fixed some issues

added new pose/turn detections
new helper classes
define-flags for libEigen

Assertions.h

@@ -70,6 +70,13 @@ namespace Assert {
 		}
 	}
 
+	template <typename T, typename U, typename V, typename STR> static inline void isNear(const T v1, const U v2, const V delta, const STR err) {
+		if (std::abs(v1-v2) > delta) {
+			std::stringstream ss; ss << "\nexpected " << v1 << " +/- " << delta << " but is " << v2 << "\n";
+			doThrow(err+ss.str());
+		}
+	}
+
 	template <typename T, typename STR> static inline void isBetween(const T v, const T min, const T max, const STR err) {
 		if (v < min || v > max) {
 			std::stringstream ss; ss << "\n[" << min << ":" << max << "] but is " << v << "\n";

CMakeLists.txt

@@ -119,7 +119,7 @@ ADD_EXECUTABLE(
 # needed external libraries
 TARGET_LINK_LIBRARIES(
 	${PROJECT_NAME}
-#	gtest
+	gtest
 #	pthread
 	${EXTRA_LIBS}
 )

Exception.h

@@ -5,7 +5,8 @@
 #include <string>
 
 #ifdef ANDROID
-#include <QMessageBox>
+//include <QMessageBox>
+#include <QtDebug>
 #endif
 
 class Exception : public std::exception {
@@ -22,7 +23,10 @@ public:
 
 		// TODO better solution?
         #ifdef ANDROID
-		QMessageBox::question(nullptr, "Exception", str.c_str(), QMessageBox::Ok);
+		    qDebug() << "-------- ERROR --------";
+			qDebug() << str.c_str();
+			qDebug() << "------------------------";
+		//QMessageBox::question(nullptr, "Exception", str.c_str(), QMessageBox::Ok);
         #endif
 
 	}

data/Timestamp.h

@@ -11,29 +11,51 @@ struct Timestamp {
 private:
 
 	/** internal timestamp in milliseconds */
-	int64_t _ms;
+	//int64_t _ms;
+	int64_t _us;
 
-	/** HIDDEN ctor. use factory methods */
+	/** hidden ctor. for internal methods only */
-	explicit Timestamp(const int64_t ms) : _ms(ms) {;}
+	Timestamp(int64_t us) : _us(us) {;}
 
 public:
 
 	/** empty ctor */
-	explicit Timestamp() : _ms(0) {;}
+	explicit Timestamp() : _us(0) {;}
 
 
+	/** get timestamp from the given value which represents microseconds */
+	static inline Timestamp fromUS(const int64_t us)	{
+		Timestamp ts;
+		ts._us = us;
+		return ts;
+	}
 	/** get timestamp from the given value which represents milliesconds */
-	static inline Timestamp fromMS(const int64_t ms)	{return Timestamp(ms);}
+	static inline Timestamp fromMS(const int64_t ms)	{
+		Timestamp ts;
+		ts._us = ms * 1000;
+		return ts;
+	}
 
 	/** get timestamp from the given value which represents seconds */
-	static inline Timestamp fromSec(const float sec)	{return Timestamp(sec*1000);}
+	static inline Timestamp fromSec(const float sec)	{
+		Timestamp ts;
+		ts._us = static_cast<int64_t>(sec * 1000 * 1000);
+		return ts;
+	}
+
+	/** get timestamp from the given value which represents a sample rate in hz */
+	static inline Timestamp fromHz(const float hz)	{
+		const float sec = 1.0f / hz;
+		return Timestamp::fromSec(sec);
+	}
 
 	/** get timestamp for the current unix-time */
 	static inline Timestamp fromUnixTime() {
 		auto now = std::chrono::system_clock::now();
 		auto duration = now.time_since_epoch();
-		auto millis = std::chrono::duration_cast<std::chrono::milliseconds>(duration).count();
+		//auto millis = std::chrono::duration_cast<std::chrono::milliseconds>(duration).count();
-		return Timestamp(millis);
+		auto micros = std::chrono::duration_cast<std::chrono::microseconds>(duration).count();
+		return Timestamp::fromUS(micros);
 	}
 
 	/** get timestamp for the current system-time */
@@ -46,44 +68,50 @@ public:
 
 public:
 
+	/** get finest available value */
+	inline int64_t finest() const {return _us;}
+
+	/** get timestamp in microseconds */
+	inline int64_t us() const {return _us;}
+
 	/** get timestamp in milliseconds */
-	inline int64_t ms() const {return _ms;}
+	inline int64_t ms() const {return _us/1000;}
 
 	/** get timestamp in seconds */
-	inline float sec() const {return _ms/1000.0f;}
+	inline float sec() const {return _us/1000.0f/1000.0f;}
 
 
 
 public:
 
 	/** is this timestamp zero? */
-	bool isZero() const {return _ms == 0;}
+	bool isZero() const {return _us == 0;}
 
 	/** equal? */
-	bool operator == (const Timestamp& o) const {return _ms == o._ms;}
+	bool operator == (const Timestamp& o) const {return _us == o._us;}
 
 	/** not equal? */
-	bool operator != (const Timestamp& o) const {return _ms != o._ms;}
+	bool operator != (const Timestamp& o) const {return _us != o._us;}
 
 	/** smaller than the given one? */
-	bool operator < (const Timestamp& o) const {return _ms < o._ms;}
+	bool operator < (const Timestamp& o) const {return _us < o._us;}
-	bool operator <= (const Timestamp& o) const {return _ms <= o._ms;}
+	bool operator <= (const Timestamp& o) const {return _us <= o._us;}
 
 	/** greater than the given one? */
-	bool operator > (const Timestamp& o) const {return _ms > o._ms;}
+	bool operator > (const Timestamp& o) const {return _us > o._us;}
-	bool operator >= (const Timestamp& o) const {return _ms >= o._ms;}
+	bool operator >= (const Timestamp& o) const {return _us >= o._us;}
 
 
 
-	Timestamp operator - (const Timestamp& o) const {return Timestamp(_ms - o._ms);}
+	Timestamp operator - (const Timestamp& o) const {return Timestamp(_us - o._us);}
-	Timestamp& operator -= (const Timestamp& o) {_ms += o._ms; return *this;}
+	Timestamp& operator -= (const Timestamp& o) {_us += o._us; return *this;}
 
-	Timestamp operator + (const Timestamp& o) const {return Timestamp(_ms + o._ms);}
+	Timestamp operator + (const Timestamp& o) const {return Timestamp(_us + o._us);}
-	Timestamp& operator += (const Timestamp& o) {_ms += o._ms; return *this;}
+	Timestamp& operator += (const Timestamp& o) {_us += o._us; return *this;}
 
-	template <typename T> Timestamp operator * (const T val) const {return Timestamp(_ms * val);}
+	template <typename T> Timestamp operator * (const T val) const {return Timestamp(_us * val);}
 
-	template <typename T> Timestamp operator / (const T val) const {return Timestamp(_ms / val);}
+	template <typename T> Timestamp operator / (const T val) const {return Timestamp(_us / val);}
 
 //	/** cast to float */
 //	operator float () const {return sec();}

floorplan/3D/objects/MTLReader.h

@@ -29,7 +29,7 @@ public:
 		;
 	}
 
-	/** read .obj from the given file */
+	/** read .mtl from the given file */
 	void readFile(const std::string& file) {
 		std::ifstream is(file);
 		std::string line;
@@ -37,7 +37,12 @@ public:
 		is.close();
 	}
 
-	/** read obj from the given data string (.obj file contents) */
+	/** read mtl from the given data string (.mtl file contents) */
+	void readData(const char* data) {
+		readData(std::string(data));
+	}
+
+	/** read mtl from the given data string (.mtl file contents) */
 	void readData(const std::string& data) {
 		std::stringstream is(data);
 		std::string line;

floorplan/3D/objects/OBJReader.h

@@ -65,6 +65,11 @@ public:
 		is.close();
 	}
 
+	/** read obj from the given data string (.obj file contents) */
+	void readData(const char* data) {
+		readData(std::string(data));
+	}
+
 	/** read obj from the given data string (.obj file contents) */
 	void readData(const std::string& data) {
 		std::stringstream is(data);

geo/Point2.h

@@ -78,6 +78,9 @@ inline float dot(const Point2 p1, const Point2 p2) {
 	return (p1.x*p2.x) + (p1.y*p2.y);
 }
 
+inline float determinant(const Point2 p1, const Point2 p2) {
+	return (p1.x*p2.y) - (p1.y*p2.x);
+}
 
 inline void swap(Point2& p1, Point2& p2) {
 	std::swap(p1.x, p2.x);

grid/factory/GridImportance.h

@@ -11,7 +11,7 @@
 #include "../../nav/dijkstra/Dijkstra.h"
 #include "../../nav/dijkstra/DijkstraPath.h"
 
-#include "../../math/Distributions.h"
+#include "../../math/distribution/Normal.h"
 
 
 

grid/walk/GridWalkLightAtTheEndOfTheTunnel.h

@@ -5,7 +5,7 @@
 #include "../Grid.h"
 
 #include "../../math/DrawList.h"
-#include "../../math/Distributions.h"
+#include "../../math/distribution/Normal.h"
 #include "../../math/DrawList.h"
 
 #include "../../nav/dijkstra/Dijkstra.h"

grid/walk/GridWalkWeighted.h

@@ -5,7 +5,7 @@
 #include "../Grid.h"
 
 #include "../../math/DrawList.h"
-#include "../../math/Distributions.h"
+#include "../../math/distribution/Normal.h"
 #include "../../math/DrawList.h"
 
 /**

grid/walk/v2/modules/WalkModuleHeading.h

@@ -7,7 +7,9 @@
 #include "../../../../Assertions.h"
 
 #include "../../../../geo/Heading.h"
-#include "../../../../math/Distributions.h"
+#include "../../../../math/distribution/Normal.h"
+#include "../../../../math/distribution/LUT.h"
+#include "../../../../math/distribution/VonMises.h"
 
 
 #include "../../../../geo/Heading.h"

grid/walk/v2/modules/WalkModuleRelativePressureControl.h

@@ -6,7 +6,7 @@
 #include "WalkStateHeading.h"
 
 #include "../../../../geo/Heading.h"
-#include "../../../../math/Distributions.h"
+#include "../../../../math/distribution/Normal.h"
 #include "../../../../Assertions.h"
 
 

main.cpp

@@ -111,7 +111,7 @@ int main(int argc, char** argv) {
 	//::testing::GTEST_FLAG(filter) = "*Matrix4*";
 	//::testing::GTEST_FLAG(filter) = "*Sphere3*";
 
-	::testing::GTEST_FLAG(filter) = "*FIRComplex*";
+	::testing::GTEST_FLAG(filter) = "*Quaternion*";
 	//::testing::GTEST_FLAG(filter) = "Timestamp*";
 
 	//::testing::GTEST_FLAG(filter) = "*RayTrace3*";

math/FixedFrequencyInterpolator.h

@@ -70,7 +70,7 @@ public:
 			while(nextOutput < cur.ts) {
 
 				// interpolation rate
-				const float percent = (nextOutput.ms() - last.ts.ms()) / (float) (diff.ms());
+				const float percent = (nextOutput.finest() - last.ts.finest()) / (float) (diff.finest());
 
 				// sanity checks
 				Assert::isNotNaN(percent, "detected NaN for interpolation");

math/Floatingpoint.h

@@ -0,0 +1,219 @@
+#ifndef FLOATINGPOINT_H
+#define FLOATINGPOINT_H
+
+#include "../Assertions.h"
+
+template <typename T> struct FP {
+
+	T val;
+
+public:
+
+	FP(int val) : val(val) {;}
+	FP(size_t val) : val(val) {;}
+	FP(float val) : val(val) {;}
+	FP(double val) : val(val) {;}
+
+	FP(const FP<float>& o) : val(o.val) {;}
+	FP(const FP<double>& o) : val(o.val) {;}
+
+	FP(const volatile FP<float>& o) : val(o.val) {;}
+	FP(const volatile FP<double>& o) : val(o.val) {;}
+
+	//template <typename U> explicit FP(const FP<U>& o) : val(o.val) {;}
+
+	//operator FP<float>() const {return FP<float>(val);}
+	operator FP<double>() const {return FP<double>(val);}
+
+	operator float() const {return static_cast<float>(val);}
+	operator double() const {return static_cast<double>(val);}
+
+
+	FP& operator += (const FP o) {
+		checkAddSub(val, o.val);
+		val += o.val;
+		return *this;
+	}
+
+	FP& operator -= (const FP o) {
+		checkAddSub(val, o.val);
+		val -= o.val;
+		return *this;
+	}
+
+	FP& operator *= (const FP o) {
+		val *= o.val;
+		return *this;
+	}
+
+	FP& operator /= (const FP o) {
+		val /= o.val;
+		return *this;
+	}
+
+	/** -------- X -------- */
+
+	FP operator - () const {
+		return FP(-val);
+	}
+
+	FP operator + (const FP o) const {
+		checkAddSub(val, o.val);
+		return FP(val+o.val);
+	}
+
+	FP operator - (const FP o) const {
+		checkAddSub(val, o.val);
+		return FP(val-o.val);
+	}
+
+	FP operator * (const FP o) const {
+		return FP(val*o.val);
+	}
+
+	FP operator / (const FP o) const {
+		return FP(val/o.val);
+	}
+
+	FP& operator = (const FP o) {
+		this->val = o;
+		return *this;
+	}
+
+
+	volatile FP& operator = (const FP& o) volatile {
+		this->val = o;
+		return *this;
+	}
+
+
+
+	bool operator == (const FP o) const {
+		return val == o.val;
+	}
+
+	bool operator != (const FP o) const {
+		return val != o.val;
+	}
+
+
+
+
+	friend std::ostream& operator << (std::ostream& stream, const FP<T>& fp) {
+		stream << fp.val;
+		return stream;
+	}
+
+private:
+
+	static inline void checkAddSub(const T a, const T b) {
+		const int x = expDiff(a,b);
+		Assert::isTrue(x <= 8, "invalid precision for +/-");
+	}
+
+	static inline int expDiff(const T a, const T b) {
+		int x, y;
+		frexp(a, &x);
+		frexp(b, &y);
+		const int d = (std::max(x,y) - std::min(x,y)) / 3;		// 3 exponents in binary per 10 in decimal?
+		return d;
+	}
+
+
+
+};
+
+inline FP<double>	operator + (const FP<float>& a, const FP<double>& b)	{return FP<double>(a.val + b.val);}
+inline FP<double>	operator + (const FP<double>& a, const FP<float>& b)	{return FP<double>(a.val + b.val);}
+inline FP<float>	operator + (const FP<float>& a, const float b)			{return a + FP<float>(b);}
+inline FP<float>	operator + (const float a, const FP<float>& b)			{return FP<float>(a) + b;}
+inline FP<double>	operator + (const FP<float>& a, const double b)			{return a + FP<double>(b);}
+inline FP<double>	operator + (const double a, const FP<float>& b)			{return FP<double>(a) + b;}
+inline FP<double>	operator + (const FP<double>& a, const float b)			{return a + FP<double>(b);}
+inline FP<double>	operator + (const float a, const FP<double>& b)			{return FP<double>(a) + b;}
+inline FP<double>	operator + (const FP<double>& a, const double b)		{return a + FP<double>(b);}
+inline FP<double>	operator + (const double a, const FP<double>& b)		{return FP<double>(a) + b;}
+
+inline FP<double>	operator - (const FP<float>& a, const FP<double>& b)	{return FP<double>(a.val - b.val);}
+inline FP<double>	operator - (const FP<double>& a, const FP<float>& b)	{return FP<double>(a.val - b.val);}
+inline FP<float>	operator - (const FP<float>& a, const float b)			{return a - FP<float>(b);}
+inline FP<float>	operator - (const float a, const FP<float>& b)			{return FP<float>(a) - b;}
+inline FP<double>	operator - (const FP<float>& a, const double b)			{return a - FP<double>(b);}
+inline FP<double>	operator - (const double a, const FP<float>& b)			{return FP<double>(a) - b;}
+inline FP<double>	operator - (const FP<double>& a, const float b)			{return a - FP<double>(b);}
+inline FP<double>	operator - (const float a, const FP<double>& b)			{return FP<double>(a) - b;}
+inline FP<double>	operator - (const FP<double>& a, const double b)		{return a - FP<double>(b);}
+inline FP<double>	operator - (const double a, const FP<double>& b)		{return FP<double>(a) - b;}
+
+inline FP<double>	operator / (const FP<float>& a, const FP<double>& b)	{return FP<double>(a.val / b.val);}
+inline FP<double>	operator / (const FP<double>& a, const FP<float>& b)	{return FP<double>(a.val / b.val);}
+inline FP<float>	operator / (const FP<float>& a, const float b)			{return a / FP<float>(b);}
+inline FP<float>	operator / (const float a, const FP<float>& b)			{return FP<float>(a) / b;}
+inline FP<double>	operator / (const FP<float>& a, const double b)			{return a / FP<double>(b);}
+inline FP<double>	operator / (const double a, const FP<float>& b)			{return FP<double>(a) / b;}
+inline FP<double>	operator / (const FP<double>& a, const float b)			{return a / FP<double>(b);}
+inline FP<double>	operator / (const float a, const FP<double>& b)			{return FP<double>(a) / b;}
+inline FP<double>	operator / (const FP<double>& a, const double b)		{return a / FP<double>(b);}
+inline FP<double>	operator / (const double a, const FP<double>& b)		{return FP<double>(a) / b;}
+
+inline FP<double>	operator * (const FP<float>& a, const FP<double>& b)	{return FP<double>(a.val * b.val);}
+inline FP<double>	operator * (const FP<double>& a, const FP<float>& b)	{return FP<double>(a.val * b.val);}
+inline FP<float>	operator * (const FP<float>& a, const float b)			{return a * FP<float>(b);}
+inline FP<float>	operator * (const float a, const FP<float>& b)			{return FP<float>(a) * b;}
+inline FP<double>	operator * (const FP<float>& a, const double b)			{return a * FP<double>(b);}
+inline FP<double>	operator * (const double a, const FP<float>& b)			{return FP<double>(a) * b;}
+inline FP<double>	operator * (const FP<double>& a, const float b)			{return a * FP<double>(b);}
+inline FP<double>	operator * (const float a, const FP<double>& b)			{return FP<double>(a) * b;}
+inline FP<double>	operator * (const FP<double>& a, const double b)		{return a * FP<double>(b);}
+inline FP<double>	operator * (const double a, const FP<double>& b)		{return FP<double>(a) * b;}
+
+inline FP<float>	operator / (const FP<float>& a, const int b)			{return a / FP<float>(b);}
+inline FP<float>	operator / (const FP<float>& a, const size_t b)			{return a / FP<float>(b);}
+
+inline FP<double>	operator / (const FP<double>& a, const int b)			{return a / FP<double>(b);}
+inline FP<double>	operator / (const FP<double>& a, const size_t b)		{return a / FP<double>(b);}
+
+
+//template <typename T, typename U> FP<T> operator + (const FP<T>& a, const U b) {return a + FP<T>(b);}
+//template <typename T, typename U> FP<T> operator + (const U a, const FP<T>& b) {return FP<T>(a) + b;}
+
+//template <typename T, typename U> FP<T> operator - (const FP<T>& a, const U b) {return a - FP<T>(b);}
+//template <typename T, typename U> FP<T> operator - (const U a, const FP<T>& b) {return FP<T>(a) - b;}
+
+//template <typename T, typename U> FP<T> operator * (const FP<T>& a, const U b) {return a * FP<T>(b);}
+//template <typename T, typename U> FP<T> operator * (const U a, const FP<T>& b) {return FP<T>(a) * b;}
+
+//template <typename T, typename U> FP<T> operator / (const FP<T>& a, const U b) {return a / FP<T>(b);}
+//template <typename T, typename U> FP<T> operator / (const U a, const FP<T>& b) {return FP<T>(a) / b;}
+
+
+
+namespace std {
+	template<class T> FP<T> pow (const FP<T>& x, const FP<T>& y) {
+		return FP<T>(std::pow(x.val, y.val));
+	}
+	template<class T> FP<T> pow (const FP<T>& x, const T& y) {
+		return FP<T>(std::pow(x.val, y));
+	}
+	template<class T> FP<T> sqrt (const FP<T> x) {
+		return FP<T>(std::sqrt(x.val));
+	}
+	template<class T> bool isnan(FP<T> x) {
+		return std::isnan(x.val);
+	}
+}
+
+#ifdef WITH_FP
+    using FPFloat = FP<float>;
+    using FPDouble = FP<double>;
+    using FPDefault = FPFloat;
+#else
+    using FPFloat = float;
+    using FPDouble = double;
+    using FPDefault = double;
+#endif
+
+
+
+
+#endif // FLOATINGPOINT_H

math/KahanSum.h

@@ -0,0 +1,84 @@
+#ifndef KAHANSUM_H
+#define KAHANSUM_H
+
+#include <vector>
+
+template <typename T> class KahanSum {
+
+private:
+
+	const T zero;
+
+	/** current sum */
+	T sum;
+
+	/** current compensation */
+	T comp;
+
+
+public:
+
+	/** ctor with zero element */
+	KahanSum(const T zero) : zero(zero), sum(zero), comp(zero) {
+
+	}
+
+	KahanSum& operator += (const T val) {
+		add(val);
+		return *this;
+	}
+
+	KahanSum& operator -= (const T val) {
+		sub(val);
+		return *this;
+	}
+
+	T get() const {
+		return sum;
+	}
+
+private:
+
+#define NO_OPT	__attribute__((optimize("-O0")))
+
+	/** adjust the sum */
+	void add(const T val) NO_OPT {
+		const T y = val - comp;
+		const T t = sum + y;
+		comp = (t-sum) - y;				// very important line
+		sum = t;
+	}
+
+	/** adjust the sum */
+	void sub(const T val) NO_OPT {
+		const T y = val - comp;
+		const T t = sum - y;
+		comp = (t-sum) + y;				// very important line
+		sum = t;
+	}
+
+public:
+
+	static T get(const std::vector<T>& values, const T zero = T()) {
+		return get(values.data(), values.size(), zero);
+	}
+
+	static T get(const T* values, const size_t cnt, const T zero = T()) {
+
+		T sum = zero;
+		volatile T comp = zero;
+		for (size_t i = 0; i < cnt; ++i) {
+			const T inp = values[i];
+			const volatile T y = inp - comp;
+			const volatile T t = sum + y;
+			comp = (t-sum) - y;
+			sum = t;
+		}
+
+		return sum;
+
+	}
+
+};
+
+#endif // KAHANSUM_H

math/Matrix3.h

@@ -4,6 +4,7 @@
 
 #include <initializer_list>
 #include <cmath>
+#include "../Assertions.h"
 
 class Matrix3 {
 
@@ -24,30 +25,72 @@ public:
 		return Matrix3( {1,0,0, 0,1,0, 0,0,1} );
     }
 
-//    static Matrix3 getRotationDeg(const float degX, const float degY, const float degZ) {
+	static Matrix3 getRotationDeg(const float degX, const float degY, const float degZ) {
-//        return getRotationRad(degX/180.0f*M_PI, degY/180.0f*M_PI, degZ/180.0f*M_PI);
+		return getRotationRad(degX/180.0f*M_PI, degY/180.0f*M_PI, degZ/180.0f*M_PI);
-//    }
+	}
 
-//    static Matrix4 getRotationRad(const float radX, const float radY, const float radZ) {
+	static Matrix3 getRotationRad(const float radX, const float radY, const float radZ) {
 
-//        const float g = radX; const float b = radY; const float a = radZ;
+		const float g = radX; const float b = radY; const float a = radZ;
-//        const float a11 = std::cos(a)*std::cos(b);
+		const float a11 = std::cos(a)*std::cos(b);
-//        const float a12 = std::cos(a)*std::sin(b)*std::sin(g)-std::sin(a)*std::cos(g);
+		const float a12 = std::cos(a)*std::sin(b)*std::sin(g)-std::sin(a)*std::cos(g);
-//        const float a13 = std::cos(a)*std::sin(b)*std::cos(g)+std::sin(a)*std::sin(g);
+		const float a13 = std::cos(a)*std::sin(b)*std::cos(g)+std::sin(a)*std::sin(g);
-//        const float a21 = std::sin(a)*std::cos(b);
+		const float a21 = std::sin(a)*std::cos(b);
-//        const float a22 = std::sin(a)*std::sin(b)*std::sin(g)+std::cos(a)*std::cos(g);
+		const float a22 = std::sin(a)*std::sin(b)*std::sin(g)+std::cos(a)*std::cos(g);
-//        const float a23 = std::sin(a)*std::sin(b)*std::cos(g)-std::cos(a)*std::sin(g);
+		const float a23 = std::sin(a)*std::sin(b)*std::cos(g)-std::cos(a)*std::sin(g);
-//        const float a31 = -std::sin(b);
+		const float a31 = -std::sin(b);
-//        const float a32 = std::cos(b)*std::sin(g);
+		const float a32 = std::cos(b)*std::sin(g);
-//        const float a33 = std::cos(b)*std::cos(g);
+		const float a33 = std::cos(b)*std::cos(g);
-//        return Matrix4({
+		return Matrix3({
-//            a11,	a12,	a13,	0,
+		    a11,	a12,	a13,
-//            a21,	a22,	a23,	0,
+		    a21,	a22,	a23,
-//            a31,	a32,	a33,	0,
+		    a31,	a32,	a33,
-//            0,		0,		0,		1
+		});
-//        });
 
-//    }
+	}
+	static Matrix3 getRotationVec(const float nx, const float ny, const float nz, const float mag) {
+		Assert::isNotNaN(nx, "detected NaN");
+		Assert::isNotNaN(ny, "detected NaN");
+		Assert::isNotNaN(nz, "detected NaN");
+		Assert::isNotNaN(mag, "detected NaN");
+		const float c = std::cos(mag);
+		const float s = std::sin(mag);
+		return Matrix3({
+		    c+nx*nx*(1-c),		nx*ny*(1-c)+nz*s,		nx*nz*(1-c)-ny*s,
+		    ny*nx*(1-c)-nz*s,	c+ny*ny*(1-c),			ny*nz*(1-c)+nx*s,
+		    nz*nx*(1-c)+ny*s,	nz*ny*(1-c)-nx*s,		c+nz*nz*(1-c)
+		});
+	}
+	static Matrix3 getRotationRadX(const float x) {
+		return Matrix3({
+		    1,		0,		0,
+		    0,		cos(x),	-sin(x),
+		    0,		sin(x),	cos(x)
+		});
+	}
+	static Matrix3 getRotationRadY(const float y) {
+		return Matrix3({
+		    cos(y),	0,		sin(y),
+		    0,		1,		0,
+		    -sin(y),0,		cos(y)
+		});
+	}
+	static Matrix3 getRotationRadZ(const float z) {
+		return Matrix3({
+		    cos(z),	-sin(z),	0,
+		    sin(z),	cos(z),		0,
+		    0,		0,			1
+		});
+	}
+
+
+	Matrix3 transposed() const {
+		return Matrix3({
+		    data[0], data[3], data[6],
+		    data[1], data[4], data[7],
+		    data[2], data[5], data[8]
+		});
+	}
 
     static Matrix3 getTranslation(const float x, const float y) {
         return Matrix3({
@@ -126,6 +169,27 @@ struct Vector3 {
 		return Vector3(x/v, y/v, z/v);
 	}
 
+	Vector3& operator += (const Vector3 o) {
+		this->x += o.x;
+		this->y += o.y;
+		this->z += o.z;
+		return *this;
+	}
+
+	Vector3& operator -= (const Vector3 o) {
+		this->x -= o.x;
+		this->y -= o.y;
+		this->z -= o.z;
+		return *this;
+	}
+
+//	Vector& operator = (const float val) {
+//		this->x = val;
+//		this->y = val;
+//		this->z = val;
+//		return *this;
+//	}
+
     bool operator == (const Vector3 o) const {
         return (x==o.x) && (y==o.y) && (z==o.z);
     }

math/MovingAverageTS.h

@@ -4,6 +4,7 @@
 #include <vector>
 #include "../data/Timestamp.h"
 #include <algorithm>
+#include "KahanSum.h"
 
 template <typename T> class MovingAverageTS {
 
@@ -22,14 +23,19 @@ private:
 	/** the value history for the window-size */
 	std::vector<Entry> history;
 
+	const T zero;
+
 	/** current sum */
 	T sum;
 
+	/** more exact running summation of many values */
+	KahanSum<T> kSum;
+
 public:
 
 
 	/** ctor with the window-size to use */
-	MovingAverageTS(const Timestamp window, const T zeroElement) : window(window), sum(zeroElement) {
+	MovingAverageTS(const Timestamp window, const T zeroElement) : window(window), zero(zeroElement), sum(zeroElement), kSum(zeroElement) {
 
 	}
 
@@ -41,6 +47,7 @@ public:
 
 		// adjust sum
 		sum += data;
+		kSum += data;
 
 		// remove too-old history entries
 		const Timestamp oldest = ts - window;
@@ -48,6 +55,7 @@ public:
 
 			// adjust sum
 			sum -= history.front().value;
+			kSum -= history.front().value;
 
 			// remove from history
 			history.erase(history.begin());
@@ -56,11 +64,31 @@ public:
 
 	}
 
-	/** get the current average */
+	/** get the current average (with increasing error due to float sum!) */
-	T get() const {
+	T getOldAPX() const {
 		return sum / history.size();
 	}
 
+	/** get the current average */
+	T get() const {
+		return kSum.get() / history.size();
+	}
+
+//	T get() const {
+
+//		T sum = zero;
+//		volatile T comp = zero;
+//		for (const auto e : history) {
+//			T inp = e.value;
+//			T y = inp - comp;
+//			T t = sum + y;
+//			comp = (t-sum) - y;
+//			sum = t;
+//		}
+
+//		return sum / history.size();
+
+//	}
 
 };
 

math/MovingMinMaxTS.h

@@ -0,0 +1,73 @@
+#ifndef MOVINGMINMAXTS_H
+#define MOVINGMINMAXTS_H
+
+#include <vector>
+#include "../data/Timestamp.h"
+#include <algorithm>
+
+template <typename T> class MovingMinMaxTS {
+
+private:
+
+	/** timestamp -> value combination */
+	struct Entry {
+		Timestamp ts;
+		T value;
+		Entry(const Timestamp ts, const T& value) : ts(ts), value(value) {;}
+	};
+
+	/** the regional window to use */
+	Timestamp window;
+
+	/** the value history for the window-size */
+	std::vector<Entry> history;
+
+	/** current sum */
+	T sum;
+
+public:
+
+
+	/** ctor with the window-size to use */
+	MovingMinMaxTS(const Timestamp window, const T zeroElement) : window(window), sum(zeroElement) {
+
+	}
+
+	/** add a new entry */
+	void add(const Timestamp ts, const T& data) {
+
+		// append to history
+		history.push_back(Entry(ts, data));
+
+		// remove too-old history entries
+		const Timestamp oldest = ts - window;
+		while(history.front().ts < oldest) {
+
+			// remove from history
+			history.erase(history.begin());
+
+		}
+
+	}
+
+	/** get the current min element */
+	T getMin() const {
+		auto comp = [] (const Entry& e1, const Entry& e2) {return e1.value < e2.value;};
+		auto it = std::min_element(history.begin(), history.end(), comp);
+		return it->value;
+	}
+
+	/** get the current max element */
+	T getMax() const {
+		auto comp = [] (const Entry& e1, const Entry& e2) {return e1.value < e2.value;};
+		auto it = std::max_element(history.begin(), history.end(), comp);
+		return it->value;
+	}
+
+	T getRange() const {
+		return getMax() - getMin();
+	}
+
+};
+
+#endif // MOVINGMINMAXTS_H

math/MovingStdDevTS.h

@@ -10,8 +10,8 @@ template <typename T> class MovingStdDevTS {
 
 private:
 
-	MovingAverageTS<T> avg;
+	MovingAverageTS<double> avg;
-	MovingAverageTS<T> avg2;
+	MovingAverageTS<double> avg2;
 
 
 public:
@@ -36,9 +36,10 @@ public:
 	/** get the current std-dev */
 	T get() const {
 
-		const T e = avg.get();
+		const double e = avg.get();
-		const T e2 = avg2.get();
+		const double e2 = avg2.get();
-		const T var = e2 - e*e;
+		const double var = e2 - e*e;
+		//if (var < 0) {return 0;}
 		return std::sqrt(var);
 
 	}

math/Quaternion.h

@@ -0,0 +1,197 @@
+#ifndef QUATERNION_H
+#define QUATERNION_H
+
+#include "Matrix3.h"
+
+class Quaternion {
+
+public:
+
+	float w;
+	float x, y, z;
+
+	/** empty ctor */
+	Quaternion() : w(1.0f), x(0.0f), y(0.0f), z(0.0f) {
+		;
+	}
+
+	/** valued ctor */
+	Quaternion(float w, float x, float y, float z) :  w(w), x(x), y(y), z(z) {
+		;
+	}
+
+	/** construct from Euler angles in radians */
+	static Quaternion fromEuler(float x, float y, float z) {
+		Quaternion q;
+		q.setEuler(x,y,z);
+		return q;
+	}
+
+	static Quaternion fromAxisAngle(float angle, float x, float y, float z) {
+		const float qx = x * std::sin(angle/2);
+		const float qy = y * std::sin(angle/2);
+		const float qz = z * std::sin(angle/2);
+		const float qw = std::cos(angle/2);
+		return Quaternion(qw,	qx,qy,qz);
+	}
+
+
+	void normalize() {
+		*this *= 1.0 / std::sqrt( x*x + y*y + z*z + w*w );
+	}
+
+	inline float dotProduct(const Quaternion& q2) const {
+		return (x * q2.x) + (y * q2.y) + (z * q2.z) + (w * q2.w);
+	}
+
+
+	/** linear interpolation between q1 and q2 */
+	static Quaternion lerp( Quaternion q1, Quaternion q2, float time) {
+		const float scale = 1.0f - time;
+		return (q1*scale) + (q2*time);
+	}
+
+	/** spherical interpolation between q1 and q2 */
+	static Quaternion slerp( Quaternion q1, Quaternion q2, float time, float threshold = 0.05)  {
+
+		float angle = q1.dotProduct(q2);
+
+		// make sure we use the short rotation
+		if (angle < 0.0f) {
+			q1 *= -1.0f;
+			angle *= -1.0f;
+		}
+
+		if (angle <= (1-threshold)) {
+			// spherical interpolation
+			const float theta = acosf(angle);
+			const float invsintheta = 1.0/(sinf(theta));
+			const float scale = sinf(theta * (1.0f-time)) * invsintheta;
+			const float invscale = sinf(theta * time) * invsintheta;
+			return (q1*scale) + (q2*invscale);
+		} else {
+			// linear interpolation
+			return Quaternion::lerp(q1,q2,time);
+		}
+
+	}
+
+
+	/** multiply by scalar */
+	Quaternion& operator *= (float val) {
+		x *= val;
+		y *= val;
+		z *= val;
+		w *= val;
+		return *this;
+	}
+
+	/** multiply by scalar */
+	Quaternion operator * (float val) const {
+		return Quaternion(w*val, x*val, y*val, z*val);
+	}
+
+	/** multiply by other quaterion */
+	Quaternion& operator *= (const Quaternion& other) {
+		return (*this = other * (*this));
+	}
+
+	/** multiply by other quaterion */
+	Quaternion operator * (const Quaternion& other) const {
+		Quaternion tmp;
+		tmp.w = (other.w * w) - (other.x * x) - (other.y * y) - (other.z * z);
+		tmp.x = (other.w * x) + (other.x * w) + (other.y * z) - (other.z * y);
+		tmp.y = (other.w * y) + (other.y * w) + (other.z * x) - (other.x * z);
+		tmp.z = (other.w * z) + (other.z * w) + (other.x * y) - (other.y * x);
+		return tmp;
+	}
+
+	/** add two quaternions */
+	Quaternion operator + (const Quaternion& b) const {
+		return Quaternion(w+b.w,		x+b.x, y+b.y, z+b.z);
+	}
+
+
+	/** set from euler angles (in radians) */
+	void setEuler(float x, float y, float z) {
+
+		double angle;
+
+		angle = x * 0.5;
+		const double sr = std::sin(angle);
+		const double cr = std::cos(angle);
+
+		angle = y * 0.5;
+		const double sp = std::sin(angle);
+		const double cp = std::cos(angle);
+
+		angle = z * 0.5;
+		const double sy = std::sin(angle);
+		const double cy = std::cos(angle);
+
+		const double cpcy = cp * cy;
+		const double spcy = sp * cy;
+		const double cpsy = cp * sy;
+		const double spsy = sp * sy;
+
+		this->x = (float)(sr * cpcy - cr * spsy);
+		this->y = (float)(cr * spcy + sr * cpsy);
+		this->z = (float)(cr * cpsy - sr * spcy);
+		this->w = (float)(cr * cpcy + sr * spsy);
+		normalize();
+
+	}
+
+	/** convert to euler angles */
+	Vector3 toEuler() const {
+
+		Vector3 res;
+
+		const double sqw = w*w;
+		const double sqx = x*x;
+		const double sqy = y*y;
+		const double sqz = z*z;
+		const double test = 2.0 * (y*w - x*z);
+
+		if (near(test, 1.0)) {
+			// heading = rotation about z-axis
+			res.z = (float) (-2.0*atan2(x, w));
+			// bank = rotation about x-axis
+			res.x = 0;
+			// attitude = rotation about y-axis
+			res.y = (float) (M_PI/2.0);
+		} else if (near(test, -1.0)) {
+			// heading = rotation about z-axis
+			res.z = (float) (2.0*std::atan2(x, w));
+			// bank = rotation about x-axis
+			res.x = 0;
+			// attitude = rotation about y-axis
+			res.y = (float) (M_PI/-2.0);
+		} else {
+			// heading = rotation about z-axis
+			res.z = (float) std::atan2(2.0 * (x*y + z*w),(sqx - sqy - sqz + sqw));
+			// bank = rotation about x-axis
+			res.x = (float) std::atan2(2.0 * (y*z + x*w),(-sqx - sqy + sqz + sqw));
+			// attitude = rotation about y-axis
+			res.y = (float) std::asin( clamp(test, -1.0, 1.0) );
+		}
+
+		return res;
+
+	}
+
+private:
+
+	static inline bool near(double d1, double d2) {
+		return std::abs(d1-d2) < 0.00001;
+	}
+
+	static inline double clamp(double val, double min, double max) {
+		if (val < min) {return min;}
+		if (val > max) {return max;}
+		return val;
+	}
+
+};
+
+#endif // QUATERNION_H

math/distribution/NormalN.h

@@ -3,6 +3,7 @@
 
 #include <cmath>
 #include <random>
+#include <vector>
 
 #include <eigen3/Eigen/Dense>
 
@@ -20,23 +21,28 @@ namespace Distribution {
         Eigen::VectorXd mu;
         Eigen::MatrixXd sigma;
 
-        const double _a;
+		double _a;
-        const Eigen::MatrixXd _sigmaInv;
+		Eigen::MatrixXd _sigmaInv;
 
-        const Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> eigenSolver;
+		Eigen::MatrixXd transform;
-        Eigen::MatrixXd transform; //can i make this const?
 
-        Random::RandomGenerator gen;
+		Random::RandomGenerator gen;
-        std::normal_distribution<> dist;
+		std::normal_distribution<> dist;
 
     public:
 
-        /** ctor */
+		/** empty ctor */
-        NormalDistributionN(const Eigen::VectorXd mu, const Eigen::MatrixXd sigma) :
+		NormalDistributionN() {
-            mu(mu), sigma(sigma), _a( 1.0 / std::sqrt( (sigma * 2.0 * M_PI).determinant() ) ), _sigmaInv(sigma.inverse()), eigenSolver(sigma) {
+			;
+		}
 
-            transform = eigenSolver.eigenvectors() * eigenSolver.eigenvalues().cwiseSqrt().asDiagonal();
+		/** ctor */
-        }
+		NormalDistributionN(const Eigen::VectorXd mu, const Eigen::MatrixXd sigma) :
+		    mu(mu), sigma(sigma), _a( 1.0 / std::sqrt( (sigma * 2.0 * M_PI).determinant() ) ), _sigmaInv(sigma.inverse()) {
+
+			const Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> eigenSolver(sigma);
+			transform = eigenSolver.eigenvectors() * eigenSolver.eigenvalues().cwiseSqrt().asDiagonal();
+		}
 
         /** get probability for the given value */
         double getProbability(const Eigen::VectorXd val) const {
@@ -50,12 +56,12 @@ namespace Distribution {
         }
 
         /** get the mean vector */
-        const Eigen::VectorXd getMu(){
+	    const Eigen::VectorXd getMu() const {
             return this->mu;
         }
 
         /** get covariance matrix */
-        const Eigen::MatrixXd getSigma(){
+	    const Eigen::MatrixXd getSigma() const {
             return this->sigma;
         }
 
@@ -71,6 +77,34 @@ namespace Distribution {
             this->mu = mu;
         }
 
+		/** return a NormalN based on given data */
+		static NormalDistributionN getNormalNFromSamples(const std::vector<std::vector<double>>& data) {
+
+			int numAttrs = data[0].size();
+			Eigen::MatrixXd eCovar = Eigen::MatrixXd::Zero(numAttrs, numAttrs);
+			Eigen::VectorXd eSum = Eigen::VectorXd::Zero(numAttrs);
+			Eigen::VectorXd eAvg = Eigen::VectorXd::Zero(numAttrs);
+
+			// mean
+			for (const std::vector<double>& vec : data) {
+				const Eigen::Map<Eigen::VectorXd> eVec((double*)vec.data(), vec.size());
+				eSum += eVec;
+			}
+			eAvg = eSum / data.size();
+
+			// covariance
+			for (const std::vector<double>& vec : data) {
+				const Eigen::Map<Eigen::VectorXd> eVec((double*)vec.data(), vec.size());
+				const Eigen::VectorXd eTmp = (eVec - eAvg);
+				eCovar += eTmp * eTmp.transpose();
+			}
+			eCovar /= data.size();
+
+			return NormalDistributionN(eAvg, eCovar);
+
+		}
+
+
         /** return a NormalN based on given data */
         static NormalDistributionN getNormalNFromSamples(const Eigen::MatrixXd& data) {
 
@@ -98,7 +132,7 @@ namespace Distribution {
                 return NormalDistributionN(mean, cov);
         }
 
-		std::vector<Point2> getContour2(const double percentWithin) {
+		std::vector<Point2> getContour2(const double percentWithin) const {
 
 			const int degreesOfFreedom = 2;	// 2D distribution
 			const ChiSquared<double> chi(degreesOfFreedom);
@@ -114,7 +148,7 @@ namespace Distribution {
 
 			std::vector<Point2> res;
 
-			std::cout << sigma << std::endl;
+			//std::cout << sigma << std::endl;
 			Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> solver(this->sigma);
 
 			Eigen::Vector2d evec1 = solver.eigenvectors().col(0);
@@ -127,7 +161,8 @@ namespace Distribution {
 				const float rad = deg / 180.0f * M_PI;
 				Eigen::Vector2d pos =
 						std::cos(rad) * std::sqrt(mul * eval1) * evec1 +
-						std::sin(rad) * std::sqrt(mul * eval2) * evec2;
+				        std::sin(rad) * std::sqrt(mul * eval2) * evec2 +
+				        this->mu;
 				res.push_back(Point2(pos(0), pos(1)));
 			}
 

math/dsp/iir/BiQuad.h

@@ -29,7 +29,7 @@ namespace IIR {
 		/** filter the given amplitude of the given channel (history) */
 		Scalar filter( const Scalar aIn ) {
 
-			Scalar aOut = 0;
+			Scalar aOut = Scalar();	// zero
 			aOut += aIn   *(b0a0);
 			aOut += in[0] *(b1a0);
 			aOut += in[1] *(b2a0);

math/filter/Complementary.h

@@ -0,0 +1,74 @@
+#ifndef COMPLEMENTARY_H
+#define COMPLEMENTARY_H
+
+#include "../dsp/iir/BiQuad.h"
+#include "../../math/stats/SampleRateEstimator.h"
+
+namespace Filter {
+
+	template <typename T> class Complementary {
+
+	private:
+
+		const float fLo;
+		const float fHi;
+
+		IIR::BiQuad<T> lp;
+		IIR::BiQuad<T> hp;
+
+		SampleRateEstimator slp;
+		SampleRateEstimator shp;
+
+		T slow;
+		T fast;
+
+	public:
+
+		/** ctor with transition frequency and sample-rate */
+		Complementary(const float fLo, const float fHi) : fLo(fLo), fHi(fHi), slow(), fast() {
+			//adjust();
+		}
+
+		void addSlow(const Timestamp ts, const T& slow) {
+			slp.update(ts);
+			this->slow = lp.filter(slow);
+			adjustLP();
+		}
+
+		void addFast(const Timestamp ts, const T& fast) {
+			shp.update(ts);
+			this->fast = hp.filter(fast);
+			adjustHP();
+		}
+
+		T get() const {
+			return slow+fast;
+		}
+
+		T getLo() const {
+			return slow;
+		}
+
+		T getHi() const {
+			return fast;
+		}
+
+	private:
+
+		void adjustLP() {
+			const float freqLP = slp.getCurHz();
+			//std::cout << freqLP << ":" << freqHP << std::endl;
+			if (freqLP > fLo*2) {lp.setLowPass(fLo, 0.707, freqLP);}
+		}
+
+		void adjustHP() {
+			const float freqHP = slp.getCurHz();
+			//std::cout << freqLP << ":" << freqHP << std::endl;
+			if (freqHP > fHi*2) {hp.setHighPass(fHi, 0.707, freqHP);}
+		}
+
+	};
+
+}
+
+#endif // COMPLEMENTARY_H

math/stats/SampleRateEstimator.h

@@ -0,0 +1,41 @@
+#ifndef SAMPLERATEESTIMATOR_H
+#define SAMPLERATEESTIMATOR_H
+
+#include "../../data/Timestamp.h"
+
+class SampleRateEstimator {
+
+private:
+
+	const double a = 0.99;
+	double curHz = 0;
+	Timestamp tsLast;
+
+public:
+
+	float update(const Timestamp ts) {
+
+		// first
+		if (tsLast.isZero()) {
+			tsLast = ts;
+			return 0;
+		}
+
+		const double diffSec = static_cast<double>((ts-tsLast).sec());
+		tsLast = ts;
+
+		if (diffSec != 0) {
+			curHz = a*curHz + (1-a) * (1.0/diffSec);
+		}
+
+		return static_cast<float>(curHz);
+
+	}
+
+	float getCurHz() const {
+		return static_cast<float>(curHz);
+	}
+
+};
+
+#endif // SAMPLERATEESTIMATOR_H

sensors/gps/GPSData.h

@@ -3,18 +3,19 @@
 
 #include "../../data/Timestamp.h"
 #include "../../geo/EarthPos.h"
+#include "../../math/Floatingpoint.h"
 
 struct GPSData {
 
 	/** time this measurement was received (NOT the GPS-time) */
 	Timestamp tsReceived;
 
-	float lat;			// deg
+	FPDefault lat;			// deg
-	float lon;			// deg
+	FPDefault lon;			// deg
-	float alt;			// m above sea-level
+	FPDefault alt;			// m above sea-level
 
-	float accuracy;		// m [might be NAN]
+	FPDefault accuracy;		// m [might be NAN]
-	float speed;		// m/s [might be NAN]
+	FPDefault speed;		// m/s [might be NAN]
 
 	/** ctor for invalid/unknown data */
 	GPSData() : tsReceived(), lat(NAN), lon(NAN), alt(NAN), accuracy(NAN), speed(NAN) {;}
@@ -49,7 +50,7 @@ struct GPSData {
 
 private:
 
-	static inline bool EQ_OR_NAN(const float a, const float b) {return (a==b) || ( (a!=a) && (b!=b) );}
+	static inline bool EQ_OR_NAN(const FPDefault a, const FPDefault b) {return (a==b) || ( (a!=a) && (b!=b) );}
 
 };
 

sensors/imu/AccelerometerData.h

@@ -3,20 +3,23 @@
 
 #include <cmath>
 #include <sstream>
+#include "../../math/Floatingpoint.h"
 
 
 /** data received from an accelerometer sensor */
 struct AccelerometerData {
 
-	float x;
+	FPDefault x;
-	float y;
+	FPDefault y;
-	float z;
+	FPDefault z;
 
 	AccelerometerData() : x(0), y(0), z(0) {;}
 
-	AccelerometerData(const float x, const float y, const float z) : x(x), y(y), z(z) {;}
+	AccelerometerData(const FPDefault x, const FPDefault y, const FPDefault z) : x(x), y(y), z(z) {;}
 
-	float magnitude() const {
+	//AccelerometerData(const FPDefault x, const FPDefault y, const FPDefault z) : x(x), y(y), z(z) {;}
+
+	FPDefault magnitude() const {
 		return std::sqrt( x*x + y*y + z*z );
 	}
 
@@ -34,22 +37,24 @@ struct AccelerometerData {
 		return *this;
 	}
 
-	AccelerometerData operator - (const AccelerometerData& o) const {
+
-		return AccelerometerData(x-o.x, y-o.y, z-o.z);
+	AccelerometerData operator + (const AccelerometerData o) const {
+		return AccelerometerData(x+o.x, y+o.y, z+o.z);
 	}
 
-	AccelerometerData operator / (const float val) const {
+	AccelerometerData operator - (const AccelerometerData& o) const {
-		return AccelerometerData(x/val, y/val, z/val);
+		return AccelerometerData(x-o.x, y-o.y, z-o.z);
 	}
 
 	AccelerometerData operator * (const float val) const {
 		return AccelerometerData(x*val, y*val, z*val);
 	}
 
-	AccelerometerData operator + (const AccelerometerData o) const {
+	AccelerometerData operator / (const float val) const {
-		return AccelerometerData(x+o.x, y+o.y, z+o.z);
+		return AccelerometerData(x/val, y/val, z/val);
 	}
 
+
 	std::string asString() const {
 		std::stringstream ss;
 		ss << "(" << x << "," << y << "," << z << ")";
@@ -68,7 +73,7 @@ struct AccelerometerData {
 
 private:
 
-	static inline bool EQ_OR_NAN(const float a, const float b) {return (a==b) || ( (a!=a) && (b!=b) );}
+	static inline bool EQ_OR_NAN(const FPDefault a, const FPDefault b) {return (a==b) || ( (a!=a) && (b!=b) );}
 
 };
 

sensors/imu/CompassData.h

@@ -4,16 +4,16 @@
 
 #include <cmath>
 #include <sstream>
-
+#include "../../math/Floatingpoint.h"
 
 /** data received from a compass sensor */
 struct CompassData {
 
 	/** azimuth angle. NAN if not available */
-	float azimuth = NAN;
+	FPDefault azimuth = NAN;
 
 	/** describes the sensor's quality */
-	float quality01 = 0;
+	FPDefault quality01 = 0;
 
 
 	/** empty ctor */
@@ -49,7 +49,7 @@ struct CompassData {
 
 private:
 
-	static inline bool EQ_OR_NAN(const float a, const float b) {return (a==b) || ( (a!=a) && (b!=b) );}
+	static inline bool EQ_OR_NAN(const FPDefault a, const FPDefault b) {return (a==b) || ( (a!=a) && (b!=b) );}
 
 };
 

sensors/imu/CompassDetection.h

@@ -2,18 +2,21 @@
 #define INDOOR_IMU_COMPASSDETECTION_H
 
 #include "MagnetometerData.h"
-#include "PoseDetection.h"
+#include "PoseProvider.h"
+#include "TurnProvider.h"
 
 #include "../../data/Timestamp.h"
 #include "../../math/MovingAverageTS.h"
 #include "../../math/MovingStdDevTS.h"
 #include "../../geo/Point3.h"
 #include "../../Assertions.h"
+#include "../../geo/Angle.h"
 
 #include "CompassDetectionPlot.h"
 
 #include <cmath>
 #include <vector>
+#include "../../math/dsp/iir/BiQuad.h"
 
 
 /**
@@ -33,21 +36,37 @@ private:
 //		Timestamp lastEstimation;
 //	} orientation;
 
-	MovingAverageTS<MagnetometerData> avgIn = MovingAverageTS<MagnetometerData>(Timestamp::fromMS(150), MagnetometerData(0,0,0));
+	MovingAverageTS<MagnetometerData> avgIn;
 
 	//MovingStdDevTS<MagnetometerData> stdDev = MovingStdDevTS<MagnetometerData>(Timestamp::fromMS(2000), MagnetometerData(0,0,0));
 	MovingStdDevTS<float> stdDev = MovingStdDevTS<float>(Timestamp::fromMS(1500), 0);
 
-	PoseDetection* pose = nullptr;
+
+
+	const PoseProvider* pose = nullptr;
+	const TurnProvider* turn = nullptr;
+
 	int numMagReadings = 0;
 
+	bool stable;
+
+	MovingStdDevTS<float> stdDevForSigma = MovingStdDevTS<float>(Timestamp::fromMS(500), 0);
+	float lastHeading = 0;
+	float curSigma = 0;
+
 public:
 
 	/** ctor */
-	CompassDetection(PoseDetection* pose) : pose(pose) {
+	CompassDetection(const PoseProvider* pose, const TurnProvider* turn, const Timestamp avgFrame = Timestamp::fromMS(500)) :
+	    pose(pose), turn(turn), avgIn(avgFrame, MagnetometerData(0,0,0)) {
 		;
 	}
 
+	/** get the current uncertainty estimation */
+	float getSigma() {
+		return curSigma + pose->getSigma() + turn->getSigma();
+	}
+
 	/** add magnetometer readings, returns the current heading, or NAN (if unstable/unknown) */
 	float addMagnetometer(const Timestamp& ts, const MagnetometerData& mag) {
 
@@ -73,30 +92,38 @@ public:
 
 		// calculate angle
 		// https://aerocontent.honeywell.com/aero/common/documents/myaerospacecatalog-documents/Defense_Brochures-documents/Magnetic__Literature_Application_notes-documents/AN203_Compass_Heading_Using_Magnetometers.pdf
-		const float mx = curMag.x;
+		const float mx = (curMag.x);
-		const float my = curMag.y;
+		const float my = (curMag.y);
 		const float tmp = std::atan2(my, mx);
 		//const float tmp = (my > 0) ? (M_PI*0.5 - std::atan(mx/my)) : (M_PI*1.5 - atan(mx/my));
 
 		// http://www.magnetic-declination.com/
 		// http://davidegironi.blogspot.de/2013/01/avr-atmega-hmc5883l-magnetometer-lib-01.html
 		const float declination = 3.0f / 180.0f * M_PI;		// GERMANY!
-		const float curHeading = - tmp + declination;
+		//const float declination = 0;		// GERMANY!
+		float curHeading = Angle::makeSafe_2PI(- tmp + declination);
+
 		float resHeading;
-		bool stable = true;
+		stable = true;
 
 		// calculate standard-deviation within a certain timeframe
-		stdDev.add(ts, curHeading);
+		const float curDiff = Angle::getSignedDiffRAD_2PI(curHeading, lastHeading);
+		stdDev.add(ts, curDiff);
+		stdDevForSigma.add(ts, curDiff);
+		curSigma = (5.0f/180.0f*(float)M_PI) + stdDevForSigma.get()*10;
+		lastHeading = curHeading;
+
+
 
 		// if the standard-deviation is too high,
 		// the compass is considered unstable
-		if (numMagReadings < 250 || stdDev.get() > 0.30) {
+//		if (numMagReadings < 250 || stdDev.get() > 0.30) {
-			resHeading = NAN;
+//			resHeading = NAN;
-			stable = false;
+//			stable = false;
-		} else {
+//		} else {
 			resHeading = curHeading;
 			stable = true;
-		}
+//		}
 
 		#ifdef WITH_DEBUG_PLOT
 			plot.add(ts, curHeading, stable, mag, curMag);
@@ -107,6 +134,7 @@ public:
 
 	}
 
+
 };
 
 #endif // INDOOR_IMU_COMPASSDETECTION_H

sensors/imu/CompassDetectionPlot.h

@@ -22,7 +22,7 @@
 
 		K::Gnuplot gp1;
 		K::Gnuplot gp2;
-		K::GnuplotMultiplot multiplot = K::GnuplotMultiplot(1,2);
+		//K::GnuplotMultiplot multiplot = K::GnuplotMultiplot(1,2);
 
 		K::GnuplotPlot plotMagRaw;
 		K::GnuplotPlotElementLines lineMagRawX;
@@ -47,8 +47,8 @@
 			gp1 << "set autoscale xfix\n";
 			gp2 << "set size ratio -1\n";
 
-			multiplot.add(&plotMagRaw);
+			//multiplot.add(&plotMagRaw);
-			multiplot.add(&plotMagFix);
+			//multiplot.add(&plotMagFix);
 
 			plotMagRaw.setTitle("Magnetometer (raw)");
 			plotMagRaw.add(&lineMagRawX); lineMagRawX.getStroke().getColor().setHexStr("#ff0000"); lineMagRawX.setTitle("x");
@@ -106,7 +106,7 @@
 				gp1 << "set arrow 1 from screen 0.85,0.85 to screen " << ax << "," << ay << "\n";
 				gp1 << "set object 2 circle at screen 0.85,0.85 radius screen 0.1 \n";
 
-				gp1.draw(multiplot);
+				gp1.draw(plotMagFix);
 				gp1.flush();
 
 				gp2.draw(plotMagScatter);

sensors/imu/GravityData.h

@@ -3,20 +3,20 @@
 
 #include <cmath>
 #include <sstream>
-
+#include "../../math/Floatingpoint.h"
 
 /** data received from an accelerometer sensor */
 struct GravityData {
 
-	float x;
+	FPDefault x;
-	float y;
+	FPDefault y;
-	float z;
+	FPDefault z;
 
     GravityData() : x(0), y(0), z(0) {;}
 
     GravityData(const float x, const float y, const float z) : x(x), y(y), z(z) {;}
 
-	float magnitude() const {
+	FPDefault magnitude() const {
 		return std::sqrt( x*x + y*y + z*z );
 	}
 
@@ -38,7 +38,7 @@ struct GravityData {
         return GravityData(x-o.x, y-o.y, z-o.z);
 	}
 
-    GravityData operator / (const float val) const {
+	GravityData operator / (const FPDefault val) const {
         return GravityData(x/val, y/val, z/val);
 	}
 
@@ -60,7 +60,7 @@ struct GravityData {
 
 private:
 
-	static inline bool EQ_OR_NAN(const float a, const float b) {return (a==b) || ( (a!=a) && (b!=b) );}
+	static inline bool EQ_OR_NAN(const FPDefault a, const FPDefault b) {return (a==b) || ( (a!=a) && (b!=b) );}
 
 };
 

sensors/imu/GyroscopeData.h

@@ -3,6 +3,7 @@
 
 #include <cmath>
 #include <sstream>
+#include "../../math/Floatingpoint.h"
 
 /**
  * data received from a gyroscope sensor
@@ -10,14 +11,14 @@
  */
 struct GyroscopeData {
 
-	float x;
+	FPDefault x;
-	float y;
+	FPDefault y;
-	float z;
+	FPDefault z;
 
 	GyroscopeData() : x(0), y(0), z(0) {;}
 
 	/** ctor from RADIANS */
-	GyroscopeData(const float x, const float y, const float z) : x(x), y(y), z(z) {;}
+	GyroscopeData(const FPDefault x, const FPDefault y, const FPDefault z) : x(x), y(y), z(z) {;}
 
 	float magnitude() const {
 		return std::sqrt( x*x + y*y + z*z );
@@ -41,7 +42,7 @@ struct GyroscopeData {
 
 private:
 
-	static inline bool EQ_OR_NAN(const float a, const float b) {return (a==b) || ( (a!=a) && (b!=b) );}
+	static inline bool EQ_OR_NAN(const FPDefault a, const FPDefault b) {return (a==b) || ( (a!=a) && (b!=b) );}
 
 };
 

sensors/imu/MagnetometerData.h

@@ -4,20 +4,21 @@
 
 #include <cmath>
 #include <sstream>
+#include "../../math/Floatingpoint.h"
 
 /**
  * data received from a magnetometer sensor
  */
 struct MagnetometerData {
 
-	float x;
+	FPDefault x;
-	float y;
+	FPDefault y;
-	float z;
+	FPDefault z;
 
 	MagnetometerData() : x(0), y(0), z(0) {;}
 
 	/** ctor from RADIANS */
-	MagnetometerData(const float x, const float y, const float z) : x(x), y(y), z(z) {;}
+	MagnetometerData(const FPDefault x, const FPDefault y, const FPDefault z) : x(x), y(y), z(z) {;}
 
 	std::string asString() const {
 		std::stringstream ss;
@@ -29,7 +30,7 @@ struct MagnetometerData {
 		return (x == x) && (y == y) && (z == z);
 	}
 
-	bool operator == (const GyroscopeData& o ) const {
+	bool operator == (const MagnetometerData& o ) const {
 		return	EQ_OR_NAN(x, o.x) &&
 				EQ_OR_NAN(y, o.y) &&
 				EQ_OR_NAN(z, o.z);
@@ -53,22 +54,27 @@ struct MagnetometerData {
 		return *this;
 	}
 
-	MagnetometerData operator * (const MagnetometerData& o) const {
+
-		return MagnetometerData(x*o.x, y*o.y, z*o.z);
+	MagnetometerData operator + (const MagnetometerData& o) const {
+		return MagnetometerData(x+o.x, y+o.y, z+o.z);
 	}
 
 	MagnetometerData operator - (const MagnetometerData& o) const {
 		return MagnetometerData(x-o.x, y-o.y, z-o.z);
 	}
 
-	MagnetometerData operator / (const float val) const {
+	MagnetometerData operator * (const MagnetometerData& o) const {
+		return MagnetometerData(x*o.x, y*o.y, z*o.z);
+	}
+
+	MagnetometerData operator / (const FPDefault val) const {
 		return MagnetometerData(x/val, y/val, z/val);
 	}
 
 
 private:
 
-	static inline bool EQ_OR_NAN(const float a, const float b) {return (a==b) || ( (a!=a) && (b!=b) );}
+	static inline bool EQ_OR_NAN(const FPDefault a, const FPDefault b) {return (a==b) || ( (a!=a) && (b!=b) );}
 
 };
 

sensors/imu/PoseDetection.h

@@ -5,6 +5,7 @@
 
 #include "../../data/Timestamp.h"
 
+#include "../../math/MovingStdDevTS.h"
 #include "../../math/MovingAverageTS.h"
 #include "../../math/MovingMedianTS.h"
 #include "../../math/Matrix3.h"
@@ -14,12 +15,13 @@
 //#include <eigen3/Eigen/Dense>
 
 #include "PoseDetectionPlot.h"
+#include "PoseProvider.h"
 
 /**
  * estimate the smartphones world-pose,
  * based on the accelerometer's data
  */
-class PoseDetection {
+class PoseDetection : public PoseProvider {
 
 
 	/** live-pose-estimation using moving average of the smartphone's accelerometer */
@@ -29,7 +31,7 @@ class PoseDetection {
 		MovingAverageTS<AccelerometerData> avg;
 
 		EstMovingAverage(const Timestamp window) :
-			avg(MovingAverageTS<AccelerometerData>(window, AccelerometerData())) {
+		    avg(window, AccelerometerData()) {
 
 			// start approximately
 			addAcc(Timestamp(), AccelerometerData(0,0,9.81));
@@ -45,26 +47,82 @@ class PoseDetection {
 			return avg.get();
 		}
 
+//		/** get the current rotation matrix estimation */
+//		//Eigen::Matrix3f get() const {
+//		Matrix3 get() const {
+
+//			// get the current acceleromter average
+//			const AccelerometerData avgAcc = avg.get();
+//			//const Eigen::Vector3f avg(avgAcc.x, avgAcc.y, avgAcc.z);
+//			const Vector3 avg(avgAcc.x, avgAcc.y, avgAcc.z);
+
+//			// rotate average-accelerometer into (0,0,1)
+//			//Eigen::Vector3f zAxis; zAxis << 0, 0, 1;
+//			const Vector3 zAxis(0,0,1);
+//			const Matrix3 rotMat = getRotationMatrix(avg.normalized(), zAxis);
+//			//const Matrix3 rotMat = getRotationMatrix(zAxis, avg.normalized());	// INVERSE
+//			//const Eigen::Matrix3f rotMat = getRotationMatrix(avg.normalized(), zAxis);
+
+//			// just a small sanity check. after applying to rotation the acc-average should become (0,0,1)
+//			//Eigen::Vector3f aligned = (rotMat * avg).normalized();
+//			const Vector3 aligned = (rotMat * avg).normalized();
+//			Assert::isBetween(aligned.norm(), 0.95f, 1.05f, "result distorted");
+//			Assert::isTrue((aligned-zAxis).norm() < 0.1f, "deviation too high");
+
+//			return rotMat;
+
+//		}
+
+		// FOR TESTING
 		/** get the current rotation matrix estimation */
 		//Eigen::Matrix3f get() const {
 		Matrix3 get() const {
 
+			// https://stackoverflow.com/questions/18558910/direction-vector-to-rotation-matrix
 			// get the current acceleromter average
 			const AccelerometerData avgAcc = avg.get();
 			//const Eigen::Vector3f avg(avgAcc.x, avgAcc.y, avgAcc.z);
-			const Vector3 avg(avgAcc.x, avgAcc.y, avgAcc.z);
+			const Point3 vZ = Point3(avgAcc.x, avgAcc.y, avgAcc.z).normalized();
+			const Point3 vX = cross(Point3(0,1,0), vZ).normalized();//Point3(avgAcc.z, -avgAcc.y, avgAcc.x);
+			//const Point3 v2 = cross(v3, vx).normalized();
+			const Point3 vY = cross(vZ, vX).normalized();
 
-			// rotate average-accelerometer into (0,0,1)
+			Matrix3 rotMat({
-			//Eigen::Vector3f zAxis; zAxis << 0, 0, 1;
+			    vX.x, vY.x, vZ.x,
-			const Vector3 zAxis(0,0,1);
+			    vX.y, vY.y, vZ.y,
-			const Matrix3 rotMat = getRotationMatrix(avg.normalized(), zAxis);
+			    vX.z, vY.z, vZ.z,
-			//const Matrix3 rotMat = getRotationMatrix(zAxis, avg.normalized());	// INVERSE
+			});
-			//const Eigen::Matrix3f rotMat = getRotationMatrix(avg.normalized(), zAxis);
+
+			// above transposed = inverse matrix = undo rotation
+			rotMat = rotMat.transposed();
+
+//			// https://stackoverflow.com/questions/18558910/direction-vector-to-rotation-matrix
+//			// get the current acceleromter average
+//			const AccelerometerData avgAcc = avg.get();
+//			//const Eigen::Vector3f avg(avgAcc.x, avgAcc.y, avgAcc.z);
+//			const Point3 vZ = Point3(-avgAcc.x, -avgAcc.y, -avgAcc.z).normalized();
+//			const Point3 vX = cross(vZ, Point3(0,1,0)).normalized();//Point3(avgAcc.z, -avgAcc.y, avgAcc.x);
+//			//const Point3 v2 = cross(v3, vx).normalized();
+//			const Point3 vY = cross(vX, vZ).normalized();
+
+//			Matrix3 rotMat({
+//			    vX.x, vY.x, vZ.x,
+//			    vX.y, vY.y, vZ.y,
+//			    vX.z, vY.z, vZ.z,
+//			});
+
+//			//rotMat = Matrix3::getRotationDeg(180, 0, 0) * rotMat;
+//			//rotMat = Matrix3::getRotationDeg(0, 0, 180) * rotMat;
+
+//			// above transposed = inverse matrix = undo rotation
+//			//rotMat = rotMat.transposed();
 
 			// just a small sanity check. after applying to rotation the acc-average should become (0,0,1)
-			//Eigen::Vector3f aligned = (rotMat * avg).normalized();
+			const Vector3 zAxis(0,0,1);
-			const Vector3 aligned = (rotMat * avg).normalized();
+			const Vector3 inp(avgAcc.x, avgAcc.y, avgAcc.z);
-			Assert::isTrue((aligned-zAxis).norm() < 0.1f, "deviation too high");
+			const Vector3 aligned = (rotMat * inp).normalized();
+			Assert::isBetween(aligned.norm(), 0.95f, 1.05f, "result distorted");
+			//Assert::isTrue((aligned-zAxis).norm() < 0.10f, "deviation too high");
 
 			return rotMat;
 
@@ -120,22 +178,24 @@ class PoseDetection {
 //	};
 
 
-
 private:
 
 	struct {
-		//Eigen::Matrix3f rotationMatrix = Eigen::Matrix3f::Identity();
 		Matrix3 rotationMatrix = Matrix3::identity();
+		float curSigma = 0;
 		bool isKnown = false;
 		Timestamp lastEstimation;
 	} orientation;
 
 	/** how the pose is estimated */
 	//LongTermMovingAverage est = LongTermMovingAverage(Timestamp::fromMS(1250));
-	EstMovingAverage est = EstMovingAverage(Timestamp::fromMS(450));
+	EstMovingAverage est;
 	//EstMovingMedian est = EstMovingMedian(Timestamp::fromMS(300));
 
+	MovingStdDevTS<float> stdDevForSigma = MovingStdDevTS<float>(Timestamp::fromMS(500), 0);
+
 	#ifdef WITH_DEBUG_PLOT
+	    int plotLimit = 0;
 		PoseDetectionPlot plot;
 	#endif
 
@@ -143,22 +203,46 @@ private:
 public:
 
 	/** ctor */
-	PoseDetection() {
+	PoseDetection(const Timestamp delay = Timestamp::fromMS(450)) : est(delay) {
-		;
+        #ifdef WITH_DEBUG_PLOT
+		    plot.setName("PoseDetection1");
+        #endif
 	}
 
 	/** get the smartphone's rotation matrix */
-	const Matrix3& getMatrix() const {
+	const Matrix3& getMatrix() const override {
 		return orientation.rotationMatrix;
 	}
 
 	/** is the pose known and stable? */
-	bool isKnown() const {
+	bool isKnown() const override {
 		return orientation.isKnown;
 	}
 
+	Matrix3 getMatrixGyro() const {
+		return Matrix3::identity();
+	}
+
+	Matrix3 getMatrixAcc() const {
+		return orientation.rotationMatrix;
+	}
+
+	/** current uncertainty */
+	float getSigma() const {
+		return orientation.curSigma;
+	}
+
+
 	void addAccelerometer(const Timestamp& ts, const AccelerometerData& acc) {
 
+		// uncertainty
+		const Vector3 curAcc = Vector3(acc.x, acc.y, acc.z);
+		float angleDiff = std::acos(curAcc.normalized().dot(Vector3(0,0,1)));
+		if (!std::isnan(angleDiff)) {
+			stdDevForSigma.add(ts, angleDiff);
+			orientation.curSigma = stdDevForSigma.get()*1;
+		}
+
 		// add accelerometer data
 		est.addAcc(ts, acc);
 
@@ -169,7 +253,10 @@ public:
 
 		// debug-plot (if configured)
 		#ifdef WITH_DEBUG_PLOT
-			plot.add(ts, est.getBase(), orientation.rotationMatrix);
+		    if (++plotLimit > 5) {
+				plot.add(ts, est.getBase(), orientation.rotationMatrix);
+				plotLimit = 0;
+			}
 		#endif
 
 	}

sensors/imu/PoseDetection2.h

@@ -0,0 +1,301 @@
+#ifndef POSEDETECTION2_H
+#define POSEDETECTION2_H
+
+
+#include "AccelerometerData.h"
+#include "GyroscopeData.h"
+
+#include "../../data/Timestamp.h"
+
+//#include "../../math/MovingAverageTS.h"
+//#include "../../math/MovingMedianTS.h"
+#include "../../math/Matrix3.h"
+
+#include "../../math/filter/Complementary.h"
+
+#include "../../geo/Point3.h"
+
+//#include "../../math/FixedFrequencyInterpolator.h"
+
+#include "PoseDetectionPlot.h"
+#include "PoseProvider.h"
+
+/**
+ * estimate the smartphones world-pose,
+ * based on the accelerometer's data
+ *
+ * https://robotics.stackexchange.com/questions/6953/how-to-calculate-euler-angles-from-gyroscope-output
+ */
+class PoseDetection2 : public PoseProvider {
+
+private:
+
+	struct {
+		//Eigen::Matrix3f rotationMatrix = Eigen::Matrix3f::Identity();
+		Matrix3 rotationMatrix = Matrix3::identity();
+		bool isKnown = false;
+		Timestamp lastEstimation;
+	} orientation;
+
+	/** how the pose is estimated */
+	//LongTermMovingAverage est = LongTermMovingAverage(Timestamp::fromMS(1250));
+	//EstMovingAverage est = EstMovingAverage(Timestamp::fromMS(450));
+	//EstMovingMedian est = EstMovingMedian(Timestamp::fromMS(300));
+
+	#ifdef WITH_DEBUG_PLOT
+		PoseDetectionPlot plot;
+		PoseDetectionPlotAngles plotAngles;
+	#endif
+
+	Vector3 lastGyroReading;
+	Timestamp lastGyroReadingTS;
+
+	//FixedFrequencyInterpolator<Vector3> interpolAcc;
+	//FixedFrequencyInterpolator<Vector3> interpolGyro;
+
+	Filter::Complementary<Vector3> filter;
+
+	//std::vector<Vector3> accBuf;
+	//std::vector<Vector3> gyroBuf;
+
+
+
+	Vector3 curAccel;
+
+	bool firstAccel = true;
+	Vector3 curAccel_rad;
+	Vector3 curGyroSum_rad;
+
+	//Matrix3 curGyroMatrix = Matrix3::identity();
+
+	static constexpr float splitFreq = 2.5;
+	static constexpr float sRate = 50;
+	static constexpr int sRateTS = 1000/sRate;
+
+
+public:
+
+	/** ctor */
+	//PoseDetection2() : interpolAcc(Timestamp::fromMS(sRateTS)), interpolGyro(Timestamp::fromMS(sRateTS)), filter(splitFreq, sRate) {
+	PoseDetection2() : filter(1, 2.5) {
+        #ifdef WITH_DEBUG_PLOT
+		    plot.setName("PoseDetection2");
+        #endif
+	}
+
+	/** get the smartphone's rotation matrix */
+	const Matrix3& getMatrix() const override {
+		return orientation.rotationMatrix;
+	}
+
+	/** is the pose known and stable? */
+	bool isKnown() const override {
+		return orientation.isKnown;
+	}
+
+
+	float angleX_old_rad = 0;
+	float angleY_old_rad = 0;
+
+
+	void addAccelerometer(const Timestamp& ts, const AccelerometerData& acc) {
+
+		// https://theccontinuum.com/2012/09/24/arduino-imu-pitch-roll-from-accelerometer/#docs
+
+		float angleX_rad = std::atan2( acc.y, acc.z);
+		float angleY_rad = std::atan2(-acc.x, std::sqrt(acc.y*acc.y + acc.z*acc.z));
+		float angleZ_rad = 0;
+
+		if (std::abs(angleX_rad-angleX_old_rad) > M_PI) {angleX_rad += 2*M_PI;}
+		if (std::abs(angleY_rad-angleY_old_rad) > M_PI) {angleY_rad += 2*M_PI;}
+
+		angleX_old_rad = angleX_rad;
+		angleY_old_rad = angleY_rad;
+
+//		float angleX_rad = std::atan2(acc.y, std::sqrt(acc.x*acc.x + acc.z*acc.z));
+//		float angleY_rad = std::atan2(-acc.x, std::sqrt(acc.y*acc.y + acc.z*acc.z));
+//		float angleZ_rad = 0;
+
+//		Point2 ref(0,1);
+//		Point2 xz( acc.x, acc.z);
+//		Point2 yz(-acc.y, acc.z);
+//		float angleY_rad = std::atan2( determinant(ref,xz), dot(ref,xz) );
+//		float angleX_rad = std::atan2( determinant(ref,yz), dot(ref,yz) );
+//		float angleZ_rad = 0.0;
+
+//		float angleX_rad =  std::atan2(acc.y, acc.z);
+//		float angleY_rad = -std::atan2(acc.x, acc.z);
+//		float angleZ_rad = 0;//-std::atan2(acc.y, acc.x);
+
+
+		//		float angleX2_rad = (angleX1_rad > 0) ? (angleX1_rad - 2*M_PI) : (angleX1_rad + 2*M_PI);
+//		float angleY2_rad = (angleY1_rad > 0) ? (angleY1_rad - 2*M_PI) : (angleY1_rad + 2*M_PI);
+//		float angleX_rad = (std::abs(curAngle_rad.x-angleX1_rad) < std::abs(curAccel_rad.x-angleX2_rad)) ? (angleX1_rad) : (angleX2_rad);
+//		float angleY_rad = (std::abs(curAngle_rad.y-angleY1_rad) < std::abs(curAccel_rad.y-angleY2_rad)) ? (angleY1_rad) : (angleY2_rad);
+
+		curAccel = Vector3(acc.x, acc.y, acc.z);
+		curAccel_rad = Vector3(angleX_rad, angleY_rad, angleZ_rad);
+
+		//curAccel_rad = Matrix3::getRotationRad(0,0,-angleZ_rad) * Vector3(angleX_rad, angleY_rad, angleZ_rad);
+
+
+		if (firstAccel) {
+			curGyroSum_rad = curAccel_rad;
+			firstAccel = false;
+		}
+
+
+
+	}
+
+
+
+
+	void addGyroscope(const Timestamp& ts, const GyroscopeData& gyro) {
+
+		Vector3 vec(gyro.x, gyro.y, gyro.z);
+
+		// ignore the first reading completely, just remember its timestamp
+		if (lastGyroReadingTS.isZero()) {lastGyroReadingTS = ts; return;}
+
+		// time-difference between previous and current reading
+		const Timestamp curDiff = ts - lastGyroReadingTS;
+		lastGyroReadingTS = ts;
+
+		// fast sensors might lead to delay = 0 ms. filter those values
+		if (curDiff.isZero()) {return;}
+
+		// current area
+		const Vector3 curArea =	(lastGyroReading * curDiff.sec());
+
+//		// update sum
+//		curAngle_rad += curArea;
+//		curGyroSum_rad += curArea;
+
+//		// PAPER
+		const float dx = 1 * lastGyroReading.x +	std::sin(curGyroSum_rad.x)*std::sin(curGyroSum_rad.y)/std::cos(curGyroSum_rad.y)*lastGyroReading.y +	std::cos(curGyroSum_rad.x)*std::sin(curGyroSum_rad.y)/std::cos(curGyroSum_rad.y)*lastGyroReading.z;
+		const float dy =							std::cos(curGyroSum_rad.x)*lastGyroReading.y +															-std::sin(curGyroSum_rad.x)*lastGyroReading.z;
+		const float dz =							std::sin(curGyroSum_rad.x)/std::cos(curGyroSum_rad.y)*lastGyroReading.y +								std::cos(curGyroSum_rad.x)/std::cos(curGyroSum_rad.y)*lastGyroReading.z;
+		curGyroSum_rad.x += dx*curDiff.sec();
+		curGyroSum_rad.y += dy*curDiff.sec();
+		curGyroSum_rad.z += dz*curDiff.sec();
+
+
+//		// PAPER
+//		const Vector3 n = lastGyroReading / lastGyroReading.norm();
+//		const float mag = lastGyroReading.norm() * curDiff.sec();
+//		if (mag != 0) {
+//			curGyroMatrix = Matrix3::getRotationVec(n.x, n.y, n.z, mag).transposed() * curGyroMatrix;
+//		}
+
+		// DEBUG PLOT
+
+
+		// update old reading
+		lastGyroReading = vec;
+
+		update(ts);
+
+
+
+	}
+
+	Matrix3 getMatrixGyro() const {
+		return Matrix3::getRotationRad(curGyroSum_rad.x, curGyroSum_rad.y, curGyroSum_rad.z);
+	}
+
+	Matrix3 getMatrixAcc() const {
+		return Matrix3::getRotationRad(curAccel_rad.x, curAccel_rad.y, curAccel_rad.z);
+	}
+
+private:
+
+	Vector3 curAngle_rad;
+	int cnt = 0;
+
+	void update(const Timestamp ts) {
+
+
+		// complementary filter		x = alpha * x + (1-alpha) * y;
+		const float alpha = 0.98f;
+		//curAngle_rad = curAngle_rad*alpha + curAccel_rad*(1-alpha);
+		//curAngle_rad = curAccel_rad;
+		//curAngle_rad = curGyroSum_rad;
+
+		//std::cout << curGyroSum_rad.x <<" " << curGyroSum_rad.y << " " << curGyroSum_rad.z << std::endl;
+
+		//curAngle_rad = filter.get();
+
+		filter.addSlow(ts, curAccel_rad);
+		filter.addFast(ts, curGyroSum_rad);
+
+		static Vector3 fused;
+		static Vector3 pref;
+		Vector3 diff = curGyroSum_rad - pref;
+		fused = (fused+diff) * alpha + curAccel_rad * (1-alpha);
+		pref = curGyroSum_rad;
+
+		// update
+		//orientation.rotationMatrix = Matrix3::getRotationRad(curAccel_rad.x, curAccel_rad.y, curAccel_rad.z); //getMatrixFor(cur);
+		//orientation.rotationMatrix = Matrix3::getRotationRad(curGyroSum_rad.x, curGyroSum_rad.y, curGyroSum_rad.z); //getMatrixFor(cur);
+		//orientation.rotationMatrix = curGyroMatrix;
+		//orientation.rotationMatrix = Matrix3::getRotationRadZ(curGyroSum_rad.z) * Matrix3::getRotationRadX(curGyroSum_rad.x) * Matrix3::getRotationRadY(curGyroSum_rad.y);
+		//orientation.rotationMatrix = Matrix3::getRotationRad(curGyroSum_rad.x, curGyroSum_rad.y, curGyroSum_rad.z);
+		orientation.rotationMatrix = Matrix3::getRotationRad(fused.x, fused.y, 0); //getMatrixFor(cur);
+
+
+		orientation.isKnown = true;
+		orientation.lastEstimation = ts;
+
+		// debug-plot (if configured)
+        #ifdef WITH_DEBUG_PLOT
+		    plot.add(ts, curAccel, orientation.rotationMatrix);
+			if (++cnt % 2 == 0) {
+				plotAngles.addAcc(ts, curAccel_rad.x, curAccel_rad.y);
+				plotAngles.addGyro(ts, curGyroSum_rad.x, curGyroSum_rad.y);
+				plotAngles.addFused(ts, fused.x, fused.y);
+			}
+        #endif
+
+	}
+
+//	/** get the current rotation matrix estimation */
+//	Matrix3 getMatrixFor(const Vector3 cur) const {
+
+//		// rotate average-accelerometer into (0,0,1)
+//		//Eigen::Vector3f zAxis; zAxis << 0, 0, 1;
+//		const Vector3 zAxis(0,0,1);
+//		const Matrix3 rotMat = getRotationMatrix(cur.normalized(), zAxis);
+//		//const Matrix3 rotMat = getRotationMatrix(zAxis, avg.normalized());	// INVERSE
+//		//const Eigen::Matrix3f rotMat = getRotationMatrix(avg.normalized(), zAxis);
+
+//		// just a small sanity check. after applying to rotation the acc-average should become (0,0,1)
+//		//Eigen::Vector3f aligned = (rotMat * avg).normalized();
+//		const Vector3 aligned = (rotMat * cur).normalized();
+//		Assert::isTrue((aligned-zAxis).norm() < 0.1f, "deviation too high");
+
+//		return rotMat;
+
+//	}
+
+//	/** get a matrix that rotates the vector "from" into the vector "to" */
+//	static Matrix3 getRotationMatrix(const Vector3& from, const Vector3 to) {
+
+//		// http://math.stackexchange.com/questions/293116/rotating-one-3d-vector-to-another
+
+//		const Vector3 v = from.cross(to) / from.cross(to).norm();
+//		const float angle = std::acos( from.dot(to) / from.norm() / to.norm() );
+
+//		Matrix3 A({
+//			0.0f,	-v.z,	v.y,
+//			v.z,	0.0f,	-v.x,
+//			-v.y,	v.x,	0.0f
+//		});
+
+//		return Matrix3::identity() + (A * std::sin(angle)) + ((A*A) * (1-std::cos(angle)));
+
+//	}
+
+};
+
+#endif // POSEDETECTION2_H

sensors/imu/PoseDetection3.h

@@ -0,0 +1,179 @@
+#ifndef POSEDETECTION3_H
+#define POSEDETECTION3_H
+
+#include "AccelerometerData.h"
+#include "GyroscopeData.h"
+
+#include "../../data/Timestamp.h"
+#include "../../math/Matrix3.h"
+#include "../../math/Quaternion.h"
+
+#include "../../geo/Point3.h"
+
+#include "PoseDetectionPlot.h"
+#include "PoseProvider.h"
+
+
+class PoseDetection3 : public PoseProvider {
+
+private:
+
+	struct {
+		//Eigen::Matrix3f rotationMatrix = Eigen::Matrix3f::Identity();
+		Matrix3 rotationMatrix = Matrix3::identity();
+		bool isKnown = false;
+		Timestamp lastEstimation;
+	} orientation;
+
+	#ifdef WITH_DEBUG_PLOT
+		PoseDetectionPlot plot;
+		PoseDetectionPlotAngles plotAngles;
+	#endif
+
+	Vector3 lastGyroReading;
+	Timestamp lastGyroReadingTS;
+
+public:
+
+	/** ctor */
+	PoseDetection3() {
+		#ifdef WITH_DEBUG_PLOT
+			plot.setName("PoseDetection3");
+		#endif
+	}
+
+	/** get the smartphone's rotation matrix */
+	const Matrix3& getMatrix() const override {
+		return orientation.rotationMatrix;
+	}
+
+	/** is the pose known and stable? */
+	bool isKnown() const override {
+		return orientation.isKnown;
+	}
+
+
+	bool first = true;
+
+	Quaternion qGyro = Quaternion(1, 0,0,0);
+	Quaternion qGyroUpdate;
+	Quaternion qAccel;
+	Quaternion qFiltered;
+
+	void addAccelerometer(const Timestamp& ts, const AccelerometerData& acc) {
+
+		const Vector3 vec(-acc.x, -acc.y, acc.z);
+		const Vector3 v = vec.normalized();
+
+
+		const float mag = -std::acos(v.dot(Vector3(0,0,1)));//-std::acos(v.z); << same
+		const Vector3 n = Vector3(v.y, -v.x, 0).normalized();
+		qAccel = Quaternion::fromAxisAngle(mag, n.x, n.y, n.z);
+
+		//const float magY = std::atan2(acc.x, acc.z);
+		//const float magX = std::atan2(acc.y, acc.z);
+		//qAccel = Quaternion::fromAxisAngle(magX, 1, 0, 0) * Quaternion::fromAxisAngle(-magY, 0, 1, 0);
+
+
+
+		//Vector3 dv = qAccel.toEuler();
+		//dv.z = 0;
+		//std::cout << dv.x << " " << dv.y << " " << dv.z << std::endl;
+
+		// for plotting
+		if (first) {
+			qGyro = qAccel;
+			first = false;
+		}
+
+		int i = 0; (void) i;
+
+	}
+
+
+
+
+	void addGyroscope(const Timestamp& ts, const GyroscopeData& gyro) {
+
+		Vector3 vec(gyro.x, gyro.y, gyro.z);
+
+		// ignore the first reading completely, just remember its timestamp
+		if (lastGyroReadingTS.isZero()) {lastGyroReadingTS = ts; return;}
+
+		// time-difference between previous and current reading
+		const Timestamp curDiff = ts - lastGyroReadingTS;
+		lastGyroReadingTS = ts;
+
+		// fast sensors might lead to delay = 0 ms. filter those values
+		if (curDiff.isZero()) {return;}
+
+		// current area
+		//const Vector3 curArea =	(lastGyroReading * curDiff.sec());
+
+
+		// length of the rotation vector
+		const float theta =  curDiff.sec() * lastGyroReading.norm();
+		const Vector3 v = lastGyroReading.normalized();
+		lastGyroReading = vec;
+
+		if (theta == 0) {return;}
+		qGyroUpdate = Quaternion::fromAxisAngle(theta, v.x, v.y, v.z);// qUpdate(cos(theta/2),		v.x * sin(theta/2), v.y * sin(theta/2), v.z * sin(theta/2));
+
+		// update
+		qGyro = qGyroUpdate * qGyro;
+
+
+
+		update(ts);
+
+	}
+
+	Matrix3 getMatrixAcc() const {
+		Vector3 r = qAccel.toEuler();
+		return Matrix3::getRotationRad(r.x, r.y, r.z);
+	}
+	Matrix3 getMatrixGyro() const {
+		Vector3 r = qGyro.toEuler();
+		return Matrix3::getRotationRad(r.x, r.y, r.z);
+	}
+
+private:
+
+	Vector3 curAngle_rad;
+	int cnt = 0;
+
+	void update(const Timestamp ts) {
+
+
+		//Quaternion qFused = qGyro;
+		//qFiltered = qAccel;
+		//Quaternion qFused = (qGyro * alpha) + (qAccel * (1-alpha));
+		qFiltered = Quaternion::lerp(qFiltered*qGyroUpdate, qAccel, 0.05);
+		//qFiltered = Quaternion::fromAxisAngle(qAccel.w*0.02, qAccel.x, qAccel.y, qAccel.z) * (qFiltered * qGyroUpdate) * 0.98;
+
+		Vector3 fused = qFiltered.toEuler();
+		//std::cout << fused.x <<" " << fused.y << " " << fused.z << std::endl;
+
+		// update
+		orientation.rotationMatrix = Matrix3::getRotationRad(fused.x, fused.y, fused.z); //getMatrixFor(cur);
+
+
+		orientation.isKnown = true;
+		orientation.lastEstimation = ts;
+
+		// debug-plot (if configured)
+		#ifdef WITH_DEBUG_PLOT
+		    plot.add(ts, Vector3(0,0,0), orientation.rotationMatrix);
+			if (++cnt % 2 == 0) {
+				plotAngles.addAcc(ts, qAccel.toEuler().x, qAccel.toEuler().y);
+				plotAngles.addGyro(ts, qGyro.toEuler().x, qGyro.toEuler().y);
+				plotAngles.addFused(ts, fused.x, fused.y);
+			}
+		#endif
+
+	}
+
+
+};
+
+#endif // POSEDETECTION3_H

sensors/imu/PoseDetectionPlot.h

@@ -17,19 +17,103 @@
 	#include "../../math/Matrix3.h"
 	#include "AccelerometerData.h"
 
+    class PoseDetectionPlotAngles {
+
+		Timestamp plotRef;
+		Timestamp lastPlot;
+
+		K::Gnuplot gp;
+
+		K::GnuplotPlot plotAcc;
+
+		K::GnuplotPlotElementLines lineAccX;
+		K::GnuplotPlotElementLines lineAccY;
+
+		K::GnuplotPlotElementLines lineGyroX;
+		K::GnuplotPlotElementLines lineGyroY;
+
+		K::GnuplotPlotElementLines lineFusedX;
+		K::GnuplotPlotElementLines lineFusedY;
+
+	public:
+
+		PoseDetectionPlotAngles() {
+
+			gp << "set autoscale xfix\n";
+
+			plotAcc.setTitle("Accelerometer");
+
+			plotAcc.add(&lineFusedX); lineFusedX.getStroke().getColor().setHexStr("#990000"); lineFusedX.setTitle("FusedX");lineFusedX.getStroke().setWidth(3);
+			plotAcc.add(&lineFusedY); lineFusedY.getStroke().getColor().setHexStr("#09900"); lineFusedY.setTitle("FusedY");	lineFusedY.getStroke().setWidth(3);
+
+			plotAcc.add(&lineAccX); lineAccX.getStroke().getColor().setHexStr("#ff8888"); lineAccX.setTitle("AccX");		lineAccX.getStroke().setType(K::GnuplotDashtype::DOTTED);		lineAccX.getStroke().setWidth(2);
+			plotAcc.add(&lineAccY); lineAccY.getStroke().getColor().setHexStr("#88ff88"); lineAccY.setTitle("AccY");		lineAccY.getStroke().setType(K::GnuplotDashtype::DOTTED);		lineAccY.getStroke().setWidth(2);
+
+			plotAcc.add(&lineGyroX); lineGyroX.getStroke().getColor().setHexStr("#ff8888"); lineGyroX.setTitle("GyroX");	lineGyroX.getStroke().setType(K::GnuplotDashtype::DASHED);		lineGyroX.getStroke().setWidth(2);
+			plotAcc.add(&lineGyroY); lineGyroY.getStroke().getColor().setHexStr("#88ff88"); lineGyroY.setTitle("GyroY");	lineGyroY.getStroke().setType(K::GnuplotDashtype::DASHED);		lineGyroY.getStroke().setWidth(2);
+
+			plotAcc.getKey().setVisible(true);
+
+		}
+
+		void addAcc(Timestamp ts, float x, float y) {
+			if (plotRef.isZero()) {plotRef = ts;}
+			const Timestamp tsPlot = (ts-plotRef);
+			lineAccX.add( K::GnuplotPoint2(tsPlot.ms(), x) );
+			lineAccY.add( K::GnuplotPoint2(tsPlot.ms(), y) );
+		}
+
+		void addGyro(Timestamp ts, float x, float y) {
+			if (plotRef.isZero()) {plotRef = ts;}
+			const Timestamp tsPlot = (ts-plotRef);
+			lineGyroX.add( K::GnuplotPoint2(tsPlot.ms(), x) );
+			lineGyroY.add( K::GnuplotPoint2(tsPlot.ms(), y) );
+		}
+
+		void addFused(Timestamp ts, float x, float y) {
+			if (plotRef.isZero()) {plotRef = ts;}
+			const Timestamp tsPlot = (ts-plotRef);
+			lineFusedX.add( K::GnuplotPoint2(tsPlot.ms(), x) );
+			lineFusedY.add( K::GnuplotPoint2(tsPlot.ms(), y) );
+			if (++cnt % 40 == 0) {flush(ts);}
+		}
+
+
+
+	private:
+
+		int cnt = 0;
+
+		void flush(Timestamp ts) {
+			cleanup(ts);
+			gp.draw(plotAcc);
+			gp.flush();
+		}
+
+		// remove old  entries
+		void cleanup(Timestamp ts) {
+			const Timestamp tsPlot = (ts-plotRef);
+			const Timestamp tsOldest = tsPlot - Timestamp::fromMS(3000);
+			auto remove = [tsOldest] (const K::GnuplotPoint2 pt) {return pt.x < tsOldest.ms();};
+			lineAccX.removeIf(remove);
+			lineAccY.removeIf(remove);
+			lineGyroX.removeIf(remove);
+			lineGyroY.removeIf(remove);
+			lineFusedX.removeIf(remove);
+			lineFusedY.removeIf(remove);
+		}
+
+
+
+	};
+
 	class PoseDetectionPlot {
 
 		Timestamp plotRef;
 		Timestamp lastPlot;
 
-		K::Gnuplot gp1;
 		K::Gnuplot gp2;
 
-		K::GnuplotPlot plotAcc;
-		K::GnuplotPlotElementLines lineAccX;
-		K::GnuplotPlotElementLines lineAccY;
-		K::GnuplotPlotElementLines lineAccZ;
-
 		K::GnuplotSplot plotPose;
 		K::GnuplotSplotElementLines linePose;
 		//K::GnuplotSplotElementEmpty emptyPose;
@@ -41,14 +125,9 @@
 		/** ctor */
 		PoseDetectionPlot() {
 
-			gp1 << "set autoscale xfix\n";
+			//gp1 << "set autoscale xfix\n";
 			gp2 << "set view equal xyz\n";
 
-			plotAcc.setTitle("Accelerometer");
-			plotAcc.add(&lineAccX); lineAccX.getStroke().getColor().setHexStr("#ff0000"); lineAccX.setTitle("gyroX");
-			plotAcc.add(&lineAccY); lineAccY.getStroke().getColor().setHexStr("#00ff00"); lineAccY.setTitle("gyroY");
-			plotAcc.add(&lineAccZ); lineAccZ.getStroke().getColor().setHexStr("#0000ff"); lineAccZ.setTitle("gyroZ");
-
 			plotPose.setTitle("Pose");
 			plotPose.getView().setEnabled(false);
 			plotPose.add(&linePose);
@@ -58,6 +137,10 @@
 			plotPose.getAxisY().setRange(-8,+8);
 			plotPose.getAxisZ().setRange(-8,+8);
 
+			plotPose.getAxisX().setLabel("x");
+			plotPose.getAxisY().setLabel("y");
+			plotPose.getAxisZ().setLabel("z");
+
 			const float a = 0.05; const float b = 0.95;
 			pose = {
 				{{0, 0, 0},{1, 0, 0},{1, 1, 0},{0, 1, 0},{0, 0, 0}}, // boden
@@ -85,17 +168,20 @@
 
 		}
 
+		void setName(const std::string& name) {
+			plotPose.setTitle(name);
+		}
+
+		void add(Timestamp ts, const Vector3& avg, const Matrix3& rotation) {
+			add(ts, AccelerometerData(avg.x, avg.y, avg.z), rotation);
+		}
+
 		void add(Timestamp ts, const AccelerometerData& avg, const Matrix3& rotation) {
 
 			if (plotRef.isZero()) {plotRef = ts;}
 			const Timestamp tsPlot = (ts-plotRef);
 			const Timestamp tsOldest = tsPlot - Timestamp::fromMS(5000);
 
-			// acc
-			lineAccX.add( K::GnuplotPoint2(tsPlot.ms(), avg.x) );
-			lineAccY.add( K::GnuplotPoint2(tsPlot.ms(), avg.y) );
-			lineAccZ.add( K::GnuplotPoint2(tsPlot.ms(), avg.z) );
-
 			if (lastPlot + Timestamp::fromMS(50) < tsPlot) {
 				lastPlot = tsPlot;
 
@@ -128,20 +214,18 @@
 				const Vector3 vx = rotation * Vector3(2,0,0);
 				const Vector3 vy = rotation * Vector3(0,3,0);
 				const Vector3 vz = rotation * Vector3(0,0,5);
+				const Vector3 vA = Vector3(avg.x, avg.y, -avg.z) * 1;
 				linePose.clear();
 				linePose.addSegment(K::GnuplotPoint3(0,0,0), K::GnuplotPoint3(vx.x, vx.y, vx.z));
 				linePose.addSegment(K::GnuplotPoint3(0,0,0), K::GnuplotPoint3(vy.x, vy.y, vy.z));
 				linePose.addSegment(K::GnuplotPoint3(0,0,0), K::GnuplotPoint3(vz.x, vz.y, vz.z));
+				linePose.addSegment(K::GnuplotPoint3(0,0,0), K::GnuplotPoint3(vA.x, vA.y, vA.z));
 
-				// remove old accelerometer entries
+				gp2 << "set label 91 at " << vx.x << "," << vx.y << "," << vx.z << " 'x' \n";
-				auto remove = [tsOldest] (const K::GnuplotPoint2 pt) {return pt.x < tsOldest.ms();};
+				gp2 << "set label 92 at " << vy.x << "," << vy.y << "," << vy.z << " 'y' \n";
-				lineAccX.removeIf(remove);
+				gp2 << "set label 93 at " << vz.x << "," << vz.y << "," << vz.z << " 'z' \n";
-				lineAccY.removeIf(remove);
+				gp2 << "set label 99 at " << vA.x << "," << vA.y << "," << vA.z << " 'accel' \n";
-				lineAccZ.removeIf(remove);
 
-				// raw accelerometer
-				gp1.draw(plotAcc);
-				gp1.flush();
 
 				// 3D pose
 				gp2.draw(plotPose);

sensors/imu/PoseProvider.h

@@ -0,0 +1,43 @@
+#ifndef POSEPROVIDER_H
+#define POSEPROVIDER_H
+
+#include "../../math/Matrix3.h"
+
+class PoseProvider {
+
+public:
+
+	virtual const Matrix3& getMatrix() const = 0;
+
+	virtual float getSigma() const = 0;
+
+	virtual bool isKnown() const = 0;
+
+};
+
+
+class PoseProviderDummy : public PoseProvider {
+
+	Matrix3 mat = Matrix3::identity();
+
+public:
+
+	virtual const Matrix3& getMatrix() const override {
+		return mat;
+	}
+
+	Matrix3 getMatrixGyro() const {
+		return mat;
+	}
+
+	Matrix3 getMatrixAcc() const {
+		return mat;
+	}
+
+	virtual bool isKnown() const override {
+		return true;
+	}
+
+};
+
+#endif // POSEPROVIDER_H

sensors/imu/StepDetection2.h

@@ -1,7 +1,6 @@
 #ifndef STEPDETECTION2_H
 #define STEPDETECTION2_H
 
-
 #include "AccelerometerData.h"
 #include "../../data/Timestamp.h"
 
@@ -52,6 +51,8 @@ private:
 
 	float threshold = 0.50;
 
+	float curFiltered = 0;
+
 	#ifdef WITH_DEBUG_PLOT
 		K::Gnuplot gp;
 		K::GnuplotPlot plot;
@@ -109,6 +110,10 @@ public:
 
 	}
 
+	float getCurFiltered() const {
+		return curFiltered;
+	}
+
 	/** does the given data indicate a step? */
 	bool add(const Timestamp ts, const AccelerometerData& acc) {
 
@@ -118,6 +123,7 @@ public:
 		auto onResample = [&] (const Timestamp ts, const AccelerometerData data) {
 
 			const float mag = data.magnitude();
+			Assert::isNotNaN(mag, "detected NaN magnitude");
 
 			// use long-term average to center around zero
 			avg.add(ts, mag);
@@ -128,6 +134,8 @@ public:
 //			if (f != f) {return;}
 			const float f = biquad.filter(mag0);
 			const float fMag = f;
+			curFiltered = fMag;
+			Assert::isNotNaN(fMag, "detected NaN filtered magnitude");
 
 			const bool isMax = locMax.add(fMag);
 
@@ -173,6 +181,8 @@ public:
 
 		};
 
+		//qDebug() << ts.ms() << " ---" << acc.x << " " << acc.y << " " << acc.z;
+
 		// ensure fixed sampling rate for FIR freq filters to work!
 		interpol.add(ts, acc, onResample);
 

sensors/imu/TurnDetection.h

@@ -4,11 +4,11 @@
 #include "GyroscopeData.h"
 #include "AccelerometerData.h"
 #include "../../data/Timestamp.h"
-#include "../../math/MovingAverageTS.h"
+#include "../../math/MovingStdDevTS.h"
 #include "../../math/Matrix3.h"
 
 #include "../../geo/Point3.h"
-#include "PoseDetection.h"
+#include "PoseProvider.h"
 
 //#include <eigen3/Eigen/Dense>
 
@@ -19,12 +19,13 @@
 
 
 #include "../../Assertions.h"
+#include "TurnProvider.h"
 
-class TurnDetection {
+class TurnDetection : public TurnProvider {
 
 private:
 
-	PoseDetection* pose = nullptr;
+	PoseProvider* pose = nullptr;
 
 	//std::vector<GyroscopeData> gyroData;
 	//Eigen::Vector3f prevGyro = Eigen::Vector3f::Zero();
@@ -32,6 +33,10 @@ private:
 
 	Timestamp lastGyroReading;
 
+	float curSigma = 0;
+
+	MovingStdDevTS<float> stdDevForSigma = MovingStdDevTS<float>(Timestamp::fromMS(500), 0);
+
 	#ifdef WITH_DEBUG_PLOT
 		TurnDetectionPlot plot;
 	#endif
@@ -39,7 +44,7 @@ private:
 public:
 
 	/** ctor */
-	TurnDetection(PoseDetection* pose) : pose(pose) {
+	TurnDetection(PoseProvider* pose) : pose(pose) {
 		;
 	}
 
@@ -65,6 +70,11 @@ public:
 //	} driftEst;
 
 
+	/** get the current uncertainty estimation */
+	float getSigma() const override {
+		return curSigma;
+	}
+
 	float addGyroscope(const Timestamp& ts, const GyroscopeData& gyro) {
 
 		// ignore the first reading completely, just remember its timestamp
@@ -90,17 +100,20 @@ public:
 		const Vector3 curGyro = pose->getMatrix() * vec;
 		//driftEst.removeDrift(ts, curGyro);
 
+
 		// area
 		//const Eigen::Vector3f area =
 		const Vector3 area =
 
-				// Trapezoid rule (should be more accurate but does not always help?!)
+		    // Trapezoid rule (should be more accurate but does not always help?!)
-				//(prevGyro * curDiff.sec()) +					// squared region
+		    //(prevGyro * curDiff.sec()) +					// squared region
-				//((curGyro - prevGyro) * 0.5 * curDiff.sec());	// triangle region to the next (enhances the quality)
+		    //((curGyro - prevGyro) * 0.5 * curDiff.sec());	// triangle region to the next (enhances the quality)
 
-				// just the rectangular region
+		    // average (is the same as above)
-				(prevGyro * curDiff.sec());		// BEST?!
+		    //((curGyro+prevGyro)/2 * curDiff.sec());
 
+		    // just the rectangular region
+		    (prevGyro * curDiff.sec());		// BEST?!
 
 		//}
 
@@ -112,9 +125,14 @@ public:
 		const float delta = area.z;
 
 		#ifdef WITH_DEBUG_PLOT
-			plot.add(ts, delta, gyro, curGyro);
+		    plot.addRelative(ts, delta, gyro, curGyro);
 		#endif
 
+		//stdDevForSigma.add(ts, prevGyro.z);	// ignore delta T. directly us radians-per-sec as sigma
+		//curSigma = stdDevForSigma.get();
+		const float radPerSec = 1.0f / 180.0f * M_PI;
+		curSigma = radPerSec + std::abs(prevGyro.z * 0.05);	// constant of 1deg/sec + 5% of current turn rate
+
 		// done
 		return delta;
 

sensors/imu/TurnDetection2.h

@@ -0,0 +1,117 @@
+#ifndef TURNDETECTION2_H
+#define TURNDETECTION2_H
+
+
+#include "GyroscopeData.h"
+#include "AccelerometerData.h"
+#include "../../data/Timestamp.h"
+#include "../../math/MovingAverageTS.h"
+#include "../../math/Matrix3.h"
+
+#include "../../geo/Point3.h"
+#include "PoseProvider.h"
+
+//#include <eigen3/Eigen/Dense>
+
+#include <cmath>
+#include <vector>
+
+#include "TurnDetectionPlot.h"
+
+
+#include "../../Assertions.h"
+
+/** THIS WILL NOT WORK AS EXPECTED! */
+class TurnDetection2 {
+
+private:
+
+	PoseProvider* pose = nullptr;
+
+	Vector3 sumSinceStart = Vector3(0,0,0);
+
+	Timestamp lastGyroReadingTS;
+	Vector3 lastGyroReading = Vector3(0,0,0);
+
+	bool first = true;
+	Matrix3 poseMat = Matrix3::identity();
+
+	float curRes = 0;
+
+	#ifdef WITH_DEBUG_PLOT
+		TurnDetectionPlot plot;
+	#endif
+
+public:
+
+	/** ctor */
+	TurnDetection2(PoseProvider* pose) : pose(pose) {
+		;
+	}
+
+
+	float addGyroscope(const Timestamp& ts, const GyroscopeData& gyro) {
+
+
+
+		// ignore the first reading completely, just remember its timestamp
+		if (lastGyroReadingTS.isZero()) {lastGyroReadingTS = ts; return curRes;}
+
+		// time-difference between previous and current reading
+		const Timestamp curDiff = ts - lastGyroReadingTS;
+		lastGyroReadingTS = ts;
+
+		// fast sensors might lead to delay = 0 ms. filter those values
+		if (curDiff.isZero()) {return curRes;}
+
+		// current area
+		//const Eigen::Vector3f area =
+		const Vector3 curArea =
+
+		        // Trapezoid rule (should be more accurate but does not always help?!)
+		        //(prevGyro * curDiff.sec()) +					// squared region
+		        //((curGyro - prevGyro) * 0.5 * curDiff.sec());	// triangle region to the next (enhances the quality)
+
+		        // just the rectangular region
+		        (lastGyroReading * curDiff.sec());		// BEST?!
+
+		//}
+
+		// adjust sum
+		sumSinceStart = sumSinceStart + curArea;
+
+		// update the previous value
+		lastGyroReading = Vector3(gyro.x, gyro.y, gyro.z);
+
+
+		// TESTING
+		const float sign = (curArea.z < 0) ? (-1) : (+1);
+		const float mag = curArea.norm();
+		return (mag * sign);
+
+
+//		// ignore readings until the first orientation-estimation is available
+//		// otherwise we would use a wrong rotation matrix which yields wrong results!
+//		if (!pose->isKnown()) {return curRes;}
+//		if (first) {poseMat = pose->getMatrix(); first = false;}
+
+//		// rotate the sum since start into our desired coordinate system, where the smartphone lies flat on the ground
+//		const Vector3 angles = pose->getMatrix() * sumSinceStart;
+//		//const Vector3 angles = poseMat * sumSinceStart;
+
+//		// rotation = z-axis only!
+//		//const float delta = area(2);
+//		curRes = angles.z;
+
+//		#ifdef WITH_DEBUG_PLOT
+//		    plot.addAbsolute(ts, curRes, gyro, sumSinceStart);
+//		#endif
+
+//		// done
+//		return curRes;
+
+	}
+
+};
+
+#endif // TURNDETECTION2_H

sensors/imu/TurnDetectionPlot.h

@@ -69,7 +69,7 @@
 
 		}
 
-		void add(Timestamp ts, const float delta, const GyroscopeData& gyro, const Vector3& gyroFixed) {
+		void addRelative(Timestamp ts, const float delta, const GyroscopeData& gyro, const Vector3& gyroFixed) {
 
 			plotCurHead += delta;
 
@@ -114,6 +114,49 @@
 
 		}
 
+		void addAbsolute(Timestamp ts, const float curHead, const GyroscopeData& gyro, const Vector3& gyroFixed) {
+
+			if (plotRef.isZero()) {plotRef = ts;}
+			const Timestamp tsPlot = (ts-plotRef);
+			const Timestamp tsOldest = tsPlot - Timestamp::fromMS(5000);
+
+			// raw gyro
+			lineGyroRawX.add( K::GnuplotPoint2(tsPlot.ms(), gyro.x) );
+			lineGyroRawY.add( K::GnuplotPoint2(tsPlot.ms(), gyro.y) );
+			lineGyroRawZ.add( K::GnuplotPoint2(tsPlot.ms(), gyro.z) );
+
+			// adjusted gyro
+			lineGyroFixX.add( K::GnuplotPoint2(tsPlot.ms(), gyroFixed.x) );
+			lineGyroFixY.add( K::GnuplotPoint2(tsPlot.ms(), gyroFixed.y) );
+			lineGyroFixZ.add( K::GnuplotPoint2(tsPlot.ms(), gyroFixed.z) );
+
+			if (lastPlot + Timestamp::fromMS(50) < tsPlot) {
+
+				lastPlot = tsPlot;
+
+				auto remove = [tsOldest] (const K::GnuplotPoint2 pt) {return pt.x < tsOldest.ms();};
+				lineGyroRawX.removeIf(remove);
+				lineGyroRawY.removeIf(remove);
+				lineGyroRawZ.removeIf(remove);
+				lineGyroFixX.removeIf(remove);
+				lineGyroFixY.removeIf(remove);
+				lineGyroFixZ.removeIf(remove);
+
+				const float ax = 0.85 + std::cos(curHead)*0.1;
+				const float ay = 0.85 + std::sin(curHead)*0.1;
+				gp1 << "set arrow 1 from screen 0.85,0.85 to screen " << ax << "," << ay << "\n";
+				gp1 << "set object 2 circle at screen 0.85,0.85 radius screen 0.1 \n";
+
+				//gp1.draw(plotGyroRaw);	// raw only
+				gp1.draw(plotGyroFix);	// fixed only
+				//gp1.draw(multiplot);	// both
+
+				gp1.flush();
+
+			}
+
+		}
+
 	};
 
 #endif

sensors/imu/TurnProvider.h

@@ -0,0 +1,12 @@
+#ifndef TURN_PROVIDER_H
+#define TURN_PROVIDER_H
+
+class TurnProvider {
+
+public:
+
+	virtual float getSigma() const = 0;
+
+};
+
+#endif // TURN_PROVIDER_H

sensors/pressure/BarometerData.h

@@ -3,28 +3,67 @@
 
 
 #include <cmath>
+#include "../../math/Floatingpoint.h"
 
 /** data received from a barometer sensor */
 struct BarometerData {
 
-	float hPa;
+	FPDefault hPa;
 
 	explicit BarometerData() : hPa(0) {;}
 
-	explicit BarometerData(const float hPa) : hPa(hPa) {;}
+	explicit BarometerData(const FPDefault hPa) : hPa(hPa) {;}
 
 	/** valid data? */
 	bool isValid() const {
-		return hPa == hPa;
+		return !std::isnan(hPa);
 	}
 
 	bool operator == (const BarometerData& o ) const {
 		return EQ_OR_NAN(hPa, o.hPa);
 	}
 
+public:
+
+	static constexpr double R = 8.31447;	// universal gas constant for air,		newton meter / mol kelvin
+	static constexpr double L = 0.0065;	// standard temperature lapse rate,			degree kelven per meter
+	static constexpr double g = 9.80665;	// gravity constant,					meter per square second
+	static constexpr double M = 0.0289644;	// molar mass for dry air,				kg / mol
+	static constexpr double P0 = 1013.25;	// pressure at mean sea level,			hPa
+	static constexpr double T0 = 288.15;		// temperature at mean sea level,		kelvin
+
+	/** hPa->meter assuming a constant 1013.25 at 0m as reference */
+	static FPDefault hpaToMeter(const FPDefault pressure) {
+		return static_cast<FPDefault>(
+		    (T0/L) * (std::pow(static_cast<FPDouble>(pressure)/P0, -(R*L)/(g*M))-1.0)
+		);
+	}
+
+	/** hPa->meter by using the given pressure pRef at hRef as reference */
+	static FPDefault hpaToMeter(const FPDefault pressure, const FPDefault PRef, const FPDefault hRef) {
+		return static_cast<FPDefault>(
+		    hRef + (T0/L) * (std::pow(static_cast<FPDouble>(pressure)/PRef, -(R*L)/(g*M))-1.0)
+		);
+	}
+
+	/** meter->hPa assuming a constant 1013.25 at 0m as reference */
+	static FPDefault meterTohPa(const FPDefault altitude) {
+		return static_cast<FPDefault>(
+		    P0 * std::pow(T0 / (T0+L*altitude), (g*M)/(R*L))
+		);
+	}
+
+	/**  meter->hPa by using the given pressure pRef at hRef as reference */
+	static FPDefault meterTohPa(const FPDefault altitude, const FPDefault PRef, const FPDefault hRef) {
+		return static_cast<FPDefault>(
+		    PRef * std::pow(T0 / (T0+L*(altitude-hRef)), (g*M)/(R*L))
+		);
+	}
+
+
 private:
 
-	static inline bool EQ_OR_NAN(const float a, const float b) {return (a==b) || ( (a!=a) && (b!=b) );}
+	static inline bool EQ_OR_NAN(const FPDefault a, const FPDefault b) {return (a==b) || ( (a!=a) && (b!=b) );}
 
 };
 

tests/math/TestDistribution.cpp

@@ -1,7 +1,15 @@
 #ifdef WITH_TESTS
 
 #include "../Tests.h"
-#include "../../math/Distributions.h"
+#include "../../math/distribution/Normal.h"
+#include "../../math/distribution/Bessel.h"
+#include "../../math/distribution/LUT.h"
+#include "../../math/distribution/VonMises.h"
+#include "../../math/distribution/Exponential.h"
+#include "../../math/distribution/NormalCDF.h"
+#include "../../math/distribution/Region.h"
+#include "../../math/distribution/Triangle.h"
+
 #include "../../misc/Time.h"
 
 template <typename Dist> void benchDist(Dist dist) {

tests/math/TestQuaternion.cpp

@@ -0,0 +1,82 @@
+#ifdef WITH_TESTS
+
+#include "../Tests.h"
+#include "../../math/Quaternion.h"
+
+const float d = 0.00001;
+
+TEST(Quaternion, fromEuler) {
+
+	Quaternion q1 = Quaternion::fromEuler(0,0,0);
+
+
+}
+
+TEST(Quaternion, mul1) {
+
+	Quaternion q1 = Quaternion::fromEuler(0.5,0,0);
+	Quaternion q2 = Quaternion::fromEuler(0.3,0,0);
+	Quaternion q3 = q1*q2;
+	ASSERT_NEAR(0.8, q3.toEuler().x, d);
+	ASSERT_NEAR(0.0, q3.toEuler().y, d);
+	ASSERT_NEAR(0.0, q3.toEuler().z, d);
+
+}
+
+TEST(Quaternion, mul2) {
+
+	Quaternion q1 = Quaternion::fromEuler(0.5, 0.0, 0.0);
+	Quaternion q2 = Quaternion::fromEuler(0.0, 0.3, 0.0);
+	Quaternion q3 = Quaternion::fromEuler(0.0, 0.0, 0.2);
+	Quaternion q4 = q1*q2*q3;
+	ASSERT_NEAR(0.5, q4.toEuler().x, d);
+	ASSERT_NEAR(0.3, q4.toEuler().y, d);
+	ASSERT_NEAR(0.2, q4.toEuler().z, d);
+
+}
+
+TEST(Quaternion, toEuler) {
+
+
+
+	Quaternion q1 = Quaternion::fromEuler(0,0,0);
+	ASSERT_NEAR(0, q1.toEuler().x, d);
+	ASSERT_NEAR(0, q1.toEuler().y, d);
+	ASSERT_NEAR(0, q1.toEuler().z, d);
+
+	{
+		Quaternion q2 = Quaternion::fromEuler(0.2, 1.0, 1.2);
+		ASSERT_NEAR(0.2, q2.toEuler().x, d);
+		ASSERT_NEAR(1.0, q2.toEuler().y, d);
+		ASSERT_NEAR(1.2, q2.toEuler().z, d);
+	}
+
+	{
+		Quaternion q = Quaternion::fromEuler(0.5, 0, 0);
+		ASSERT_NEAR(0.5, q.toEuler().x, d);
+		ASSERT_NEAR(0.0, q.toEuler().y, d);
+		ASSERT_NEAR(0.0, q.toEuler().z, d);
+	}{
+		Quaternion q = Quaternion::fromEuler(0, 0.5, 0);
+		ASSERT_NEAR(0.0, q.toEuler().x, d);
+		ASSERT_NEAR(0.5, q.toEuler().y, d);
+		ASSERT_NEAR(0.0, q.toEuler().z, d);
+	}{
+		Quaternion q = Quaternion::fromEuler(0, 0, 0.5);
+		ASSERT_NEAR(0.0, q.toEuler().x, d);
+		ASSERT_NEAR(0.0, q.toEuler().y, d);
+		ASSERT_NEAR(0.5, q.toEuler().z, d);
+	}{
+		Quaternion q = Quaternion::fromEuler(-0.5, 0, 0.5);
+		ASSERT_NEAR(-0.5, q.toEuler().x, d);
+		ASSERT_NEAR(0.0, q.toEuler().y, d);
+		ASSERT_NEAR(0.5, q.toEuler().z, d);
+	}
+
+}
+
+
+
+
+
+#endif

tests/math/distribution/TestNormalN.cpp

@@ -1,4 +1,5 @@
 #ifdef WITH_TESTS
+#ifdef WITH_EIGEN
 
 #include "../../Tests.h"
 #include "../../../math/divergence/KullbackLeibler.h"
@@ -74,4 +75,5 @@ TEST(NormalN, multivariateGaussSampleData) {
 }
 
 #endif
+#endif
 

tests/math/divergence/TestJensenShannon.cpp

@@ -1,4 +1,5 @@
 #ifdef WITH_TESTS
+#ifdef WITH_EIGEN
 
 #include "../../Tests.h"
 #include "../../../math/divergence/JensenShannon.h"
@@ -92,3 +93,4 @@ TEST(JensenShannon, generalFromSamples) {
 }
 
 #endif
+#endif

tests/math/divergence/TestKullbackLeibler.cpp

@@ -1,4 +1,5 @@
 #ifdef WITH_TESTS
+#ifdef WITH_EIGEN
 
 #include "../../Tests.h"
 #include "../../../math/divergence/KullbackLeibler.h"
@@ -301,3 +302,4 @@ TEST(KullbackLeibler, generalFromSamples) {
 }
 
 #endif
+#endif

tests/sensors/imu/TestTurnDetection.cpp

@@ -1,5 +1,6 @@
 #ifdef WITH_TESTS
 
+#ifdef TODO
 #include "../../Tests.h"
 
 #include "../../../sensors/imu/TurnDetection.h"
@@ -67,5 +68,5 @@ TEST(TurnDetection, xx) {
 
 }
 
-
+#endif
 #endif

tests/smc/merging/mixing/TestMixingSamplerDivergency.cpp

@@ -1,4 +1,5 @@
 #ifdef WITH_TESTS
+#ifdef WITH_EIGEN
 
 #include "../../../../smc/merging/mixing/MixingSamplerDivergency.h"
 #include "../../../../smc/filtering/ParticleFilterMixing.h"
@@ -142,5 +143,5 @@ namespace K {
 }
 
 
-
+#endif
 #endif