Not much

tex/chapters/3_ftm.tex

@@ -37,12 +37,13 @@
 \section{Wi-Fi Range Measurements}
 \label{sec:ftm}
 
-An obvious approach to estimate a location is to measure the distance between the current unknown position and a known position.
+An obvious approach to estimate a location is to measure the distance between the current unknown position and known positions.
 Given multiple measurements to different reference points an absolute position in a local coordinate system can be found.
 With ideal distance measurements to several known positions it is straightforward to calculate the current position.
-However, in the present of noisy and imperfect measurements estimating a accurate position is a challenging problem.
+However, in the present of noisy and imperfect measurements estimating a precise position is a challenging problem.
+%TODO Harte bruch 
 For a smartphone based indoor localization system using the existing Wi-Fi infrastructure is a reasonable choice.
-In this work signal strength based and signal propagation time based distance measurements are considered.
+In this work signal strength and signal propagation time based distance measurements are considered.
 
 \subsection{Received Signal Strength Indication}
 % TODO dBm vs dB??
@@ -133,9 +134,10 @@ However, to account for the signal processing delay of the initiator's hardware
 When the ACK frame is received at the responder at time $t_4$ the responder can calculate the round trip time of the signal by subtracting $t_1$ from $t_4$.
 To exclude the processing delay of the initiator the difference between $t_2$ and $t_3$ is subtracted from the total round trip time, which results in the propagation delay of the signal
 \begin{equation}
-  \text{ToF} = (t_4-t_1) - (t_3-t_2) % TODO besseres Symbol als RTT
+  \text{ToF} = (t_4-t_1) - (t_3-t_2) \text{.} % TODO besseres Symbol als RTT
 \end{equation}
 
+Measuring ToF only once is usually not sufficient. 
 While RF power is relatively simple to measure, obtaining accurate ToF values at a small resolution like nanoseconds needs much more caution, as the measurements are sensitive to noise.
 Relatively small deviations from the real time value result in a vast error in the distance estimate, \eg a measurement error of \SI{10}{ns} results in a distance error of \SI{3}{m}.
 For this reason the above outlined procedure is repeated multiple times to reduce the impact of noise.
@@ -145,9 +147,13 @@ In fact, a single FTM measurement or burst instance, consists of many FTM-ACK ex
 \end{equation}
 
 After calculating the average ToF the responder transfers the result to the initiator where the result can be processed by an application.
-With increasing $n$ the impact of noise is lessened, but the time until the FTM measurement is available for the consuming software increases.
+With increasing $n$ the impact of noise is lessened, but the delay until the FTM measurement is available for the consuming software increases.
 Therefore, the actual choice of the value of $n$ is a trade-off between precision and measurement delay.
 
+Assuming that the signal propagates constantly at the speed of light the distance between initiator and responder is trivially given with
+\begin{equation}
+  d = \frac{\text{ToF}}{2} \cdot c
+\end{equation}
 %TODO ToF -> distance ToF/2 * c
 %TODO IEEE 802.11-2016 6.3.58.1
 
@@ -170,6 +176,6 @@ To allow much finer resolution the receiver uses super resolution methods to all
 In addition to distance measurements the \ieeWifiFTM standard defines a format to transfer location information about the responder.
 This allows to add new access points dynamically to the localization system without updating the initiators, \ie smartphone, as the access point can be configured to know its position and can transmit this information to the smartphone.
 
-Error sources:
-multipath propagation, noise, finite sample rate
+%Error sources:
+%multipath propagation, noise, finite sample rate