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@@ -1,31 +1,116 @@
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%\section{Wi-Fi Range Measurements}
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%\label{sec:ftm}
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%
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%Ganz grundsätzlich zwei drei Sätze dazu. Distanzen sind gut für Lokalisierung weil... Kurz die Unterschiede der Beiden.
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%
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%\subsection{Fine Timing Measurement}
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%\begin{itemize}
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% \item New IEEE 802.11mc standard to measure round trip time from client to access point.
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% \item Theory, protocol.
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% \item Expected error behavior
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%\end{itemize}
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%
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%
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%FTM defines a protocol to measure the round trip time between an initiator and a responder, e.g. a smartphone based client and access point.
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%For data privacy reasons the responder is always passive and only the initiator can trigger time measurements.
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%
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%\subsection{Received Signal Strength Indication}
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%
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%Klassisch RSSI mit Log Distance Modell...
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%steckt die rssi in das log distance modell und bekommt eine distanz raus. baby easy
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%
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%\subsection{Measurement Pre-Filtering}
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%
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%<zeige fehlerplots mit range messungen>
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%
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%wenn man sich die messungen nun ansithet, dann... argumentiere kalmanfilter über diese range messungsplots und begründe warum er die messdaten stabiler macht.
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%kalman auf rssi ist erstmal nicht so klug weil kalman linear und rssi nicht linear sind. in LOS konditionen ist rssi logritmisch und in NLOS ganz was anders... nicht-linear halt
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%in den späteren evaluatieren werden wir uns aber dennoch raw vs pre-filtering ansehen, um ein bessere gefühl dafür zu bekommen was es in welcher situation bringt
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%
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%Filter measurements per AP with simple Kalman filter before localization
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%
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%RSSI leichter messbar und einfach gegegeben, aber abhänigi von umgebung - coarsely quantized
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%RTT deutlich komplexer zu messen, daher eigener FTM Standard. Super-resolution?!
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\section{Wi-Fi Range Measurements}
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\label{sec:ftm}
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Ganz grundsätzlich zwei drei Sätze dazu. Distanzen sind gut für Lokalisierung weil... Kurz die Unterschiede der Beiden.
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\subsection{Fine Timing Measurement}
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\begin{itemize}
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\item New IEEE 802.11mc standard to measure round trip time from client to access point.
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\item Theory, protocol.
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\item Expected error behavior
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\end{itemize}
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FTM defines a protocol to measure the round trip time between an initiator and a responder, e.g. a smartphone based client and access point.
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For data privacy reasons the responder is always passive and only the initiator can trigger time measurements.
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A obvious approach to estimate a location is to measure the distance between the current unknown position and a known position.
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Given multiple measurements to different reference points an absolute position in a local coordinate system can be found.
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With ideal distance measurements it is straightforward to calculate the current position.
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However, in the present of noise and imperfect measurements estimating a accurate position is a challenging problem.
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\subsection{Received Signal Strength Indication}
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% TODO dBm vs dB??
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Klassisch RSSI mit Log Distance Modell...
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steckt die rssi in das log distance modell und bekommt eine distanz raus. baby easy
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Received Signal Strength Indication (RSSI) is a measure of the received RF power and is obtained by the radio hardware at the antenna connector using an analog-to-digital converter.
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It is usually expressed in \si{\dBm} and quantified to integer values.
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For indoor localization RSSI is often used to deduce the distance from a smartphone to the access point, because it is virtually always available on common devices.
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The \docLogDistance{} model is commonly used to predict the signal strength $s$ at a given distance $d$.
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Which is formally given with
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\begin{equation}
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s = \mTXP - 10 \mPLE \log_{10}{\frac{\mMdlDist}{\mMdlDist_0}} + \mathcal{X} \text{,}
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\label{eq:logDistModel}
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\end{equation}
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where $\mTXP$ denotes the sending power of the AP at reference distance $\mMdlDist_0$ (\eg \si{1}{m}) in \si{\dBm}, $\mPLE$ is the path loss exponent, which value needs to be empirically chosen for the given environment.
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The added zero-mean Gaussian random variable $\mathcal{X}$ models signal fading and random channel noise in \si{\decibel}.
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\subsection{Measurement Pre-Filtering}
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The \docLogDistance{} model can be reformulated to compute the distance $d$ based on the RSSI $s$ with
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\begin{equation}
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d = 10^{(\mTXP-s) / 10\mPLE}
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\end{equation}
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<zeige fehlerplots mit range messungen>
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In free space the value of the path loss exponent is $\mPLE=2$.
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In indoor scenarios $\mPLE$ accounts for the architecture around the AP, thus a single global factor is chosen for the whole building.
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%This restricts the \docLogDistance{} model to a uniform view on the complete environment and does not allow to differentiate between different types of materials, and ignores which walls are actually transmitted the signal.
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wenn man sich die messungen nun ansithet, dann... argumentiere kalmanfilter über diese range messungsplots und begründe warum er die messdaten stabiler macht.
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kalman auf rssi ist erstmal nicht so klug weil kalman linear und rssi nicht linear sind. in LOS konditionen ist rssi logritmisch und in NLOS ganz was anders... nicht-linear halt
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in den späteren evaluatieren werden wir uns aber dennoch raw vs pre-filtering ansehen, um ein bessere gefühl dafür zu bekommen was es in welcher situation bringt
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This restricts the \docLogDistance{} model to a uniform view on the whole environment and does not take the actual propagation path of the signal into account.
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Therefore it is not possible
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not allow to differentiate between different types of materials, and ignores which walls are actually transmitted the signal.
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Filter measurements per AP with simple Kalman filter before localization
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In order to take walls into account the model must include the power loss of every traversed wall, which results in the wall-attenuation factor model \cite{TODO}.
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Often the dampening factors of walls are unknown and hard to measure.
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Additionally, the computation of the wall-attenuation factor model requires costly intersection tests with the geometry of the environment which can be intractable to perform on a regular smartphone.
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Another approach is to take measurements at known positions distributed throughout the building.
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These fingerprints can then be used in the localization phase to obtain the current position with a nearest neighbour search.
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Given the current RSSI value the most likely position is the one which has
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This method includes the characteristics of the environment into the prerecorded fingerprints.
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Recording the fingerprints is a time-consuming and tedious process for large buildings and needs to be redone whenever the environment changes significantly.
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However, RSSI values are often coarsely quantized, depend heavily on the environment, differ from device to device, and are affected by the interferences.
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- free space loss
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- walls
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, also dynamic obstacles like persons can interfere with the signal.
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\subsection{Fine Timing Measurement}
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Time-based distance measurements are based on successive timestamps taken at the sender and receiver site.
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The difference of the two timestamps is the time the signal took to travel from the sender to the receiver.
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Multiplied by the propagation speed of light results in the distance between the two nodes.
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The propagation speed of the signal depends on the propagation medium and is slower in media with higher relative permittivity, like concrete walls, compared to air.
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However, for most indoor environments the signal propagation speed can be assumed to be constant, as the total travel distance in non-air media is usually negligible short compared to the travel distance in air \cite{marcaletti2014filtering}.
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For that reason, time of flight (ToF) measurements are more robust compared to received power measurements.
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While RF power is relatively simple to measure, obtaining accurate ToF values at small resolutions like nanoseconds needs much more caution, as the measurements are sensitive to noise.
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Relatively small deviations from the real time value result in a large error in the distance estimate, \eg a error of 1ns results in xx meter.
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Therefore, distance estimates can greatly differ from the ideal euclidean distance.
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The accuracy of distance estimate depends on the ability of the hardware to detect the line-of-sight signal.
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In an indoor environment it is very common that a signal will reach the receiver from different paths with different lengths.
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The prime example is a signal which reaches the receiver via a direct line-of-sight propagation plus two reflected paths of the same length.
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As the reflected paths have the same length and phase they constructively interfere at the receiver resulting in a higher receiving power compared to the direct connection.
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The difficulty in such multipath scenarios is to distinguish the direct path from the reflected paths.
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Here the limiting factor is the sampling rate of the receiving hardware.
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Given 802.11xxx the channel bandwidth is 20 mhz which results in a sampling rate of
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In order to measure the ToF the hardware needs to detect the direct line-of-sight signal
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However, obtaining accurate ToF measurements of the line-of-sight signal in heavy multipath environment like indoors is not easy.
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Error sources:
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multipath propagation, noise, finite sample rate
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