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Publication# One Step Impulse Radio Ultra-WideBand Positioning Algorithm

Abstract

We consider the problem of positioning estimation with impulse radio (IR) ultra-wideband (UWB) radio under dense multipaths and additive Gaussian noise environments. Most popular positioning algorithms first estimate certain parameters (such as time of arrival (TOA), angle of arrival (AOA) and time difference of arrival (TDOA)) from the received signals. These parameters are then used to estimate the targeted position. In practice, the estimation of these parameters is not errors free and the distribution of the errors is difficult to model exactly. In contrast, we propose a novel one-step approach, which estimates the position and channels directly and jointly from the received signals of the used base stations. We use a Bayesian approach where the prior distribution of the channels follows the IEEE 802.15.4a channel model to estimate the joint posterior probability density function (pdf) of the channels, the targeted position and the transmit time. One application of the joint posterior pdf of the channels, the targeted position and the transmit time is the position determination with classical posterior estimator (such as minimum mean square error estimator (MMSE)). For computing the joint posterior pdf of the channels, the targeted position and the transmit time, we derived an algorithm which is based on sampling-importance resampling and the expectation maximization technique. Furthermore, we propose a reduced-complexity architecture of the proposed IR UWB localization system using our proposed algorithm. The algorithm can be easily implemented on hardware. Numerical evaluations under the IEEE 802.15.4a channel model are presented to demonstrate the good performance of the proposed estimator.

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John Farserotu, Jean-Yves Le Boudec, Hai Zhan

We consider the problem of ranging with Impulse Radio (IR) Ultra-WideBand (UWB) radio under weak Line Of Sight (LOS) environments and additive Gaussian noise. We use a Bayesian approach where the prior distribution of the channel follows the IEEE 802.15.4a channel model, to estimate the joint posterior probability density function (pdf) of the channel and the targeted distance. One of applications of the joint posterior pdf of the channel and the targeted distance is the ranging determination with classical posterior estimators (such as Minimum Mean Square Error Estimator (MMSE)). For computing the joint posterior pdf of the channel and the targeted distance, we derived a novel algorithm which is based on importance sampling and expectation maximum techniques. Furthermore, we propose a reduced-complexity architecture of IR UWB ranging system using our proposed algorithm. The complexity analysis of the algorithm shows the proposed algorithm is a low-complexity one. Numerical evaluations under the IEEE 802.15.4a channel model are presented to demonstrate the good performance of the proposed estimator.

In this thesis, we focus on Impulse Radio (IR) Ultra-WideBand (UWB) ranging and positioning techniques under indoor propagation environments. IR-UWB, a new carrierless communication scheme using impulses, is a candidate technology for future communication, ranging and positioning applications. Recent progress on both the technical and regulatory side of this technology has made this possible [1][2][3]. The fine time resolution of UWB signals has created a vision of novel ranging and positioning applications to augment existing narrowband systems operating in dense multipath environments [4][5][6]. We propose a high-resolution IR-UWB ranging algorithm based on Maximum Likelihood (ML) when the noise is additive Gaussian noise or multi-user interference. First, we pose the ranging problem as an ML estimation problem for the channel delays and their amplitudes at the receiver. We evaluate the ranging by translating the received delay estimates into an estimate of the distance. Then, we use the same transformation as the first step of Iterative Quadratic Maximum Likelihood (IQML) and we transform the ML problem into another optimization problem that avoids the estimation of the amplitude coefficients. We solve the remaining optimization problem with a gradient descent approach (Pseudo-Quadratic Maximum Likelihood (PQML) algorithm). Most previous works assume the distribution of the targeted distance is a uniform distribution (for example [7], [8] and [9]). In contrast to the previous works, we propose that the distribution of the targeted distance, which is not necessarily a uniform distribution, should depend on the geometry of the indoor environments of interest. We propose a Bayesian detection algorithm where the prior distribution of the channel follows the IEEE 802.15.4a channel model to identify whether the received signal is Line-Of-Sight (LOS) signal or a Non-Line-Of-Sight (NLOS) signal. If it is a LOS signal, we use a Bayesian estimation approach to estimate the joint posterior probability density function (pdf) of the channel and the targeted distance. We use this pdf function to estimate the ranging with Minimum Mean Square Error Estimator (MMSE). For computing the joint posterior pdf of the channel and the targeted distance, we derive a novel algorithm based on Sampling and Importance Resampling (SIMR) and Expectation Maximum (EM) techniques. Furthermore, we propose a reduced-complexity architecture of an IR-UWB ranging system by using our proposed algorithms. We also implement the Bayesian ranging algorithm on the Xinlix ML410 Field-Programmable Gate Array (FPGA) board. The used FPGA resources show that the Bayesian ranging algorithm is a low-complexity algorithm. We derive a novel Ziv-Zakai lower bound for IR-UWB ranging error that depends on the geometry of the indoor environments of interest. In contrast to the work in [7], we do not introduce, during our derivation process, any approximation for our log-likelihood function. Therefore, we obtain a more accurate Ziv-Zakai lower bound for the IR-UWB ranging error with IEEE 802.15.4a channel models. Based on the geometry of the indoor environments of interest, we can find the "best" position of the base station that provides the lowest Ziv-Zakai lower bound of the IR-UWB ranging error. Our bound can also be used in real environments with the channel measurements from real environments. We also propose that the distribution of the targeted position should depend on the geometry of the indoor environments of interest. We propose a novel one-step approach that estimates the position and channels directly and jointly from the received signals of the used base stations. We use a Bayesian approach where the prior distribution of the channels follows the IEEE 802.15.4a channel model to estimate the joint posterior pdf of the channels, the targeted position and the transmit time. One application of the joint posterior pdf of the channels, the targeted position and the transmit time is the determination of the position with classical posterior estimator (such as MMSE). For computing the joint posterior pdf of the channels, the targeted position and the transmit time, we derived an algorithm that is based on SIMR and EM techniques. We derive Ziv-Zakai position error lower bounds for a one-step positioning scheme, a Time Of Arrival (TOA)-based positioning scheme and a Time Difference Of Arrival (TDOA)-based positioning scheme. As our derived bounds depend on the geometry of the indoor environments of interest, our bounds can also be used in real environments with the channel measurements from real environments. Multi-User Interference (MUI) statistical models for IR-UWB systems can be important in providing an accurate estimate of the channel state. As such, it can have a major impact on the overall system performance. In the literature, MUI in the time domain is often approximated with Middleton class A and Gaussian Mixture Models. We use measurements from an indoor IR-UWB testbed to assess the validity of these models. We analyzed the statistical properties of IR-UWB MUI with the measurements from real indoor environments.

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We consider the problem of ranging with impulse radio (IR) ultra-wideband (UWB) radio under dense multipaths propagation environments and additive Gaussian noise. We propose a Bayesian detection algorithm where the prior distribution of the channel follows the IEEE 802.15.4a channel model, to identify whether the received signal is a Line-of-Sight (LOS) signal or a Non-Line-of-Sight (NLOS) signal. If it is a LOS signal, we use a Bayesian estimation approach to estimate the joint posterior probability density function (pdf) of the channel and the targeted distance. One of applications of the joint posterior pdf of the channel and the targeted distance is the ranging determination with classical posterior estimators (such as Minimum Mean Square Error Estimator (MMSE)). For computing the joint posterior pdf of the channel and the targeted distance, we derived a novel algorithm which is based on importance sampling and expectation maximum techniques. Numerical evaluations under the IEEE 802.15.4a channel model are presented to demonstrate the good performance of the proposed algorithms.