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Publication# A Novel Bayesian Impulse Radio Ultra-WideBand Ranging Algorithm

Abstract

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.

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Ultra-wideband

Ultra-wideband (UWB, ultra wideband, ultra-wide band and ultraband) is a radio technology that can use a very low energy level for short-range, high-bandwidth communications over a large portion of th

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathema

Estimator

In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (th

John Farserotu, Jean-Yves Le Boudec, Hai Zhan

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.

John Farserotu, Jean-Yves Le Boudec, Hai Zhan

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.

John Farserotu, Jean-Yves Le Boudec, Hai Zhan

We propose a high-resolution ranging algorithm for impulse radio (IR) ultra-WideBand (UWB) communication systems in additive white Gaussian noise. We formulate the ranging problem as a maximum- likelihood (ML) estimation problem for the channel delays and amplitudes at the receiver. Then we translate the obtained delay estimates into an estimate of the distance. The ML estimation problem is a non-linear problem and is hard to solve. Some previous works focus on finding alternative estimation procedures, for example by denoising. In contrast, we tackle the ML estimation problem directly. First, 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. Second, we solve the remaining optimization problem with a gradient descent approach (pseudo-quadratic maximum likelihood (PQML) algorithm). To demonstrate the good performance of the proposed estimator, we present the numerical evaluations under the IEEE 802.15.4a channel model. We show that our algorithm performs significantly better than previously published heuristics. We also derive a reduced complexity version of the algorithm algorithm, which will be implemented on the Xinlix field-programmable gate array (FPGA) board in the future. We test the approach in a real weak line of sight (LOS) propagation environment and obtained good accuracy for the ranging.