Target Localization in the Presence of Multipaths

A delayed version of a bandlimited signal can be represented by convolving a sinc function and the signal itself. By using this property, a novel constrained LMS algorithm that estimates the difference in arrival times of signal at two spatially separated receivers with multipath propagations is developed. The time delay obtained can be used to localize targets in sonar and radar systems. Introduction and Problem Formulation : The process of planar localization involves determining the bearing and range of a target by either passive or active means. In this application, all receivers and signal source are assumed to be in the same plane. The critical part of designing an optimal estimator for source position is the accurate computation of the time delay of the signal between pairs of receivers[1]. Chan et al[2] introduced a parameter estimation approach to time delay estimation by modeling the delay as a FIR filter whose coefficients are samples of a sinc function. This approach brings many parameter estimation algorithms, some of them adaptive, to the solution of the delay estimation problem. However, signal usually arrives at each individual omnidirectional receiver through more than one path. In this letter, we propose a constrained adaptive algorithm to estimate the delay when each 1 This paper is a postprint of a paper submitted to and accepted for publication in Electronics Letters and is subject to Institution of Engineering and Technology Copyright. The copy of record is available at IET Digital Library. receiver sees a signal plus an attenuated and delayed signal arose from multipath transmission. For simplicity, we consider a two-path model which is free of additive noise. Given the received signals, where is a bandlimited white Gaussian process and is the delay to be estimated. The multipaths are characterized by and , the attenuation constants, and and , the multipath delays respectively. Obviously, the multipath delays should be greater than 0 and the attenuation constants must lie between 0 and 1. These signals can also be expressed, via the convolution theorem, as where the infinity sign in the summation can be replaced by an integer which is chosen large enough to minimize truncation error[3]. The proposed configuration of the time delay estimator is shown in Figure 1. We first process and by the filter blocks and to give and respectively. The desired transfer function of and are and . That is, , , and for . The immediate filter outputs, and , will then become x(k) = s(k) + α1s(k − Δ1) (1a) y(k) = s(k − D) + α2s(k − D − Δ2) (1b)