Noise Effects On The IRWLS Algorithm Performance For Time Delay Estimation

Abstract

Underwater target tracking is considered from the point of view of dealingwith problems resultingfrom the residuals obtained due to fitting models using the least squares procedures. Robust regression procedures appear to outperform the least squares procedures when the errors are noii Gaussian and also have improved performances for Gaussian errors. Filters based on the Iteratively Reweighted Least Squares method have been proposed. The present paper is concerned with exploring the effects of noise levels on the performance of the IRWLS algorithm. AMonte-Carlo simulation using synthetic records is performed and best candidate robust functions are detailed. I. INTRODUCTION Time delay (and its time variation) of a received signal are used in estimating target location in tracking systems. An integral part of the system is a time delay estimator (TDE) which converts the received data to measurable indicators which are further processed so that estimates of time delays are smoothed and related to values for target localization. Kalman filtering has been applied to target tracking as detailed in (1). The problem of evaluating the noise statistics manifested by the state covariance matrix Q and the measurement error covariance matrix R of Kalman filtering has recognized for some time (2-31. Proposed procedures involve a considerable computational effort that may be avoided by using robust estimation techniques. Kalman-based approaches estimate the target ran e approach adopted in this research is to obtain estimates of the time delay differences from the available measurements a:. an intermediate step. This then is followed by evaluating the desired target range. In (4), the generalized Kalman filtering approach to the problem is introduced. The approach attempts to achieve a trade-off between accuracy and stability of estimates. For non Gaussian errors, the performance of least squares estimators is far from being optimal. Efforts have been made to improve the performance of the least squares procedures for non Gaussian errors, and to enhance their performance for the Gaussian errors (5). The application of the iteratively reweighted least squares (IRWLS) method to the target tracking problem is proposed in (6). The paper reports improved results using the IRWLS method over those obtained using Kalman filtering. We discuss the effects of noise levels on proposed filters for time delay estimation. The filters are based on the Andrews' and Fair weighting functions of the IRWLS. We offer computational results to illustrate and compare the performance of the two filters with that of the ordinary least squares method. directly from the available measured time delays. T E e 11. THE ESTIMATION PROBLEM