A Maximum Likelihood Time Delay Estimator in a Multipath Environment Using Importance Sampling

Abstract

In this paper, we present a new implementation of the maximum likelihood criterion for the estimation of the time delays in a multipath environment and then extend it to the estimation of the time difference of arrival when the transmitted signal is unknown. The new technique implements the concept of importance sampling (IS) to find the global maximum of the compressed likelihood function in a modest computational manner. It thereby avoids traditional complex multidimensional grid search or initialization-dependent iterative methods. Indeed, one of the most interesting features is that it transforms the multi-dimensional search inherent to multipath propagation into a much simpler one-dimensional optimization problem in the delays dimension. Moreover, it guarantees convergence to the global maximum, contrarily to the popular iterative implementation of the maximum likelihood criterion by the well known expectation maximization (EM) algorithm. Comparisons with some other methods such as the EM algorithm, MUSIC and accelerated random search (ARS) demonstrates the superiority of the proposed IS-based multipath delay estimator in terms of estimation performance and complexity.