Complexity reduction in the parametric estimation of superimposed signal replicas

Abstract

The estimation of the delays and angles of arrival of several superimposed signal replicas requires a high computational burden, which is reduced in practice by employing sub-optimal estimators or by exploiting a specific structure of the problem. In this paper, we propose to reduce the computational burden by looking beforehand for a data representation of small size, which is obtained from an a priori distribution of the parameters. This distribution, being different to the distribution of the parameters in the estimation problem itself, summarises the information about their range of variation. The data reduction can be regarded as the result of applying a Karhunen–Loève expansion. Focusing on the delay parameterisation, we show how this data reduction can be performed efficiently. We present the adaptation of the TLS-ESPRIT algorithm for delay estimation, and of the deterministic Maximum Likelihood estimator to this data reduction. In order to calculate the latter estimator, we discuss the application of Newton-type methods.