ML estimation under misspecified number of signals

Abstract

The maximum likelihood (ML) approach for estimating direction of arrival (DOA) is a well known and popular technique in array processing. Its statistical properties such as consistency and efficiency have been extensively studied in the literature. A common assumption made in previous works is that the assumed number of signals equals the true one. However, this information is not always available and usually needs to be estimated together with the DOA parameter. Thus it is crucial to know whether ML estimator provides any significant information when we are not certain about the number signals. In this work, we show that ML estimator under misspecified number of signals converges to a well defined limit. In the case of well separated sources, components of ML estimates coincide with the true parameters. Our theoretical analysis is validated by numerical experiments.