Stochastic Maximum Likelihood Estimation Under Misspecified Numbersof Signals

The maximum likelihood (ML) approach for estimating direction of arrival (DOA) plays an important role in array processing. Its consistency and efficiency have been well established in the literature. A common assumption is that the number of signals is known. In many applications, this information is not available and needs to be estimated. However, the estimated number of signals does not always coincide with the true number of signals. Thus, it is crucial to know whether the ML estimator provides any relevant information about DOA parameters under a misspecified number of signals. In a previous study by this author ["ML estimation under misspecified number of signals," presented at the Thirty-Ninth Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, November 2005], he focused on the deterministic signal model and showed that the ML estimator under a misspecified number of signals converges to a well defined limit. Under mild conditions, the ML estimator converges to the true parameters. In the current correspondence, we extend those results to the stochastic signal model and validate our analysis by simulations.