Analysis of subspace fitting and ML techniques for parameter estimation from sensor array data

Signal parameter estimation from sensor array data is a problem that is encountered in many engineering applications. Under the assumption of Gaussian distributed emitter signals, the so-called stochastic maximum likelihood (ML) technique is known to be statistically efficient, i.e., the estimation error covariance attains the Cramer-Rao bound (CRB) asymptotically. Herein, it is shown that also the multidimensional signal subspace method, termed weighted subspace fitting (WSF), is asymptotically efficient. This also results in a novel, compact matrix expression for the CRB on the estimation error variance. The asymptotic analysis of the ML and WSF methods is extended to deterministic emitter signals. The asymptotic properties of the estimates for this case are shown to be identical to the Gaussian emitter signal case, i.e., independent of the actual signal waveforms. Conclusions, concerning the modeling aspect of the sensor array problem are drawn.