Signal waveform estimation in the presence of uncertainties about the steering vector

The problem of signal waveform estimation using an array of sensors where there exist uncertainties about the steering vector of interest is presented in this paper. This problem occurs in many situations, including arrays undergoing deformations, uncalibrated arrays, scattering around the source, etc. In this paper, we assume that some statistical knowledge about the variations of the steering vector is available. Within this framework, two approaches are proposed depending on whether the signal is assumed to be deterministic or random. In the former case, the maximum likelihood estimator is derived. It is shown that it amounts to a beamforming-like processing of the observations and an iterative algorithm is presented to obtain the ML weight vector. For random signals, a Bayesian approach is advocated and we derive maximum a posteriori estimators. Numerical examples are provided to illustrate the performances of the estimators.