Bearing estimation for a distributed source: modeling, inherent accuracy limitations and algorithms

The problem of using sensor array measurements to estimate the bearing of a radiating source surrounded by local scatterers is considered. The concept of “partial coherence” is introduced to account for temporal as well as spatial correlation effects often encountered in a Rayleigh fading-type propagation channel formed between a source and sensor array elements. A simple parametric model for temporal channel correlation is presented, yielding an overall spatio-temporal channel model that is more realistic than formerly proposed models (which assume either full or zero temporal channel correlation). Thus, previously proposed “distributed source” models for bearing estimation problems are generalized to a parametric spatio-temporal model for what will be called “partially coherently distributed (PCD) sources.” A study of the associated Cramer–Rao Bound (CRB) is undertaken for a simple but illustrative problem formulation. The inherent limitations in bearing estimation accuracy for this spatiotemporal problem are seen to lie between the cases of zero and full temporal correlation, becoming more severe as temporal channel correlation increases. In addition, the associated maximum likelihood estimators for source bearing are proposed, and their performance is compared with that predicted by the CRB.