Optimum and Suboptimum Bearing Estimation for Deterministic and Random Signals in Normal Noise Fields
David Middleton · The Journal of the Acoustical Society of America · 1967
A general theory of maximum likelihood estimation (MLE) of bearing angle and associated measures of the location of signal sources by passive reception is constructed for arbitrary arrays and normal noise fields, extending earlier work. We distinguish two important classes of input signal: known and unknown signal waveforms. Explicit results are obtained for (unconditional) maximum likelihood estimators (UMLE's) of signal amplitude and waveform, and for the (log) likelihood functionals which must be further maximized by choice of bearing-angle parameters (through search procedures) for a priori distributions of parameters. Performance of the optimum bearing estimator (OBE) is measured in terms of the variance of the estimates, involving a matrix of order appropriate to the number of parameters to be estimated. For threshold cases where noise processes can be regarded as stationary, with sample-size large and array elements treated as point sensors, further results are obtained. Examples illustrating the critical role of a priori probabilities are provided, and comparison of the OBE with a suboptimum system (BDI) is made.