Comparison of two efficient ML algorithms for high resolution sources tracking-time recursive implementation

A comparison is made of two fast Newton-Gauss algorithms for implementation of the exact maximum-likelihood (ML) and an approximate ML (AML) previously introduced by the authors (1989). The AML is impeded by the need of an eigenvalue decomposition of the covariance matrix, but it exhibits better robustness and a lower signal-to-noise ratio (SNR) threshold. The availability of efficient ML algorithms opens the way to interesting recursive or adaptive tracking methods. If an a priori Gaussian probability is assumed for bearing parameters, the algorithm can be easily modified, and it provides the updated estimates and their posteriori covariance. A dynamic model may be also introduced, and then all the requirements for building a Kalman-like recursive estimation scheme for fast moving sources tracking are presented. The update may be made with a small number of snapshots, even a single one, when the a priori covariance has converged to a small enough value. This one snapshot case is very interesting, since the ML algorithm then takes a much simplified form