Passive synthetic aperture processing as a Kalman filter problem

Abstract

Passive synthetic aperture processing of a towed array is basically the coherent processing of the array data over a given length of time which, based on the speed of tow, translates into an equivalent increase in aperture length, and therefore a concomitant increase in spatial gain. The Kalman filter formalism is particularly suited to this task for four reasons. First, it coherently updates the measurements based on a comparison of their predicted values, based on a signal model, and subsequent measurements taken at a later time, in a recursive manner. Second, it allows in principle any signal model, i.e., not simply plane waves. Third, it generates a minimum variance estimate not only on the desired bearings, but any desired (observable) model parameters. Finally, it avoids the explicit construct of a beamformer, thus permitting the precision of the estimates to have no lower limit (such as the spatial bin size of a beamformer) other than the minimum variance obtainable under the given signal to noise conditions. Samples of multiple bearing estimations based on synthetic data will be shown. Also, a general formalism will be presented that allows direct estimation and update of certain signal model parameters.