A convergence analysis of an adaptive underwater passive tracking system

The ability of the adaptive filtering system to converge to an unbiased estimate cf those target parameters of interest such as range and depth is examined. Passive target measurements make use of difference in signal arrival time between geometrically separated sensor systems such as those described in Knapp and Carter (1976), Hassab and Boucher (1976), Hassab (1976), McCabe and Moose (1981). While generally good results of different simulated tracking scenarios have been reported upon in Moose (1983), and Moose and Dailey (1983) these results are valid only for the geometries that were specifically simulated. Thus a theoretical investigation is necessary to examine filter convergence after an initial target detection or target maneuver has occurred. Due to the complexity of the nonlinear data generation and tracking system shown for the vertical plane, and not shown, though very similar for range and bearing in the horizontal ocean plane the convergence analysis is part analytic and part computer analysis. Preliminary results show that the tracking systems converge, but converge with a small bias that is both geometry and signal to noise ratio dependent.