A convergence analysis of a passive underwater tracking system with nonlinear feedback

The basic signal processing structure of a new passive underwater tracking system incorporating nonlinear feedback [1], [2] is modeled, and its ability to converge to an unbiased estimate of target range is examined. Target measurements are derived using difference of arrival times between passive sensor systems geometrically separated. The range tracking system utilizes a nonlinear signal processor to first linearize and invert the noisy time delay measurements. This eliminates the need for extended Kalman filtering techniques and allows the use of a more basic-type state estimator [1]. However, the processed measurements now contain both nonstationary and non-Gaussian measurement errors. To help compensate for these effects, the tracking system incorporates nonlinear feedback from output to input, in order to help maintain a zero-mean measurement error process. Thus, a theoretical investigation is necessary to examine overall tracking system convergence after an initial target detection and/or target maneuver has occurred. The convergence analysis is performed using two separate tracking models. The first model is a scalar first-order low-pass filter. The second model is a vector Kalman-type state estimator. Although the estimator is linear, the overall tracking system is nonlinear due to the non-linear bias removal feedback and the data linearization system. This inherent complexity requires the convergence analysis to be both analytic and make extensive use of computer simulation analysis. Results show that each system converges, but with a small bias that is both geometry and signal-to-noise ratio dependent.