Hermite Polynomial Uncorrelated Conversion Filter for Bearings-Only Tracking

Abstract

Passive bearings-only target tracking is a challenging estimation problem due to high nonlinearity and low observability. In this paper, a novel Hermite polynomial uncorrelated conversion filter is proposed within the linear minimum mean square error framework to improve the target tracking performance. The uncorrelated conversion is a nonlinear transformation of the original measurement that is uncorrelated with it. It can be regarded as a pseudomeasurement to augment the measurement space so that additional information can be exploited to update the state estimate in a nonlinear way. Due to the orthogonality property of the Hermite polynomials in the probability domain, each uncorrelated conversion is constructed as a Hermite polynomial, which is not only uncorrelated with the original measurement but also uncorrelated with other Hermite polynomial uncorrelated conversions automatically. This method enables a systematic way to generate multiple uncorrelated conversions. Moreover, it is shown that, under the linear measurement model, the Hermite polynomial uncorrelated conversion filter is equivalent to the linear minimum mean square error estimator. The simulation results illustrate the superiority of the Hermite polynomial uncorrelated conversion filter over the conventional nonlinear Gaussian filters in the sense of the root mean square error and consistency.