Converted Measurement Trackers for Systems with Nonlinear Measurement Functions

Converted measurement tracking is a technique that filters in the coordinate system where the underlying process of interest is linear and Gaussian, and requires the measurements to be nonlinearly transformed to fit. The goal of the transformation is to allow for tracking in the coordinate system that is most natural for describing system dynamics. There are two potential issues that arise when performing converted measurement tracking. The first is conversion bias that occurs when the measurement transformation introduces a bias in the expected value of the converted measurement. The second is estimation bias that occurs because the estimate of the converted measurement error covariance is correlated with the measurement noise, leading to a biased Kalman gain. The goal of this research is to develop a new approach to converted measurement tracking that eliminates the conversion bias and mitigates the estimation bias. This new decorrelated unbiased converted measurement (DUCM) approach is developed and applied to numerous tracking problems applicable to sonar and radar systems. The resulting methods are compared to the current state of the art based on their mean square error (MSE) performance, consistency and performance with respect to the posterior Cramer-Rao lower bound