Gaussian Mixture Representation of 3- D Phased Array Radar Measurements in Sine Space
Michael Kowalski, Dale Blair, Paul A. Miceli · 2023
When measurement errors are more than two orders of magnitude larger in crossrange (i.e., angle) than in range, the representation of the posterior distribution with a single Gaussian covariance is inaccurate for tracking applications. Measurements are a nonlinear function of the Cartesian track states, and this nonlinearity must be addressed to achieve near optimal estimates with a consistent covariance. Gaussian mixture models have been shown to be an effective tool for modeling the posterior distribution when a single Gaussian is not sufficient [1]. An effective method to find the Maximum Likelihood (ML) solution to the parameters describing the Gaussian mixture model around a converted distribution is Expectation Maximization (EM) [3]. The application of EM tools to radar measurements has been restricted to polar and spherical measurements [8], [10], while phased array measurements are in range and sine space. In this work, the EM algorithm is used to find the ML estimates of the parameters of a Gaussian mixture representation of the 3-D sine space measurements in 3-D Cartesian space. The mixture models are shown to greatly reduce the Kullback-Leibler diver-gence of the true and model distributions when compared to a single Gaussian. The nuances of the distributions are examined, such as the presence of a skew in the distribution, and a lookup table is proposed as a computationally efficient component of a Gaussian mixture filter. The Gaussian mixtures are shown to be effective in reducing the adverse effects of the nonlinearity in sensor measurements when tracking with a Gaussian mixture filter.