Gaussian Mixture Representation of 3- D Phased Array Radar Measurements in Sine Space

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.