Efficient Gaussian Mixture Modeling of Long-Range 2-D Radar Measurements

In some practical radar systems of interest, the standard EKF linearization approach applied to a nonlinear measurement transformation is ineffective. In particular, if measurements are performed in polar coordinates and the crossrange error is much greater than the range error, then the true error region in Cartesian space is no longer well approximated by a Gaussian distribution. This effect is known as the “contact lens” problem, and various approaches have been proposed to alleviate it, including particle and Gaussian mixture (GM) filters. In this work, a method is presented for modeling Cartesian converted measurement distributions, which suffer from the contact lens effect using Maximum Likelihood (ML) GM parameters. In order to allow an efficient implementation of this process in a GM Kalman filter, a normalization of the ML parameters is introduced so that parameters can be computed offline and efficiently stored in a lookup table. Simulation results are presented to illustrate the method and confirm the results.