Maximum likelihood mixture modeling for three-dimensional non-Gaussian measurements
Benjamin Davis, William Dale Blair · 2018
In long-range radar tracking problems with precise range measurements, the Extended Kalman Filter (EKF) tracking algorithm commonly used with non-linear radar measurements fails to achieve good performance. This is due to the fact that this algorithm approximates the measurement error distribution in Cartesian space using a Gaussian distribution when the true distribution is highly non-Gaussian, a situation which is referred to as the "contact-lens" problem in the literature. A recently developed technique uses Maximum Likelihood (ML) to fit Gaussian Mixture (GM) parameters to the non-Gaussian Cartesian measurement distribution in 2D. This approach was applied in a new GM Kalman filter which provides excellent range estimation performance at a fraction of the cost of a particle filter. This paper extends the ML modeling approach to three dimensional radar measurements. This presents a greater difficulty because the ML GM fits to a 3D radar measurement in Cartesian space have widely varying geometries compared to ML fits to a 2D measurement.