Gaussian mixture presentation of measurements for long-range radar tracking

In long-range radar tracking, the measurement uncertainty region has a thin and curved shape in Cartesian space due to the fact that the measurement is accurate in range but inaccurate in angle. Such a shape reflects grievous measurement nonlinearity, which can lead to inconsistency in tracking performance and significant tracking errors in traditional nonlinear filters, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). In this paper, we propose a modified version of the Gaussian Mixture Measurement-Integrated Track Splitting (GMM-ITS) filter to deal with the nonlinearity of measurements in long-range radar tracking. Not only is the state probability density function (pdf) approximated by a set of Gaussian track components, but the likelihood function (LF) is approximated by several Gaussian measurement components. In this way, both the state pdf and LF in the proposed filter have more accurate approximation than traditional filters that approximate measurements using just one Gaussian distribution. Simulation experiments show that the proposed filter can successfully avoid the inconsistency problem and also obtain high tracking accuracy in both 2-D (with range-angle measurements) and 3-D (with range-direction-cosine measurements) long-range radar tracking.