Adaptive Gaussian mixture modeling for tracking of long range targets

Long-range radar systems providing precise range measurements experience degraded tracking performance due to the non-Gaussian nature of their measurement distribution when converted to Cartesian space. The unbiased transform and unscented Kalman filter have been used to obtain an unbiased track and improved track covariance consistency. However, debiasing the mean and inflating the covariance results in range estimates with larger errors than the measurements, along with an excessive gating region that leads to a higher probability of false alarm gating and measurement-to-track association errors. The Measurement Covariance Adaptive Extended Kalman Filter (MCAEKF) follows a similar covariance inflation strategy and suffers from similar problems. More recently, Tian and Bar-Shalom investigated the representation of the contact-lens like distribution of the precise range measurements by a Gaussian mixture. This technique increased the number of Gaussian components used to represent the contact-lens distribution until a consistency criterion dependent on the curvature of the distribution was reached. In this paper, the number of Gaussians needed to control the Kullback-Leibler (K-L) divergence of the mixture approximation from the true distribution is studied as a function of the curvature of the measurement distribution. Additionally, the track state estimate is also represented by a Gaussian mixture using an adaptive technique based on K-L divergence for selecting the number of Gaussians. This adaptive GM filter is then implemented and the results show that it produces track range estimates with error that is not degraded with respect to the accuracy of the input range measurements.