Enhanced GMM-based Filtering with Measurement Update Ordering and Innovation-based Pruning

The Gaussian mixture model (GMM) has been extensively investigated in nonlinear/non-Gaussian filtering problems. This paper presents two enhancements for GMM-based nonlinear filtering techniques, namely, the adaptive ordering of the measurement update and normalized innovation square (NIS)-based mixture component management. The first technique selects the order of measurement update by maximizing the marginal measurement likelihood to improve performance. The second approach takes the filtering history of a mixture component into account and prunes those components with NIS larger than a threshold to eliminate their impact on the filtering posterior. The advantage of the proposed enhancements is illustrated via simulations that consider source tracking using the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements received at two unmanned aerial vehicles (UAVs). A GMM-cubature quadrature Kalman filter (CQKF) is implemented and its performances with different measurement update and mixture component management strategies are compared. The superior performance obtained via the use of the two proposed techniques is demonstrated.