Gaussian mixture probability hypothesis density filter against measurement origin uncertainty

Abstract

The Gaussian mixture probability hypothesis density (GM-PHD) filter is a promising solution to the multi-target tracking (MTT) problem, which successfully integrates target detection, tracking, and identification. Despite its wide applicability and computational efficiency, the existing GM-PHD filter can lose the estimates of the targets frequently in heavily cluttered and/or low signal-to-noise ratio (SNR) environments. This is mainly attributed to insufficient consideration of uncertainties around whether a measurement is from a target or not in the GM-PHD filter. Specifically, at each time step, the GM-PHD filter generates new Gaussian components corresponding to individual measurements which have the same estimate error covariances regardless of whether the measurement is from a target or not, so that it can lose the estimates of targets when the clutter density is high and/or the detection probability is low. To address this problem, a new covariance update equation is proposed. This equation computes the estimate error covariance of a newly generated Gaussian component corresponding to each measurement conditioned on the uncertainty in the measurement origin, i.e. whether: (1) measurement is clutter; (2) measurement is originated from a target; and (3) there is no measurement. The performance of the proposed GM-PHD algorithm is demonstrated with illustrative MTT scenarios with different noise conditions.