Binomial splitting Gaussian mixture implementation of the unscented Kalman probability hypothesis density filter

Abstract

In this work, we present a binomial splitting Gaussian mixture unscented Kalman probability hypothesis density (BSGM-UKPHD) filter. The BSGM-UKPHD filter applies a binomial splitting strategy to the original Gaussian mixture unscented Kalman probability hypothesis density (GM-UKPHD) filter, to gain performance promotion when the measurement function is nonlinear. The binomial splitting approximates every Gaussian component of the predicted probability hypothesis density (PHD) with a sum of weighted Gaussian distributions that have smaller covariance. Thus the state update of the nonlinear measurements will cause smaller errors. The binomial splitting preserves the mean and covariance of the original Gaussian distribution, and uses weights from the standardized binomial distribution. Simulation results show that, the proposed BSGM-UKPHD filter outperforms the GM-UKPHD filter and the Gaussian mixture extended Kalman PHD (GM-EKPHD) filter.