Gaussian mixture implementations of probability hypothesis density filters for non-linear dynamical models

The probability hypothesis density (PHD) filter is a multiple- target filter for recursively estimating the number of targets and their state vectors from sets of observations. The filter is able to operate in environments with false alarms and missed detections. Two distinct algorithmic implementations of this technique have been developed. The first of which, called the particle PHD filter, requires clustering techniques to provide target state estimates which can lead to inaccurate estimates and is computationally expensive. The second algorithm, called the Gaussian mixture PHD (GM-PHD) filter does not require clustering algorithms but is restricted to linear-Gaussian target dynamics, since it uses the Kalman filter to estimate the means and covariances of the Gaussians. This article provides a review of Gaussian filtering techniques for non-linear filtering and shows how these can be incorporated within the Gaussian mixture PHD filters. Finally, we show some simulated results of the different variants.