Gaussian Particle Implementations of Probability Hypothesis Density Filters

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. Extensions for the GM-PHD filter allow for mildly non-linear dynamics using extended and Unscented Kalman filters. A new particle implementation of the PHD filter which does not require clustering to determine target states is presented here. The PHD is approximated by a mixture of Gaussians, as in the GM-PHD filter but the transition density and likelihood function can be non-linear. The resulting filter no longer has a closed form solution so Monte Carlo integration is applied for approximating the prediction and update distributions. This is calculated using a bank of Gaussian particle filters, similar to the procedure used with the Gaussian sum particle filter. The new algorithm is derived here and presented with simulated results.