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

• Published in: IET Seminar on Target Tracking and Data Fusion: Algorithms and Applications pp. 19 - 28
• Main Authors: Clark, D, Ba-Tuong Vo, Ba-Ngu Vo, Godsill, S
• Format: Conference Proceeding
• Language: English
• Published: Stevenage IET 2008
• Subjects: Filtering methods in signal processing; Interpolation and function approximation (numerical analysis); Other topics in statistics; Signal processing theory; clustering techniques; probability; Gaussian mixture implementations; Kalman filter; particle filtering (numerical methods); nonlinear filters; recursively estimation; target state estimates; nonlinear dynamical systems; state vectors; Gaussian filtering techniques; Gaussian mixture PHD filter; multiple-target filter; linear-Gaussian target dynamics; Gaussian processes; target tracking; recursive estimation; state estimation; nonlinear filtering; Kalman filters; nonlinear dynamical models; probability hypothesis density filters; particle PHD filter
• ISBN: 0863419100; 9780863419102
• DOI: 10.1049/ic:20080053

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.