PHD和CPHD是最优或次最优滤波器？

问：PHD和CPHD是最优或次最优滤波器？

答：PHD是次最优滤波器，它是最优递归多目标非线性滤波器的矩近似。

This type of approach allows the problem of estimating multiple targets in clutter and uncertain associations to be cast in a Bayesian filtering framework [16], which in turn results in an optimal multi-target Bayesian filter [1].

As is the case in many nonlinear Bayesian estimation problems, the optimal multi-target Bayesian filter is infeasible to implement except for simple examples and an important contribution of FISST is to provide structured tools in the form of the statistical moments of an RFS. The first-order moment of an RFS is called probability hypothesis density (PHD), and it is an intensity function defined over the state space of the targets. The so-called PHD filter [16,17] propagates in time PHDs corresponding to the set of target states as an approximation of the optimal multi-target Bayesian filter. A practical implementation of the PHD filter is provided by approximating the PHDs with Gaussian mixtures (GM) [18] which results in the Gaussian-mixture PHD (GM-PHD) filter. In the recent work [19], Mahler presented an extension of the PHD filter to also handle extended targets of the type presented in [2].

 

With finite set statistics (FISST), Mahler introduced a set theoretic approach in which targets and measurements are modeled using random finite sets (RFS). The approach allows multiple target tracking in the presence of clutter and with uncertain associations to be cast in a Bayesian framework [11], resulting in an optimal multi-target Bayes filter [2].

 

The PHD filter is a suboptimal but computationally tractable alternative to the RFS Bayes multi-target filter. It is a recursion that only propagates the PHD or the intensity function of the RFS of targets [3].

 

[1]. Granstrom, K., et al. (2012). "Extended Target Tracking using a Gaussian-Mixture PHD Filter." IEEE Transactions on Aerospace and Electronic Systems 48(4): 3268-3286.

[2]. Granstrom, K. and U. Orguner (2012). "A phd Filter for Tracking Multiple Extended Targets Using Random Matrices." IEEE Transactions on Signal Processing 60(11): 5657-5671.

[3]. K. Panta, D. E. Clark, and B.-N. Vo, "Data association and track management for the gaussian mixture probability hypothesis density filter," IEEE Transactions on Aerospace and Electronic Systems, vol. 45, no. 3, pp. 1003-1016, 2009, doi: 10.1109/TAES.2009.5259179. 

 

 

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