## Rao-Blackwellized Particle Filter for Multiple Target Tracking (2005)

Venue: | Information Fusion Journal |

Citations: | 32 - 3 self |

### BibTeX

@ARTICLE{Särkkä05rao-blackwellizedparticle,

author = {Simo Särkkä and Aki Vehtari and Jouko Lampinen},

title = {Rao-Blackwellized Particle Filter for Multiple Target Tracking},

journal = {Information Fusion Journal},

year = {2005},

volume = {8},

pages = {2007}

}

### OpenURL

### Abstract

In this article we propose a new Rao-Blackwellized particle filtering based algorithm for tracking an unknown number of targets. The algorithm is based on formulating probabilistic stochastic process models for target states, data associations, and birth and death processes. The tracking of these stochastic processes is implemented using sequential Monte Carlo sampling or particle filtering, and the e#ciency of the Monte Carlo sampling is improved by using Rao-Blackwellization.

### Citations

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Citation Context ...ance matrices Rk,j can be different for each target. Non-linear measurement models can be used by replacing the non-linear model with a locally linearized model as in the extended Kalman filter (EKF) =-=[2,6]-=- or by using the unscented transformation as in the unscented Kalman filter (UKF) [29]. • Target dynamics are linear Gaussian p(xk,j | xk−1,j) = N(xk,j | Ak−1,jxk−1,j, Qk−1,j), (5) where the transitio... |

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Citation Context ...be used by replacing the non-linear model with a locally linearized model as in the extended Kalman filter (EKF) [2,6] or by using the unscented transformation as in the unscented Kalman filter (UKF) =-=[29]-=-. • Target dynamics are linear Gaussian p(xk,j | xk−1,j) = N(xk,j | Ak−1,jxk−1,j, Qk−1,j), (5) where the transition matrix Ak−1,j and process noise covariance matrix Qk−1,j may be different for differ... |

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Citation Context ...particular form for the birth and death models. The approximation based on limiting the number of births and deaths on each time step is also discussed in [19]. The particle filtering based method in =-=[20]-=- uses exponential (Poisson) models for target appearance and disappearance a bit similarly to our method. The branching particle based solution [21] also models target appearance as a stochastic (Mark... |

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Citation Context ...is unbiased. Another way, which is also used in our simulation system, is adaptive resampling, in which the effective number of particles, which is estimated from the variance of the particle weights =-=[24]-=- is used for monitoring the need for resampling. The performance of the SIR algorithm is also dependent on the importance distribution π(·), which is an approximation of the posterior distribution of ... |

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Citation Context ...cking in the case of an unknown number of targets. A tractable implementation of the framework is to use the first order moment of the multi-target posterior, the probability hypothesis density (PHD) =-=[15]-=- as an approximation. SMC based implementations of the PHD have been reported, for example, in the articles [16] [17]. In the SMC based method presented in the article [13] the extension to an unknown... |

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Citation Context ...der moment of the multi-target posterior, the probability hypothesis density (PHD) [15] as an approximation. SMC based implementations of the PHD have been reported, for example, in the articles [16] =-=[17]-=-. In the SMC based method presented in the article [13] the extension to an unknown number of targets is based on hypothesis testing. Because the algorithm generates estimates of data association prob... |

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Citation Context ... enhance the computational efficiency, heuristic methods such as gating, hypothesis merging, clustering and several other strategies can be employed. Probabilistic multiple hypothesis tracking (PMHT) =-=[10]-=- is a modification of the MHT, where the data associations are assumed to be independent over the target tracks. This way the computational complexity of the method is substantially reduced, but it is... |

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Citation Context ...the sense that it minimizes the variance of the importance weights. One way of improving the efficiency of SMC is to use Rao-Blackwellization. The idea of the Rao-Blackwellized particle filter (RBPF) =-=[25,5,23]-=- is that sometimes it is possible to evaluate some of the filtering equations analytically and the others with Monte Carlo sampling instead of computing everything with pure sampling. According to the... |

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Citation Context ...st order moment of the multi-target posterior, the probability hypothesis density (PHD) [15] as an approximation. SMC based implementations of the PHD have been reported, for example, in the articles =-=[16]-=- [17]. In the SMC based method presented in the article [13] the extension to an unknown number of targets is based on hypothesis testing. Because the algorithm generates estimates of data association... |

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Citation Context ... applications. By tuning the resampling algorithm and possibly changing the order of weight computation and sampling, accuracy and computational efficiency of the algorithm could possibly be improved =-=[27]-=-. An important issue is that sampling could be more efficient without replacement, such that duplicate samples are not stored. There is also evidence that in some situations it is more efficient to us... |

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Citation Context ...pling instead of computing everything with pure sampling. According to the Rao-Blackwell theorem this leads to estimators with less variance than what could be obtained with pure Monte Carlo sampling =-=[26]-=-. An intuitive way of understanding this is that the marginalization replaces the finite Monte Carlo particle set representation with an infinite closed form particle set, which is always more accurat... |

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Citation Context ...E-mail: jouko.lampinen@hut.fi, Tel: +358 9 451 4827, Fax: +358 9 451 4830. Preprint submitted to Elsevier Science 22 September 2005s1 Introduction This article is an extended version 4 of the article =-=[1]-=-, in which we proposed a Rao-Blackwellized particle filtering based multiple target tracking algorithm called Rao-Blackwellized Monte Carlo data association (RBMCDA). In this article we extend the RBM... |

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Citation Context ...ual division is often done in literature. In the article [1] we presented a solution to first two of these problems using Rao-Blackwellized particle filtering together with classical filtering theory =-=[2,6]-=-. The main contribution of this article is to solve the problem of estimating the number of targets. In the next two sections we shall present a short review of the existing methods for data associati... |

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Citation Context ...sed in [19]. The particle filtering based method in [20] uses exponential (Poisson) models for target appearance and disappearance a bit similarly to our method. The branching particle based solution =-=[21]-=- also models target appearance as a stochastic (Markov) process. The tracking of an unknown number of targets is also closely related to model selection. An application of SMC methods to estimating th... |

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Citation Context ...appeared from the surveillance area. The detection of the appearance of a new target is based on testing the hypothesis between association with the old targets and with the new target. 4sThe article =-=[18]-=- presents a SMC based method, which is similar to our method except that a plain particle presentation of the joint posterior distribution is used. In the method, birth and death moves in particle pro... |

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Citation Context ...uplicate samples are not stored. There is also evidence that in some situations it is more efficient to use a simple deterministic algorithm for preserving the N most likely particles. In the article =-=[28]-=- it is shown that in digital demodulation, where the sampled space is discrete and the optimization criterion is the minimum error, the deterministic algorithm performs better. 6s2 RBMCDA with a Known... |

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Citation Context ...ty hypothesis density (PHD) [15] as an approximation. SMC based implementations of the PHD have been reported, for example, in the articles [16] [17]. In the SMC based method presented in the article =-=[13]-=- the extension to an unknown number of targets is based on hypothesis testing. Because the algorithm generates estimates of data association probabilities, these estimates can be used for approximatin... |

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Citation Context ... likelihood of the association with the existing targets is too low. A track is deleted when its likelihood becomes too low compared to the other tracks. Random sets and finite set statistics (FISST) =-=[14]-=- provide a very general framework for Bayesian modeling of multiple target tracking in the case of an unknown number of targets. A tractable implementation of the framework is to use the first order m... |

1 |
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Citation Context ...cle. Due to the plain particle presentation, the method in the article [18] is also applicable to the more general case of target tracking without explicit thresholding of measurements. The method in =-=[19]-=- also resembles our method, except that the article does not suggest any particular form for the birth and death models. The approximation based on limiting the number of births and deaths on each tim... |

1 |
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Citation Context ...ocess. The tracking of an unknown number of targets is also closely related to model selection. An application of SMC methods to estimating the number of RBF network weights from data is presented in =-=[22]-=-. In this article, we extend the SMC based RBMCDA method [1] to tracking an unknown number of targets. The extension is based on modeling the birth and death stochastic processes, such that track form... |