## Tracking Multiple Objects with Particle Filtering (2000)

Citations: | 82 - 4 self |

### BibTeX

@MISC{Hue00trackingmultiple,

author = {C. Hue and J. -p. Le Cadre and P. Prez},

title = {Tracking Multiple Objects with Particle Filtering},

year = {2000}

}

### Years of Citing Articles

### OpenURL

### Abstract

We address the problem of multitarget tracking encountered in many situations in signal or image processing. We consider stochastic dynamic systems detected by observation processes. The difficulty lies on the fact that the estimation of the states requires the assignment of the observations to the multiple targets. We propose an extension of the classical particle filter where the stochastic vector of assignment is estimated by a Gibbs sampler. This algorithm is used to estimate the trajectories of multiple targets from their noisy bearings, thus showing its ability to solve the data association problem. Moreover this algorithm is easily extended to multireceiver observations where the receivers can produce measurements of various nature with different frequencies.

### Citations

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Citation Context ... cope with heavy clutter, and is very easy to implement. Such filters have been used in very different areas for Bayesian filtering, under different names: the bootstrap filter for target tracking in =-=[7]-=- and the Condensation algorithm in computer vision [8] are two examples among others. In earliest studies, the algorithm was only composed of two periods: the particles were predicted according to the... |

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Citation Context ...¢ i =1,:::,M, i t =P(K j t = i) forallj =1,:::,mt is the discrete probability that any measurement is associated with the ith target. To solve the data association some assumptions are commonly made =-=[28]-=-. A1. One measurement can originate from one target or from the clutter. A2. One target can produce zero or one measurement at one time. The assumption (A1) expresses that the association is exclusive... |

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Citation Context ...sociations must be exhaustively enumerated. This leads to an NP-hard problem because the number of possible associations increases exponentially with time, as in the multiple hypotheses tracker (MHT) =-=[1]-=-. To cope with this problem, pruning and gating eliminate the less likely hypotheses but can unfortunately eliminate good ones as well. In the joint probabilistic data association filter (JPDAF) [2], ... |

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Citation Context ...t. Such filters have been used in very different areas for Bayesian filtering, under different names: the bootstrap filter for target tracking in [7] and the Condensation algorithm in computer vision =-=[8]-=- are two examples among others. In earliest studies, the algorithm was only composed of two periods: the particles were predicted according to the state equation during the prediction step; then their... |

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Citation Context ...n [13] to track multiple objects but the algorithm is very dependent of the observation model and is only applied for two objects. In the same context, a Bayesian multiple-blob tracker called BraMBLe =-=[14]-=- has just been proposed. It deals with a varying number of objects which are depth-ordered thanks to a 3-D state space. Lately, in mobile robotic [15], a set of particle filters for each target connec... |

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Citation Context ...he correction step. Up to a constant, (6) comes down to adjust the weight of predictions by multiplying it by the likelihood p(yt j xt ). In the most general setting of sequential Monte Carlo methods =-=[16]-=-, the displacement of particles is obtained by sampling from an appropriate density f which might depend on the data as well. The general algorithm is summarized in Fig. 1. The density L is often mult... |

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Citation Context ...e found in [16, 20, 21]. Some convergence results of the empirical distributions to the posterior distribution on the path space have been proved when the number N of particles tends towards infinity =-=[22, 23]-=-. In the path space (R nx ) t+1 , each particle s n t at time t can be considered to be a discrete path of length t + 1. Compared with the particle filter presented in Fig. 1, particle filtering in th... |

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Citation Context ..., a Bayesian multiple-blob tracker called BraMBLe [14] has just been proposed. It deals with a varying number of objects which are depth-ordered thanks to a 3-D state space. Lately, in mobile robotic =-=[15]-=-, a set of particle filters for each target connected by a statistical data association has been proposed. We propose here a general algorithm for MTT in the passive sonar context. This work is organi... |

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Citation Context ...eriod. The corresponding algorithm of particle filter with systematic resampling is described in Fig. 2. To measure the degeneracy of the algorithm, theeffectivesamplesizeN eff has been introduced in =-=[20, 21]-=-. We can estimate this quantity by ˆN eff =1= P N n=1 (qn t )2 which measures the number of meaningful particles. As advocated in [16], the resampling can be done only if ˆ N eff <N threshold . This e... |

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Citation Context ...en developed to accomplish this resampling whose final goal is to enforce particles in areas of high likelihood. The frequency of this resampling has also been studied. Also the use of kernel filters =-=[9]-=- has been introduced to regularize the sum of Dirac densities associated to the particles when the dynamic noise of the state equation was too low [10]. Despite this long history of studies, in which ... |

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Citation Context ...d, the extension of the particle filter to multiple target tracking has progressively received attention only in the last five years. Such extensions have first been claimed theoretically feasible in =-=[11, 12]-=- but the examples chosen only dealt with one single target. In computer vision a probabilistic exclusion principle has been developed in [13] to track multiple objects but the algorithm is very depend... |

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Citation Context ...ies the exhaustive enumeration of all possible associations at the current time step. When the association variables are instead supposed statistically independent like in the probabilistic MHT (PMHT =-=[3, 4]-=-), the complexity is reduced. For instance in [3, 4], the algorithm is presented as an incomplete data problem solved by an EM algorithm. There is no measurement gating as in the JPDAF and all the ass... |

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Citation Context ...d, the extension of the particle filter to multiple target tracking has progressively received attention only in the last five years. Such extensions have first been claimed theoretically feasible in =-=[11, 12]-=- but the examples chosen only dealt with one single target. In computer vision a probabilistic exclusion principle has been developed in [13] to track multiple objects but the algorithm is very depend... |

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Citation Context ...eal with significant clutter and spurious objects for target tracking [12] and guidance [18]. The weighted sum of Dirac laws is then approximated by a Gaussian mixture obtained by a clustering method =-=[19]-=-. The particle sets enable one to estimate any functional of Xt in particular the two first moments with g(x)=x and g(x)=x2 , respectively. The mean can be used to estimate the position of one object ... |

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Citation Context ...iven these assignment probabilities, the particle weights can be evaluated. The particle filters are then dependent through the evaluation of the assignment probabilities. The algorithms presented in =-=[29, 30]-=- are both applied to target tracking. The state space of each particle is the concatenation of the state space of each target and the likelihood of the measurements given a particle is derived accordi... |

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Citation Context ...e found in [16, 20, 21]. Some convergence results of the empirical distributions to the posterior distribution on the path space have been proved when the number N of particles tends towards infinity =-=[22, 23]-=-. In the path space (R nx ) t+1 , each particle s n t at time t can be considered to be a discrete path of length t + 1. Compared with the particle filter presented in Fig. 1, particle filtering in th... |

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Citation Context ...t deal with classical bearings-only problems. The object is then a “point-object” in the x-y plane. In the context of a slowly maneuvering target, we have chosen a nearly constant-velocity model (see =-=[24]-=- for a review of the principal dynamical models used in this domain). A. The Model The state vector Xt represents the coordinates and the velocities in the x-y plane: Xt =(xt ,yt ,vxt ,vyt ). The disc... |

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Citation Context ...ies the exhaustive enumeration of all possible associations at the current time step. When the association variables are instead supposed statistically independent like in the probabilistic MHT (PMHT =-=[3, 4]-=-), the complexity is reduced. For instance in [3, 4], the algorithm is presented as an incomplete data problem solved by an EM algorithm. There is no measurement gating as in the JPDAF and all the ass... |

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Citation Context ...mated targets in the estimation procedure. Two main ways have been found in the literature to estimate the parameters of such a mixture: the EM method (and its stochastic version, the SEM algorithm =-=[31]-=-) and the Data Augmentation method. The second one amounts in fact to a Gibbs sampler. In [3—5] the EM algorithm is extended and applied to multitarget tracking. This method implies that the vectors ... |

25 |
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Citation Context ...nce of significant clutter. Several hypotheses about the object position can then be kept if the set of particles splits into several subsets. This is where the great strength of this filter lies. In =-=[17]-=- for instance, the measurement vector Yt consists of a set of detected features along line measurements. The assumed underlying generative model affects each feature either to the target boundary, or ... |

15 |
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(Show Context)
Citation Context ...iven these assignment probabilities, the particle weights can be evaluated. The particle filters are then dependent through the evaluation of the assignment probabilities. The algorithms presented in =-=[29, 30]-=- are both applied to target tracking. The state space of each particle is the concatenation of the state space of each target and the likelihood of the measurements given a particle is derived accordi... |

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Citation Context ...eriod. The corresponding algorithm of particle filter with systematic resampling is described in Fig. 2. To measure the degeneracy of the algorithm, theeffectivesamplesizeN eff has been introduced in =-=[20, 21]-=-. We can estimate this quantity by ˆN eff =1= P N n=1 (qn t )2 which measures the number of meaningful particles. As advocated in [16], the resampling can be done only if ˆ N eff <N threshold . This e... |

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Citation Context ...Metropolis-Hasting algorithm with the proposal densities being the conditional distributions, and the acceptance probability being consequently always equal to one. The interested reader can refer to =-=[37]-=- for an introduction to Markov chain Monte Carlo simulation methods and also for a presentation of the EM algorithm. For µ t =(Xt ,Kt ,¦ t ), the method consists in generating a Markov chain that conv... |

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Citation Context ...o measurement gating as in the JPDAF and all the associations are considered. The results are then satisfactory when the measurement equation is linear and when the trajectories are deterministic. In =-=[5]-=- the algorithm is extended to the tracking of maneuvering targets with an hidden “model-switch” process controlled by a Markov probability structure. A comparison of the PMHT with the JPDAF is describ... |

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Citation Context ...also been studied. Also the use of kernel filters [9] has been introduced to regularize the sum of Dirac densities associated to the particles when the dynamic noise of the state equation was too low =-=[10]-=-. Despite this long history of studies, in which the ability of particle filter to track multiple posterior modes is claimed, the extension of the particle filter to multiple target tracking has progr... |

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Citation Context ...g of maneuvering targets with an hidden “model-switch” process controlled by a Markov probability structure. A comparison of the PMHT with the JPDAF is described in a practical two-target scenario in =-=[6]-=-, focusing on the mean-square estimation errors and the percentage of lost tracks. Unfortunately, the above algorithms do not cope with nonlinear models and non-Gaussian noises. IEEE TRANSACTIONS ON A... |

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