Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Illustrative example on contaminant cloud tracking <s> Contour tracking for a single source emission is addressed in this paper. This problem is solved by estimating the contour boundary positions using a set of particle filters. The use of Sequential Monte Carlo techniques enables the tracking to performed when the measurements are noisy and the tracking results also includes the estimation uncertainly. The proposed technique is illustrated for a SCIPUFF generated single emission scenario and simulation experiments showed the successful tracking throughout the tracking period. <s> BIB001 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Illustrative example on contaminant cloud tracking <s> In this paper, we address the problem of detection and tracking of multiple contaminant clouds. We develop a stochastic extension of the Gaussian puff model to characterize evolution of the average atmospheric pollutant concentration. To perform the sequential inference on this difficult problem, we propose a Markov Chain Monte Carlo (MCMC)-based Particle algorithm. Numerical simulations illustrate the ability of the algorithm to detect and track multiple contaminant clouds. <s> BIB002
The presented Gaussian mixture sequential MCMC technique has been also successfully applied to pollutant cloud tracking in BIB002 . The tracking of contaminant clouds can also be seen as an extended object tracking problem. The capability to monitor and track contaminant clouds is indeed a problem of great importance. Nowadays, the threat of pollution due to the release, either accidentally or deliberately, of Chemical, Biological, Radiological or Nuclear (CBRN) agents is high. Indeed, many rogue nations and terror groups seek to employ asymmetric warfare and some groups will be attracted by the use of chemical weapons to achieve major impact. As a consequence, rapid detection and early response to a release of a CBRN agent could dramatically reduce the extent of human exposure. In BIB002 , the authors propose an inference algorithm within a Bayesian framework to track directly the contaminant concentration, instead of some contaminant boundary as in BIB001 , thus providing more information about the actual situation. More precisely, the concentration of pollutant is expressed in this work using the following parametric function: . (16) This formulation of the concentration field of interest is motivated by two widely used dispersion models: the Gaussian Puff Model and the Gaussian Puff Particle Model. The parameters of each Gaussian shape, involved in Eq. (16) evolve independently over time as follows: where φ(.|ν, σ 2 ) is the truncated normal distribution with mean ν and variance σ 2 defined on [0, +∞) to ensure the positivity of the weight variable. The mean vector transition probability is a random walk with a linear drift depending on the wind velocity v and the covariance matrix is assumed to be a Wishart random matrix with a scaling matrix Dτ (D is the pollutant diffusion matrix) and a number of degrees of freedom n. τ = t k − t k−1 corresponds to the sampling interval between t k and t k−1 . As in the previous example of large group tracking, the problem consists in estimating sequentially the evolution of a sum of dynamic multivariate Gaussian components. The only difference is in the likelihood function. For chemical, biological or radiological source term estimation, several sensors allow to measure the concentration in the atmosphere like the LCAD (Lightweight Chemical Agent Detector) and the MCAD (Mobile Chemical Agent Detector) but one of the most data rich sensors currently available is the LIght Distance And Ranging (LIDAR) sensor. The observations from sensors can be generally written as a nonlinear function of the concentration field and noises that take into account both the dispersion model uncertainty and the measurement error: In a Bayesian framework, the aim is thus to compute the poste- , N t k |Z 1:k ) where z 1:k is the observation set from time 1 to t k in order to give estimate of the parameters involved in the concentration field. The main challenging difficulty in this problem is the fact that we have to deal with unknown and time-varying number of Gaussian shapes for the concentration as well as nonlinearity and non-Gaussianity in the model. In BIB002 , the authors propose algorithm to identify and track these multiple contaminant clouds based on a sequential Monte Carlo Markov Chain (MCMC) mechanization which approximates the filtering distribution of interest. To illustrate the results obtained by this sequential MCMC in this context, the scenario studied in this section consists of one cloud modeled by 3 Gaussian shapes then at time t = 150 s, an other cloud modeled by one Gaussian puff appears in the observation scene. The synthetic data are generated using the stochastic Gaussian puff model described by Eqs. (17)- (19) . In the sequential MCMC algorithm used to track the contaminant clouds, all Gaussian shapes are initialized as inactive in order to allow the algorithm to identify all the Gaussian shapes necessary to model the actual contaminant clouds. The maximum number of Gaussian shapes in the algorithm is set to N max = 5. For each complete LIDAR scan, 4000 MCMC iterations are performed with burn-in of 1000 iterations. All 4000 MCMC output are kept as particle approximation to posterior distribution. Fig. 7 illustrates true concentration of the cloud (on the left column), the results from the Gaussian mixture sequential MCMC technique (in the middle column) in time steps respectively 108, 307 and 557 and the measurements obtained with an LIDAR (in the rightmost column). From this figure it can be recognized that the filtering algorithm is able to adequately identify and track the contaminant clouds in a difficult scenario with heavy clutter.