{"id":201,"date":"2012-08-08T21:25:31","date_gmt":"2012-08-08T21:25:31","guid":{"rendered":"http:\/\/www-sop.inria.fr\/members\/Fabien.Campillo\/?page_id=201"},"modified":"2023-10-06T13:10:31","modified_gmt":"2023-10-06T13:10:31","slug":"smc-demos","status":"publish","type":"page","link":"http:\/\/localhost:8888\/wordpress\/software\/smc-demos\/","title":{"rendered":"Sequential Monte Carlo (particle filtering) for tracking"},"content":{"rendered":"

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A set of matlab applications of particle filtering for applications in tracking developed in the context of lectures given from 2005 to 2010. The code has been\u00a0registered in 2009 at the Agence pour la Protection des Programmes (APP) [reference\u00a0IDDN.FR.001.28003.000.S.P.2009.000.31235].<\/p>\n

See\u00a0gitlab repository<\/a>.<\/p>\n

SMC are a class of algorithms for approximate inference in dynamic models. They are used to estimate the state of a system over time, given a sequence of noisy measurements. The basic idea of SMC methods is to represent the probability distribution over the state of the system at each time step using a set of weighted samples, or particles. The particles are propagated through time using the dynamics of the system, and their weights are updated based on the measurements that are made. The weights are used to approximate the true distribution, and they can be used to compute various statistics of interest, such as the mean and covariance of the state. SMC methods are useful because they allow us to make inferences about the state of a system in a computationally efficient manner, without requiring us to compute the true distribution explicitly. They have been applied in many fields.<\/p>\n

Documentation: you can read the lecture notes\u00a0“Mod\u00e8les de Markov cach\u00e9s et filtrate particular”\u00a0(last chapter) of a course I gave at the Universit\u00e9 du Sud Toulon-Var. The 2006 version if in the CEL website [link<\/a>], the 2007 version is here<\/a>.<\/p>\n\n\n

Context<\/h1>\n\n\n\n

In all these examples a mobile is describe by its state \"X_t\" in \"\mathbb{R}^n\" at time \"t\" which is a Markov process described by a Markov transition kernel \"Q_t(x,dx')\" with:<\/p>\n

  <\/span>   <\/span>\"\[<\/p><\/p>\n

for example it could be given by an SDE<\/p>\n

  <\/span>   <\/span>\"\[<\/p><\/p>\n

The observation process is \"Y_k\" which is the observation of \"X_t\" at time \"t_k\" given by:<\/p>\n

  <\/span>   <\/span>\"\[<\/p><\/p>\n

with \"0=t_0<t_1<t_2<\cdots\".<\/p>\n\n\n\n

Target tracking with angle only and obstacles<\/h1>\n\n\n\n
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\"\"The original idea for this nice example came from<\/span> [Simon Maskell](http:\/\/www.simonmaskell.com\/).<\/span><\/em><\/p>\n<\/div>\n

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The idea is to follow a mobile on the plane. We have \"S\" observation stations (squares) and \"L\" obstacles (black segments) that hide the movement of the mobile.<\/p>\n

The measures are the angle of the line of sight plus noise. <\/p>\n

In the video, we place 1) the observations stations, 2) the obstacles, then 3) we plot the trajectory of the mobile, and 4) we simulate the observations, finally 5) we plot the evolution of the particles of the approximation of the nonlinear filter.<\/p>\n

We notice the ability of the particle filter to handle non Gaussian situations. <\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n

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