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Bayesian estimation for target tracking, Part III: Monte Carlo filters

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Abstract This is the third part of a three part article series examining methods for Bayesian estimation and tracking. In the first part we presented the general theory of Bayesian estimation where we showed that Bayesian estimation methods can be divided into two very general classes: a class where the observation‐conditioned posterior densities are propagated in time through a predictor/corrector method and a second class where the first two moments are propagated in time, with state and observation moment prediction steps followed by state moment update steps that use the latest observations. In the second part, we make the assumption that all densities are Gaussian and, after applying an affine transformation and approximating all nonlinear functions by interpolating polynomials, we recover the sigma point class of Kalman filters. In this third part, we show that approximating a non‐Gaussian density by a set of Monte Carlo samples drawn from an importance density leads to particle filter methods, where the posterior density is propagated in time and moment integrals are approximated by sample moments. These methods include the sequential importance sampling bootstrap, optimal, and auxiliary particle filters and more general Monte Carlo particle filters. WIREs Comput Stat 2012 doi: 10.1002/wics.1210 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

Example of the creation of w(x).

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Combination particle filter that uses a sigma point Kalman filter as an importance density.

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Process flow diagram for the GPF.

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Principle of resampling. Top: Samples drawn from q (dashed red line) with associated normalized importance weights depicted by bullets with radii proportional to normalized weights (the target density corresponding to p is plotted as the solid green line). Middle: After resampling, all particles have the same importance weight and some have been duplicated. Bottom: Samples have been regularized using a Kernel density estimator that resamples and moves.

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Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

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