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Bayesian estimation for target tracking: part II, the Gaussian sigma‐point Kalman filters

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Abstract This is the second part of a three part article 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 this 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, including the unscented, spherical simplex, and Gauss‐Hermite Kalman filters. In part 3, we will show that approximating a density by a set of Monte Carlo samples leads to particle filter methods, where the posterior density is propagated in time and moment integrals are approximated by sample moments. WIREs Comput Stat 2012 doi: 10.1002/wics.1215 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

Three‐dimensional uniform grid of vector sigma points lying on the unit sphere.

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Process flow for all sigma‐point Kalman filters.

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Two‐dimensional nested grid of vector sigma points for Hermite numerical integration.

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Uniform grid of vector sigma points on a simplex in one, two, and three dimensions.

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

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