By Anton J. Haug
A sensible method of estimating and monitoring dynamic platforms in real-worl applications
Much of the literature on appearing estimation for non-Gaussian platforms is brief on sensible technique, whereas Gaussian equipment frequently lack a cohesive derivation. Bayesian Estimation and Tracking addresses the distance within the box on either debts, offering readers with a accomplished review of tools for estimating either linear and nonlinear dynamic platforms pushed through Gaussian and non-Gaussian noices.
Featuring a unified method of Bayesian estimation and monitoring, the booklet emphasizes the derivation of all monitoring algorithms inside a Bayesian framework and describes powerful numerical tools for comparing density-weighted integrals, together with linear and nonlinear Kalman filters for Gaussian-weighted integrals and particle filters for non-Gaussian instances. the writer first emphasizes certain derivations from first ideas of eeach estimation process and is going directly to use illustrative and certain step by step directions for every technique that makes coding of the monitoring clear out basic and simple to understand.
Case reviews are hired to show off purposes of the mentioned subject matters. furthermore, the booklet provides block diagrams for every set of rules, permitting readers to increase their very own MATLAB® toolbox of estimation methods.
Bayesian Estimation and Tracking is a superb ebook for classes on estimation and monitoring equipment on the graduate point. The publication additionally serves as a priceless reference for examine scientists, mathematicians, and engineers looking a deeper knowing of the topics.
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Additional info for Bayesian Estimation and Tracking: A Practical Guide
Sequential Monte Carlo Methods in Practice. New York, NY: Springer-Verlag; 2001. 5. Papoulis A. Probability, Random Variables, and Stochastic Processes, 4th ed. McGraw-Hill; 2002. 6. Bar Shalom Y, Li XR, Kirubarajan T. Estimation with Application to Tracking and Navigation: Theory, Algorithms and Software. Wiley; 2001. 7. Candy JV. Bayesian Signal Processing: Classical, Modern, and Particle Filtering Methods. Hoboken, NJ: Wiley; 2009. 8. Ristic B, Arulampalam S, Gordon N. Beyond the Kalman Filter: Particle Filters for Tracking Applications.
In this section, we will review methods for numerically approximating such nonlinear functions. This section begins with a review of scalar methods that are then extended into multiple dimensions. All of the approximations to a nonlinear function are essentially expansions of the nonlinear function into a polynomial with arbitrary coefficients. Specification of the exact form of the coefficients depends on the application, the desired accuracy and other computational considerations. Issues related to the specification of these coefficients for estimation and tracking applications will be addressed in a later chapters on specific methods for the evaluation of density-weighted integrals.
1 BAYESIAN INFERENCE Inference methods consist of estimating the current values for a set of parameters based on a set of observations or measurements. The estimation procedure can follow one of two models. The first model assumes that the parameters to be estimated, usually unobservable, are nonrandom and constant during the observation window but the observations are noisy and thus have random components. The second model assumes that the parameters are random variables that have a prior probability and the observations are noisy as well.