Nonlinear bayesian filtering with applications to estimation and navigation

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Title: Nonlinear bayesian filtering with applications to estimation and navigation
Author: Lee, Deok-Jin
Abstract: In principle , general approaches to optimal nonlinear filtering can be described in a unified way from the recursive Bayesian approach . The central idea to this recur - sive Bayesian estimation is to determine the probability density function of the state vector of the nonlinear systems conditioned on the available measurements . However , the optimal exact solution to this Bayesian filtering problem is intractable since it requires an infinite dimensional process . For practical nonlinear filtering applications approximate solutions are required . Recently efficient and accurate approximate non - linear filters as alternatives to the extended Kalman filter are proposed for recursive nonlinear estimation of the states and parameters of dynamical systems . First , as sampling -based nonlinear filters , the sigma point filters , the unscented Kalman fil - ter and the divided difference filter are investigated . Secondly , a direct numerical nonlinear filter is introduced where the state conditional probability density is calcu - lated by applying fast numerical solvers to the Fokker -Planck equation in continuous - discrete system models . As simulation -based nonlinear filters , a universally effective algorithm , called the sequential Monte Carlo filter , that recursively utilizes a set of weighted samples to approximate the distributions of the state variables or param - eters , is investigated for dealing with nonlinear and non -Gaussian systems . Recentparticle filtering algorithms , which are developed independently in various engineer - ing fields , are investigated in a unified way . Furthermore , a new type of particle filter is proposed by integrating the divided difference filter with a particle filtering framework , leading to the divided difference particle filter . Sub -optimality of the ap - proximate nonlinear filters due to unknown system uncertainties can be compensated by using an adaptive filtering method that estimates both the state and system error statistics . For accurate identification of the time -varying parameters of dynamic sys - tems , new adaptive nonlinear filters that integrate the presented nonlinear filtering algorithms with noise estimation algorithms are derived . For qualitative and quantitative performance analysis among the proposed non - linear filters , systematic methods for measuring the nonlinearities , biasness , and op - timality of the proposed nonlinear filters are introduced . The proposed nonlinear optimal and sub -optimal filtering algorithms with applications to spacecraft orbit es - timation and autonomous navigation are investigated . Simulation results indicate that the advantages of the proposed nonlinear filters make these attractive alterna - tives to the extended Kalman filter .
URI: http : / /hdl .handle .net /1969 .1 /2269
Date: 2005-08-29

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Nonlinear bayesian filtering with applications to estimation and navigation. Available electronically from http : / /hdl .handle .net /1969 .1 /2269 .

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