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Description:
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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 . |