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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/2269 |
| Date | 29 August 2005 |
| Creators | Lee, Deok-Jin |
| Contributors | Alfriend, Kyle T. |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 2072696 bytes, electronic, application/pdf, born digital |
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