Kalman filtering with state constraints: a survey of linear and nonlinear algorithms
Kalman filtering with state constraints: a survey of linear and nonlinear algorithms
- Author(s): D. Simon
- DOI: 10.1049/iet-cta.2009.0032
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- Author(s): D. Simon 1
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Affiliations:
1: Department of Electrical and Computer Engineering, Cleveland State University, Cleveland, USA
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Affiliations:
1: Department of Electrical and Computer Engineering, Cleveland State University, Cleveland, USA
- Source:
Volume 4, Issue 8,
August 2010,
p.
1303 – 1318
DOI: 10.1049/iet-cta.2009.0032 , Print ISSN 1751-8644, Online ISSN 1751-8652
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The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications include the extended Kalman filter, the unscented Kalman filter, and the particle filter. Although the Kalman filter and its modifications are powerful tools for state estimation, we might have information about a system that the Kalman filter does not incorporate. For example, we may know that the states satisfy equality or inequality constraints. In this case we can modify the Kalman filter to exploit this additional information and get better filtering performance than the Kalman filter provides. This paper provides an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications. If both the system and state constraints are linear, then all of these different approaches result in the same state estimate, which is the optimal constrained linear state estimate. If either the system or constraints are nonlinear, then constrained filtering is, in general, not optimal, and different approaches give different results.
Inspec keywords: Kalman filters; Gaussian noise; state estimation; constraint theory
Other keywords:
Subjects: Other topics in statistics; Other topics in statistics; Signal processing theory; Filtering methods in signal processing
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