Kalman Filtering with State Equality Constraints

Daniel J. Simon; Tien Li Chia

doi:10.1109/7.993234

Kalman Filtering with State Equality Constraints

Daniel J. Simon
, Tien Li Chia

ControlSoft, Inc.

Research output: Contribution to journal › Article › peer-review

Abstract

Kalman filters are commonly used to estimate the states of a dynamic system. However, in the application of Kalman filters there is often known model or signal information that is either ignored or dealt with heuristically. For instance, constraints on state values (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. A rigorous analytic method of incorporating state equality constraints in the Kalman filter is developed. The constraints may be time varying. At each time step the unconstrained Kalman filter solution is projected onto the state constraint surface. This significantly improves the prediction accuracy of the filter. The use of this algorithm is demonstrated on a simple nonlinear vehicle tracking problem

Original language	American English
Journal	IEEE Transactions on Aerospace and Electronic Systems,
Volume	38
DOIs	https://doi.org/10.1109/7.993234
State	Published - Jan 1 2002

Keywords

Kalman filtering
Maximum probability method
Mean square minimization
Nonlinear filtering
Nonlinear vehicle tracking problem
Prediction accuracy
State equality constraints
State estimation
Time varying constraints
Unconstrained filter solution

Disciplines

Electrical and Computer Engineering

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10.1109/7.993234License: CC BY

Kalman Filtering with State Equality ConstraintsFinal published version, 1.02 MBLicense: CC BY

Cite this

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title = "Kalman Filtering with State Equality Constraints",

abstract = " Kalman filters are commonly used to estimate the states of a dynamic system. However, in the application of Kalman filters there is often known model or signal information that is either ignored or dealt with heuristically. For instance, constraints on state values (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. A rigorous analytic method of incorporating state equality constraints in the Kalman filter is developed. The constraints may be time varying. At each time step the unconstrained Kalman filter solution is projected onto the state constraint surface. This significantly improves the prediction accuracy of the filter. The use of this algorithm is demonstrated on a simple nonlinear vehicle tracking problem",

keywords = "Kalman filtering, Maximum probability method, Mean square minimization, Nonlinear filtering, Nonlinear vehicle tracking problem, Prediction accuracy, State equality constraints, State estimation, Time varying constraints, Unconstrained filter solution",

author = "Simon, \{Daniel J.\} and Chia, \{Tien Li\}",

note = "Simon, D. Tien Li Chia. (2002). Kalman filtering with state equality constraints. Aerospace and Electronic Systems, IEEE Transactions on, 38(1), 128-136, doi: 10.1109/7.993234.",

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N2 - Kalman filters are commonly used to estimate the states of a dynamic system. However, in the application of Kalman filters there is often known model or signal information that is either ignored or dealt with heuristically. For instance, constraints on state values (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. A rigorous analytic method of incorporating state equality constraints in the Kalman filter is developed. The constraints may be time varying. At each time step the unconstrained Kalman filter solution is projected onto the state constraint surface. This significantly improves the prediction accuracy of the filter. The use of this algorithm is demonstrated on a simple nonlinear vehicle tracking problem

AB - Kalman filters are commonly used to estimate the states of a dynamic system. However, in the application of Kalman filters there is often known model or signal information that is either ignored or dealt with heuristically. For instance, constraints on state values (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. A rigorous analytic method of incorporating state equality constraints in the Kalman filter is developed. The constraints may be time varying. At each time step the unconstrained Kalman filter solution is projected onto the state constraint surface. This significantly improves the prediction accuracy of the filter. The use of this algorithm is demonstrated on a simple nonlinear vehicle tracking problem

KW - Kalman filtering

KW - Maximum probability method

KW - Mean square minimization

KW - Nonlinear filtering

KW - Nonlinear vehicle tracking problem

KW - Prediction accuracy

KW - State equality constraints

KW - State estimation

KW - Time varying constraints

KW - Unconstrained filter solution

UR - https://engagedscholarship.csuohio.edu/enece_facpub/158

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VL - 38

JO - IEEE Transactions on Aerospace and Electronic Systems,

JF - IEEE Transactions on Aerospace and Electronic Systems,

ER -

Kalman Filtering with State Equality Constraints

Abstract

Keywords

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