Performance Sensitivity Analysis of a Kalman Filter Using Adjoint Functions

A method is proposed for determining the performance sensitivity of a Kalman filter with respect to small variations in the parameters of both a 'real world' reference model and an assumed filter model. It is shown that a sizable reduction in computational effort may be achieved using the...

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Bibliographic Details
Main Author: Clark, Ronald R
Format: Report
Language:English
Subjects:
ADAPTIVE CONTROL SYSTEMS
AUTOMATIC
CONTROL
CONTROL THEORY
INERTIAL NAVIGATION
INSTRUMENTATION
KALMAN FILTERS
MATHEMATICAL MODELS
MATRICES(MATHEMATICS)
NUMERICAL ANALYSIS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
SENSITIVITY
SENSITIVITY ANALYSIS
Theoretical Mathematics
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Description
Summary:A method is proposed for determining the performance sensitivity of a Kalman filter with respect to small variations in the parameters of both a 'real world' reference model and an assumed filter model. It is shown that a sizable reduction in computational effort may be achieved using the adjoint method presented here to calculate the local performance sensitivities for a large number of parameters rather than using more direct methods. In the report, equations for the covariance functions of the combined filter and reference system are found and adjoint equations corresponding to the linear perturbation equations of the system covariance functions determined. An expression is found for the change in a performance index in terms of the adjoint functions and small, possibly time-varying, changes in the parameters of the combined system. (Author)