Selection of noise parameters for Kalman filter
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Ka-Veng Yuen (Èî¼ÒÈÙ),
Ka-In Hoi (Ðí¼ÎÏÍ) and Kai-Meng Mok (ĪÆôÃ÷)
Department of Civil and Environmental
Engineering, University of Macau, China
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Abstract: The Bayesian probabilistic approach is
proposed to estimate the process noise and measurement noise parameters for a
Kalman filter. With state vectors and covariance matrices estimated by the
Kalman filter, the likehood of the measurements can be constructed as a function
of the process noise and measurement noise parameters. By maximizing the
likelihood function with respect to these noise parameters, the optimal values
can be obtained. Furthermore, the Bayesian probabilistic approach allows the
associated uncertainty to be quantified. Examples using a
single-degree-of-freedom system and a ten-story building illustrate the proposed
method. The effect on the performance of the Kalman filter due to the selection
of the process noise and measurement noise parameters was demonstrated. The
optimal values of the noise parameters were found to be close to the actual
values in the sense that the actual parameters were in the region with
significant probability density. Through these examples, the Bayesian approach
was shown to have the capability to provide accurate estimates of the noise
parameters of the Kalman filter, and hence for state estimation.
Keywords: Bayesian inference; Kalman filter;
measurement noise; process noise; state estimatio
