A suboptimal Kalman filter considering error analysis
MOTOYASU NAGATA · International Journal of Systems Science · 1979
There are many occasions when approximate design of the Kalman filter is inevitable in the identification. This paper proposes the algorithms for two kinds of suboptimal Kalman filters based on the error analysis of the filter. It is rare that each noise added to the dynamical equation, or the measurement equation may be regarded as sequentially correlated in the practical situation. The suboptimal Kalman filter is constructed in order to replace the sequentially correlated measurement noise by the appropriate white measurement noise. The concept of the design for the proposed filter is delineated. The covariance of the estimation error due to the replacement of the measurement noise, called the actual covariance, is derived in the form of the differential equation. This is the known result of the error analysis of the Kalman filter. Secondly, the stationary condition is assumed on the actual covariance in place of the usual optimal covariance of the estimation error. One suboptimal Kalman filter with the gain from the stationary condition is obtained, which is called the modified stationary Kalman filter. Thirdly, the performance loss of the actual covariance is minimized with respect to the filter gain under the restraint of the differential equation of the actual covariance. The gain of the other suboptimal Kalman filter is derived from the minimization condition. Furthermore, numerical examples are carried out to test the validity of the modified stationary Kalman filter.