Analysis of Bias,Variance and Mean Square Estimation Error in Reduced Order Filters.

摘要

The Kalman filter gives the optimal minimum variance,unbiased estimate of the system state. It is shown in this paper that for a ROF one cannot in general obtain an unbiased estimator. The conditional mean of the estimation error is non-zero and,therefore,the true covariance of the estimation error is not equal to the second moment of the estimation error as implied in some previous work. This problem of bias is recognized in the work of several references;however,the reduced order problem was not addressed. It is shown that a reduced order filter in general will be biased. The equations for the second moment,true covariance,and bias are presented for the continuous dynamics,continuous measurement and continuous dynamics,discrete measurement ROF problem. The results include the subcases of continuous and impulsive control. (Author)