Optimal reduced-order observer-estimators

An optimal reduced-order filter (in the sense of minimum error variance) which can provide a full vector of state estimates for systems where the dimension of the measurement vector is smaller than that of the state vector and no measurements are noise-free is presented. The optimal reduced-order filter is constructed using two-step L-K transformations for optimization. In step one, a K-transformation is utilized to construct an optimal-observer-type subfilter with order of n-m. An L-transformation is then used to build an optimal complementary subfilter with order m. The L and K matrices are determined to minimize the estimate error variances at each step. The order of the optimal reduced-order filter which combines two subfilters is max(n-m,m). When the dimension of the measurement vector is the same as that of state vector. the optimal reduced-order filter is then the Kalman filter (full order). Since two subfilters can be implemented by two processors in parallel, the proposed filter is computationally efficient.<>