两段卡尔曼估值器及最优条件研究

The Study of Two-Stage Kalman Estimator and Its Optimal Conditions

考虑了具有ARMA模型随机偏差的两段卡尔曼估值器的最优条件问题。首先给出了增广状态的最优卡尔曼滤波和两段卡尔曼估值器 ;其次证明了在一定的代数约束条件下 ,两段卡尔曼估值器和增广状态的最优卡尔曼滤波是等价的 ;最后 ,由于给定的代数约束条件在实际系统中是受限制的 ,因此结论表明两段卡尔曼估值器是次优的。

The optimality of two-stage state estimation in the presence of ARMA model random bias is studied. First, the optimal augmented state Kalman filter and the two-stage Kalman estimator are given. Second, under and algebraic constraint condition, the equivalence between the two-stage Kalman estimator and the optimal augmented state Kalman filter is proved. Finally, because the given algebraic constraint is restrictive in practice, thus, the results of the paper indirectly indicate that two-stage Kalman estimator will be sub optimal.