不确定噪声方差定常系统保性能鲁棒Kalman滤波器

对带不确定噪声方差线性定常系统鲁棒Kalman滤波,提出一般的统一的保性能鲁棒性概念.用Lyapunov方程方法,提出两类保性能极大极小鲁棒稳态Kalman滤波器.一类是寻求不确定噪声方差最大扰动域(鲁棒域),使得对于扰动域内的所有扰动,确保系统滤波精度偏差的最大下界是零,最小上界是所预置的精度偏差指标;另一类是在预置噪声方差有界扰动域内,寻求滤波精度偏差的最大下界和最小上界.通过引入不确定噪声方差扰动的参数化表示,问题转化为相应的非线性与线性最优化问题,可分别用Lagrange乘数法和线性规划(LP)方法求解.应用于跟踪系统的仿真例子验证了所提结果的正确性和有效性.

Guaranteed-cost robust Kalman filters for time-invariant systems with uncertain noise variances

For the robust Kalman filtering of linear time-invariant systems with uncertain noise variances, the concept of general and unified guaranteed-cost robustness of Kalman filtering is presented, and two classes of guaranteed cost mini-max robust steady-state Kalman filters are presented by using the Lyapunov equation approach. One class is to find the maximal perturbation region (robust region) of uncertain noise variances such that for all admissible perturbations in this region the accuracy deviations are guaranteed to have zero as the maximal lower bound and the prescribed accuracy deviation index as the minimal upper bound. The other class is to find the maximal lower bound and the minimal upper bound of the accuracy deviations over the prescribed bounded perturbation region of noise variances. The problems are converted into corresponding nonlinear and linear optimization problems by introducing the parameterized representation of noise variances perturbations. They are solved by Lagrange multiplier method and linear programming (LP) approach, respectively. A simulation example applied to tracking system validates the correctness and effectiveness of the proposed method.