不确定系统鲁棒稳态白噪声反卷积平滑器

摘要

对于带不确定噪声方差的线性离散时不变随机系统，根据极大极小鲁棒估计原理，基于带噪声方差保守上界的最坏情形保守系统，应用 Kalman 滤波和最优白噪声估计理论，提出了一种鲁棒稳态白噪声反卷积平滑器。对于所有容许的不确定噪声方差，保证它的实际平滑误差方差阵有一个最小上界。基于 Lyapunov 方程方法证明了它的鲁棒性和鲁棒精度关系。一个数值仿真例子验证了所提出结果的正确性和有效性。%For the linear discrete time-invariant stochastic system with uncertain noise variances,according to the minimax robust estimation principle,based on the worst-case conservative system with the conservative upper bounds of noise variances,applying Kalman filter and the optimal white noise estimation theory,a robust steady-state white noise deconvolution smoother is presented.Its actual smoothing error variances are guaran-teed to have a minimal upper bound for all admissible uncertain noise variances.Its robustness and the robust accuracy relation are proved based on the Lyapunov equation approach.A simulation example is given to verify the correctness and effectiveness of the proposed results.