不确定系统鲁棒稳态白噪声反卷积平滑器

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。

Robust steady-state white noise deconvolution smoother for uncertain systems

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 guaranteed 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.