不确定多通道信号鲁棒稳态估计  

Robust Steady-State Estimation for Uncertain Multichannel Signal

作　　者：陶贵丽 李爽 王雪梅 刘文强 TAO Guili;LI Shuang;WANG Xuemei;LIU Wenqiang(College of Media Engineering,Communication University of Zhejiang,Hangzhou 310018;School of Information and Electronic Engineering(Sussea Artificial Intelligence Institute),Zhejiang Gongshang University,Hangzhou 310018)

机构地区：[1]浙江传媒学院媒体工程学院,杭州310018 [2]浙江工商大学信息与电子工程学院(萨塞克斯人工智能学院),杭州310018

出　　处：《系统科学与数学》2022年第10期2794-2816,共23页Journal of Systems Science and Mathematical Sciences

基　　金：浙江省教育厅科研项目(Y202147323);黑龙江省自然科学基金项目(LH2019F035);国家自然科学基金项目(61803148);浙江省新型网络标准及应用技术重点实验室(2013E10012)资助课题。

摘　　要：对于一类具有随机参数矩阵、不确定噪声方差、一步随机时滞、丢包和丢失观测的多通道自回归(Autoregressive,AR)信号系统,文章研究其鲁棒稳态Kalman滤波问题.应用状态空间方法,增广方法和虚拟噪声技术,混合不确定AR信号模型被转换为仅带不确定噪声方差和相同过程以及观测噪声的状态空间模型.根据极大极小鲁棒估计原理,基于带不确定噪声方差保守上界的最坏情形系统,提出了鲁棒稳态Kalman一步和多步信号预报器.证明了所提出的信号预报器的鲁棒性,即对于所有容许的不确定性,信号预报器的实际稳态预报误差方差被保证有相应的最小上界.仿真例子验证了所提出方法的正确性和有效性.This paper studies the robust steady-state Kalman filtering problem for a class of multichannel autoregressive(AR)signal with random parameter matrices,uncertain noise variances,one-step random delay,packet dropouts,and missing measurements.Using the state space method,augmented method,and the fictitious noise technique,the mixed uncertain AR signal model under study is converted into a state space model only with uncertain noise variances and same process and measurement noises.In the light of the minimax robust estimation principle,based on the worstcase system with conservative upper bounds of uncertain noise variances,the robust steady-state Kalman one-step and multi-step signal predictors are proposed.The robustness of the proposed signal predictors is proved,such that for all admissible uncertainties,the actual steady-state estimation error variances of signal predictors are guaranteed to have the corresponding minimal upper bounds.A simulation example verifies the correctness and effectiveness of the proposed methods.

关 键 词：多通道自回归信号 鲁棒稳态预报器 随机参数矩阵 一步随机时滞 丢包 不确定噪声方差 

分 类 号：O212.1[理学—概率论与数理统计] TN911.7[理学—数学]