基于间歇测量的状态估计稳定性和精度研究
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摘要
针对分布式控制系统状态估计过程出现的测量值丢失问题,量化分析了测量值丢失对估计稳定性和精度的影响。首先,根据随机测量模型重新推导带测量值丢失的卡尔曼滤波器,得到估计误差协方差迭代式;然后,将随机误差协方差迭代式建模为修正的黎卡提微分方程,提出了估计稳定性和精度分析方法;最后,列举不同的系统实例,证明临界包到达率的存在性,当测量值到达率大于临界值时,平均误差协方差从发散过渡到有界,进而得到估计精度与包达率之间的函数关系。
This paper quantitatively analyzed the influence of the loss of measured values on the stability and accuracy of the estimation for the loss of measured values in the state estimation process of distributed control systems. Firstly,it deduced a Kalman filter with measurement loss,and a estimation error covariance iterative based on the stochastic measurement model.Then,it modeled the random error covariance iteration as a modified Riccati differential equation,and proposed the Kalman filter estimation stability theory. Finally,it gaven some different system examples to show the existence of the critical arrival rate of the distributed control system,when the arrival rate of the measured value is greater than the critical value,the mean error covariance transits from divergence to boundedness,and obtains the function relationship between the state estimation accuracy and the packet arrival rate.
This paper quantitatively analyzed the influence of the loss of measured values on the stability and accuracy of the estimation for the loss of measured values in the state estimation process of distributed control systems. Firstly,it deduced a Kalman filter with measurement loss,and a estimation error covariance iterative based on the stochastic measurement model.Then,it modeled the random error covariance iteration as a modified Riccati differential equation,and proposed the Kalman filter estimation stability theory. Finally,it gaven some different system examples to show the existence of the critical arrival rate of the distributed control system,when the arrival rate of the measured value is greater than the critical value,the mean error covariance transits from divergence to boundedness,and obtains the function relationship between the state estimation accuracy and the packet arrival rate.
引文
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[9]Huang Minyi,Dey S.Stability of Kalman filtering with Markovian packet losses[J].Automatica,2007,43(4):598-607.
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[14]Moayedi M,Foo Y K,Soh Y C.Adaptive Kalman filtering in networked systems with random sensor delays,multiple packet dropouts and missing measurements[J].IEEE Trans on Signal Processing,2010,58(3):1577-1588.
[15]Sinopoli B,Schenato L,Franceschetti M,et al.Kalman filtering with intermittent observations[J].IEEE Trans on Automatic Control,2004,49(9):1453-1464.
[16]Hadjicostis C N,Touri R.Feedback control utilizing packet dropping network links[C]//Proc of the 41st IEEE Conference on Decision and Control.Piscataway,NJ:IEEE Press,2002:1205-1210.
[2]陈军勇,邬依林,祁恬.无线传感器网络分布式量化卡尔曼滤波[J].控制理论与应用,2011,28(12):1729-1739.
[3]孙言强,王晓东,周兴铭.无线网络中的干扰攻击[J].软件学报,2012,23(5):1207-1221.
[4]Welch G,Bishop G.An introduction to the Kalman filter[D].Chapel Hill:University of North Carolina,2006.
[5]Wong W S,Brockett R W.Systems with finite communication bandwidth constraints.I.State estimation problems[J].IEEE Trans on Automatic Control,1997,42(9):1294-1299.
[6]Wong W S,Brockett R W.Systems with finite communication bandwidth constraints.II.Stabilization with limited information feedback[J].IEEE Trans on Automatic Control,1999,44(5):1049-1053.
[7]Shi Ling,Epstein M,Murray R M.Kalman filtering over a packetdropping network:a probabilistic perspective[J].IEEE Trans on Automatic Control,2010,55(3):594-604.
[8]Zhang Huanshui,Song Xinming,Shi Ling.Convergence and mean square stability of suboptimal estimator for systems with measurement packet dropping[J].IEEE Trans on Automatic Control,2012,57(5):1248-1253.
[9]Huang Minyi,Dey S.Stability of Kalman filtering with Markovian packet losses[J].Automatica,2007,43(4):598-607.
[10]Jin Zhipu,Gupta V,Murray R M.State estimation over packet dropping networks using multiple description coding[J].Automatica,2006,42(9):1441-1452.
[11]Micheli M.Random sampling of a continuous-time stochastic dynamical system:analysis,state estimation,and applications[C]//Proc of the 15th International Symposium on Mathematical Theory of Networks and Systems.2002:206-207.
[12]Micheli M,Jordan M I.Random sampling of a continuous time stochastic dynamical system[C]//Proc of the 15th Intlernational Symposium on Mathematical Theory of Networks and Systems.2002.
[13]Wang Ting,Guo Di,Cai Chunyang,et al.Clock synchronization in wireless sensor networks:analysis and design of error precision based on lossy networked control perspective[J].Mathematical Problems in Engineering,2015,2015(2):1-17.
[14]Moayedi M,Foo Y K,Soh Y C.Adaptive Kalman filtering in networked systems with random sensor delays,multiple packet dropouts and missing measurements[J].IEEE Trans on Signal Processing,2010,58(3):1577-1588.
[15]Sinopoli B,Schenato L,Franceschetti M,et al.Kalman filtering with intermittent observations[J].IEEE Trans on Automatic Control,2004,49(9):1453-1464.
[16]Hadjicostis C N,Touri R.Feedback control utilizing packet dropping network links[C]//Proc of the 41st IEEE Conference on Decision and Control.Piscataway,NJ:IEEE Press,2002:1205-1210.