Title :
Estimation with Information Loss: Asymptotic Analysis and Error Bounds
Author :
Shi, Ling ; Epstein, Michael ; Tiwari, Abhishek ; Murray, Richard M.
Author_Institution :
Control and Dynamical Systems, California Institute of Technology; Pasadena, CA91125, Tel:
Abstract :
In this paper, we consider a discrete time state estimation problem over a packet-based network. In each discrete time step, the measurement is sent to a Kalman filter with some probability that it is received or dropped. Previous pioneering work on Kalman filtering with intermittent observation losses shows that there exists a certain threshold of the packet dropping rate below which the estimator is stable in the expected sense. That work assumes that packets are dropped independently between all time steps. However we give a completely different point of view. On the one hand, it is not required that the packets are dropped independently but just that the information gain πg, defined to be the limit of the ratio of the number of received packets n during N time steps as N goes to infinity, exists. On the other hand, we show that for any given πg, as long as πg> 0, the estimator is stable almost surely, i.e. for any given Ε > 0, the error covariance matrix Pkis bounded by a finite matrix M, with probability 1 -Ε.We also give explicit formula for the relationship between M and Ε. We consider the case where the observation matrix is invertible.
Keywords :
Centralized control; Communication system control; Control systems; Covariance matrix; Error analysis; H infinity control; Information analysis; Kalman filters; State estimation; State feedback;
Conference_Titel :
Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on
Print_ISBN :
0-7803-9567-0
DOI :
10.1109/CDC.2005.1582324