Stability Analysis of Multi-Sensor Kalman Filtering over Lossy Networks

Abstract

This paper studies the remote Kalman filtering problem for a distributed system setting with multiple sensors that are located at different physical locations. Each sensor encapsulates its own measurement data into one single packet and transmits the packet to the remote filter via a lossy distinct channel. For each communication channel, a time-homogeneous Markov chain is used to model the normal operating condition of packet delivery and losses. Based on the Markov model, a necessary and sufficient condition is obtained, which can guarantee the stability of the mean estimation error covariance. Especially, the stability condition is explicitly expressed as a simple inequality whose parameters are the spectral radius of the system state matrix and transition probabilities of the Markov chains. In contrast to the existing related results, our method imposes less restrictive conditions on systems. Finally, the results are illustrated by simulation examples.

Robust Distributed Kalman Filtering: On the Choice of the Local Tolerance

“…Since the nominal model in Equation ( 5) does not coincide with the actual one and each node k can only exploit information shared by its neighbors l ∈ N k , the aim of distributed robust Kalman filtering is to compute a prediction xk,t of the state x t for every node k by using only the local information, taking into account the model uncertainty. In the case that the node k has access to all measurements across all the nodes in the network, then xk,t coincides with Equation (4) which can be written, using the parameterization in Equations ( 6) and (7) as…”

“…On the other hand, its implementation is very expensive in terms of data transmission; indeed, we require that all sensors can exchange their measurements. Such a limitation disappears by considering distributed filtering [1][2][3][4][5][6][7][8][9]. The key idea is that the communication among the nodes is limited.…”

Optimal Fusion Estimation with Multi-Step Random Delays and Losses in Transmission

“…Random failures in the transmission of measured data, together with the inaccuracy of the measurement devices, cause often the degradation of the estimator performance in networked systems. In light of these concerns, the estimation problem with one or even several network-induced uncertainties is recently attracting considerable attention, and the design of new fusion estimation algorithms has become an active research topic (see, e.g., [ 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 ] and references therein). In addition, some recent advances on the estimation, filtering and fusion for networked systems with network-induced phenomena can be reviewed in [ 14 , 15 ], where a detailed overview of this field is presented.…”

Networked Fusion Filtering from Outputs with Stochastic Uncertainties and Correlated Random Transmission Delays

“…These additional transmission uncertainties can spoil the fusion estimators performance and motivate the need of designing fusion estimation algorithms that take their effects into consideration. In recent years, in response to the popularity of networked stochastic systems, the fusion estimation problem from observations with random delays and packet dropouts, which may happen during the data transmission, has been one of the mainstream research topics (see, e.g., [ 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 ], and references therein). All the above papers on signal estimation with random transmission delays assume independent random delays in each sensor and mutually independent delays between the different network sensors; in [ 31 ] this restriction was weakened and random delays featuring correlation at consecutive sampling times were considered, thus allowing to deal with common practical situations (e.g., those in which two consecutive observations cannot be delayed).…”