A linear distributed filter inspired by the Markovian jump linear system filtering problem

Abstract

In this paper we introduce a consensus-based distributed filter, executed by a sensor network, inspired by the Markovian jump linear system filtering theory. We show that the optimal filtering gains of the Markovian jump linear system can be used as an approximate solution of the optimal distributed filtering problem. This parallel allows us to interpret each filtering gain corresponding to a mode of operation of the Markovian jump linear system as a filtering gain corresponding to a sensor in the network. The approximate solution can be implemented distributively and guarantees a quantifiable level of performance.

Distributed detectability and filter design in homogeneous sensor networks

“…Olfati-Saber et al( [6], [7], [8]), Alriksson et al( [9]), and Subbotin et al( [10]) combined the standard Kalman filter with consensus protocol to develop consensus-based Kalman filter. Matei and Baras([11], [12]), Millán et al([13]) combined Luenberger-like observers with consensus strategies to present a distributed filter for linear time-invariant process. Matei and Baras( [11], [12]) provided a distributed detectability condition for completely connected network and an LMIs-based condition using Markovian jump linear system theory for general topology, respectively.…”

“…Matei and Baras([11], [12]), Millán et al([13]) combined Luenberger-like observers with consensus strategies to present a distributed filter for linear time-invariant process. Matei and Baras( [11], [12]) provided a distributed detectability condition for completely connected network and an LMIs-based condition using Markovian jump linear system theory for general topology, respectively. They proposed a suboptimal distributed filter by quadratic optimization approach.…”

Dynamic output‐feedback stabilisation for Markovian jump systems with incomplete transition description and input quantisation: linear matrix inequality approach

“…In recent years, Markovian jump systems (MJSs) have been widely studied due to the fact that MJSs are appropriate to represent many real-world systems subject to random abrupt variations in their structures. Thus, a lot of problems about MJSs with mode transition applied by a Markov process have been studied [1][2][3][4][5][6]. Besides, MJSs have found applications in many practical systems such as electric power systems [7], networked systems [8] and manufacturing systems [9].…”

Less conservative stabilization conditions for Markovian jump systems with incomplete knowledge of transition probabilities and input saturation

“…Over the past decades, Markovian jump systems (MJSs) have received considerable attention due to the fact that MJSs are proper to express many dynamic systems subject to random abrupt variations in their structures. Thus, many researchers have studied about MJSs with the mode transition applied by a Markov stochastic process . Besides, MJSs have been widely applied in many practical applications such as manufacturing systems , networked control systems , lossy sensor network , and so on.…”