Weighted Average Consensus Filtering for Continuous-Time Linear Systems With Asynchronous Sensor Measurements

In practical sensor networks, especially heterogeneous sensor networks, sensor nodes may have distinct sampling periods and initial sampling time instants, probably their observations are also nonuniform. However, the distributed consensus state estimation problem for continuous-time linear systems in such asynchronous sensor networks has not been addressed in the literature. To solve this problem, this article proposes a consensus filtering algorithm for distributed state estimation over asynchronous sensor networks based on the weighted average consensus strategy. First, asynchronous measurements at each sensor node within a given filtering interval are transformed to the consensus filtering time instant according to the continuous-time system dynamics. Statistical characteristics of converted measurement noises are carefully exploited as well as their cross-correlations induced by the synchronization procedure. It is also discovered that the converted measurement noises are one-step correlated with the discretized process noise. Second, measurements after synchronization are used to update local estimates at sensor nodes with the above correlations taken into account and weighted average consensus iterations are performed based on information interactions of sensor nodes with their neighbors. Finally, the estimation error of the proposed asynchronous consensus filtering algorithm is proved to be exponential mean-square bounded, and its effectiveness is evaluated by a simulation example.