Distributed Recursive State Estimation Over Sensor Networks Under the Push-Pull-Based Gossip Protocol: A Locally Minimum Variance Approach

Abstract

This paper addresses the problem of distributed recursive state estimation over sensor networks utilizing the gossip protocol, where communication resources are conserved by allowing each node to randomly select neighboring nodes for data exchange. An easily implementable and scalable mathematical model is developed for the push-pull-based gossip protocol, facilitating bidirectional data exchange. Random variables are introduced to characterize node selection, with their probability distributions considered as customizable protocol parameters. Distributed state estimators integrated with the gossip protocol are subsequently formulated within the framework of recursive estimation. The relationship between estimation error and gossip protocol parameters is analyzed, leading to the derivation of computationally efficient upper bounds for estimation error covariance matrices. Estimator gains are then designed to minimize the traces of these upper bounds, thereby enhancing estimation accuracy. Furthermore, performance analysis is conducted to establish the monotonicity of estimation precision with respect to noise intensity. Finally, numerical simulations are presented to validate the effectiveness of the proposed method.