Partial Diffusion Kalman Filtering for Distributed State Estimation in Multiagent Networks

Abstract

Many problems in multiagent networks can be solved through distributed learning (state estimation) of linear dynamical systems. In this paper, we develop a partial-diffusion Kalman filtering (PDKF) algorithm, as a fully distributed solution for state estimation in the multiagent networks with limited communication resources. In the PDKF algorithm, every agent (node) is allowed to share only a subset of its intermediate estimate vectors with its neighbors at each iteration, reducing the amount of internode communications. We analyze the stability of the PDKF algorithm and show that the algorithm is stable and convergent in both mean and mean-square senses. We also derive a closedform expression for the steady-state mean-square deviation criterion. Furthermore, we show theoretically and by numerical examples that the PDKF algorithm provides a trade-off between the estimation performance and the communication cost that is extremely profitable.

Performance Analysis of Distributed Kalman Filtering With Partial Diffusion Over Noisy Network

“…(iii) (Ergodicity). The matrices {F, H k } are detectable for every k and {F, GQ 1 2 } is stabilizable [26]. Under Assumption 3-(iii), P k,i|i−1 converges to P − k and P k,i|i converges to P k , for all k. Under these assumptions, the matrices F i , G i and D i also converge in steady-state, and their steady-state values are given by P lim…”

“…The PDKF algorithm proposed in [26] is shown by Algorithm 2. For every agent k, the objective of PDKF implementation is to recursively estimate the unknown state x i ∈ R M , while sharing a subset of its intermediate estimate vector with its neighbors l ∈ N k .…”

“…At every time instant i, the agents run Kalman filtering algorithm for diffusion step and communicate to their neighbors the intermediate estimate for aggregation step. Equation (6) is utilized to aggregate the partially received intermediate Algorithm 2 Partial Diffusion Kalman Filter [26] Initialization:x k,0|−1 = 0 and P k,0|−1 = Π 0 For i ≥ 0, every node k computes…”

“…Among these methods, we focus on partial diffusion Kalman filter (PDKF) algorithm proposed at [26]. The PDKF algorithm consists of an adaptation phase and a combination phase.…”

“…The results proposed in [26] are based on the assumption that the communications among the nodes are ideal, i.e., the information transmitted correctly among them. In practice, however, the performance of the adaptive networks is strongly affected by the presence of such a link state, where the communication links are noisy.…”