ODEFTC: Optimal Distributed Estimation based on Fixed-Time Consensus
Irene Perez-Salesa, Rodrigo Aldana‐López, Carlos Sagüés · Information Fusion · 2024
Distributed state estimation has been a significant research topic in recent years due to its applications for multi-robot and large-scale systems. Several approaches have been proposed in the context of continuous-time systems with stochastic noise, with limitations regarding observability, assumptions on the noise bounds, or requirements to pre-compute auxiliary global information offline. Moreover, many of these approaches are suboptimal with respect to a centralized implementation, and optimal proposals only apply to time-invariant systems. The present work proposes the ODEFTC algorithm for distributed state estimation based on fixed-time consensus. The proposal computes state estimates and corresponding covariance matrices online, making it suitable for time-variant systems. We verify the stability of the proposal through formal analysis, and we show that the optimal centralized solution, given by the Kalman-Bucy filter, can be recovered asymptotically. Additionally, we provide numerical results and an in-depth statistical and numerical discussion to show the advantages of our proposal against other approaches in the literature.