Decentralized Online Estimation Breakthrough: Additive Noise Overcome with SDE Stability

This paper tackles the challenge of decentralized online parameter estimation when nodes communicate over a directed graph (digraph) and suffer from additive measurement and communication noises. The authors model each agent's local linear measurements as having random measurement matrices, and the communication links introduce additive noise. To analyze convergence, they reformulate the problem as a non-autonomous linear stochastic differential equation (SDE) with random time-varying coefficients. Using numerical approximation theory, they derive conditions for asymptotic stability of the SDE, which directly translates to convergence of the estimation algorithm.

A key finding is that the algorithm's gains can be tuned to guarantee mean square convergence provided the measurement matrices and the communication graph collectively satisfy a stochastic spatial-temporal persistence of excitation condition. This condition ensures that sufficiently diverse information is gathered over time and across nodes. The researchers also examine a special case where the measurement matrices follow a Markov chain, demonstrating the theoretical results with a numerical example. This work provides a rigorous foundation for deploying decentralized estimation in sensor networks, autonomous systems, and distributed AI where noise is unavoidable.