Continuous-Time Decentralized Online Estimation With Additive Noises
For multi-agent systems requiring decentralized estimation, this work provides convergence guarantees under realistic noisy communication, but the approach is incremental as it extends existing persistence of excitation ideas to continuous-time stochastic settings.
This paper tackles decentralized online parameter estimation with additive communication noises over fixed digraphs, proving mean square convergence under a stochastic spatial-temporal persistence of excitation condition. Numerical examples validate the theoretical results.
We study a decentralized online estimation problem with additive communication noises over the fixed digraph. Each node has a linear measurement of an unknown parameter with random measurement matrices and runs a continuous-time online estimation algorithm. We transform the convergence analysis of the algorithm into the stability analysis of the non-autonomous linear stochastic differential equation (SDE) with random time-varying coefficients, and develop the asymptotic stability by numerical approximation theory. Based on the stability results, we show that the algorithm gains can be properly designed to ensure mean square convergence if the measurement matrices and the communication graph satisfy the stochastic spatial-temporal persistence of excitation condition. Furthermore, a special case where the measurement matrices contain a Markov chain is investigated, and the theoretical results are demonstrated by a numerical example.