Scalable Distributed Data-Driven State Estimation Algorithm via Gaussian Processes With Guaranteed Stability

In this article, we focus on the scalable distributed data-driven state estimation problem using Gaussian processes (GPs). The framework includes two parts: 1) the data-driven training approach and 2) the state-estimation architecture. First, the objective is to obtain the transition and measurement functions of the considered state-space model by a data-driven training strategy via distributed GPs. In particular, to improve the training efficiency, we employ an online conditioning algorithm, which reduces the computational burden significantly. Then, all nodes exchange their own trained GPs with their respective neighbors. Furthermore, to achieve consensus on local trained GPs, we propose a Wasserstein weighted average consensus algorithm, which differs from the current Kullback-Leibler average consensus on probability densities. Second, based on the training results, we propose a distributed state estimation algorithm to perform fresh state estimation. After obtaining the state estimation results (mean and covariance) and exchanging them with their neighboring nodes, we then execute the Wasserstein weighted average to achieve consensus on state estimations. Also, we analyze the stability and robustness of the proposed distributed state estimation by using GP. Finally, numerical and real-world examples are provided to validate the effectiveness of the proposed training method and data-driven state estimation algorithms.