Stability of distributed extended Kalman filters

The need for faster and more robust parameter estimates in the smart grid, together with the growth in multi-sensor distributed measurements has motivated the development of distributed extended Kalman filtering (EKF) algorithms. However, fundamental theoretical insights about the convergence and stability of these distributed extended Kalman filtering algorithms are still lacking. To this end, we provide the mean square stability analysis of a class of complex-valued distributed extended Kalman filters. Specifically, we consider the diffusion augmented complex EKF (D-ACEKF) algorithm, as the algorithm caters for widely linear models and non-circular noise, a pre-requisite for modern smart grid applications. Our results provide physically meaningful interpretations of the role of the degree of nonlinearity of the state transition and observation functions, noise level in the system and the initialisation error in the stability of the D-ACEKF.