Distributed Outlier-Robust extended Kalman filter for wireless sensor networks

The Distributed Kalman Filter (DKF) has shown outstanding performance in Gaussian noise environments, making it a suitable choice for handling Gaussian noise in state estimation problems through information fusion among nodes in sensor network. Nevertheless, when the measured value is contaminated by an outlier in nonlinear systems, it causes a situation where non-Gaussian noise is present, which will lead to degradation of the conventional DKF's performance. Therefore, to solve the problem of outlier in nonlinear systems, a centralized outlier-robust extended Kalman filter (C-OR-EKF) is developed, which adopts the M-estimation cost function as the optimal criterion to deal with the error in the filtering process. The M-estimation effectively removes the effect of large outliers, thus making the algorithm robust against non-Gaussian noise. Furthermore, to reduce the node communication burden, a distributed outlier-robust extended Kalman filter (D-OR-EKF) is proposed. Moreover, the mean error and mean square error behavior of C-OR-EKF and D-OR-EKF are analyzed separately to determine the stability of the proposed methods. Finally, by conducting experiments in a nonlinear system and an IEEE 14 system, the D-OR-EKF based on different cost functions of M-estimation is compared with the existing distributed robust Kalman filter. The experimental results show that the proposed algorithms effectively handle the problem of state estimation in non-Gaussian noise environment.