Robust node position estimation algorithms for wireless sensor networks based on improved adaptive Kalman filters

The Kalman filter (KF) is an optimal state estimator for position observation systems with noise; therefore, it is typically used to estimate the location of a node in a wireless sensor network (WSN) in a noisy environment. The precision of noise statistics largely determines the localization accuracy of the KF, and the statistics of noise are often unknown or time-varying in a real WSN. Therefore, the adaptive Kalman filter (AKF) is utilized for awareness of the statistical parameters of noise. However, the node position estimation (NPE) algorithm based on the state-of-the-art AKF typically lacks robustness and becomes inaccurate in the case of simultaneously perceiving the statistics of process noise and measurement noise. This study proposes a robust NPE algorithm based on an improved adaptive extended Kalman filter (RNPE-IAEKF) and another robust NPE algorithm based on an improved adaptive unscented Kalman filter (RNPE-IAUKF). The RNPE-IAEKF algorithm has low computing complexity, while the RNPE-IAUKF algorithm has high positioning accuracy. Our proposed algorithms solve the problems of poor robustness and low accuracy of the NPE algorithm based on the adaptive extended Kalman filter (NPE-AEKF) and the NPE algorithm based on the adaptive unscented Kalman filter (NPE-AUKF). In addition, the RNPE-IAEKF and the RNPE-IAUKF do not lose robustness upon simultaneous perception of the statistics of process noise and measurement noise, which is strictly proven in theory. The results of practical experiments and numerical simulations demonstrate that regardless of the placement of a static target node, the mobility of a mobile target node, and the number of anchor nodes, the RNPE-IAEKF improves upon the positioning accuracy and convergence speed of the NPE-AEKF by at least 28% and 29%, respectively and that the RNPE-IAUKF increases the localization accuracy and convergence rate of the NPE-AUKF by at least 32% and 37%.