Abstract

Distributed Kalman filter (DKF) is an effective method to solve the problem of state estimation in multi-sensor systems. However, the accuracy of conventional DKF may be influenced by the non-Gaussian noises and the accumulated errors in local Kalman filters (LKFs). To encounter the above challenges, a tightly coupled DKF with covariance intersection is proposed. In our method, using the computation outputs of LKFs, a Gaussian Mixture Model is formulated to address the influence of non-Gaussian noises. In order to reduce the cumulative errors from LKFs, covariance intersection fusion is utilized. Furthermore, an index-Huber function is designed to reduce the impact of large covariance generated by the LKFs. Several simulation and real-world experiments are conducted to show the effectiveness of our methods. The method we proposed outperforms three other DKF algorithms in the metrics of RMSE and cumulative error. In addition, a real-world multi-sensor state estimation experiment is conducted on a hexapod robot.

Method

A novel tightly coupled DKF algorithm utilizing covariance intersection is proposed to correct local filters. Different from previous work, we focus more on the effect of GMM weights on fusion accuracy and the cumulative error of local filter. In our method, GMM is adopted to handle non-Gaussian priors. The local filters in our framework may be Kalman filter and its variants, including extended Kalman filter (EKF), unscented Kalman filter (UKF), etc. The proposed method is adapted to solve the problem of state estimation and information fusion for systems with multiple sensor nodes under non-Gaussian noise, such as power network, vehicle tracking, and robotics.

Fig. 1 The framework of the proposed tightly coupled DKF. The GMM is composed of the local Kalman filter results after outlier detection and the weights are computed through maximum likelihood estimation. The covariance intersection is utilized to minimize the trace of covariance matrix in the local Kalman filter.

Result

RMSE w.r.t. timestep of different methods in the simulation experiment with 10 sensor nodes and 15 sensor nodes. The experiment results demonstrate that our tightly coupled DKF outperforms other methods, and verify the effectiveness of the proposed covariance intersection and index-Huber function.

he real-world robot system with multiple sensors, including 3 IMU sensors, 18 torque sensors, and 18 joint encoders. The estimated velocity of the robot from T-DKF (tightly coupled DKF) and L-DKF (loosely coupled DKF) in different timesteps. The velocity estimated directly from the IMU fluctuates considerably, but the GMM fusion results reduce the effect of IMU noise.