A novel matrix block algorithm based on cubature transformation fusing variational Bayesian scheme for position estimation applied to MEMS navigation system

Abstract

It is great significant for autonomous underwater vehicle (AUV) to obtain its position in real time. Great developments in low-cost inertial navigation system (INS) have been made due to outstanding merits in micro-electro-mechanical system (MEMS) technologies. The navigation errors of the MEMS grade inertial measurement unit (IMU) increase greatly over time because of the complex and changeable marine environment. The measurement noise plays an important role in state estimation with high accuracy. However, the accuracy of measurement noise will be degraded due to larger MEMS sensors’ errors. To solve the problem above, a novel algorithm which fuses variational Bayesians into nonlinear filtering is proposed. Firstly, the position information is augmented to the measurement vector. The measurement functions are divided into linear and nonlinear. Secondly, the variational Bayesian (VB) method is used to estimate the probability density function of the state vector, predicted error covariance matrix and measurement noise matrix. In the case of calculating the second order moment estimation, the cubature transformation is used to determine nonlinear integral equations, and the linear integral equations are derived by the Kalman filter. Finally, the accurate state vector and error covariance matrix are obtained. The real underwater experiments are performed and experiment results show that the proposed algorithm has better performance in aspect of positioning accuracy of AUV and robustness than the traditional algorithms.