Variational Bayesian Adaptive Kalman Filter for Integrated Navigation with Unknown Process Noise Covariance

Abstract

In the application of integrated navigation by using Inertial measurement Units (IMUs) and Global Navigation Satellite System (GNSS), magnetometers and barometer, the process noise of IMU s is usually unstable and considered to be unknown, because temperature and vibration may cause the divergence or an incorrect result of Kalman filter algorithm, especially with the low-cost sensors. To solve the problem of unstable process noise covariance, a Variational Bayesian Adaptive Kalman Filter for integrated navigation is presented in this paper. Given that the conjugate prior distribution of unknown process noise covariance is assumed to be inverse Wishart distribution, Variational Bayesian (VB) method can estimate system state and process noise covariance simultaneously. Based on the idea of VB method, the novel Variational Bayesian adaptive Extended Kalman Filter (VBEKF -P) and Variational Bayesian adaptive Unscented Kalman Filter (VBUKF - P) are implemented and applied to compensate the instability. The comparison experimental results show that VBEKF-P and VBUKF-P can guarantee estimation accuracy and stability under the condition of underestimated process noise covariance, but with the expense of five to ten times of computational complexity.