SINS/EM Log Integrated Navigation With Variable-Structure Multiple Model Adaptive Kalman Filter

When integrating a strapdown inertial navigation system (SINS) with an electromagnetic log (EM Log) for navigation purposes, the presence of ocean current and time-varying measurement noise from EM Log can introduce significant errors into the integrated system. To mitigate the adverse effects caused by the EM Log, an expected-mode augmentation variable-structure multiple model adaptive Kalman filter (EMA-VSMM-AKF) algorithm is proposed to integrate data from SINS and EM Log. In this algorithm, the ocean current velocity is modeled as a first-order Markov process, and the unknown time-varying measurement noise variance is assumed to follow an inverse Gamma (IG) distribution, which serves as the conjugate prior distribution for noise statistics. The main challenges faced by the proposed EMA-VSMM-AKF algorithm lie in handling the exponential growth term in the interacting multiple model (IMM) input interaction procedure and dealing with the coupling between the state vector and measurement noise variance in the likelihood function. These challenges are overcome by employing a merging scheme through maximum likelihood estimation and variational Bayesian (VB) approximation. The feasibility of the proposed EMA-VSMM-AKF algorithm is assessed through simulation test and sea experiment. Furthermore, its performance is evaluated and compared to the improved Sage-Husa filter in a sea experiment. The computation time for both methods is similar, while the EMA-VSMM-AKF algorithm exhibits a remarkable improvement of over 20% in the root-mean-square error of position.