Variational robust filter with a heavy-tailed mixture model for GNSS/INS tightly coupled integration

In the tightly coupled integration of global navigation satellite systems (GNSS) and inertial navigation systems (INS) within complex environments, harsh observation conditions, signal multipath effects, and unknown pulse interference can easily lead to non-stationary heavy-tailed measurement noise. To address this challenge, in this paper, we first construct a heavy-tailed mixture (HM) model that is insensitive to prior noise statistics for modeling the likelihood probability density function. Subsequently, an improved variational Bayesian (VB) method is introduced to decouple the variational posterior updates for the state vector and the unknown parameters. Finally, an HM model-based variational robust filter (HMRKF) for GNSS/INS tightly coupled integration is proposed. The experimental results demonstrate that the HMRKF can adaptively infer the accurate measurement noise covariance matrix using the pre-selected measurement set and observation information, achieving an optimal estimation performance among the six schemes evaluated. Compared to the extended Kalman filter, the position, velocity, and yaw accuracy of the HMRKF are 56.66%, 76.35%, and 80.62% better, respectively. Additionally, the computational complexity of the improved VB method is more than 30% lower compared to the conventional VB method, significantly alleviating the algorithm's computational burden. Therefore, the proposed HMRKF can ensure the integrated system's navigation accuracy and robustness within non-stationary heavy-tailed noise environments.