A novel adaptive Gaussian sum cubature Kalman filter with time-varying non-Gaussian noise for GNSS/SINS tightly coupled integrated navigation system

The Gaussian sum cubature Kalman filter (GSCKF) based on Gaussian mixture model (GMM) is a critical nonlinear non-Gaussian filter for data fusion of global navigation satellite system/strapdown inertial navigation systems (GNSS/SINS) tightly coupled integrated navigation system. However, the stochastic model of non-Gaussian noise in practical operating environments is not static, but rather time-varying. So if the GMM of GSCKF cannot be adjusted adaptively, it will lead to a decrease in estimation accuracy. To address this issue, we propose a novel adaptive GSCKF (AGSCKF) based on the dynamic adjustment of GMM. By analyzing the impact of GMM displacement parameter on the fitting accuracy of non-Gaussian noise, a novel algorithm for GMM displacement parameter adaptive adjustment is proposed using a cost function. Then this novel algorithm is applied to overcome the limitations of GSCKF under time-varying non-Gaussian noise environment, thereby improving the filtering performance. The simulation and experimental results indicate that the proposed AGSCKF exhibits significant advantage in changeable environments affected by time-varying non-Gaussian noise, which is applied to GNSS/SINS tightly coupled integrated navigation system data fusion can improve estimation accuracy and adaptability without sacrificing significant computational complexity.