An Improved Gaussian Sum Extended Kalman Filter With Colored Noise for GNSS/SINS Tightly Coupled Positioning and Attitude Determination Systems

The Gaussian sum extended Kalman filter (GSEKF), as a nonlinear non-Gaussian filter, disregards the impact of colored noise components in non-Gaussian noise engendered by external interference, which may compromise the estimation accuracy in global navigation satellite system/strapdown inertial navigation system (GNSS/SINS) tightly coupled positioning and attitude determination systems. To address this problem, an improved Gaussian sum extended Kalman filter with colored noise (colored-GSEKF) is proposed to refine the random model by approximating non-Gaussian noise using Gaussian mixture models and whitening the colored noise components within the non-Gaussian colored noise through state and measurement augmentation. This improved algorithm further enhances the accuracy and stability of the filtering estimation in non-Gaussian colored noise environments. Simulations and experimental results indicate that the proposed colored-GSEKF exhibits superior accuracy in modeling a random model in non-Gaussian colored noise environments. By applying this filter to GNSS/SINS tightly coupled positioning and attitude determination systems utilized on unmanned aerial vehicles influenced by non-Gaussian colored noise, the estimation accuracy and stability can be improved.