A novel Gaussian sum quaternion constrained cubature Kalman filter algorithm for GNSS/SINS integrated attitude determination and positioning system

The quaternion cubature Kalman filter (QCKF) algorithm has emerged as a prominent nonlinear filter algorithm and has found extensive applications in the field of GNSS/SINS integrated attitude determination and positioning system (GNSS/SINS-IADPS) data processing for unmanned aerial vehicles (UAV). However, on one hand, the QCKF algorithm is predicated on the assumption that the random model of filter algorithm, which follows a white Gaussian noise distribution. The noise in actual GNSS/SINS-IADPS is not the white Gaussian noise but rather a ubiquitous non-Gaussian noise. On the other hand, the use of quaternions as state variables is bound by normalization constraints. When applied directly in nonlinear non-Gaussian system without considering normalization constraints, the QCKF algorithm may result in a mismatch phenomenon in the filtering random model, potentially resulting in a decline in estimation accuracy. To address this issue, we propose a novel Gaussian sum quaternion constrained cubature Kalman filter (GSQCCKF) algorithm. This algorithm refines the random model of the QCKF by approximating non-Gaussian noise with a Gaussian mixture model. Meanwhile, to account for quaternion normalization in attitude determination, a two-step projection method is employed to constrain the quaternion, which consequently enhances the filtering estimation accuracy. Simulation and experimental analyses demonstrate that the proposed GSQCCKF algorithm significantly improves accuracy and adaptability in GNSS/SINS-IADPS data processing under non-Gaussian noise conditions for Unmanned Aerial Vehicles (UAVs).