Application of the Adaptive Mixed-Order Cubature Particle Filter Algorithm Based on Matrix Lie Group Representation for the Initial Alignment of SINS
N. Wang, Fanming Liu · Information · 2025
Under large azimuth misalignment conditions, the initial alignment of strapdown inertial navigation systems (SINS) is challenged by the nonlinear characteristics of the error model. Traditional particle filter (PF) algorithms suffer from the inappropriate selection of importance density functions and severe particle degeneration, which limit their applicability in high-precision navigation. To address these limitations, this paper proposes an adaptive mixed-order spherical simplex-radial cubature particle filter (MLG-AMSSRCPF) algorithm based on matrix Lie group representation. In this approach, attitude errors are represented on the matrix Lie group SO(3), while velocity errors and inertial sensor biases are retained in Euclidean space. Efficient bidirectional conversion between Euclidean and manifold spaces is achieved through exponential and logarithmic maps, enabling accurate attitude estimation without the need for Jacobian matrices. A hybrid-order cubature transformation is introduced to reduce model linearization errors, thereby enhancing the estimation accuracy. To improve the algorithm’s adaptability in dynamic noise environments, an adaptive noise covariance update mechanism is integrated. Meanwhile, the particle similarity is evaluated using Euclidean distance, allowing the dynamic adjustment of particle numbers to balance the filtering accuracy and computational load. Furthermore, a multivariate Huber loss function is employed to adaptively adjust particle weights, effectively suppressing the influence of outliers and significantly improving the robustness of the filter. Simulation and the experimental results validate the superior performance of the proposed algorithm under moving-base alignment conditions. Compared with the conventional cubature particle filter (CPF), the heading accuracy of the MLG-AMSSRCPF algorithm was improved by 31.29% under measurement outlier interference and by 39.79% under system noise mutation scenarios. In comparison with the unscented Kalman filter (UKF), it yields improvements of 58.51% and 58.82%, respectively. These results demonstrate that the proposed method substantially enhances the filtering accuracy, robustness, and computational efficiency of SINS, confirming its practical value for initial alignment in high-noise, complex dynamic, and nonlinear navigation systems.