Robust Simultaneous Localization and Mapping in Non-Gaussian Environments Using Gaussian-Manifold–Projected Structure–Spectrum Regularized Cubature Kalman Filter

Abstract

To address the challenges of non-Gaussian process disturbances, observation contamination, and numerical degeneration of high-dimensional covariance matrices in outdoor large-scale mobile mapping and simultaneous localization and mapping (SLAM), this paper proposes a Gaussian-manifold–based structure–spectrum dual-domain regularized cubature Kalman filter, termed GM-SSDRCKF-SLAM. From an information-geometric perspective, the local approximation of the non-Gaussian posterior is formulated as a Kullback–Leibler divergence minimizing projection onto a statistical manifold. On this basis, a geometrically consistent recursive estimation framework is established by combining the tangent-space pose error modeling on the planar pose manifold. In the prediction stage, Student’s t–based local Gaussianization and L-curve–guided truncated singular value stabilization are introduced to mitigate the effects of heavy-tailed process noise and covariance spectral degeneration. In the observation stage, the Akaike Information Criterion and Bayesian Information Criterion–guided adaptive feature-landmark selection together with Student’s t robust weighting is used to jointly suppress abnormal measurements, weakly informative features, and redundant state expansion. Comparative experiments under multiple non-Gaussian noise settings are conducted on both a classical simulation environment and the Victoria Park real data set. Under severe observation contamination, GM-SSDRCKF reduces position root mean square error (RMSE) by 86.2% and 52.1% and orientation RMSE by 90.3% and 72.7%, relative to CKF-SLAM and Student’s t CKF-SLAM, respectively. Under coupled non-Gaussian disturbances, the corresponding reductions are 81.7% and 49.3% in position RMSE and 88.5% and 72.7% in orientation RMSE. In the real-world Victoria Park experiments, additional comparisons with invariant EKF-SLAM and robust GraphSLAM further demonstrate the advantage of the proposed method. Averaged over two real-data cases, GM-SSDRCKF reduces position RMSE by 85.3%, 68.2%, 70.1%, and 47.0% relative to CKF-SLAM, Student’s t CKF-SLAM, invariant EKF-SLAM, and robust GraphSLAM, respectively. The proposed method also yields shorter localization-error tails, more consistent normalized average estimation error squared behavior, and more stable covariance spectra. These results demonstrate that reliable SLAM in complex non-Gaussian environments requires the coordinated treatment of posterior approximation, geometric consistency, state-structure regulation, and covariance spectral stabilization.