Robust cubature Kalman filter based on generalized hyperbolic distribution for SLAM under colored heavy-tailed measurement noise

The effectiveness of existing filter-based simultaneous localization and mapping (SLAM) algorithms will deteriorate under non-Gaussian measurement noise, especially when dealing with the colored heavy-tailed characteristics. In this paper, we present a novel robust cubature Kalman filter based on the generalized hyperbolic distribution for SLAM under colored heavy-tailed measurement noise. Within the proposed algorithm, the measurement differencing method is adopted to whiten the colored noise, and subsequently, the additive heavy-tailed noise is modeled by the generalized hyperbolic distribution, which contains several typical heavy-tailed distributions as special cases. We utilize the variational Bayesian inference method to jointly estimate the system state together with the measurement noise parameters, and the one-step smoothing estimation method is utilized to estimate the state vector at the previous moment to enhance the estimation accuracy. To address the varying number of landmark points observed at different moments, we perform sequential processing during the measurement update process, and this method also reduces the computational complexity. The proposed algorithm creates a flexible framework for the state estimation of nonlinear systems under colored and variable heavy-tailed noise, with several existing algorithms serving as special cases. The superior performance of the proposed algorithm in terms of estimation accuracy and robustness is validated through simulations and experiments.