Research of Extended Dimension Embedded CKF-SLAM Base on Truncated Singular Value Decomposition

In response to the problem of the filtering error of the CKF algorithm increasing linearly with the dimensionality of the state space, resulting in difficulty in propagating multiplicative noise, and the instability of the system caused by outliers in the system state driven model and observation data, this paper proposes an Extended Dimensional Embedded Cubature Kalman Filter algorithm based on the Truncated Singular Value Decomposition (TSVD-AECKF). Firstly, Singular Value Decomposition (SVD) is used instead of Cholesky Decomposition in the CKF algorithm to suppress the non-positivity of the system state covariance matrix; Considering the impact of small singular values on stability, this paper adopts the truncation method and provides a method for determining the truncation threshold; Secondly, the system noise is added to the state variable, and the embedded cubature criterion is used to improve the traditional CKF while expanding its dimensions; Finally, through simulation experiments, TSVD-AECKF was compared with other SLAM methods, and the results showed that this method can effectively suppress positioning errors that increase with the dimension of the state space, enhance the filter's ability to resist noise data interference, and thereby improve the robustness and stability of the mapping.