Xu Hanghang, Chen Yijin, Song Wenhui, Wang Lianchao
College of Geoscience and Surveying Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China.
Sensors (Basel). 2024 Dec 5;24(23):7800. doi: 10.3390/s24237800.
Simultaneous localization and mapping (SLAM) faces significant challenges due to high computational costs, low accuracy, and instability, which are particularly problematic because SLAM systems often operate in real-time environments where timely and precise state estimation is crucial. High computational costs can lead to delays, low accuracy can result in incorrect mapping and localization, and instability can make the entire system unreliable, especially in dynamic or complex environments. As the state-space dimension increases, the filtering error of the standard cubature Kalman filter (CKF) grows, leading to difficulties in multiplicative noise propagation and instability in state estimation results. To address these issues, this paper proposes an extended-dimensional embedded CKF based on truncated singular-value decomposition (TSVD-AECKF). Firstly, singular-value decomposition (SVD) is employed instead of the Cholesky decomposition in the standard CKF to mitigate the non-positive definiteness of the state covariance matrix. Considering the effect of small singular values on the stability of state estimation, a method is provided to truncate singular values by determining the truncation threshold using the Akaike information criterion (AIC). Furthermore, the system noise is embedded into the state variables, and an embedding volume criterion is used to improve the conventional CKF while extending the dimensionality. Finally, the proposed algorithm was validated and analyzed through both simulations and real-world experiments. The results indicate that the proposed method effectively mitigates the increase in localization error as the state-space dimension grows, enhancing time efficiency by 55.54%, and improving accuracy by 35.13% compared to the standard CKF algorithm, thereby enhancing the robustness and stability of mapping.
同时定位与地图构建（SLAM）由于计算成本高、精度低和稳定性差而面临重大挑战，这些问题尤为棘手，因为SLAM系统通常在实时环境中运行，及时且精确的状态估计至关重要。高计算成本会导致延迟，低精度会导致地图构建和定位错误，而稳定性差会使整个系统不可靠，尤其是在动态或复杂环境中。随着状态空间维度的增加，标准容积卡尔曼滤波器（CKF）的滤波误差会增大，导致乘性噪声传播困难以及状态估计结果不稳定。为了解决这些问题，本文提出了一种基于截断奇异值分解的扩展维嵌入式CKF（TSVD-AECKF）。首先，在标准CKF中采用奇异值分解（SVD）代替乔列斯基分解，以减轻状态协方差矩阵的非正定问题。考虑到小奇异值对状态估计稳定性的影响，提供了一种通过使用赤池信息准则（AIC）确定截断阈值来截断奇异值的方法。此外，将系统噪声嵌入到状态变量中，并使用嵌入量准则在扩展维度的同时改进传统的CKF。最后，通过仿真和实际实验对所提算法进行了验证和分析。结果表明，所提方法有效地减轻了随着状态空间维度增加而导致的定位误差增加，与标准CKF算法相比，时间效率提高了55.54%，精度提高了35.13%，从而增强了地图构建的鲁棒性和稳定性。
