平方根容积卡尔曼滤波在移动机器人 SLAM 中的应用

针对机器人同时定位与地图构建（SLAM）问题，提出基于平方根容积卡尔曼滤波的SLAM算法．该算法主要特点是使用平方根容积卡尔曼滤波计算SLAM后验概率密度， 以减小线性化误差，达到提高SLAM定位精度的目的．提出的算法通过传递平方根因子代替系统协方差矩阵，因而在计算中避免了耗费时间的Cholesky分解， 提高了算法效率．实验部分使用扩展型卡尔曼滤波SLAM（EKF-SLAM）、无迹卡尔曼滤波SLAM（UKF-SLAM）和所提出的算法进行了对比．实验结果表明： 较之EKF-SLAM，容积卡尔曼滤波的精度提高了1倍；相比UKF-SLAM，SCKF-SLAM节省1/4计算资源．

For simultaneous localization and mapping (SLAM) of robots, a new solution is proposed, named square-root cubature Kalman filter based SLAM algorithm (SCKF-SLAM). The main contribution of the proposed algorithm is that the SLAM posterior probability density is calculated by using the square root cubature Kalman filter in order to reduce linearization error and improve SLAM accuracy. Instead of covariance matrixes, square-root factors are used in the proposed SLAM algorithm to avoid the time-consuming Cholesky decompositions and improve the calculation efficiency. In experiments, the proposed algorithm is compared with extended Kalman filter SLAM (EKF-SLAM) and unscented Kalman filter SLAM (UKF-SLAM). The results show that compared with EKF-SLAM, precision of SCKF-SLAM is doubled, and compared with UKF-SLAM, SCKF-SLAM saves a quarter of computation resources.