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中文摘要：
针对移动机器人同步定位与地图构建（simultaneous localization and mapping，SLAM）存在的计算量大、数值不稳定等问题，结合容积卡尔曼滤波（cubature Kalman filter，CKF）原理，设计了一种基于平方根CKF（square root cubature Kalman filter，SRCKF）的SLAM算法（SRCKF-SLAM）．SRCKF-SLAM算法通过移动机器人运动模型和观测模型进行预测和观测，并以目标状态均值和协方差的平方根进行迭代更新，确保了协方差矩阵的对称性和半正定性，改进了数值精度和稳定性．仿真实验结果表明，相比CKF-SLAM算法，SRCKF-SLAM算法的均方根误差降低了14％，一致性区域内点数的百分比提高了36％，SRCKF-SLAM算法有效地满足了移动机器人SLAM导航需求．
英文摘要：
In order to solve the large computing cost and numerical instabilities of simultaneous localization and mapping （SLAM）, a square root cubature Kalman filter （SRCKF） based SLAM algorithm （SRCKF-SLAM） for mobile robots is designed according to cubature Kalman filter （CKF） principle. The SRCKF-SLAM algorithm accomplishes prediction and observation through motion model and observation model, and it is updated iteratively by propagating square root factors of the mean and covariance of the state variable, which guarantees the symmetry and positive semi-definiteness of the covariance matrix and therefore improves numerical accuracy and stability. The simulation experiments show that, compared with the CKF-SLAM algorithm, the root-mean square error of the SRCKF-SLAM algorithm decreases 14%, and the percentage of points in consistency area increases 36%, therefore the SRCKF-SLAM algorithm effectively satisfies the requirement of SLAM navigation of mobile robots.
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