中文摘要：

针对移动机器人同时定位与地图创建（Simultaneous localization and mapping, SLAM）中的FastSLAM算法, 存在非线性系统线性化处理和计算雅可比矩阵的缺点, 本文提出了基于Sterling多项式插值处理非线性系统的SLAM方法. 该方法基于Rao-Blackwellized粒子滤波框架, 利用中心差分滤波方法产生改进的建议分布函数, 提高了机器人位姿估计的精度; 利用中心差分滤波初始化特征和更新地图中的特征, 提高了地图创建的精度; 针对实际应用中存在虚假特征的情况 提出了一种有效的地图管理方法. 在同等粒子数的情况下, 该方法改进了SLAM结果的精度. 基于仿真和实际数据的实验结果验证了该方法的有效性.

英文摘要：

There are two serious drawbacks in FastSLAM （Simultaneous localization and mapping）, which are the derivation of the Jacobian matrices and the linear approximations of nonlinear functions. To overcome the serious drawbacks of the previous frameworks, this paper provides a robust SLAM algorithm based on the Sterling polynomial interpolation. It uses the central difference filter （CDF） to compute the proposal distribution in Rao-Blackwellized particle filter, then to initialize and update each feature state. For practical application, an effective mechanism for feature management is proposed. This approach improves the state estimation accuracy, and requires a smaller number of particles than previous approaches. Both simulation and experimental results are used to validate the effectiveness of the proposed algorithm.