Wang Miao, Liu Weifeng, Wen Chenglin
School of Electrical and Control Engineering, Shaanxi University of Science and Technology, Xi'an 710021, China.
School of Automation, Guangdong University of Petrochemical Technology, Maoming 525000, China.
Sensors (Basel). 2022 Jul 26;22(15):5590. doi: 10.3390/s22155590.
Multi-robot motion and observation generally have nonlinear characteristics; in response to the problem that the existing extended Kalman filter (EKF) algorithm used in robot position estimation only considers first-order expansion and ignores the higher-order information, this paper proposes a multi-robot formation trajectory based on the high-order Kalman filter method. The joint estimation method uses Taylor expansion of the state equation and observation equation and introduces remainder variables on this basis, which effectively improves the estimation accuracy. In addition, the truncation error and rounding error of the filtering algorithm before and after the introduction of remainder variables, respectively, are compared. Our analysis shows that the rounding error is much smaller than the truncation error, and the nonlinear estimation performance is greatly improved.
多机器人运动与观测一般具有非线性特征；针对机器人位置估计中现有的扩展卡尔曼滤波器（EKF）算法仅考虑一阶展开而忽略高阶信息的问题，本文提出一种基于高阶卡尔曼滤波方法的多机器人编队轨迹。联合估计方法利用状态方程和观测方程的泰勒展开，并在此基础上引入余项变量，有效提高了估计精度。此外，分别比较了引入余项变量前后滤波算法的截断误差和舍入误差。分析表明，舍入误差远小于截断误差，非线性估计性能得到极大提升。
