基于LU分解的增广信息滤波机器人协同定位

在增广信息滤波机器人协同定位算法中，通常对联合分布的信息矩阵采用Cholesky方法进行分解。基于Cholesky分解的增广信息滤波对联合分布的信息矩阵的正定对称性要求很高，在联合分布的信息矩阵不满足正定对称性的情况下，求逆产生异常，影响联合分布的信息恢复，系统的鲁棒性下降。本文提出了一种基于LU分解的增广信息滤波算法，保证了机器人协同定位算法精度的同时，有效解决了联合分布的信息矩阵分解异常问题，最后对机器人系统可观测性进行分析。利用MATLAB软件平台对算法进行仿真验证。结果表明，该算法保证了机器人协同定位精度，提高了机器人系统的鲁棒性。

Expanded information filtering robot co-localization based on LU decomposition

In the co-localization algorithm of augmented information filtering robot, the Cholesky method is usually used to decompose the information matrix of the joint distribution. The augmented information filtering based on Cholesky decomposition has high requirements for the positive definite symmetry of the information matrix of the joint distribution, and in the case that the information matrix of the joint distribution does not meet the positive definite symmetry, the inversion produces anomalies, affects the information recovery of the joint distribution, and the robustness of the system decreases. An augmented information filtering algorithm based on LU decomposition was proposed, which ensures the accuracy of the robot co-localization algorithm, effectively solves the problem of information matrix decomposition anomaly of joint distribution, and finally the observability of the robot system was analyzed. The MATLAB software platform was used to simulate and verify the algorithm. The results show that the algorithm ensures the cooperative positioning accuracy of the robot and improves the robustness of the robot system.