基于几何解释的集群AUV协同定位误差及编队构型分析

Analyzing of Cooperative Locating Error and Formation Configuration of AUV Based on Geometric Interpretation

针对利用Cramer-Rao不等式下界评价集群AUV定位性能不直观的问题,基于几何椭圆提出了定位性能评价标准的几何解释方法。利用Fisher信息矩阵代替Cramer-Rao不等式,通过奇异值分解将先验信息矩阵与量测信息矩阵合成为后验信息矩阵,并利用椭圆对其进行几何表示,基于后验信息椭圆面积建立定位性能评价函数。通过分析性能评价函数,设计了单主、双主以及三主AUV集群的最优编队构型,并对三主AUV集群编队提出了特殊编队构型,其较最优编队构型的定位性能相差不大的情况下,更容易实现。仿真实验验证了最优编队构型具有更高的定位精度以及特殊编队构型的有效性。

Because the evaluation of the location performance of AUVs with the lower bound of the Cramer-Rao inequality is not intuitive,the geometric interpretation method is proposed based on geometric ellipse.The Fisher information matrix is used to replace the Cramer-Rao inequality.The priori information matrix and the measurement information matrix are synthesized into the posterior information matrix through singular value decomposition.The geometric ellipse is used to geometrically represent the posterior information matrix.The posterior information ellipse area is used to establish the location performance evaluation function.By analyzing the performance evaluation function,the optimal formation configurations of single-master,dual-master and three-master AUVs are designed.The implementation of the special formation configuration for the three-master AUV formation proposed in the paper is easier,while the location performance of the optimal formation configuration is not much inferior.The simulation results verify that the optimal formation configuration has a higher location accuracy and that the special formation configuration is effective.