基于条件数的多自主水下航行器协同定位系统可观测度分析

Observability Analysis of Cooperative Localization System for MAUV Based on Condition Number

针对基于移动长基线的多自主水下航行器(MAUV)协同定位系统,建立了MAUV的2D运动学模型与距离量测方程。利用基于Lie导数的非线性系统可观测性理论,得到协同定位系统可观测矩阵及MAUV编队的不可观测航行路径。利用奇异值分解(SVD)理论获得系统可观测矩阵的条件数,建立了协同定位系统可观测度的评价函数,并在不同MAUV航行队形对系统可观测度进行仿真分析。结果表明,系统可观测度随着MAUV航行队形的不同而变化,从而为通过变换队形来提高协同定位性能提供了有效的参考依据。

For the multiple autonomous underwater vehicle （MAUV） cooperative localization system based on the moving long baseline, the 2D kinematic models and range measurement equations of MAUV are established. The observability theory of nonlinear system based on Lie derivatives is used to derive the observability matrix of the cooperative localization system and describe the unobservable trajectories of MAUV system. The evaluation function for the observability metric of the localization system is given u- sing the condition number of observability matrix obtained from singular value decomposition（SVD） theo- ry. Finally, a series of simulation experiments are designed to analyze the system observability under the different MAUV formations. The results show that the system observability change with the MAUV forma- tion, which provides an effective reference to improve the performance of cooperative localization system by transforming the MAUV formation.