多无人机编队异常检测的稀疏优化算法

Sparse Optimization Algorithm in Multi-UAV Formation Anomaly Detection

针对多无人机编队的异常检测问题,为避免多假设检验及概率不等式的复杂性,将异常检测问题转化为一个线性未知参数矢量的辨识过程。在有无异常检测个数的先验条件下,分别构造极大似然辨识问题和非凸的稀疏优化问题,利用最优必要条件求解最优估计值。采用松弛法将非凸稀疏优化规划成易于求解的凸优化问题。针对凸优化问题中的范数形式,分别应用最优必要条件和快速梯度算法来近似估计最优值,并分析快速梯度算法的收敛不等式。最后用仿真算例验证所提方法的有效性。

To avoid any multi-hypothesis test and the complexity of some probability inequalities, the anomaly detection problem can be converted to the identification of a linear unknown parameter vector. Under priori condition about the number of the anomaly detection, a maximum likelihood identification problem and a non-convex sparse optimization problem are constructed. Then the optimum necessary condition is applied to solve the optimum estimation, and a solvable convex optimization is obtained from the non-convex sparse optimization by adopting a relaxation method. For different norm forms in the convex optimization, the optimum necessary condition and the fast gradient algorithm are respectively used to estimate the optimum values, and some convergence inequalities of the fast gradient algorithm are analyzed. Finally, the effectiveness of the proposed method is verified by the simulation example results.