Variance-Constrained State Estimation for Nonlinearly Coupled Complex Networks
针对非线性耦合复杂网络，提出一种基于扩展卡尔曼滤波的方差约束状态估计器，通过优化误差协方差上界确定增益矩阵，并证明估计误差均方有界。
This paper studies the state estimation problem for nonlinearly coupled complex networks. A variance-constrained state estimator is developed by using the structure of the extended Kalman filter, where the gain matrix is determined by optimizing an upper bound matrix for the estimation error covariance despite the linearization errors and coupling terms. Compared with the existing estimators for linearly coupled complex networks, a distinct feature of the proposed estimator is that the gain matrix can be derived separately for each node by solving two Riccati-like difference equations. By using the stochastic analysis techniques, sufficient conditions are established which guarantees the state estimation error is bounded in mean square. A numerical example is provided to show the effectiveness and applicability of the proposed estimator.