State estimation for nonlinearly coupled complex networks with application to multi-target tracking

This paper is concerned with the state estimation problem for a class of nonlinearly coupled complex networks with random coupling strengths. The coupling strengths are assumed to be chosen from a set of uniform distributions with non-negative means. The estimator is developed for each node 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. It is shown that the gain matrix can be derived separately for each node by solving two Riccati-like difference equations. By using the stochastic analysis technique, a sufficient condition is established which guarantees the boundedness of the estimation errors. As an application, we show how the nonlinearly coupled complex networks can be used to describe the target motions with interacting behaviors and the proposed estimator can be used to derive the state estimates of the targets. A numerical example is provided to verify the effectiveness of the proposed estimator.