A rigorous performance analysis is dedicated to the distributed Kalman filtering fusion with feedback for distributed recursive state estimators of dynamic systems. It is shown that the Kalman filtering track fusion formula with feedback is, like the track fusion without feedback, exactly equivalent to the corresponding centralized Kalman filtering formula. Moreover, the so-called P matrices in the feedback Kalman filtering at both local trackers and fusion center are still the covariance matrices of tracking errors. Although the feedback here cannot improve the performance at the fusion center, the feedback does reduce the covariance of each local tracking error. The above results can be extended to a hybrid track fusion with feedback received by a part of the local trackers.

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Efficient computation of the largest eigenvalue and the smallest eigenvalue of a real symmetric matrix is a very important problem in engineering. Using neural networks to complete these operations is in an asynchronous manner and can achieve high performance. This paper proposes a concise functional neural network (FNN) expressed as a differential equation and designs steps to do this work. Firstly, the mathematical analytic solution of the equation is received, and then the convergence properties of this FNN are fully gained. Finally, the computing steps are designed in detail. The proposed method can compute the smallest eigenvalue and the largest eigenvalue whether the matrix is non-definite, positive definite or negative definite. Compared with other methods based on neural networks, this FNN is very simple and concise, so it is very easy to realize.

When the activation function possesses multilevel property, the Hopfield neural network has some novel dynamical behaviors, and it is worthwhile to study. First, some properties about the activation function are obtained, on this foundation, some theoretical analysis about the quasi-equilibrium points has been made. From local and global view, some theorems about the boundedness are presented. Finally, two theorems about the first derivative of trajectory with respect to time are found, the first theorem indicates that the trajectory cannot keep increasing or decreasing for time t>to, the second theorem is about the complete stability of the trajectory.

本文提出一个基于数据关联性能评价的优化跟踪门算法，并通过它来减少跟踪门内来自非本目标的回波，最终达到提高多目标多传感器跟踪系统性能的目的。与最优跟踪门相比，经理论分析和仿真数据表明，本算法有效改善了系统的性能，尤其在强干扰、高虚警的情况下更为明显。