A new type of fast distributed Kalman consensus filtering algorithm based on local information feedback is presented to tackle filtering problems in wireless sensor networks. First, this fast filtering issues are transformed into a stochastic stability problem of the dynamic estimation errors, which can be solved by Lyapunov's second method and matrix theory. Then, two sufficient conditions about the proportional‐like feedback (double gains regulation) method and incremental Proportional‐Integral‐Derivative (PID) feedback method for the asymptotical stability of the systems are presented, respectively. Moreover, to achieve a faster convergence rate, a novel optimal method is given by combing a genetic algorithm and incremental PID. Finally, an illustrative example is presented to give a comparison of the convergence speed between the three filtering algorithms in the same condition, and verify the effectiveness and advantage of the proposed theoretical results in this article.

中文翻译：

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一种新型快速分布式卡尔曼共识滤波算法的设计与优化

针对无线传感器网络中的滤波问题，提出了一种基于局部信息反馈的新型快速分布式卡尔曼共识滤波算法。首先，这种快速滤波问题被转化为动态估计误差的随机稳定性问题，这可以通过李雅普诺夫的第二种方法和矩阵理论来解决。然后，针对系统的渐近稳定性，分别提出了关于比例式反馈（双增益调节）方法和增量式比例积分微分（PID）反馈方法的两个充分条件。此外，为了达到更快的收敛速度，结合遗传算法和增量PID给出了一种新颖的最优方法。最后，