大规模网络滤波的随机动力系统方法
A Random Dynamical Systems Approach to Filtering in Large-scale Networks
摘要：
研究了由传感器网络观测的离散线性系统的滤波问题。传感器与估计器共享公共通信介质，并且传输是比特和功率预算的。在估计器处的信号处理的条件高斯性的假设下（这可以通过观测数据包确认来确保），示出了最优均方误差滤波器的条件预测误差协方差根据非负定矩阵空间上的随机动力系统（RDS）而演变。我们的RDS形式主义不依赖于特定的介质访问协议（随机化），并且在最小分布可观测性假设下，我们表明随机条件预测误差协方差矩阵序列在分布上收敛到唯一不变分布（独立于初始滤波器状态），即，条件误差过程是遍历的。在介质访问协议的广泛假设下，我们证明了条件误差协方差序列满足马尔可夫-费勒性质，从而明确表征其不变测度的支持。在这项工作中采用的方法是足够一般的设想这种应用程序的样本路径分析更一般的混合或切换系统，现有的分析大多是基于时刻。
英文摘要：
The paper studies the problem of filtering a discrete-time linear system observed by a network of sensors. The sensors share a common communication medium to the estimator and transmission is bit and power budgeted. Under the assumption of conditional Gaussianity of the signal process at the estimator (which may be ensured by observation packet acknowledgements), the conditional prediction error covariance of the optimum mean-squared error filter is shown to evolve according to a random dynamical system (RDS) on the space of non-negative definite matrices. Our RDS formalism does not depend on the particular medium access protocol (randomized) and, under a minimal distributed observability assumption, we show that the sequence of random conditional prediction error covariance matrices converges in distribution to a unique invariant distribution (independent of the initial filter state), i.e., the conditional error process is shown to be ergodic. Under broad assumptions on the medium access protocol, we show that the conditional error covariance sequence satisfies a Markov-Feller property, leading to an explicit characterization of the support of its invariant measure. The methodology adopted in this work is sufficiently general to envision this application to sample path analysis of more general hybrid or switched systems, where existing analysis is mostly moment-based.
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