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首页> 外文期刊>Information Theory, IEEE Transactions on >Distributed Kalman Filtering Over Massive Data Sets: Analysis Through Large Deviations of Random Riccati Equations
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Distributed Kalman Filtering Over Massive Data Sets: Analysis Through Large Deviations of Random Riccati Equations

机译：海量数据集的分布式卡尔曼滤波：通过随机Riccati方程的大偏差进行分析

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摘要

This paper studies the convergence of the estimation error process and the characterization of the corresponding invariant measure in distributed Kalman filtering for potentially unstable and large linear dynamic systems. A gossip network protocol termed modified gossip interactive Kalman filtering (M-GIKF) is proposed, where sensors exchange their filtered states (estimates and error covariances) and propagate their observations via intersensor communications of rate γ̅; γ̅ is defined as the averaged number of intersensor message passages per signal evolution epoch. The filtered states are interpreted as stochastic particles swapped through local interaction. This paper shows that the conditional estimation error covariance sequence at each sensor under M-GIKF evolves as a random Riccati equation (RRE) with Markov modulated switching. By formulating the RRE as a random dynamical system, it is shown that the network achieves weak consensus, i.e., the conditional estimation error covariance at a randomly selected sensor converges weakly (in distribution) to a unique invariant measure. Further, it is proved that as γ̅ → ∞ this invariant measure satisfies the large deviation (LD) upper and lower bounds, implying that this measure converges exponentially fast (in probability) to the Dirac measure δ, where P* is the stable error covariance of the centralized (Kalman) filtering setup. The LD results answer a fundamental question on how to quantify the rate at which the distributed scheme approaches the centralized performance as the intersensor communication rate increases.
机译：本文研究了潜在的不稳定和大型线性动力系统的估计误差过程的收敛性和分布式卡尔曼滤波中相应不变性度量的特征。提出了一种称为修正八卦交互式卡尔曼滤波（M-GIKF）的八卦网络协议，其中传感器交换其滤波后的状态（估计和误差协方差），并通过传感器间通信以速率γ̅传播其观测值； γ̅定义为每个信号演化时期的传感器间消息通过的平均数量。滤波后的状态被解释为通过局部相互作用交换的随机粒子。本文表明，在M-GIKF下，每个传感器的条件估计误差协方差序列随着马尔可夫调制切换而演变成随机Riccati方程（RRE）。通过将RRE公式化为随机动力学系统，可以证明网络实现了弱共识，即，随机选择的传感器的条件估计误差协方差弱（分布）收敛到唯一不变度量。此外，证明了当γ̅→∞时，该不变测度满足大偏差（LD）的上下限，这意味着该测度以指数形式快速（概率）收敛到狄拉克测度δ，其中P *是稳定误差协方差集中式（卡尔曼）过滤设置。 LD结果回答了一个基本问题，即当传感器之间的通信速率增加时，如何量化分布式方案接近集中式性能的速率。

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