集体可检测性下的多速率分布式无迹卡尔曼滤波
Multi-Rate Distributed Unscented Kalman Filtering Under Collective Detectability
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中文总结 AI 辅助
本文针对无融合中心的非线性网络，提出多速率分布式UKF方法，基于集体可检测性实现信息扩散，在多速率采样下保持稳定且精度优于五轮协方差平均一致性。
中文摘要 AI 辅助
针对无融合中心的非线性网络，本文提出一种多速率分布式无迹卡尔曼滤波（UKF）方法。本地连续-离散UKF在公共基础网格上运行，在自身采样时刻更新，并在一跳邻域内交换估计值。在窗口式集体可检测性条件下，即使单个节点无需可观测，信息矩阵的扩散也能使商协方差保持一致有界。当集体不可观测子空间为平凡空间，且统计线性化偏差满足显式相干性界时，信息加权融合均值可产生指数有界的均方误差，且无需收缩-混合条件，这与需要该条件的算术扩散均值形成对比。一种分布式H∞变体采用固定衰减惩罚项。有限前缀可行性检查和一跳可检测性Gramian可产生一致正则化信息裕度，进而通过显式局部收缩-混合条件实现均方误差有界性。所提方法在随机非线性基准和三惯量网络上进行测试，其中每个节点至少缺失一个模态。结果表明，信息扩散的精度是五轮协方差平均一致性的五分之一通信量，在3:2多速率采样下仍保持稳定，而协方差平均一致性和扩散均值均发散，且能保持商协方差有界。
英文摘要
We develop a multi-rate distributed unscented Kalman filter for nonlinear networks without a fusion center. Local continuous-discrete UKFs run on a common base grid, update at their own sampling instants, and exchange estimates within one-hop neighborhoods. Under a windowed collective-detectability condition, diffusion of information matrices gives uniformly bounded quotient covariances although no individual node need be observable. When the collectively invisible subspace is trivial and the statistical-linearization discrepancies satisfy an explicit coherence bound, the information weighted fused mean yields exponentially bounded mean-square errors without a contraction-mixing condition. This contrasts with the arithmetic diffusiojn mean, which requires one. A distributed $H_{\infty}$ variant uses a fixed attenuation penalty. A finite-prefix feasibility check and the one-hop detectability Gramian yield a uniform regularized-information margin - an explicit local-contraction-mixing condition then yields mean-square error boundedness. The developed methods are tested on a stochastic nonlinear benchmark and a three-inertia network in which every node misses at least one mode. Information diffusion is more accurate than five-round covariance-averaging consensus at one fifth of its communication. It remains stable under 3:2 multi-rate sampling, where the covariance-averaging consensus and the diffusion mean both diverge, and it keeps the quotient covariances bounded.
