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arXiv 2006.00628eess.SYcs.SYmath.OC
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时变系统的在线状态估计

Online State Estimation for Time-Varying Systems

Guido Cavraro, Emiliano Dall'Anese, Joshua Comden, Andrey Bernstein

摘要:

本文研究了线性测量模型的时变系统的状态估计问题;特别是,本文考虑了可用测量数小于状态数的情况。代替一批线性最小二乘(LS)的方法-非常适合静态网络,其中可以收集足够数量的测量值,以获得满秩设计矩阵-本文提出了一种在线算法来估计可能随时间变化的状态,通过处理测量值和可用时。该算法的设计取决于一个广义LS成本与邻近点型正则化增强。利用以封闭形式可用的正则化LS问题的解,在线算法被写为线性动力系统,其中状态基于先前的估计和基于新的可用测量来更新。条件下的算法步骤实际上是一个收缩映射,并得出不同的噪声模型的估计误差的界限。数值模拟证实了分析结果。

英文摘要:

The paper investigates the problem of estimating the state of a time-varying system with a linear measurement model; in particular, the paper considers the case where the number of measurements available can be smaller than the number of states. In lieu of a batch linear least-squares (LS) approach -- well suited for static networks, where a sufficient number of measurements could be collected to obtain a full-rank design matrix -- the paper proposes an online algorithm to estimate the possibly time-varying state by processing measurements as and when available. The design of the algorithm hinges on a generalized LS cost augmented with a proximal-point-type regularization. With the solution of the regularized LS problem available in closed-form, the online algorithm is written as a linear dynamical system where the state is updated based on the previous estimate and based on the new available measurements. Conditions under which the algorithmic steps are in fact a contractive mapping are shown, and bounds on the estimation error are derived for different noise models. Numerical simulations are provided to corroborate the analytical findings.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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