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arXiv · 2006.00628

Online State Estimation for Time-Varying Systems

Guido Cavraro·Emiliano Dall'Anese·Joshua Comden·Andrey Bernstein
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Abstract

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.

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Guido Cavraro, Emiliano Dall'Anese, Joshua Comden, Andrey Bernstein. 2020-05-31. Online State Estimation for Time-Varying Systems. https://arxiv.org/abs/2006.00628

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