Online State Estimation for Time-Varying Systems

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4 Scopus Citations


The article investigates the problem of estimating the state of a time-varying system with a linear measurement model; in particular, the article 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 approach - well-suited for static networks, where a sufficient number of measurements could be collected to obtain a full-rank design matrix - the article 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 least-squares cost augmented with a proximal-point-type regularization. With the solution of the regularized least-squares 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.

Original languageAmerican English
Pages (from-to)5424-5431
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number10
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

NREL Publication Number

  • NREL/JA-5D00-81025


  • Asynchronous sensors
  • networked systems
  • state estimation
  • time-varying systems


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