Estimation and dynamic updating of time-varying signals with sparse variations

M. Salman Asif, Adam Charles, Justin Romberg, Christopher Rozell

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper presents an algorithm for an ℓ1-regularized Kalman filter. Given observations of a discrete-time linear dynamical system with sparse errors in the state evolution, we estimate the state sequence by solving an optimization algorithm that balances fidelity to the measurements (measured by the standard ℓ2 norm) against the sparsity of the innovations (measured using the ℓ1 norm). We also derive an efficient algorithm for updating the estimate as the system evolves. This dynamic updating algorithm uses a homotopy scheme that tracks the solution as new measurements are slowly worked into the system and old measurements are slowly removed. The effective cost of adding new measurements is a number of low-rank updates to the solution of a linear system of equations that is roughly proportional to the joint sparsity of all the innovations in the time interval of interest.

Original languageEnglish (US)
Title of host publication2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings
Pages3908-3911
Number of pages4
DOIs
StatePublished - 2011
Externally publishedYes
Event36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Prague, Czech Republic
Duration: May 22 2011May 27 2011

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Other

Other36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011
Country/TerritoryCzech Republic
CityPrague
Period5/22/115/27/11

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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