Sparsity Penalties in Dynamical System Estimation (bibtex)
by , , and
Abstract:
In this work we address the problem of state estimation in dynamical systems using recent developments in compressive sensing and sparse approximation. We formulate the traditional Kalman filter as a one-step update optimization procedure which leads us to a more unified framework, useful for incorporating sparsity constraints. We introduce three combinations of two sparsity conditions (sparsity in the state and sparsity in the innovations) and write recursive optimization programs to estimate the state for each model. This paper is meant as an overview of different methods for incorporating sparsity into the dynamic model, a presentation of algorithms that unify the support and coefficient estimation, and a demonstration that these suboptimal schemes can actually show some performance improvements (either in estimation error or convergence time) over standard optimal methods that use an impoverished model.
Reference:
Sparsity Penalties in Dynamical System EstimationA. Charles, M.S. Asif, J. Romberg and C. Rozell. In Proceedings of the Conference on Information Sciences and Systems (CISS), March 2011.
Bibtex Entry:
@InProceedings{charles.11b,
  author = 	 {Charles, A. and Asif, M.S. and Romberg, J. and Rozell, C.},
  title = 	 {Sparsity Penalties in Dynamical System Estimation},
  booktitle =	 {{Proceedings of the Conference on Information Sciences and Systems (CISS)}},
  year =	 2011,
  month = {March},
  address =	 {Baltimore, MD},
abstract = {In this work we address the problem of state estimation in dynamical systems using recent developments in compressive sensing and sparse approximation. We formulate the traditional Kalman filter as a one-step update optimization procedure which leads us to a more unified framework, useful for incorporating sparsity constraints. We introduce three combinations of two sparsity conditions (sparsity in the state and sparsity in the innovations) and write recursive optimization programs to estimate the state for each model. This paper is meant as an overview of different methods for incorporating sparsity into the dynamic model, a presentation of algorithms that unify the support and coefficient estimation, and a demonstration that these suboptimal schemes can actually show some performance improvements (either in estimation error or convergence time) over standard optimal methods that use an impoverished model.},
url =          {http://siplab.gatech.edu/pubs/charlesCISS2011.pdf}
}
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