1. Sum-of-exponentials modeling and common dynamics estimation using Tensorlab
- Author
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L. De Lathauwer, Otto Debals, Ivan Markovsky, and Electricity
- Subjects
0209 industrial biotechnology ,Mathematical optimization ,Low-rank approximation ,010103 numerical & computational mathematics ,02 engineering and technology ,01 natural sciences ,mosaic Hankel matrix ,Matrix (mathematics) ,020901 industrial engineering & automation ,Software for system identification ,0101 mathematics ,System identification ,Mathematics ,low-rank approximation ,Signal processing ,tensorlab ,SIGNAL (programming language) ,Toolbox ,Exponential sum ,Control and Systems Engineering ,Estimation and filtering ,Time series modelling ,structured data fusion ,Algorithm ,Subspace topology - Abstract
Fitting a signal to a sum-of-exponentials model is a basic problem in signal processing. It can be posed and solved as a Hankel structured low-rank matrix approximation problem. Subsequently, local optimization, subspace, and convex relaxation methods can be used for the numerical solution. In this paper, we show another approach, based on the recently developed concept of structured data fusion. Structured data fusion problems are solved in the Tensorlab toolbox by local optimization methods. The approach allows fitting of signals with missing samples and adding constraints on the model, such as fixed exponents and common dynamics in multi-channel estimation problems. These problems are non-trivial to solve by other existing methods. Tensorlab is publicly available and the results presented are reproducible.
- Published
- 2017
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