A moments-based approach to estimation and data interpolation for a class of Wiener systems

Mustafa Ayazoglu, Mario Sznaier, Constantino Lagoa, Octavia Camps

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

    4 Scopus citations

    Abstract

    This paper addresses the problems of estimating the values of both the outputs and the internal signals for a class of Wiener systems consisting of the cascade of an unknown linear time invariant systems and a known, rational, generically non-invertible nonlinearity, based solely on past input/output data corrupted by noise. This situation arises in many scenarios of practical interest where an explicit a-priori model of the linear system is not available. Examples include extracting geometric 3D structure from a sequence of 2D images (structure from motion), and nonlinear dimensionality reduction via manifold embedding. The main result of the paper is a simple, computationally efficient algorithm that is capable of handling intermittent measurements and does not entail identifying first the unknown linear dynamics. Rather, the problem of estimating the internal signals and interpolating missing data is recast into a rank-constrained feasibility problem. Although this problem depends polynomially in the data, we show that, by appealing to classical results on moments optimization, it can be reduced to a rank-constrained Linear Matrix Inequality optimization and efficiently solved using existing techniques. The potential of the proposed approach is illustrated by solving structure from motion problems using real data.

    Original languageEnglish (US)
    Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
    Pages5674-5680
    Number of pages7
    DOIs
    StatePublished - Dec 1 2010
    Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
    Duration: Dec 15 2010Dec 17 2010

    Publication series

    NameProceedings of the IEEE Conference on Decision and Control
    ISSN (Print)0191-2216

    Other

    Other2010 49th IEEE Conference on Decision and Control, CDC 2010
    CountryUnited States
    CityAtlanta, GA
    Period12/15/1012/17/10

    All Science Journal Classification (ASJC) codes

    • Control and Systems Engineering
    • Modeling and Simulation
    • Control and Optimization

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