TY - GEN
T1 - A moments-based approach to estimation and data interpolation for a class of Wiener systems
AU - Ayazoglu, Mustafa
AU - Sznaier, Mario
AU - Lagoa, Constantino
AU - Camps, Octavia
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=79953152108&partnerID=8YFLogxK
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U2 - 10.1109/CDC.2010.5717846
DO - 10.1109/CDC.2010.5717846
M3 - Conference contribution
AN - SCOPUS:79953152108
SN - 9781424477456
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5674
EP - 5680
BT - 2010 49th IEEE Conference on Decision and Control, CDC 2010
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 49th IEEE Conference on Decision and Control, CDC 2010
Y2 - 15 December 2010 through 17 December 2010
ER -