A moments-based approach to estimation and data interpolation for a class of Wiener systems
A moments-based approach to estimation and data interpolation for a class of Wiener systems
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一类维纳系统的基于矩的估计和数据插值方法
DOI：
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发表时间：
2010
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通讯作者：
O. Camps
中科院分区：
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作者：
Mustafa Ayazoglu;M. Sznaier;C. Lagoa;O. Camps
本文研究了一类Wiener系统的输出和内部信号的估计问题，该系统由一个未知的线性时不变系统和一个已知的、有理的、一般不可逆的非线性系统级联而成，仅基于过去的输入/输出数据，而输入/输出数据被噪声污染.这种情况出现在许多实际感兴趣的场景中，其中线性系统的显式先验模型不可用。例子包括从2D图像序列中提取几何3D结构（从运动中提取结构），以及通过流形嵌入进行非线性降维。本文的主要结果是一个简单的，计算效率高的算法，能够处理间歇性的测量，并不需要首先识别未知的线性动态。相反，估计内部信号和内插缺失数据的问题被改写成一个秩约束的可行性问题。虽然这个问题依赖于多项式的数据，我们表明，通过呼吁经典的矩优化结果，它可以减少到一个秩约束的线性矩阵不等式优化，并有效地解决了使用现有的技术。通过使用真实的数据解决从运动恢复结构的问题，说明了所提出的方法的潜力。
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.