Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
A subspace algorithm for the identification of discrete time frequency domain power spectra
Automatica (Journal of IFAC)
Modifications of rational transfer matrices to achieve positive realness
Signal Processing
Filtering and System Identification: A Least Squares Approach
Filtering and System Identification: A Least Squares Approach
Brief paper: An insight into instrumental variable frequency-domain subspace identification
Automatica (Journal of IFAC)
Interior-Point Method for Nuclear Norm Approximation with Application to System Identification
SIAM Journal on Matrix Analysis and Applications
Subspace-based rational interpolation of analytic functions from phase data
IEEE Transactions on Signal Processing
The power of convex relaxation: near-optimal matrix completion
IEEE Transactions on Information Theory
Foundations and Trends® in Machine Learning
Cross-spectrum based blind channel identification
IEEE Transactions on Signal Processing
Automatica (Journal of IFAC)
Robust spectral factor approximation of discrete-time frequency domain power spectras
Automatica (Journal of IFAC)
Lower Bounds on the Mean-Squared Error of Low-Rank Matrix Reconstruction
IEEE Transactions on Signal Processing
Constrained Cramér–Rao Bound on Robust Principal Component Analysis
IEEE Transactions on Signal Processing
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Subspace-based methods have been effectively used to estimate multi-input/multi-output, discrete-time, linear-time-invariant systems from noisy spectrum samples. In these methods, a critical step is splitting of two invariant subspaces associated with causal and non-causal eigenvalues of some structured matrices built from spectrum measurements via singular-value decomposition in order to determine model order. Mirror image symmetry with respect to the unit circle between the eigenvalue sets of the two invariant spaces, required by the subspace algorithms, is lost due to low signal-to-noise ratio, unmodeled dynamics, and insufficient amount of data. Consequently, the choice of model order is not straightforward. In this paper, we propose a new model order selection scheme that is insensitive to noise and undermodeling and based on the regularized nuclear norm optimization in combination with a recently developed subspace-based spectrum estimation algorithm which uses non-uniformly spaced, in frequencies, spectrum measurements. A detailed simulation study shows the effectiveness of the proposed scheme to large amplitude noise over short data records. Examples illustrating application of the proposed scheme to real-life problems are also presented. The proposed scheme can be readily integrated into frequency-domain instrumental variable subspace algorithms to estimate auto-power spectral density or cross-power spectral density function matrices from non-uniformly spaced, in frequencies, spectrum measurements.