Spectral estimation based on structured low rank matrix pencil

Abstract

This paper proposes a new parameter estimation algorithm for damped sinusoidal signals. Parameter estimation for damped sinusoidal signals with additive white noise is a problem of significant interest in many signal processing applications, like analysis of NMR data and system identification. The new algorithm estimates the signal parameters using a matrix pencil constructed from the measured data. To reduce the noise effect, rank deficient Hankel approximation of prediction matrix is used. The performance of the new algorithm is significantly improved by structured low rank approximation of prediction matrix. Computer simulations show that the noise threshold of the new algorithm is significantly better than the existing algorithms.

Calibrationless parallel imaging reconstruction based on structured low-rank matrix completion

“…When the rank of the matrix is known beforehand, Equation can be recast into the following formulation : …”

Hankel low-rank approximation and completion in time series analysis and forecasting: a brief review

“…Hankel structure in signal processing Fitting and analysing the sum-of-exponentials model is very common in signal processing and so there has been much attention on Hankel SLRA to obtain solutions in problems such as: spectral estimation [96,107], sparse signal recovery [84], and denoising particular types of signal [15,27]. Other uses of the sum-of-exponentials model include: finite rate of innovation [30], shape-from-moments [31], and superresolution [18] problems.…”

Flutter Boundary Identification from Time-Domain Simulations Using the Matrix Pencil Method

“…In this technical note, we formulate a minimum damping estimate based on the matrix pencil method and demonstrate how to compute its derivative. The matrix pencil method is a technique that can be used to robustly estimate the coefficients in a Prony series (a series of damped sinusoids) from a time-dependent signal [4,5]. These Prony series coefficients can then be used to evaluate an estimate of the minimum aeroelastic damping.…”