The constrained total least squares technique and its applications to harmonic superresolution

Abatzoglou, Theagenis J.; Mendel, Jerry M.; Harada, G.A.

doi:10.1109/78.80955

Cited by 245 publications

(166 citation statements)

References 20 publications

Supporting

Mentioning

162

Contrasting

Unclassified

Order By: Relevance

“…Linear prediction equations can be solved to estimate the parameters of multiple sinusoids and it is shown that STLS estimator corresponds to the ML estimator when noise is normally distributed [6]. Consider the case where parameters of two sinusoids which are close in frequency need to be estimated with frequencies f 1 = 0.32 Hz and f 2 = 0.30 Hz in white noise w n :…”

Section: Frequency Estimation Of Multiple Sinusoidsmentioning

confidence: 99%

Structured least squares with bounded data uncertainties

Pilancı

Arıkan

Oğuz

et al. 2009

2009 IEEE International Conference on Acoustics, Speech and Signal Processing

View full text Add to dashboard Cite

In many signal processing applications the core problem reduces to a linear system of equations. Coefficient matrix uncertainties create a significant challenge in obtaining reliable solutions. In this paper, we present a novel formulation for solving a system of noise contaminated linear equations while preserving the structure of the coefficient matrix. The proposed method has advantages over the known Structured Total Least Squares (STLS) techniques in utilizing additional information about the uncertainties and robustness in ill-posed problems. Numerical comparisons are given to illustrate these advantages in two applications: signal restoration problem with an uncertain model and frequency estimation of multiple sinusoids embedded in white noise.

show abstract

Section: Frequency Estimation Of Multiple Sinusoidsmentioning

confidence: 99%

Structured least squares with bounded data uncertainties

Pilancı

Arıkan

Oğuz

et al. 2009

2009 IEEE International Conference on Acoustics, Speech and Signal Processing

View full text Add to dashboard Cite

show abstract

“…The dependent variable is represented by vector b, in which we try keeping the correction term ∆b as small as possible while simultaneously compensating for the noise present in b by forcing Ax=b+∆b [7].…”

Section: Ols Approachmentioning

confidence: 99%

“…Using OLS technique for this problem will result in biased solution and location accuracy will decrease due to the accumulation of the system matrix errors. To alleviate this problem, a generalization of the OLS solution, called total leastsquares (TLS) [7][8][9], is utilized to remove the noise in A and b using a perturbation on A and b of the smallest Frobenius norm which makes the system of equations consistent. It is shown that in the TDOA based location problem the unknown parameters in vector x are quadratic constraint related, which could be realized via Lagrange multipliers technique to constrain the TLS solution.…”

Section: Introductionmentioning

confidence: 99%

A Quadratic Constraint Total Least-squares Algorithm for Hyperbolic Location

Yang¹,

An²,

Xu³

2008

IJCNS

View full text Add to dashboard Cite

A novel algorithm for source location by utilizing the time difference of arrival (TDOA) measurements of a signal received at spatially separated sensors is proposed. The algorithm is based on quadratic constraint total least-squares (QC-TLS) method and gives an explicit solution. The total least-squares method is a generalized data fitting method that is appropriate for cases when the system model contains error or is not known exactly, and quadratic constraint, which could be realized via Lagrange multipliers technique, could constrain the solution to the location equations to improve location accuracy. Comparisons of performance with ordinary least-squares are made, and Monte Carlo simulations are performed. Simulation results indicate that the proposed algorithm has high location accuracy and achieves accuracy close to the CramerRao lower bound (CRLB) near the small TDOA measurement error region.

show abstract

“…In fact, earlier work of STLS can be found in [12] and amendments have been made to improve the rate of convergence and reduce the computational complexity [13]- [15]. For example, Philippe et al have suggested an iterative method [16], namely, STLS2, based on Lagrange-Newton method and provided a fast implementation of the algorithm.…”

Section: Introductionmentioning

confidence: 99%

“…The structured total least squares (STLS) approach [12]- [16], which exploits the special structure involved in the over-determined system can provide efficient parameter estimates. In fact, earlier work of STLS can be found in [12] and amendments have been made to improve the rate of convergence and reduce the computational complexity [13]- [15].…”

Section: Introductionmentioning

confidence: 99%