Weighted Total Least Squares for Frequency Estimation of Real Sinusoids Based on Augmented System

Иванов, Д. В.; Zhdanov, A. I.

doi:10.1109/ewdts50664.2020.9224905

Cited by 2 publications

(2 citation statements)

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“…where 2 aa = . To solve the complete least squares problem, efficient algorithms have been developed based on SVD [13] or extended systems equivalent to normal biased systems [11,14].…”

Section: Consider the Estimation Of Parameters mentioning

confidence: 99%

“…Hyperbolic functions are closely related to exponential and trigonometric functions and can be expressed in terms of them. A large number of works are devoted to the estimation of the parameters of exponential and trigonometric functions, as well as their combinations [7][8][9][10][11]. It should be noted that a small number of works are devoted to estimating the parameters of hyperbolic functions.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of Parameters of Hyperbolic Functions with Additive Noise

Ivanov

Sandler

Chertykovtseva

2021

Materials, Computer Engineering and Education Technology

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Hyperbolic functions are widely used to write solutions to ordinary differential equations and partial differential equations. These functions are nonlinear in parameters, which makes it difficult to estimate the parameters of these functions. In the paper, two-step algorithms for estimating the parameters of hyperbolic sine and cosine (sinh and cosh) in the presence of measurement errors are proposed. At the first step, the hyperbolic function is transformed into a linear difference equation (autoregression) of the second order. Estimation in the presence of noise of observation of autoregression parameters using ordinary least square (OLS) gives biased estimates. Modifications of the two-stage estimation algorithm based on the use of the method of total least squares (TLS) and the method of extended instrumental variables (EIV), hyperbolic sine and cosine in the presence of errors in measurements are proposed. Numerical experiments have shown that the accuracy of the parameter estimation using the proposed modifications is higher than the accuracy of the estimate obtained using the ordinary least squares method (OLS).

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“…where 2 aa = . To solve the complete least squares problem, efficient algorithms have been developed based on SVD [13] or extended systems equivalent to normal biased systems [11,14].…”

Section: Consider the Estimation Of Parameters mentioning

confidence: 99%