Total least squares estimation model based on uncertainty theory

Hong-mei, Shi; Sun, Xiangqun; Wang, Shuai; Ning, Yufu

doi:10.1007/s12652-021-03671-2

Cited by 4 publications

(3 citation statements)

References 18 publications

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“…20 The total least squares method is then used to solve the extended order matrix parameters. [21][22][23][24][25] This method takes into account the noise disturbance of the observation vector and data matrix at the same time as it solves the parameters. This reduces the effect of noise on the parameter estimate and makes the enhanced spectrum more accurate.…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation in Spectral Resolution Enhancement Based on Forward–Backward Linear Prediction Total Least Square Method

Qin

Han

et al. 2023

Appl Spectrosc

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In a Fourier transform infrared (IR) spectrometer, the Michelson interference signal extrapolation method based on linear prediction is often used to improve spectral resolution. In this method, an autoregressive (AR) model is established for the Michelson interference signal in the spectrometer. Once the AR model parameters are determined, the AR process is predictable. The interference signal can be used to figure out the AR model's parameters. Based on this, the AR model can be used to extrapolate the interference signal to improve the spectral resolution. In this paper, the forward–backward linear prediction total least squares (FB-TLS) method is proposed to estimate the parameters of the AR model. The parameters that are estimated are used to improve the IR spectral resolution. By simulating different order and signal-to-noise ratio situations, the effects of the Burg, the least square, and the FB-TLS parameter estimation methods on spectral resolution enhancement are studied. The simulation results demonstrate that the FB-TLS parameter estimation method can effectively suppress noise and avoid spurious peaks. The experimental results demonstrate that the FB-TLS parameter estimation method is effective for spectral resolution enhancement technology based on linear prediction. When the FB-TLS method is used to enhance NH3 IR spectral resolution from 2 cm−1 to 1 cm−1, the spectral prediction error in the NH3 characteristic band is only 0.21% compared with the measured NH3 spectrum, whose spectral resolution is 1 cm−1.

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Section: Introductionmentioning

confidence: 99%

Parameter Estimation in Spectral Resolution Enhancement Based on Forward–Backward Linear Prediction Total Least Square Method

Qin

Han

et al. 2023

Appl Spectrosc

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“…So far, we have many methods to solve the uncertain regression model, but most of these methods only consider the error of the dependent variable, which is obviously one-sided and the accuracy and reliability of the regression equation will be affected. In 2022, Shi et al [21] proposed an uncertain total least squares estimation. The uncertain total least squares estimation improves the accuracy of the regression equation and has a good effect.…”

Section: Introductionmentioning

confidence: 99%

Robust Total Least Squares Estimation Method for Uncertain Linear Regression Model

Shi,

Zhang,

Gao

et al. 2023

Mathematics

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In data analysis and modeling, least squares and total least squares are both mathematical optimization techniques. It is noteworthy that both the least squares method and the total least squares method are used to deal with precise and random data. However, when the given data are not random, or when the data are imprecise, and only the range of the data is available, the traditional linear regression method cannot be used. This paper presents an uncertain total least squares estimation method and an uncertain robust total least squares linear regression method based on uncertainty theory and total least squares method. The uncertain total least squares estimation can fully consider errors in the given data and the uncertain robust total least squares linear regression method can effectively eliminate outliers in the data. It is possible to obtain a more reasonable fitting effect with both of these methods, as well as to solve the predicted value and the confidence interval with these two methods. In terms of robust total least squares linear regression estimation, both uncertain total least squares regression estimation and uncertain robust total least squares regression estimation are feasible based on numerical examples. There are more accurate fitting equations and more reliable results with uncertain robust least squares linear regression estimation.

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“…proposed two new uncertain linear regression models. Shi et al [23] proposed total least squares estimation model based on uncertainty theory. Uncertainty statistics also have real applications; when COVID-19 was spreading rapidly in most countries around the world, Liu Z.…”

Section: Introductionmentioning

confidence: 99%

Relative Error Linear Combination Forecasting Model Based on Uncertainty Theory

Hong-mei¹,

Wang²,

Wang³

et al. 2023

Symmetry

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The traditional combination forecasting model has good forecasting effect, but it needs precise historical data. In fact, many random events are uncertain, and much of the data are imprecise; sometimes, historical data are lacking. We need to study combination forecasting problems by means of uncertainty theory. Uncertain least squares estimation is an important technique of uncertain statistics, an important way to deal with imprecise data, and one of the best methods to solve the unknown parameters of uncertain linear regression equations. On the basis of the traditional combination forecasting method and uncertain least squares estimation, this paper proposes two kinds of uncertain combination forecasting models, which are the unary uncertain linear combination forecasting model and the uncertain relative error combination forecasting model, respectively. We set up several piecewise linear regression models according to the data of different periods and, according to certain weights, These piecewise linear regression models are combined into a unary uncertain linear combination forecasting model with a better forecasting effect. The uncertain relative error combination forecasting model is a new forecasting model that combines the traditional relative error linear forecasting model and the uncertain least squares estimation. Compared with the traditional forecasting model, the model can better deal with the forecasting problem of imprecise data. We verify the feasibility of the uncertain combination forecasting model through a numerical example. According to the data analysis, compared with the existing model, the forecasting effect of the proposed model is better.

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Total least squares estimation model based on uncertainty theory

Cited by 4 publications

References 18 publications

Parameter Estimation in Spectral Resolution Enhancement Based on Forward–Backward Linear Prediction Total Least Square Method

Parameter Estimation in Spectral Resolution Enhancement Based on Forward–Backward Linear Prediction Total Least Square Method

Robust Total Least Squares Estimation Method for Uncertain Linear Regression Model

Relative Error Linear Combination Forecasting Model Based on Uncertainty Theory

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