scholarly journals A Sort of New Improved Algorithm For Total Least Square

2015 ◽  
Vol 9 (1) ◽  
pp. 238-247
Author(s):  
Deng Yonghe
Keyword(s):  
Least Square ◽  
New Method ◽  
Unknown Parameters ◽  
Error Equation ◽  
Virtual Observation ◽  
Condition Equation ◽  
Total Least Square ◽  
Improved Algorithm

Aim to blemish of total least square algorithm based on error equation of virtual observation, this paper put forward and deduced a sort of new improved algorithm which selects essential unknown parameters among designing matrix, and then, doesn’t consider condition equation of unknown parameters among designing matrix. So, this paper perfected and enriched algorithm, and sometimes, new method of this paper is better. Finally, the results of examples showed that new mothod is viable and valid.

scholarly journals Improved Total Least Square Algorithm

2015 ◽  
Vol 9 (1) ◽  
pp. 394-399 ◽  
Author(s):  
Deng Yonghe
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Least Square ◽  
Error Equation ◽  
Virtual Observation ◽  
Straight Line ◽  
Condition Equation ◽  
Total Least Square ◽  
Three Dimensional Space ◽  
Improved Algorithm

Aim to blemish of total least square algorithm based on error equation of virtual observation,this paper proposed a sort of improved algorithm which doesn’t neglect condition equation of virtual observation,and considers both error equation and condition equation of virtual observation.So,the improved algorithm is better.Finally,this paper has fitted a straight line in three-dimensional space based on the improved algorithm.The result showed that the improved algorithm is viable and valid.

scholarly journals Retraction Note: A Sort of New Improved Algorithm For Total Least Square

2015 ◽  
Vol 9 (1) ◽  
pp. 322-322
Author(s):  
Deng Yonghe
Keyword(s):  
Peer Review ◽  
Review Process ◽  
Peer Review Process ◽  
Least Square ◽  
Ethical Practices ◽  
On Line ◽  
Total Least Square ◽  
Improved Algorithm

The Publisher and Editor have retracted this article [1] in accordance with good ethical practices. After a thorough investigations we believe that the peer review process was compromised. The article was published on-line on

scholarly journals New Method for Generating New Families of Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 726
Author(s):  
Lamya A. Baharith ◽  
Wedad H. Aljuhani
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Rate Function ◽  
New Method ◽  
Likelihood Method ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Failure Rate Function ◽  
New Approach ◽  
Numerical Studies

This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this distribution can take asymmetric and near-symmetric shapes. Various asymmetric shapes, such as decreasing, increasing, L-shaped, near-symmetrical, and right-skewed shapes, are observed for the related failure rate function, making it more tractable for many modeling applications. Some significant mathematical features of the suggested distribution are determined. Estimates of the unknown parameters of the proposed distribution are obtained using the maximum likelihood method. Furthermore, some numerical studies were carried out, in order to evaluate the estimation performance. Three practical datasets are considered to analyze the usefulness and flexibility of the introduced distribution. The proposed alpha power Weibull–exponential distribution can outperform other well-known distributions, showing its great adaptability in the context of real data analysis.

scholarly journals High Precision Position Measurement Method for Laguerre-Gaussian Beams Using a Quadrant Detector

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 4007 ◽  
Author(s):  
Qian Li ◽  
Jiabin Wu ◽  
Yunshan Chen ◽  
Jingyuan Wang ◽  
Shijie Gao ◽  
...  
Keyword(s):  
Maximum Error ◽  
Least Square ◽  
New Method ◽  
Beam Radius ◽  
Engineering Practice ◽  
Gaussian Beams ◽  
Good Prospect ◽  
Position Measurement ◽  
Beam Position ◽  
Mean Square Errors

In this paper, we propose a new method to improve the position measurement accuracy for Laguerre-Gaussian beams on a quadrant detector (QD). First, the error effects of the detector diameter and the gap size are taken into account, and the position error compensation factor is introduced into the conventional formula. Then, in order to reduce the number of parameters, the concept of effective radius is proposed. Thus, a new analytical expression is obtained with a best fit using the least square method. It is verified by simulation that this approach can reduce the maximum error by 97.4% when the beam radius is 0.95 mm; meanwhile, the root mean square errors under different radii are all less than 0.004 mm. The results of simulation show that the new method could effectively improve the accuracy of the QD measurement for different radii. Therefore, the new method would have a good prospect in the engineering practice of beam position measurements.

scholarly journals Smooth Signal Activity Detection in White Gaussian Noise: Application to P300 Detection

2021 ◽  
Author(s):  
Ali Mobaien ◽  
Reza Boostani ◽  
Negar Kheirandish
Keyword(s):  
Gaussian Noise ◽  
Signal To Noise Ratio ◽  
Hypothesis Test ◽  
White Gaussian Noise ◽  
Least Square ◽  
Unknown Parameters ◽  
Detection Scheme ◽  
Ml Estimation ◽  
Unknown Variance ◽  
Synthetic Datasets

<div>Abstract—In this research, we have proposed a new scheme to detect and extract the activity of an unknown smooth template in presence of white Gaussian noise with unknown variance. In this regard, the problem is considered a binary hypothesis test, and it is solved employing the generalized likelihood ratio (GLR) method. GLR test uses the maximum likelihood (ML) estimation of unknown parameters under each hypothesis. The ML estimation of the desired signal yields an optimization problem with smoothness constraint which is in the form of a conventional least square error estimation problem and can be solved optimally. The proposed detection scheme is studied for P300 elicitation from the background electroencephalography signal. In addition, to assume the P300 smoothness, two prior knowledge are considered in terms of positivity and approximate occurrence time of P300. The performance of the method is assessed on both real and synthetic datasets in different noise levels and compared to a conventional signal detection scheme without considering smoothness priors, as well as state-of-theart linear and quadratic discriminant analysis. The results are illustrated in terms of detection probability, false alarm rate, and accuracy. The proposed method outperforms the counterparts in low signal-to-noise ratio situations.</div>

scholarly journals Integer variables estimation problems: the Bayesian approach

1997 ◽  
Vol 40 (5) ◽  
Author(s):  
F. Sansò ◽  
G. Venuti
Keyword(s):  
Bayesian Approach ◽  
Estimation Procedure ◽  
Least Square ◽  
Unknown Parameters ◽  
Ordinary Least Square ◽  
Integer Variables ◽  
Cycle Slips ◽  
Estimation Problems ◽  
Continuous Range ◽  
Gps Observations

In geodesy as well as in geophysics there are a number of examples where the unknown parameters are partly constrained to be integer numbers, while other parameters have a continuous range of possible values. In all such situations the ordinary least square principle, with integer variates fixed to the most probable integer value, can lead to paradoxical results, due to the strong non-linearity of the manifold of admissible values. On the contrary an overall estimation procedure assigning the posterior distribution to all variables, discrete and continuous, conditional to the observed quantities, like the so-called Bayesian approach, has the advantage of weighting correctly the possible errors in choosing different sets of integer values, thus providing a more realistic and stable estimate even of the continuous parameters. In this paper, after a short recall of the basics of Bayesian theory in section 2, we present the natural Bayesian solution to the problem of assessing the estimable signal from noisy observations in section 3 and the Bayesian solution to cycle slips detection and repair for a stream of GPS measurements in section 4. An elementary synthetic example is discussed in section 3 to illustrate the theory presented and more elaborate, though synthetic, examples are discussed in section 4 where realistic streams of GPS observations, with cycle slips, are simulated and then back processed.

Modified gradient algorithm for total least square filtering

2006 ◽  
Vol 70 (1-3) ◽  
pp. 568-576 ◽  
Author(s):  
Xiangyu Kong ◽  
Chongzhao Han ◽  
Ruixuan Wei
Keyword(s):  
Least Square ◽  
Gradient Algorithm ◽  
Total Least Square
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