Feasibility study on the least square method for fitting non-Gaussian noise data

Scattered data from edge detection usually involve undesired noise which seriously affects the accuracy of ellipse fitting. In order to alleviate this kind of degradation, a method of direct least absolute deviation ellipse fitting by minimizing the ℓ1 algebraic distance is presented. Unlike the conventional ℓ2 estimators which tend to produce a satisfied performance on ideal and Gaussian noise data, while do a poor job for non-Gaussian outliers, the proposed method shows very competitive results for non-Gaussian noise. In addition, an efficient numerical algorithm based on the split Bregman iteration is developed to solve the resulting ℓ1 optimization problem, according to which the computational burden is significantly reduced. Furthermore, two classes of ℓ2 solutions are introduced as the initial guess, and the selection of algorithm parameters is studied in detail; thus, it does not suffer from the convergence issues due to poor initialization which is a common drawback existing in iterative-based approaches. Numerical experiments reveal that the proposed method is superior to its ℓ2 counterpart and outperforms some of the state-of-the-art algorithms for both Gaussian and non-Gaussian artifacts.

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Positioning Techniques in Indoor Environments Based on Stochastic Modeling of UWB Round Trip Time Measurements

10.36227/techrxiv.15016107 ◽

2021 ◽

Author(s):

Paolo Carbone

Keyword(s):

Particle Filter ◽

Gaussian Noise ◽

Additive White Gaussian Noise ◽

Least Square ◽

Indoor Environments ◽

Round Trip Time ◽

Round Trip ◽

Positioning Systems ◽

Trip Time ◽

Non Gaussian

<div><div><div><p>In this paper, a technique for modeling propagation of Ultra Wide Band (UWB) signals in indoor or outdoor environments is proposed, supporting the design of a positioning systems based on Round Trip Time (RTT) measurements and on a particle filter. By assuming that nonlinear pulses are transmitted in an Additive White Gaussian Noise Channel, and detected using a threshold based receiver, it is shown that RTT measurements may be affected by a non-Gaussian noise. RTT noise properties are analyzed, and the effects of non-Gaussian noise on the performance of a RTT based positioning system are investigated. To this aim, a classical Least Square, an extended Kalman Filter and a Particle Filter are compared when used to detect a slowly moving target in presence of the modeled noise. It is shown that, in a realistic indoor environment, the Particle Filter solution may be a competitive solution, at a price of increased computational complexity. Experimental verifications validate the presented approach.</p></div></div></div>

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Construction of Adjustment Model of Traffic Volume Forecast in The Latter Part of Expressway Operating

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.178-181.1526 ◽

2012 ◽

Vol 178-181 ◽

pp. 1526-1531

Author(s):

Ming Shun Li ◽

Zuo Hui Zhu

Keyword(s):

Linear Relationship ◽

Traffic Flow ◽

Feasibility Study ◽

Least Square Method ◽

Traffic Volume ◽

Least Square ◽

Adjustment Model ◽

Traffic Flow Forecast ◽

Method Model ◽

Flow Forecast

This paper focuses on the problem of serious deviation about predicted traffic flow on the feasibility study stage of expressway,puts forward an idea to compare and analyse the predicted traffic flow in feasibility study stage and the actual traffic after project operation,introducts least square method model, and finds out the linear relationship between them, thus predicts traffic flow of expressway operation. Finally, the calculation is made by combining with concrete expressway project,which proves that this method is usefull to improving the accuracy of the traffic flow forecast.

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The Technology Research Based on Least Square Method for Extracting Quadric Surface

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.220-223.2342 ◽

2012 ◽

Vol 220-223 ◽

pp. 2342-2345

Author(s):

Y. W. Chen ◽

H. X. Zhang ◽

W. Y. Zhang

Keyword(s):

Point Cloud ◽

Least Square Method ◽

Least Square ◽

Single Type ◽

Point Cloud Data ◽

Quadric Surface ◽

Cloud Data ◽

Computation Efficiency ◽

Noise Data ◽

Linear Least Square

In this paper, the discrete point cloud data is directly used to extract quadric surface, with the single type of the point cloud data, the surface is firstly recognized. And then, according to different types of quadric surface, using the geometric parameter equation, the technology of extracting quadric surface can be achieved based on least square method. The results of the study show that: For normal data or less noisy data, the accuracy of calculation of linear least square method is the highest. For the nonlinear square method, on the other hand, the calculation precision is the lowest. However, the computational efficiency of the nonlinear least square method is higher than the linear least square method. The least square laws are more sensitive to noise data. With the increasing of the increased noise data, the extraction accuracy of the results will be affected by certain influence, but its computation efficiency is higher. Research results to practical engineering application of least square method to extract the quadratic surface have certain guiding significance.

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European Option Based on Least-Squares Method under Non-Extensive Statistical Mechanics

Entropy ◽

10.3390/e21100933 ◽

2019 ◽

Vol 21 (10) ◽

pp. 933

Author(s):

Limin Liu ◽

Yingying Cui

Keyword(s):

Statistical Mechanics ◽

Least Squares ◽

Least Squares Method ◽

Gaussian Model ◽

Closed Form Solution ◽

Least Square Method ◽

Form Solution ◽

Least Square ◽

European Options ◽

Non Gaussian

This paper is devoted to the study of the pricing of European options under a non-Gaussian model. This model follows a non-extensive statistical mechanics which can better describe the fractal characteristics of price movement in the financial market. Moreover, we present a simple but precise least-square method for approximation and obtain a closed-form solution of the price of European options. The advantages of this technique are illustrated by numerical simulation, which shows that the least-squares method is better compared with Borland’s two methods in 2002 and 2004.

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Positioning Techniques in Indoor Environments Based on Stochastic Modeling of UWB Round Trip Time Measurements

10.36227/techrxiv.15016107.v1 ◽

2021 ◽

Author(s):

Paolo Carbone

Keyword(s):

Particle Filter ◽

Gaussian Noise ◽

Additive White Gaussian Noise ◽

Least Square ◽

Indoor Environments ◽

Round Trip Time ◽

Round Trip ◽

Positioning Systems ◽

Trip Time ◽

Non Gaussian

<div><div><div><p>In this paper, a technique for modeling propagation of Ultra Wide Band (UWB) signals in indoor or outdoor environments is proposed, supporting the design of a positioning systems based on Round Trip Time (RTT) measurements and on a particle filter. By assuming that nonlinear pulses are transmitted in an Additive White Gaussian Noise Channel, and detected using a threshold based receiver, it is shown that RTT measurements may be affected by a non-Gaussian noise. RTT noise properties are analyzed, and the effects of non-Gaussian noise on the performance of a RTT based positioning system are investigated. To this aim, a classical Least Square, an extended Kalman Filter and a Particle Filter are compared when used to detect a slowly moving target in presence of the modeled noise. It is shown that, in a realistic indoor environment, the Particle Filter solution may be a competitive solution, at a price of increased computational complexity. Experimental verifications validate the presented approach.</p></div></div></div>

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Direct Assessment of Effective Renal Plasma Flow from Renoscintigraphy with a Gamma Camera and an On-Line Computer

Nuklearmedizin ◽

10.1055/s-0037-1620658 ◽

1981 ◽

Vol 20 (06) ◽

pp. 274-278

Author(s):

J. Liniecki ◽

J. Bialobrzeski ◽

Ewa Mlodkowska ◽

M. J. Surma

Keyword(s):

Count Rate ◽

Renal Plasma Flow ◽

Early Period ◽

Least Square Method ◽

Least Square ◽

Uptake Coefficient ◽

Positive Linear Correlation ◽

On Line ◽

Best Fit ◽

Plasma Activity

A concept of a kidney uptake coefficient (UC) of 131I-o-hippurate was developed by analogy from the corresponding kidney clearance of blood plasma in the early period after injection of the hippurate. The UC for each kidney was defined as the count-rate over its ROI at a time shorter than the peak in the renoscintigraphic curve divided by the integral of the count-rate curve over the "blood"-ROI. A procedure for normalization of both curves against each other was also developed. The total kidney clearance of the hippurate was determined from the function of plasma activity concentration vs. time after a single injection; the determinations were made at 5, 10, 15, 20, 30, 45, 60, 75 and 90 min after intravenous administration of 131I-o-hippurate and the best-fit curve was obtained by means of the least-square method. When the UC was related to the absolute value of the clearance a positive linear correlation was found (r = 0.922, ρ > 0.99). Using this regression equation the clearance could be estimated in reverse from the uptake coefficient calculated solely on the basis of the renoscintigraphic curves without blood sampling. The errors of the estimate are compatible with the requirement of a fast appraisal of renal function for purposes of clinical diagknosis.

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