Outlier elimination method based on multinomial fitting

A polynomial and order polynomial technology, applied in the field of measurement and control systems, can solve the problems of difficult to master standards and low efficiency, and achieve the effect of maintaining continuity, accurate parameters and wide application range

Inactive Publication Date: 2017-09-22
NO 719 RES INST CHINA SHIPBUILDING IND
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Problems solved by technology

The artificial method is more successful in judging the outliers with obvious errors, but this method is very inefficient a

Method used

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  • Outlier elimination method based on multinomial fitting
  • Outlier elimination method based on multinomial fitting
  • Outlier elimination method based on multinomial fitting

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Embodiment Construction

[0025] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0026] Such as figure 1 A outlier elimination method based on polynomial fitting is shown, including steps:

[0027] Step 1: Carry out n-order polynomial fitting to original measurement data, obtain coefficient matrix and fit polynomial;

[0028] From the known observation data (i=0,1,...,m), draw a rough graph—a scatter diagram, and select an appropriate number n for least squares polynomial fitting;

[0029] For the given measurement data (x i ,y i )(i=0,1,...,m), construct a function p(x) as the given data (x i ,y i ) approximate expression, so that the error r i =p(x i )-y i (i=0,1,…,m) has the smallest sum of squares, namely

[0030]

[0031] Geometrically seek the relationship with a given point (x i ,y i )(i=0,1,…,m) is the curve y=p(x) where the sum of squared distances is the smallest. The function p(x) is called the fit...

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Abstract

The invention discloses a method for eliminating outliers based on polynomial fitting, which comprises the steps of: performing n-order polynomial fitting on the original measurement data to obtain a coefficient matrix and a fitting polynomial, and draw a rough For the scatter diagram, select the appropriate number n to perform the least squares polynomial fitting, and construct a function p(x) for the given measurement data (xi, yi) as an approximate expression of the given data (xi, yi), so that The sum of squares of error ri=p(xi)-yi is the smallest, that is, i is an integer from 0 to m. Based on polynomial fitting, this method invented a method for the computer to automatically remove the outliers in the measured data, and identified and eliminated the outliers in the observed data sequence by fitting the residual sequence of the estimated value and the observed value, which is very useful for practical engineering applications. important application value.

Description

technical field [0001] The invention relates to an outlier elimination method based on polynomial fitting, which is applicable to the field of measurement and control systems such as communication and navigation. Background technique [0002] Measurement data such as communication and navigation often contain a large number of data points that seriously deviate from the measured true value, and these abnormal data are called outliers. Although the number of outliers is small, it will have a greater impact on data processing and analysis, reducing the reliability of the data. Although some filtering and smoothing methods can eliminate outliers to a certain extent, if the parameters are not well selected, it is likely that the data processing results will not be convincing due to severe distortion, or the smoothing effect will not be achieved. Therefore, before smoothing the data, the outlier points in the measurement data should be effectively identified and eliminated. The...

Claims

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Application Information

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IPC IPC(8): G06F17/17G06F17/18
CPCG06F17/17G06F17/18
Inventor 郭嵩李斌万涛张伟何晋秋李霖潘慧佘莹莹徐侃王磊李金余良甫管阳赵寅
Owner NO 719 RES INST CHINA SHIPBUILDING IND
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