Minimum chi-square estimation method

A technology of extremely small chi-square and new value, which is applied in the field of numerical analysis and reliability, and can solve the problems that the coefficient value of the smallest chi-square cannot be determined, the method mechanism is unclear, and the algorithm is not optimal, etc., so as to achieve easy programming and avoid information loss , the effect of simple method

Inactive Publication Date: 2017-12-01
BEIJING INST OF AEROSPACE CONTROL DEVICES
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  • Description
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Problems solved by technology

[0018] (1) The solution is not unique, which means that this method cannot determine the coefficient value that minimizes chi-square;
[0019] (2) The mechanism of the method is not clear, and the algorithm is not optimal
[0020] (3) It is easy to cause information loss

Method used

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Embodiment 1

[0099] Let the given argument be (x i }Corresponding measurement sequence{f i }, i=1,2,...,n; where n=10, such as figure 2 Shown is the measurement sequence given in the embodiment of the present invention; the specific values ​​of the data are shown in Table 1. Fit a linear curve and select two basis functions with The fitting function constructed by this is y(x)=a 1 x-a 2 .

[0100] Table 1

[0101]

[0102]

[0103] Using the solution method of the present invention, the initial value is a 1 = 1.857130151514106, a 2 =6.939083333409633, after 8 iterations of calculation, a is finally obtained 1 = 1.854996089750836, a 2 =6.975801527797882. That is, the a calculated from the 7th iteration 1 , A 2 The first 10 digits after the decimal point correspond to the same value, which is the optimal value. The iterative process is like image 3 Shown, where image 3 a and image 3 b respectively represents a 1 , A 2 Iterative process. Put a 1 And a 2 Substituting into the fitting functi...

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Abstract

The invention relates to a minimal chi-square estimation method, which constructs the function form of the fitting curve on the basis of a linearly independent basis function set, adopts an iterative calculation method to provide the coefficients in the function of the fitting curve, and puts The theoretical value obtained after the coefficients are substituted into the fitting function has the characteristic of the smallest chi-square. The minimal chi-square estimation method of the present invention avoids the multi-solution problem of the fminsearch function, has a unique solution and can guarantee the smallest chi-square, and ensures the solution accuracy, avoiding the problem of missing information in the solution process, and the minimal chi-square estimation method of the present invention has strong logic, easy programming, simple method and easy implementation.

Description

Technical field [0001] The invention relates to a minimal chi-square estimation method, belonging to the technical field of numerical analysis and reliability. Background technique [0002] There are many functions in scientific experiments and engineering applications, and their analytical expressions are unknown. For example, with the extension of storage time, the performance and parameters of inertial devices will change, but the change process can only be measured by a series of nodes x by experimental observation. i Value on f i . The problem now is to seek the approximation function y(x) of the test point sequence, or to use geometric language to find a curve y(x) to fit (smooth) these n points. [0003] In the related theory of fitness test, χ 2 Statistics are often used to test whether the common distribution of a group of independent samples belongs to a distribution family with specific properties. Minimal chi-square estimation refers to minimizing χ 2 The parameters o...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/15
CPCG06F17/15
Inventor 魏宗康江麒彭智宏魏珍虹
Owner BEIJING INST OF AEROSPACE CONTROL DEVICES
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