CN102800128A - Method for establishing geomorphic description precision model by utilizing gplotmatrix and regression analysis - Google Patents

Abstract

The invention relates to a method for establishing a terrain description accuracy model by using a scatter diagram matrix and regression analysis, which can effectively solve the problem of the DEM terrain description accuracy model between the digital elevation model terrain description error and its influencing factors. The technical solution is to aim at the DEM terrain The interaction between the description error and its influencing factors, but it is difficult to distinguish which factors have the greatest impact on the DEM terrain description error, what is the influence law between them, and what kind of mathematical relationship exists. Make full use of the visual image, Intuitive feature, combining mathematical modeling and visualization technology, constructing a method of establishing multivariate nonlinear data model through function fitting, and finally establishing a new DEM terrain description accuracy model, the invention not only increases the mathematical modeling Intuitive and visual features, and increase the scientificity and accuracy of visual data analysis, is an innovation in the research of digital elevation model error analysis and precision.

Description

Method of Establishing Terrain Description Accuracy Model Using Scatterplot Matrix and Regression Analysis

technical field

The invention relates to a digital elevation model, in particular to a method for establishing a terrain description accuracy model by using a scatter diagram matrix and regression analysis.

Background technique

Digital Elevation Model (DEM for short) error analysis and accuracy research has always been a hot spot of concern, and it is also an important part throughout the process of DEM modeling and application. Kubik (1998) submitted a work report on "Review and Prospect of Digital Elevation Model" at the 16th International Society for Photogrammetry and Remote Sensing (ISPRS). He pointed out that although the problem of DEM accuracy has been basically completed in theory, with the deepening of research on spatial data quality and uncertainty, the impact factors, propagation mechanism and related analysis of DEM terrain description errors still need further research.

At present, most people use the method of combining mathematical statistics and experiments to analyze the accuracy of DEM. Holmes (2000) analyzed the spatial distribution of DEM errors using histograms and discrete point maps when studying the impact of DEM errors with a 30-meter spatial resolution of the US Geological Survey on terrain features; Chen Nan and Wang Qinmin (2006 ) When analyzing the influence of different spatial resolution DEMs on the Loess Plateau on the accuracy of slope extraction, the relationship between the DEM terrain description error and spatial resolution was studied in the form of a line graph; Liu Min and Tang Guoan (2007) based on artificial rainfall experiments In the analysis of the variation characteristics of the topographic index at different development stages in the loess small watershed, the frequency distribution map of the topographic index along with rainfall erosion was drawn; when Li Jiang (2007) studied the relationship between terrain simplification and DEM topographic description error, he first used the frequency distribution map to analyze the The impact of terrain simplification on the slope, and then on this basis, using the scatter diagram to analyze the correlation between the DEM terrain description error and the average slope, and achieved good results. However, with the in-depth research on the DEM terrain description accuracy model in recent years, it is found that only the traditional mathematical statistics combined with experiments can only describe the influence of a single influencing factor on the DEM terrain description accuracy. The research on the relationship between multiple influencing factors (referring to more than two) still needs another solution.

As a visual comparison technology, visualization displays the uncertainty of data errors in front of users in a visible way, and closely links the uncertainty of data errors with map drawing and GIS spatial analysis, making users more intuitive and more intuitive. Image, more correctly understand the described object. Therefore, the significance of DEM terrain description error visualization is not only to describe the relationship between DEM terrain description error and its influencing factors, but more importantly, it can be combined with regression analysis to establish a more reasonable DEM terrain description error function model: Tang Guoan (2001) established a mathematical model of DEM terrain description error, spatial resolution, and section curvature; Wang Guangxia (2004) revised the model, and studied the functional relationship between DEM terrain description error, spatial resolution, and average slope, and further improved the The accuracy of the model. However, due to the vast territory of our country, the types of landforms are complex and changeable. As a result, when analyzing landforms such as glaciers and mountains, the fitting effect of the above precision model is not good. To test the establishment process of its accuracy model, the reasons may include two aspects: one is the terrain factor that affects the error of the DEM terrain description, which is reflected in the unreasonable selection of the terrain factor when constructing the DEM terrain description accuracy model (referring to its relationship with the DEM terrain description The error correlation is too small) or the selection of terrain factors is not enough (referring to the complexity of the DEM terrain description accuracy model, the three variables cannot reveal the essence of the model); on the other hand, the DEM terrain description accuracy model that can meet all current landform types Difficult to use a unified mathematical formula to express.

Therefore, the focus of this paper on building a multivariate data model using visualization and regression analysis is to mine the correlation features between DEM terrain description errors and their influencing factors, and to determine whether a unified DEM terrain description accuracy model can be established according to the correlation. However, there are many influencing factors on the error of DEM terrain description, how to select the most suitable influencing factors becomes the key to solve this problem. A scatterplot matrix is a visualization method that describes the relationship between two variables in multidimensional data. It can compare and analyze the correlation of different variables in a graph, and at the same time, it can visualize the correlation information of two variables, so as to facilitate the discovery and selection of the fitting function between the two variables. Therefore, the idea of scatter plot matrix and regression analysis can be used to solve the above existing problems.

Contents of the invention

In view of the above situation, in order to solve the defects of the prior art, the purpose of the present invention is to provide a method of using scatter plot matrix and regression analysis to establish a terrain description accuracy model, which can effectively solve the problem of Digital Elevation Model (Digital Elevation Model, referred to as DEM) The problem of DEM terrain description accuracy model between terrain description error and its influencing factors.

The technical problem to be solved by the present invention is: aiming at the interaction between the DEM terrain description error and its influencing factors, it is difficult to distinguish which factors have the greatest influence on the DEM terrain description error, what are the influence rules between them, and there are In order to solve the problem of mathematical relationship, a method of combining scatter plot matrix and regression analysis to establish a terrain description accuracy model is proposed. This method makes full use of the visual image and intuitive features, and combines mathematical modeling with visualization technology. A method of establishing a multivariate nonlinear data model is constructed by means of function fitting, and finally a new DEM terrain description accuracy model is established.

The technical solution of the present invention is: utilize scatter diagram matrix and regression analysis to establish the terrain description accuracy model method, the steps are as follows:

The first step is to draw a scatter matrix of digital elevation model terrain description error and its influencing factors (including spatial resolution, slope, profile curvature, relative height difference, concave-convex coefficient, slope aspect and roughness), and determine and use an influencing factor Fitting terrain description accuracy model;

(1.1) Draw the scatter diagram matrix of the digital elevation model terrain description error and its influencing factors. Let the terrain description error be Y, and the related influencing factor be X. Since there are more than one influencing factors, here we set them as X ₁ , X ₂ , …, X _k , where k represents the number of influencing factors, and k>1, draw the scatter diagram matrix of the terrain description error Y and its influencing factors X ₁ , X ₂ ,…, X _k , and at each scatter point A confidence ellipse is drawn on the graph, and the long and short radii of the ellipse reflect the correlation between the two variables, that is, the flatter the ellipse, the stronger the correlation;

(1.2) By observing the scatter diagram matrix obtained in the previous step, it is judged whether this method can be used to establish a terrain description accuracy model, that is, according to the scatter diagram characteristics of the terrain description error Y and each influencing factor X _i , where i represents the ith , and i=1, 2, ..., k, to judge whether there is a certain functional relationship between them. If the terrain description error Y and the scatter diagram features of any X _i are very chaotic, one or more polynomials cannot be used to establish the relationship between them, that is, there is no obvious relationship between Y and any X _i , Then this method cannot be used to establish a functional model between the terrain description error Y and the influencing factor X, and the modeling ends. If there is a functional relationship between the terrain description error Y and any X _i , it is further determined whether a polynomial can be used to fit the graphic features of Y and X _i ;

(1.3) If yes, judge the correlation between terrain description error Y and all influencing factors X _i that meet the current conditions, and assume that the best correlation X ₁ fitting formula (1) is selected, where n is the fitting polynomial The number of times, a ₀ , a ₁ ,..., a _n-1 , a _n , to establish a terrain description accuracy model, and the modeling ends,

$Y=\left[\begin{array}{ccccc}{a}_0& a_1& \·\·\·& a_{\mathrm{no}-1}& a_{\mathrm{no}}\end{array}\right]\&Center\; Dot;\left[\begin{array}{c}1\\ x_1^1\\ .\\ .\\ .\\ x_1^{\mathrm{no}-1}\\ x_1^{\mathrm{no}}\end{array}\right]$ Formula 1);

(1.4) If not, multiple sets of polynomials are used to fit the terrain description accuracy model respectively. First, divide the Y and _Xi scatter diagrams that meet the current conditions into several different areas. The basis for the division is that Y and _Xi in each area can be represented by a polynomial. Then, find the variable _Xi , In order to facilitate the next step of fitting, the lower the polynomial degree of fitting Y in each area, the better, that is, the scatter plot characteristics of Xi _and Y in each area are best shown as linear correlations, assuming it is X ₁ , finally, fit the formula (2) according to its graphic features, where n is the number of fitted polynomials, m is the number of fitted polynomials, that is, the number of divided areas, a _pq is the coefficient of the fitted polynomials, p represents row p, q represents column q, and p=1, 2,..., m, q=0, 1,..., n,

                            公式（2）；

Formula (2);

(1.5) A new variable A can be extracted from the coefficient matrix of formula (2), let A _q = (a _1q , a _2q ,…, a _mq ) ^T , where q represents the qth, and q=0, 1,… , n, then formula (2) can be written as formula (3), and then proceed to the second step,

$Y=\left[\begin{array}{ccccc}{A}_0& {\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="HDA00001992562300012.png"\; state="\{\{state\}\}">A</figure-callout>}}_1& \&Center\; Dot;\&Center\; Dot;\&Center\; Dot;& A_{\mathrm{no}-1}& A_{\mathrm{no}}\end{array}\right]\&Center\; Dot;\left[\begin{array}{c}1\\ x_1^1\\ .\\ .\\ .\\ x_1^{\mathrm{no}-1}\\ x_1^{\mathrm{no}}\end{array}\right]$ Formula (3);

In the second step, use the new variables A ₀ , A ₁ ... A _n-1 obtained in (1.5), A _n to replace the digital elevation model terrain description error and combine it with the remaining variables, that is, remove the X ₁ that has been fitted in the first step Perform fitting, repeat this step until a function can be used to establish a terrain description accuracy model;

(2.1) Considering that the terrain description error Y has been fitted with _X1 , it can be considered that the influence of the _X1 variable on the terrain description error has been eliminated. Therefore, in order to exclude the effect of X ₁ on A _q , in the fitting process of A _q and X _i , the value of i is 2, 3...,k, and the selection of the base in X _i should be based on X ₁ is a fixed value, that is, try to select m bases with the smallest variation range of _X1 . Finally, draw the scatter plot matrix of A _q , X ₂ , X ₃ , ..., X _k , where q represents the qth, and q=0, 1, ..., n;

(2.2) Observe the scatter diagram matrix obtained in (2.1) to judge whether this method can be used to establish a unified terrain description accuracy model. That is, according to the scatter diagram characteristics of A _q and each influencing factor _Xi , where i represents the i-th one, and i=2, 3,..., k, judge whether there is a certain functional relationship between them. If the scatter diagram features of A _q and any X _i are very chaotic, and one or more polynomials cannot be used to establish the relationship between them, that is, there is no obvious relationship between A _q and any X _i , then This method cannot be used to establish a unified functional model between the terrain description error Y and the influencing factor X. After the modeling is completed, if there is a functional relationship between A _q and any X _i , it is further determined whether a polynomial can be used to fit A _q and X _i graphic features;

，为拟合多项式的系数，继续进行第3步，(2.3) If yes, judge the correlation between A _q and all influencing factors X _i that meet the current conditions, and choose the X ₂ fitting formula (4) with the best correlation, where n ₂ is A _q fitting degree of polynomial, b ₀ , b ₁ ,…,

, To fit the coefficients of the polynomial, proceed to step 3,

$A_q=\left[\begin{array}{ccccc}{b}_0& {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HDA00001992562300012.png"\; state="\{\{state\}\}">b</figure-callout>}}_1& \&CenterDot;\&Center\; Dot;\&CenterDot;& b_{{\mathrm{no}}_2-1}& b_{{\mathrm{no}}_2}\end{array}\right]\&Center\; Dot;\left[\begin{array}{c}1\\ x_2^1\\ .\\ .\\ .\\ x_2^{{\mathrm{no}}_2-1}\\ x_2^{{\mathrm{no}}_2}\end{array}\right]$ Formula (4);

为A_q拟合多项式的系数，p₂表示第p₂行，q₂表示第q₂列，且p₂=1，2，…，m₂，q₂=0，1，…，n₂，(2.4) If not, use multiple sets of polynomials to fit the relationship model between A _q and _Xi respectively. For the method, refer to 1.4. First, divide the scatter diagram that meets the current conditions A _q and _Xi into several different areas. The division is based on the fact that A _q and _Xi of each area after division can be represented by a polynomial. Then, look for the variable X _i , in order to facilitate the next step of fitting, the lower the polynomial degree of fitting with A _q in each area, the better, that is, the scatter plot characteristics of Xi _and A _q in each area are the best If it is linear correlation, assume it is X ₂ , and use multiple functions to fit the formula (5) according to its graphic characteristics, where n ₂ is the degree of A _q fitting polynomial, m ₂ is the degree of A _q fitting polynomial number,

is the coefficient of the polynomial fitting for A _q , p ₂ represents the p _2th row, q ₂ represents the q _2th column, and p ₂ =1, 2,..., m ₂ , q ₂ =0, 1,..., n ₂ ,

                        公式（5）；

Formula (5);

=（

，

，…，）^T，其中，q₂=0，1，…，n₂，则公式（5）可写为公式（6），然后利用新获取的变量重复进行第2步，直到可以用一个函数拟合，(2.5) A series of new variables B can be extracted from the coefficient matrix of formula (5), let

=(

,

,..., ) ^T , where, q ₂ =0, 1, ..., n ₂ , then formula (5) can be written as formula (6), and then use the newly acquired variables to repeat step 2 until a function can be used to fit,

$A_q=\left[\begin{array}{ccccc}{B}_0& {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA00001992562300012.png"\; state="\{\{state\}\}">B</figure-callout>}}_1& \&CenterDot;\&CenterDot;\&CenterDot;& B_{({\mathrm{no}}_2-1)}& B_{{\mathrm{no}}_2}\end{array}\right]\&Center\; Dot;\left[\begin{array}{c}1\\ x_2^1\\ .\\ .\\ .\\ x_2^{{\mathrm{no}}_2-1}\\ x_2^{{\mathrm{no}}_2}\end{array}\right]$ Formula (6);

Step 3: sort out the fitting process of digital elevation model terrain description error Y and influencing factor X, and substitute the formula obtained in step 2 into the formula obtained in step 1 to obtain formula (7),

$Y=f(x_1,x_2,\&CenterDot;\&CenterDot;\&CenterDot;,x_K)$ Formula (7);

Among them, k represents the number of influencing factors, and k>1, the description accuracy model is completed.

Description of drawings

Fig. 1 is a flow chart of the process of establishing a DEM terrain description accuracy model using a scatter diagram matrix and regression analysis in the present invention.

Fig. 2 is the DEM terrain description error and spatial resolution, slope, profile curvature, relative height difference, concave-convex coefficient, slope aspect, and seven influencing factors of the experimental data of the four types of landforms of hills, loess, glaciers and Zhongshan in the present invention The scatterplot matrix of is used to judge and select fitting variables and fitting functions.

Figure 3 is a scatter plot matrix of DEM terrain description error and spatial resolution, which is used to more clearly identify graphic features.

Fig. 4 is a scatter diagram matrix of coefficients A ₁ , A ₀ and six topographic factors (slope, section curvature, relative height difference, concave-convex coefficient, aspect and roughness) of the DEM of the present invention with a resolution of 10 meters.

Detailed ways

The specific implementation manners of the present invention will be described in further detail below in conjunction with the accompanying drawings.

As shown in Figure 1, the specific implementation steps of the present invention are as follows:

Data preparation, first, select four pieces of contour data of hills, loess, Zhongshan and glacier with a scale of 1:50,000, and interpolate these four pieces of data into regular grid DEM data with a resolution of 10 meters , and consider it to be the true value; then, further use the newly acquired four pieces of regular grid DEM data to extract six pieces of DEM data with spatial resolutions of 20m, 30m, 40m, 50m, 60m, and 70m at equal intervals (the extracted standard reference "1:50,000 Digital Elevation Model (DEM) Production Technical Regulations"); finally, calculate the DEM terrain description error of 24 maps.

The first step is to draw the scatter plot matrix of the DEM terrain description error and its influencing factors, and judge and use an influencing factor to fit the terrain description accuracy model.

(1.1) First, draw the scatter diagram matrix of the seven influencing factors of DEM terrain description error and spatial resolution, slope, profile curvature, relative height difference, concave-convex coefficient, slope aspect, and roughness, as shown in Figure 2.

(1.2) It can be seen that there is no uniform distribution trend between the DEM terrain description error and the seven influencing factors. Therefore, it is difficult to use a function to fit the functional relationship between the DEM terrain description error and a single influencing factor, so skip Step (1.3).

(1.4) In addition, it is found that there are specific distribution characteristics between the DEM terrain description error, spatial resolution, and terrain factors at a certain stage. Basically, the distribution of DEM terrain description errors and influencing factors can be divided into four independent categories according to the terrain type. In the area of , that is, the graphical characteristics of the DEM terrain description error can be fitted with the help of multiple sets of functions, and the linear relationship between the DEM terrain description error and the resolution is more obvious. Therefore, zooming in on the scatter plots of the DEM terrain description error and spatial resolution of the four types of landforms, as shown in Figure 3, can linearly fit the relationship between the DEM terrain description error and the spatial resolution of the four types of landforms. Let E _t be the error of DEM terrain description, R be the spatial resolution, and formula (8) can be obtained by using formula (2).

${\mathrm{E.}}_t=\left[\begin{array}{cc}-0.9941& 0.1010\\ -0.7364& 0.0991\\ 0.0985& 0.1912\\ -2.0085& 0.5733\end{array}\right]\&Center\; Dot;\left[\begin{array}{c}1\\ {\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HDA00001992562300012.png"\; state="\{\{state\}\}">R</figure-callout>}}^1\end{array}\right]$ Formula (8)

(1.5) Extract the equation coefficients of formula (8), set A ₀ and A ₁ , then A ₁ = (0.1010, 0.0991, 0.1912, 0.5733) ^T , A ₀ = (-0.9941, -0.7364, 0.0985, -2.0085) ^T , that is, formula (8) can be written as formula (9) using formula (3), and proceed to the next step.

${\mathrm{E.}}_t=\left[\begin{array}{cc}{A}_0& {\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="HDA00001992562300012.png"\; state="\{\{state\}\}">A</figure-callout>}}_1\end{array}\right]\&CenterDot;\left[\begin{array}{c}1\\ {\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HDA00001992562300012.png"\; state="\{\{state\}\}">R</figure-callout>}}^1\end{array}\right]$ Formula (9)

In the second step, use the obtained new variables A ₁ and A ₀ to replace the DEM terrain description error and continue fitting with the remaining variables (referring to the six influencing factors except spatial resolution).

(2.1) Since the influence of spatial resolution on the error of DEM terrain description has been taken into account in the first step, and when the spatial resolution is fixed, the number of samples of any other influencing factor is exactly 4 (with the new variable A ₁ , the size of the base in A ₀ is equal), so here directly draw coefficients A ₁ , A ₀ and six topographic factors (slope, profile curvature, relative height difference, concave-convex coefficient, aspect and roughness of DEM with 10-meter resolution ) scatterplot matrix, as shown in Figure 4.

(2.2) It can be seen that the scatter diagram features of slope, relative height difference and equation coefficient A ₁ are obvious, while the scatter diagram characteristics of concave-convex coefficient and coefficient A ₀ are obvious, and the coefficients A ₁ and A ₀ can be respectively Regression analysis with only one polynomial.

(2.3) For the coefficient A ₁ , although the slope and the relative height difference have a certain functional relationship with it, the correlation between the relative height difference and the coefficient A ₁ is higher, and the quadratic fitting effect is better, so the relative height difference is set as H, formula (10) is obtained by using formula (4).

$A_1=\left[\begin{array}{ccc}0.1147& -0.017& 0.0047\end{array}\right]\&CenterDot;\left[\begin{array}{c}1\\ h^1\\ h^2\end{array}\right]$ Formula (10)

For the coefficient A ₀ , the linear fitting effect of the concave-convex coefficient and the coefficient A ₀ is better. Assuming that the concave-convex coefficient is C, formula (11) can be obtained by using formula (4).

$A_0=\left[\begin{array}{cc}12125& -12125\end{array}\right]\&Center\; Dot;\left[\begin{array}{c}1\\ C\end{array}\right]$ Formula (11)

In the third step, use formulas (10) and (11) to sort out formula (8), and obtain the relationship formula (12) between DEM terrain description error E _t and spatial resolution R, relative height difference H, and concave-convex coefficient C:

${\mathrm{E.}}_t=(0.0047h^2-0.017h+0.1147)-R12125C+12125$ Formula (12)

Accuracy analysis, another 12 pieces of regular grid DEM data with a resolution of 10 meters (including three pieces of hills, loess, glaciers, and Zhongshan landforms) were selected, and compared with the old formula (13) of the existing DEM terrain description accuracy model (Wang Guangxia (2004) improved DEM terrain description accuracy model, where E _t is the DEM terrain description error, R is the spatial resolution, and V is the profile curvature), the present invention uses the new DEM terrain description error and spatial resolution, relative height difference, The relationship formula (12) of the concave-convex coefficient recalculates the DEM terrain description errors of these 12 pieces of data, and the results are shown in Table 1.

${\mathrm{E.}}_t=(0.0061V+0.0027)R+0.0010V^2-0.0649+0.5695$ Formula (13)

Table 1 Calculation results of DEM terrain description error of 12 pieces of DEM data (unit: meter)

As can be seen from Table 1, the DEM terrain description error calculated by the new formula of the present invention is more consistent with the real error in glacial landforms and Zhongshan landforms. Wherein, the DEM terrain description error of Zhongshan landforms has improved by an order of magnitude, but in hilly landforms and Zhongshan landforms. For the loess landform, the fitting effects of the two sets of formulas are different. In order to further compare the advantages and disadvantages of the two sets of formulas, this paper calculates the correlation between the real error of DEM and the old formula and the new formula in hills and loess landforms, and Zhongshan and glacier landforms. Coefficients and standard deviations are shown in Table 2.

Table 2 Correlation coefficient and standard deviation between real error and DEM terrain description error calculated by old formula and new formula

It can be seen from Table 2 that although the fitting effect of the new formula on hills and loess landforms is comparable to that of the original formula, its fitting effect on glacial landforms and Zhongshan landforms has been greatly improved, reaching the goal of expanding the application range of terrain description accuracy models. Purpose. Therefore, it is scientific and effective to use the scatter plot matrix and regression analysis to establish the terrain description accuracy model.

The advantages of the present invention are:

(1) The present invention combines the visualization technology with the method of mathematical statistics, and uses the scatter plot matrix to solve the method of selecting fitting variables and fitting functions in multivariate data regression analysis, which not only increases the intuitive and vivid features of mathematical modeling , and increase the scientificity and accuracy of visual data analysis.

(2) The present invention utilizes the scatter plot matrix characteristics of multivariate data and the idea of repeated curve fitting, and proposes a method for establishing a nonlinear function model between multivariate data, which provides a basis for building multivariate data models in other fields in the future. A kind of reference and reference.

(3) The present invention establishes a DEM terrain description accuracy model, which reveals the variation rule of the DEM terrain description error and its influencing factors, which is beneficial to guide people to understand and grasp the essence of DEM accuracy.

Claims (1)

1. a method of utilizing scatter diagram matrix and regretional analysis to set up the topograph accuracy model is characterized in that, may further comprise the steps:

The 1st step; Draw the scatter diagram matrix of digital elevation model topograph error and its factor of influence; Factor of influence comprises spatial resolution, the gradient, section curvature, relative relief, concavo-convex coefficient, aspect and roughness, judges and utilizes a factor of influence match topograph accuracy model:

(1.1) the scatter diagram matrix of drafting digital elevation model topograph error and its factor of influence, establishing the topograph error is Y, relative factor of influence is X, owing to more than one of factor of influence, is made as X here respectively ₁, X ₂..., X _k, wherein, k representes the number of factor of influence, and k>1, draw topograph error Y and its factor of influence X ₁, X ₂..., X _kThe scatter diagram matrix, and on each scatter diagram, draw fiducial confidence ellipse, the correlativity of oval two variablees of long and short radius reflection, promptly ellipse is flat more, correlativity is strong more;

Can the scatter diagram matrix judgement that (1.2) obtains through observation (1.1) utilize this method to set up the topograph accuracy model, promptly according to topograph error Y and each factor of influence X _iThe scatter diagram characteristic, wherein, i representes the i number, i=1,2 ..., k judges whether there is certain functional relation between them, if topograph error Y and any X _iThe scatter diagram characteristic all show very chaotic, can't set up connecting each other between them with one or more polynomial expressions, i.e. Y and any X _iDo not have tangible relationship characteristic, then can not utilize this method to set up the function model between topograph error Y and the factor of influence X, modeling finishes, if topograph error Y and any X _iThere is funtcional relationship, then further confirms to utilize a fitting of a polynomial Y and X _iGraphic feature;

(1.3) if ability is then judged topograph error Y and satisfied all factor of influence X of precondition of working as _iCorrelativity size, and hypothesis is selected the best X of correlativity ₁Fitting formula (1), wherein, n is the number of times of polynomial fitting, a ₀, a ₁..., a _N-1, a _nBe the coefficient of polynomial fitting, set up the topograph accuracy model, modeling finishes,

$Y=\left[\begin{array}{ccccc}{a}_0& a_1& \&CenterDot;\&CenterDot;\&CenterDot;& a_{n-1}& a_n\end{array}\right]\&CenterDot;\left[\begin{array}{c}1\\ X_1^1\\ .\\ .\\ .\\ X_1^{n-1}\\ X_1^n\end{array}\right]$ Formula (1);

(1.4) if can not, then utilize many group polynomial expressions match topograph accuracy models respectively.At first, will satisfy as precondition Y and X _iScatter diagram be divided into several different zones, the foundation of division is for dividing back each regional Y and X _iCan utilize a polynomial repressentation, then, seek variable X _i,, make the degree of polynomial of itself and Y match in each zone low more good more, i.e. X for the ease of next step match _iPreferably show as linear relevantly in each regional scatter diagram characteristic with Y, suppose that it is X ₁, last, according to its graphic feature fitting formula (2), wherein, n is the number of times of polynomial fitting, m is the number of polynomial fitting, the number of regions of promptly dividing, a _PqBe the coefficient of polynomial fitting, p representes that p is capable, and q representes the q row, and p=1,2 ..., m, q=0,1 ..., n,

formula (2);

(1.5) matrix of coefficients of formula (2) can extract new variables A, establishes A _q=(a _1q, a _2q..., a _Mq) ^T, wherein, q representes q, and q=0,1 ..., n, then formula (2) can be written as formula (3), carries out for the 2nd step again,

$Y=\left[\begin{array}{ccccc}{A}_0& A_1& \&CenterDot;\&CenterDot;\&CenterDot;& A_{n-1}& A_n\end{array}\right]\&CenterDot;\left[\begin{array}{c}1\\ X_1^1\\ .\\ .\\ .\\ X_1^{n-1}\\ X_1^n\end{array}\right]$ Formula (3);

The 2nd step, the new variables A that utilizes (1.5) to obtain ₀, A ₁A _N-1, A _nReplace digital elevation model topograph error and and surplus variable, promptly remove the X of match in the 1st step ₁Carry out match, repeat this step and up to utilizing a function to set up the topograph accuracy model:

(2.1) consider topograph error Y with X ₁Function is crossed in match, can think X ₁Variable is eliminated the influence of topograph error, in order to get rid of X ₁To A _qEffect, at A _qWith X _iFit procedure in, wherein, the value of i is 2,3 ..., k, and X _iChoosing of middle base should be based on X ₁Be fixed value, promptly choose X as far as possible ₁M the base that variation range is minimum, last, draw A _q, X ₂, X ₃..., X _kThe scatter diagram matrix, wherein, q representes q, and q=0,1 ..., n;

(2.2) observe scatter diagram matrix that (2.1) obtain and judge and to utilize this method to set up unified topograph accuracy model, promptly according to A _qWith each factor of influence X _iThe scatter diagram characteristic, wherein, i representes i, and i=2,3 ..., k judges whether there is certain functional relation between them, if A _qWith any X _iThe scatter diagram characteristic all show very chaotic, can't set up connecting each other between them, i.e. A with one or more polynomial expressions _qWith any X _iDo not have tangible relationship characteristic, then can not utilize this method to set up unified topograph error Y and the function model between the factor of influence X, modeling finishes, if A _qWith any X _iThere is funtcional relationship, then further confirms to utilize a fitting of a polynomial A _qWith X _iGraphic feature;

(2.3) if ability is then judged A _qWith all influence factor X that satisfy when precondition _iCorrelativity size, and hypothesis is selected the best X of correlativity ₂Fitting formula (4), wherein, n ₂Be A _qThe number of times of polynomial fitting, b ₀, b ₁...,

,

Be the coefficient of polynomial fitting,

$A_q=\left[\begin{array}{ccccc}{b}_0& b_1& \&CenterDot;\&CenterDot;\&CenterDot;& b_{n_2-1}& b_{n_2}\end{array}\right]\&CenterDot;\left[\begin{array}{c}1\\ X_2^1\\ .\\ .\\ .\\ X_2^{n_2-1}\\ X_2^{n_2}\end{array}\right]$ Formula (4);

(2.4) if can not, then utilize many group polynomial expressions match A respectively _qWith X _iRelational model, method at first, will satisfy as precondition A with reference to (1.4) _qWith X _iScatter diagram be divided into several different zones, the foundation of division is for dividing each regional A of back _qWith X _iCan utilize a polynomial repressentation, then, seek variable X _i,, make itself and A for the ease of next step match _qThe degree of polynomial of match is low more good more in each zone, i.e. X _iWith A _qPreferably show as linear being correlated with in each regional scatter diagram characteristic, suppose that it is X ₂, and utilize a plurality of function fitting formulas (5) according to its graphic feature, and wherein, n ₂Be A _qThe number of times of polynomial fitting, m ₂Be A _qThe number of polynomial fitting,

Be A _qThe coefficient of polynomial fitting, p ₂Represent p ₂OK, q ₂Represent q ₂Row, and p ₂=1,2 ..., m ₂, q ₂=0,1 ..., n ₂,

formula (5);

(2.5) matrix of coefficients of formula (5) can extract a series of new variables B again, establishes

=( , ...,

) ^T, wherein, q ₂=0,1 ..., n ₂, then formula (5) can be written as formula (6), utilizes the variable B newly obtain to repeat for the 2nd step then, up to can using a function match,

$A_q=\left[\begin{array}{ccccc}{B}_0& B_1& \&CenterDot;\&CenterDot;\&CenterDot;& B_{(n_2-1)}& B_{n_2}\end{array}\right]\&CenterDot;\left[\begin{array}{c}1\\ X_2^1\\ .\\ .\\ .\\ X_2^{n_2-1}\\ X_2^{n_2}\end{array}\right]$ Formula (6);

The 3rd step: the fit procedure of arrangement digital elevation model topograph error Y and factor of influence X, the 2nd step gained formula is updated to the 1st step gained formula, get formula (7),

$Y=f(X_1,X_2,\&CenterDot;\&CenterDot;\&CenterDot;,X_K)$ Formula (7);

Wherein, k representes the number of factor of influence, and k>1, describe accuracy model and accomplish.

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