CN104807442A - Automatic multidimensional gross error detection method - Google Patents

Abstract

The invention discloses an automatic multidimensional gross error detection method. The automatic multidimensional gross error detection method comprises following steps: 1) laying of a leveling network is carried out, and a leveling scheme is designed; 2) field leveling is carried out; 3) a mathematical model is established based on observation data; and 4) WK diagnosis is carried out successively until no influential point is detected. It is shown by a large amount of actual leveling data that data processing efficiency can be increased greatly by subjecting original leveling observation data to a plurality of WK diagnosis, and choosing influential points into a second group for part least-square estimation. The automatic multidimensional gross error detection method is capable of increasing gross error detection speed in leveling observation greatly, is convenient for programming realization, and possesses relatively high practical value in engineering application.

Description

A kind of multidimensional Detection of Gross Errors method automatically

Technical field

The present invention relates to a kind of WK of combining Distance geometry partial least squares to carry out the method for the multidimensional Detection of Gross Errors in measurement of the level, belong to " geodesy " technical field in " Surveying Science and Technology " subject.

Background technology

Measurement of the level is a kind of the most frequently used method measuring ground point elevation.Determining that topocentric elevation is a groundwork in measuring, is carry out control survey, measure the smashed parts and one of the basic foundation of construction lofting.Carry out measurement of the level tool in engineering practice to have very great significance.

Inevitably can occur rough error in the process of measurement of the level, rough error point can affect measurement of the level data process effects, and the estimation that even can lead to errors time serious affects drawing of correct conclusion.Therefore carry out Detection of Gross Errors to measurement of the level data to be extremely necessary.

Since eighties of last century Baarda at the end of the sixties has proposed since data snooping, the detection of observation rough error, identify that with processing be the study hotspot of Measurement and Data Processing theory always.Through the continuous effort of many scholars, this theory achieves larger progress, defines two kinds of different rough error tupes: rough error be included into the average drifting mould of function model and rough error be included into the Robust filter pattern of probabilistic model.Along with the continuous progress of observation method, occur that the probability of multiple rough error increases.Study the detection of multiple rough error, identification and treatment theory and also seem abnormal important.

Partial least squares is a kind of Detection of Gross Errors method based on average drifting pattern.The method is first divided into groups to observed reading, observed reading not containing rough error is put in one group, and the observed reading containing rough error is put in another group, adjustment principle makes the quadratic sum not containing the observed reading correction of rough error minimum, instead of the quadratic sum of whole observed reading correction is minimum.But the group technology that former partial least squares adopts be search procedure one by one, greatly, especially when observed reading data volume is large, efficiency comparison is low for the method search work amount.

For search procedure search work amount is large one by one, inefficient problem, the present invention proposes and adopt WK Furthest Neighbor to carry out the method for dividing into groups.The method can search out the Highly Influential case in leveling observation data, second group that then Highly Influential case is put into partial least squares.Examples prove through a large amount of: diagnose as long as carry out several WK to original level observation data, pick out Highly Influential case and put into second group, carry out partial least squares, greatly can improve data-handling efficiency.The inventive method substantially increases the speed of multidimensional Detection of Gross Errors in leveling observation, is also easy to programming realization, and engineer applied has good practical value.

Summary of the invention

Goal of the invention: the object of the present invention is to provide a kind of multidimensional Detection of Gross Errors method in measurement of the level, uses the multidimensional rough error in the method detection measurement of the level to calculate easy, greatly can improve the efficiency of multidimensional Detection of Gross Errors.

Technical scheme: the present invention of the present invention by the following technical solutions:

The first step: lay leveling network in the region needing to carry out measurement of the level, design measurement of the level scheme, in order to ensure the quality of data, needs to carry out redundant observation;

Second step: adopt spirit-leveling instrument to carry out field data collection, obtain the n section discrepancy in elevation between each leveling point;

3rd step: utilize whole leveling observation data founding mathematical models, sets up

Function model: L=AX+ Δ (1)

Probabilistic model: E (Δ)=0, D (L)=D (Δ)=σ ₀ ²q=σ ₀ ²p ^-1(2)

In formula, L is that observation vector is tieed up in n × 1; A is that n × t maintains matrix number, and t is Essential Observations; X is that unknown parameter vector is tieed up in t × 1; Δ is that error vector is tieed up in n × 1; E () is mathematical expectation, and D () is variance---covariance matrix; σ ₀ ²for unit power variance; Q is association's factor matrices; P is power battle array.

According to minimum least square adjustment method, calculate:

The least-squares estimation of unknown parameter X:

$\hat{X}={\left(A^T\mathrm{PA}\right)}^{-1}{A}^T\mathrm{PL}---\left(3\right)$

Observed reading correction:

$V=A\hat{X}-L---\left(4\right)$

Association's factor matrices of correction:

Q _VV＝(I-H)Q _LL(5)

In formula, H is hat matrix:

H＝A(A ^TPA) ^-1A ^TP (6)

Variance of unit weight valuation:

${{\widehat{\mathrm{\σ}}}_0}^2=\frac{V^T\mathrm{PV}}{n-t}---\left(7\right)$

4th step: the WK distance value calculating each leveling observation data, each WK distance has corresponding statistic tantile, and compare, select rough error data and be placed on second group, remaining data are placed on first group;

C. the WK distance value of each observed reading:

${\mathrm{wk}}_i=\left|\frac{v_i}{{\∂}_0\left(i\right)\sqrt{Q_{V_i{V}_i}}}\right|*{\left(\frac{h_{\mathrm{ii}}}{1-h_{\mathrm{ii}}}\right)}^{\frac{1}{2}}---\left(8\right)$

V in formula _ifor i-th in (4) formula (i=1,2 ... n) correction of individual observed reading, for removing the σ of i-th observed reading ₀valuation, for i-th main diagonal element in (5) formula, h _iifor i-th main diagonal element of hat matrix H.

D. the statistic tantile of WK distance is calculated

Work as wk _i> wk _{i divides}time, i-th point is Highly Influential case.Wherein α is level of significance.

5th step: to first group of datacycle the 3rd and the 4th step in the 4th step, each circulation level of signifiance α reduces successively, as α gets 0.1,0.05,0.025,0.01,0.005,0.0025 successively ..., until do not have Highly Influential case to be detected again.Every three of the rule that α chooses successively is one group and is chosen for 0.1,0.05,0.025 another group and then choosing 1/10th of this group numeral more successively successively and connects successively, constantly circulates.

Compared with prior art, its beneficial effect is in the present invention: compared with existing partial least square method of adjustment, the present invention substantially increases the efficiency of grouping.Prove through a large amount of data instances, diagnose as long as the present invention carries out several WK to initial condition quasi-accurate observation, by the Highly Influential case diagnosed out put into second group, carry out partial least square, greatly can improve the rough error data-handling efficiency in measurement of the level, and data processing quality can be improved, obtain good data processing precision.This inventive method is convenient to programming realization, has good engineering practical value.

Accompanying drawing explanation

Fig. 1 is the level checking network schematic diagram described in embodiment.

Embodiment

Below technical solution of the present invention is described in detail, but protection scope of the present invention is not limited to described embodiment.

Embodiment 1:

When describing specific implementation process, in conjunction with certain specific embodiment, the inventive method is elaborated.Embodiment, as shown in Figure 1.

(1) leveling network is laid, design measurement of the level scheme.In order to ensure the quality of data, need to carry out redundant observation.

Concrete embodiment, leveling network is laid as shown in Figure 1, and in figure, arrow represents observed ray, and A, F are known point, and elevation is respectively 0.000m and 11.414m.

(2) adopt spirit-leveling instrument to carry out field data collection, obtain 13 sections of discrepancy in elevation between each leveling point.

Obtaining leveling observation value vector by observation is: h=[73.794,14.007,14.171,71.949,59.785,12.159,15.364,5.794,3.040,0.164,3.204,9.571,62.376] represent that (unit is m) to discrepancy in elevation truth vector, S=[2.0,1.9,1.5,1.0,1.4,1.3,1.1,2.1,1.5,1.1,1.2,0.9,1.6] each leveling line distance (unit is km) is represented.Calculating weight unit medial error is: 0.0015m, intends the rough error of-9mm, 8mm and-8mm at the 1st, 4,8 discrepancy in elevation data patrix.

(3) carry out first time WK to diagnose

Discrepancy in elevation observation number is n=13, and Essential Observations t=5, redundant observation number is r=n-t=13-5=8.Utilize whole observation data founding mathematical models, calculate the WK distance value of each observation data, calculate the statistic tantile that each WK distance is corresponding, level of significance α herein gets 0.10, the data that WK distance value is greater than tantile picked out, calculated case is as table 1:

Table 1 first time WK diagnostics table

With No. * be greater than the data of statistic tantile for WK distance value.

(4) second time WK diagnosis is carried out

If level of significance α now gets 0.05, calculated case is in table 2:

Table 2 second time WK diagnostics table

With No. * be greater than the data of statistic tantile for WK distance value.

(5) carry out third time WK to diagnose

If level of significance α now gets 0.025, calculated case is in table 3:

Table 3 third time WK diagnostics table

With No. * be greater than the data of statistic tantile for WK distance value.

(6) the 4th WK diagnosis is carried out

If level of significance α now gets 0.01, calculated case is in table 4:

Table 4 the 4th WK diagnostics table

4th time WK diagnoses the Highly Influential case number obtained to be zero, and stop WK diagnosis to this step, grouping terminates.As can be seen from above result of calculation, through four WK diagnosis, 1,4, No. 8 leveling observation value adding rough error is all detected, the 12nd discrepancy in elevation observed reading is also had to be detected in addition, this is because WK diagnosis is comparatively responsive, when more for unnecessary leveling observation, there is no large impact.

As mentioned above, although represented with reference to specific preferred embodiment and described the present invention, it shall not be construed as the restriction to the present invention self.Under the spirit and scope of the present invention prerequisite not departing from claims definition, various change can be made in the form and details to it.

Claims (2)

1. the multidimensional rough error automatic detection method in measurement of the level, is characterized in that, comprise the following steps:

1) read the leveling data of pre-set level net, described leveling data is carried out the leveling data of redundant observation;

2) step 1 is utilized) whole leveling observation data founding mathematical models of obtaining,

Function model: L=AX+ Δ (1)

Probabilistic model: E (Δ)=0, D (L)=D (Δ)=σ ₀ ²q=σ ₀ ²p ^-1(2)

In formula, L is that observation vector is tieed up in n × 1; A is that n × t maintains matrix number, and t is Essential Observations; X is that unknown parameter vector is tieed up in t × 1; Δ is that error vector is tieed up in n × 1; E () is mathematical expectation, and D () is variance---covariance matrix; σ ₀ ²for unit power variance; Q is association's factor matrices; P is power battle array.

According to least square adjustment method, calculate:

The least-squares estimation of unknown parameter X:

$\hat{X}={\left(A^T\mathrm{PA}\right)}^{-1}{A}^T\mathrm{PL}---\left(3\right)$

Observed reading correction:

$V=A\hat{X}-L---\left(4\right)$

Association's factor matrices of correction:

Q _VV＝(I-H)Q _LL(5)

In formula, H is hat matrix:

H＝A(A ^TPA) ^-1A ^TP (6)

Variance of unit weight valuation:

${{\widehat{\mathrm{\σ}}}_0}^2=\frac{V^T\mathrm{PV}}{n-t}---\left(7\right)$

3) the WK distance value of each leveling observation data is calculated, and the statistic tantile of correspondence, compare, select rough error data and be placed on second group, remaining data are placed on first group;

A. the WK distance value of each observed reading:

${\mathrm{wk}}_i=\left|\frac{v_i}{{\widehat{\mathrm{\σ}}}_0\left(i\right)\sqrt{Q_{v_i{v}_i}}}\right|*{\left(\frac{h_{\mathrm{ii}}}{1-h_{\mathrm{ii}}}\right)}^{\frac{1}{2}}---\left(8\right)$

V in formula _ifor i-th in (4) formula (i=1,2 ... n) correction of individual observed reading, for removing the σ of i-th observed reading ₀valuation, for i-th main diagonal element in (5) formula, h _iifor i-th main diagonal element in (6) formula.

B. the statistic tantile of WK distance is calculated

Work as wk _i>wk _{i divides}time, i-th point is Highly Influential case; Wherein α is level of significance.

4) if the 3rd) there is Highly Influential case to occur in step, using the 3rd) first group of data in step are as whole leveling observation datacycle the 2nd) and the 3rd) step, each circulation level of signifiance α reduces successively, as α get 0.1 successively, 0.05,0.025,0.01,0.005 ..., until do not have Highly Influential case to be detected again.If the 3rd) do not have Highly Influential case to occur in step, terminate.

2. the multidimensional Detection of Gross Errors method in measurement of the level according to claim 1, it is characterized in that described level of significance α reduces value successively, be specially and get 0.1,0.05,0.025,0.01,0.005,0.0025 successively ... be detected to there is no Highly Influential case.