CN105043342B - Unidirectional precise distance measuring triangulated height measuring method - Google Patents
Unidirectional precise distance measuring triangulated height measuring method Download PDFInfo
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Abstract
The invention provides an unidirectional precise distance measuring triangulated height measuring method. The unidirectional precise distance measuring triangulated height measuring method is mainly used for determining atmospheric vertical refraction coefficient in trigonometric leveling, and determining weighing value in network adjustment of ranging trigonometric leveling. The unidirectional precise distance measuring triangulated height measuring method mainly comprises following steps: laying of a reference point and points to be measured, and height determination of the reference point and the points to be measured; acquisition of sample data used for refraction coefficient correlativity determination; calculation of refraction coefficients of observed orientations; determination of refraction coefficient correlativity of observed orientations, and variance estimation; calculation of unidirectional distance measuring triangulated height; and weighing value determination and survey adjustment in unidirectional network adjustment of ranging trigonometric leveling. The unidirectional precise distance measuring triangulated height measuring method is suitable for height measurement in repeat and high risk environment, is capable of obtaining height of projects lack of bi-directional observation conditions, or projects used for increasing trigonometric leveling precision via determining refraction coefficient difference, or projects adopting unidirectional trigonometric leveling instead of bi-directional trigonometric leveling so as to reduce cost.
Description
Technical field
The invention belongs to Range finder triangle elevation field of measuring technique, and in particular to a kind of one-way precise Range finder triangle elevation is surveyed
Amount method.
Background technology
Although the sustainable development of current GNSS technologies provides great convenience for the acquisition of spatial data, in some specific bars
Under part, its plane positioning precision has been even up to submillimeter, but due to by geodetic height to elevation in normal transfer process high
The abnormal influence for obtaining the factor such as precision and its own certainty of measurement, limits its pushing away in higher precision measurement of higher degree field
Extensively, therefore elevation still largely uses traditional measurement means, the current degree of precision measurement of higher degree mainly has two ways, a kind of
It is the measurement of the level, another is precise distance measurement triangulated height, wherein measurement of the level precision highest, is surveyed in some Precision Elevations
Amount aspect almost can not be substituted, so, current one, second-class elevation obtain and rely primarily on precise leveling realization, but at some
Area, such as high-mountain gorge areas, the transmission of levelling elevation is extremely difficult, and some areas are even impossible
, but be just easier to realize using Range finder triangle elevation measurement, triangulated height has measure discrepancy in elevation speed soon, and measurement is simple,
The advantages of not limited by orographic condition, particularly more obvious in the larger initiative and advantages of the localities of the discrepancy in elevation, particularly in recent years, measurement sets
Standby angle measurement, range accuracy are improved constantly, and computational methods are also continuously available perfect so that Range finder triangle elevation certainty of measurement has aobvious
Write and improve, it is ripe to obtain third, fourth class elevation application using Range finder triangle elevation measuring method at present, home and abroad some
Scholar also carried out using the accurate triangulated height of range finding instead of second-class or even first order level(l)ing research or even production, such as Liaoning engineering
The Shen Chen of university, the Han Yun of China University of Geosciences, all water channels of Tianjin water power institute etc. have carried out correlative study and practice per capita, right
In the advantage for further playing triangulated height, efficient trigonometric levelling technology and Measurement and Data Processing method are persistently excavated,
With important research and application value.
But triangulated height also has the defect of its own, its influence factor mainly has two aspects, on the one hand by vertical angle
The limitation of certainty of measurement, is on the other hand mainly influenceed by atmospheric refraction and deviation of plumb line factor.Vertical angular measurement and air
Vertical refraction error is that (in application, the range finding length of side is general shorter, therefore deviation of plumb line shadow for the main error source of precise distance measurement triangulated height
Sound do not give individually consideration), with the continuous lifting of observation instrument precision, particularly sighted with automatic target detection, automatically, oneself
Dynamic angle measurement is continued to develop with range finding robot measurement, and vertical angle observation precision is significantly lifted, therefore, atmospheric refraction
Influence, in order to weaken influence of the refractive power to trigonometric levelling precision, is typically adopted as the important error source of trigonometric levelling
Effect of Refraction is weakened with the means of bilateral observation, if landform is symmetrical, is observed with the period, it is ensured that the environmental condition of measurement
It is closer to, this weakening effect is more satisfactory, but if orographic condition is asymmetric, or can not be entered in section at the same time
Row it is past, return observation, then toward, return survey during environment there occurs large change, then be difficult to preferably counteracting Atmosphere Refraction to three
The influence of angle elevation, even error can be increased under partial condition.Triangulated height refractive power relation is shown in accompanying drawing 1.It is shown as in figure from A points
Schematic diagram is observed to B points, i is instrument height, and s is that target is high, and a is vertical angle, is put down away from being D, and difference high is hAB.Due to vertical air
The influence of refractive power, sight line occur earthward or opposite direction refraction, sight line is not straight line but camber line.Dotted line is and receives in figure
To the direction of visual lines of Atmosphere Refraction influence.
Therefore, if project does not possess bilateral observation condition, especially for some personnel inconvenience reach and should not expose or
Unsuitable frequently exposed project, such as high-risk Landslide Monitoring project, limit level and to being measured to Range finder triangle elevation
Using.When being measured using unidirectional Range finder triangle elevation, due to being influenceed by factors such as atmospheric refraction, unidirectional range finding triangle is high
Cheng Jingdu is difficult to ensure that.
The content of the invention
The present invention is to provide a kind of one-way precise Range finder triangle elevation measuring method, it is therefore an objective to overcome described in background technology
Deficiency existing for unidirectional Range finder triangle elevation measurement prior art.Mainly solve SEQUENCING VERTICAL folding in Range finder triangle elevation measurement
The determination of backscatter extinction logarithmic ratio (key element such as implicit deviation of plumb line), and problem is weighed in adjustment of trigonometric leveling nekwork really.
The technical scheme is that：One-way precise Range finder triangle elevation measuring method, it is characterised in that including following step
Suddenly：
Step 1：Lay datum mark and tested point
This step is comprised the following specific steps that：
1) lays tested point according to engineering demand first, that is, lay observed object point；Opened on the basis of tested point determination
Open up the laying of datum mark, including laying for the datum mark to the direct observation of tested point and vertical for determining Real-Time Atmospheric
The laying of the reference direction point of refraction coefficient；
2) ensures that datum mark does not occur significantly deformation in a re-surveying cycle of datum mark, here using t methods of inspection pair
Each datum mark carries out displacement significance test to determine whether significantly deformation；
3) reference direction that is laid, the topographic structure that should be passed through with direction sight line to be measured and close towards situation, really
Both near-earth gas-bearing formation structures of guarantor are similar, and wherein reference direction refers to the direction determined by datum mark to reference direction point, side to be measured
To refer to determined by datum mark to tested point direction；
If 4) slip masses periphery does not meet step 2) and step 3) require datum mark, independently built in strange land
Auxiliary base point and reference direction, it is desirable to which the auxiliary base point that strange land is built should be with datum mark to tested point direction with reference direction
The topographic structure and direction that sight line is passed through are consistent, it is ensured that two places landform and direction are consistent, and illumination condition is consistent；
Step 2：Obtain datum mark and point height to be measured
After the completion of datum mark, tested point are laid, elevation known to translocation datum mark and tested point, using level or accurate survey
Away from the mode translocation of trigonometric levelling, benchmark point height wants Accurate Determining, and certainty of measurement is higher than one grade of tested point；It is to be measured
The initial height accuracy of point need to be higher than the required precision of design, and the project that the accurate elevation of tested point has difficulties is obtained for part,
Unidirectional Range finder triangle elevation measurement result is then used, the reference elevation that each inverting Vertical atmosphere re- fraction coefficient is used answers one
Cause；
Step 3：Obtaining sample data is used to determine reference direction with Vertical atmosphere re- fraction coefficient dependency relation in direction to be measured
The Range finder triangle elevation measurement sample data taken under multiple environment is related to direction to be measured to set up reference direction
Relation；By Continuous Observation datum mark and tested point direction ranging triangulated height data, using the number of passes high acquired in step 2
According to synchronously calculating lasting refraction coefficient；By the statistics to refraction coefficient, noise reduction process, set up reference direction with it is to be measured
The dependency relation in direction；Observation time avoids the cloudy day, is changed with the thermograde for ensureing complexity, it is ensured that under this observation condition
The parameter that daily observation needs is obtained, is observed using unique step, observation is encrypted in the case of air conversion acutely；
When tested point for being proposed in step 2 uses unidirectional Range finder triangle elevation, need to ensure in data acquisition
Rise, only tested point will not occur significantly deformation in the time period, for the point position for deforming, can by rising, only the time distinguish
Observation elevation, according to each moment of temporal interpolation point height to be measured；
For the project for possessing many phase Range finder triangle elevation measurement data, precision and reliability directly are carried out to these data
After inspection, calculating analysis is carried out as sample data；
The Range finder triangle elevation measurement sample data that either which kind of mode is obtained, is required to ensure every group of base for being gathered
Quasi- direction corresponds in time with direction ranging trigonometric levelling data to be measured；
Step 4：Determine each observed direction Vertical atmosphere re- fraction coefficient
The datum mark and tested point height value provided according to step 2, and the Range finder triangle elevation measurement that step 3 is obtained
Sample data, each group reference direction and Vertical atmosphere re- fraction coefficient k value in direction to be measured are solved according to equation below, wherein, each group
Reference direction direction containing auxiliary base：
K value computing formula are as follows：
K=1- [(h-STiltedly×Sinα-I+L)2R/(STiltedly×cosα)2] (2)
In above formula：H is known difference high, STiltedlyIt is oblique distance, α is vertical angle, and I is instrument height, and L is absolute altitude, and R is reference ellipsoid
Radius of curvature；
Vertical atmosphere re- fraction coefficient to being calculated carries out noise reduction process using small echo, or in regression equation parameter Estimation
During parameter Estimation, Vertical atmosphere re- fraction parameter variance m are carried out using Least Square methodk 2Estimation equation is as follows：
M in formulah 2、ms 2、ma 2、mI 2、mL 2Respectively corresponding discrepancy in elevation h, oblique distance STiltedly, vertical angle α, instrument height I, absolute altitude L
Variance；
When being calculated with tested point Continuous Observation, deformation point is then being observed, is stopping the time in the event of deforming in a short time
Point height to be measured is determined respectively, and the deformation point height at specified moment is obtained by temporal interpolation；
Step 5：Determine the dependency relation and refraction coefficient variance of reference direction and Vertical atmosphere re- fraction coefficient in direction to be measured
Estimate
On the basis of the Vertical atmosphere re- fraction coefficient k and its variance that step 4 determines, it is established that reference direction and direction to be measured
The Correlation model of Vertical atmosphere re- fraction coefficient；Both correlations are set up two methods：
Method one：Using Regression Equations reference direction and each directional correlation relation to be measured；
Method two：With reference to local near-earth gas-bearing formation distribution of temperature gradient, any direction is determined with orientation, elevation angle key element
Tested point Vertical atmosphere re- fraction coefficient computation model；
It is to be measured with each using Regression Equations reference direction based on the Vertical atmosphere re- fraction coefficient k that step 4 is calculated
The dependency relation in direction；First by drawing scatter diagram, determine that regression equation matches line style, then analyze reference direction and each
The correlation of Vertical atmosphere re- fraction coefficient in direction to be measured, the direction to be measured of related sexual satisfaction requirement is carried out according to project required precision
Screening, the principle of screening is required precision more high then higher to correlation requirement；By after correlation test, setting up reference direction
With the regression equation of each direction refraction coefficient to be measured, and the calculating of regression equation parameter and estimating for refraction coefficient variance are carried out
Calculate；
If observation station is more, pointwise determination is not easy to, then according to method two, is determined with orientation, elevation angle key element any
Direction tested point Vertical atmosphere re- fraction coefficient computation model；
Step 6：The determination of unidirectional Range finder triangle elevation
Step 5 defines the dependency relation of reference direction and direction to be measured, in each measurement process according to formula (2) really
Determine reference direction Vertical atmosphere re- fraction coefficient, in order to represent difference, the reference direction refraction coefficient without auxiliary base direction is adopted
Represented with KH：
KHi=1- [(hH-STiltedly×Sinα-I+L)2R/(STiltedly×cosα)2] (14)
In each monitoring process, by the discrepancy in elevation h for observing survey station point to datum markH, oblique distance STiltedly, vertical angle α, instrument height
I and absolute altitude L, calculates Vertical atmosphere re- fraction coefficient；
The COEFFICIENT K H that will be calculatediSubstitute into following formula：
KBi=a+bKHi (15)
In each measurement process, by measuring KHi, it is possible to obtain KBi, by KBiFollowing formula is substituted into, all directions are determined
Amendment Vee formation difference high：
hi=STiltedly×Sinαi+Ii-Li+(1-KBi)×(STiltedly×Cosαi)2/2R (16)
Step 7：Unidirectional Range finder triangle elevation net is weighed and adjustment really
Tested point is measured by two or more survey stations, can be formed and conformed to or closed path, then foundation
Closure error of elevation further corrects Vertical atmosphere re- fraction coefficient；Calculating process is as follows：
If measurement two datum marks to the discrepancy in elevation of tested point B1 is respectively h1And h2, two benchmark point heights are H1And H2, then
In the presence of following relation：
ω=H1+h1-h2-H2 (17)
ω in formula is exactly mis-tie misclosure, in theory ω=0, and then by ω, according to distance, really power is assigned to discrepancy in elevation h1And h2On,
By this numerical value, generation time formula (2) carries out the iterative calculation of k values again again；
Discrepancy in elevation observation indirect adjustment model is then set up, the optimal estimation value of each discrepancy in elevation is determined, model is as follows：
V is discrepancy in elevation observation correction；B is the coefficient matrix of adjustment Models；It is elevation unknown parameter；- f is adjustment mould
The constant term of type；Thus model determines elevation parameter
Wherein vertical adjustment is really weighed according to Range finder triangle elevation variance.
Re-surveying cycle described in step 1 refers to due to the influence of the factors such as geological movement and engineering construction, may influence
Stability to datum mark is measured, it is necessary to periodically measure control net, to find the deformation of datum mark in time and right
The datum mark for deforming assigns new Measurement results；A re-surveying cycle mentioned here refer to just duplicate measurements experience when
Between be spaced.
In the step 5, correlation determines that method is specifically to be realized with the most frequently used equation of linear regression, specifically such as
Under：
First, the premise for seeking the tropic is that variable tested point Vertical atmosphere re- fraction COEFFICIENT K B rolls over reference direction SEQUENCING VERTICAL
Backscatter extinction logarithmic ratio KH there must be linear correlation, and the index of linear correlation is correlation coefficient ρ：
Secondly, order：
KB=KH β+e (6)
As effective KB more than 2, it is necessary to carry out optimal estimation of parameters；
According to the principle of least square, parameter estimation least square solution formula is directly given：
β=(KHTPKH)-1KHTPKB (7)
Solution normal equation system is obtained：
With the multiple correlation coefficient of model to Regression Model Simulator degree comprehensive measurement：
Wherein：It is Vertical atmosphere re- fraction coefficient average value in direction to be measured,It is Vertical atmosphere re- fraction system in direction to be measured
Number calculated value；R2Bigger, i.e., closer to 1, then models fitting effect is better, and the irrelevance of equation is smaller；
Finally, its variance is evaluated：
If residual values are V, then：
V=KH β-KB (10)
The estimate of variance σ of refraction coefficient KB in direction to be measured2For：
In the step 7, the method for carrying out true power according to Range finder triangle elevation variance is as follows：
Unidirectionally Range finder triangle elevation variance evaluation formula is：
In formulams 2、ma 2、mI 2、mL 2Respectively corresponding discrepancy in elevation h, oblique distance STiltedly, vertical angle α, refraction coefficient k,
The variance yields of instrument height I and absolute altitude L, wherein ms 2、ma 2、mI 2、mL 2Variance is calculated using nominal or estimation precision,Directly use
The estimate of variance of refraction coefficient KB in direction to be measuredCalculated,
Error is σ in setting weight unit0, determine that each weights for surveying section triangulated height is：
Beneficial effects of the present invention：The present invention is design methodology, to improve unidirectional Range finder triangle elevation certainty of measurement.
The method mainly solves the determination of SEQUENCING VERTICAL refraction coefficient (implicit deviation of plumb line key element) in Range finder triangle elevation measurement, and
The problems such as being weighed really in Range finder triangle elevation net adjusted data.The method is to arrange some observation benchmark according to the tested point arranged
Point, and obtain datum mark and point height to be measured by observing.Obtain the sight synchronous with direction triangulated height to be measured of each group reference direction
Data, and benchmark point and tested point grid DEM each group reference direction and Vertical atmosphere re- fraction coefficient in direction to be measured are surveyed, and
All directions Vertical atmosphere re- fraction coefficient to being calculated carries out noise reduction process.According to each group Vertical atmosphere re- fraction after noise reduction process
Coefficient, sets up reference direction and Vertical atmosphere re- fraction coefficient Correlation model in direction to be measured, and can estimate SEQUENCING VERTICAL folding
Backscatter extinction logarithmic ratio variance.In the application, when the refraction coefficient for determining reference direction, just can obtain each according to the model set up and treat
The refraction coefficient in direction is surveyed, the direction refraction coefficient to be measured that will be obtained is substituted into triangulated height computing formula, just can obtain benchmark
Put to the tested point discrepancy in elevation and discrepancy in elevation variance yields.Last foundation discrepancy in elevation variance carries out trigonometric levelling networks and really weighs, and carries out one way range finding
Trigonometric levelling networks or elevation mixed network adjustment.
Advantages of the present invention is as follows：
1st, it is suitable to the measurement of higher degree work under repetition and high-risk environment, such as Level monitoring project is provided for a set of
High efficiency, high-precision Range finder triangle elevation solution；
2nd, measurement efficiency is higher, due to not using Bidirectional observation, can significantly reduce the field data collection time；
3rd, certainty of measurement is higher, such as measurement result and selection model reliability, can significantly attenuate due to coming and going survey environmental condition
Asymmetric, caused refraction coefficient is offset not thoroughly to the influence of result；
4th, measurement operation process is safer, because it need not carry out coming and going survey, after tested point can place prism, nobody
It is on duty, it is that continuously acquiring for danger zone Precision Elevation data provides possibility；
5th, measurement cost is lower, due to significantly improving for efficiency, more inexpensive solution is provided to repeat the measurement of higher degree
Scheme.
The present invention is described in further details below with reference to accompanying drawing.
Brief description of the drawings
Fig. 1 is triangulated height refractive power relation schematic diagram.
Fig. 2 is simulated experiment project schematic diagram.
Fig. 3 is the work flow of the inventive method.
Fig. 4 is the reference direction and Vertical atmosphere re- fraction index variation graph in direction to be measured after noise reduction.
Specific embodiment
Work flow of the invention is illustrated in figure 3, specific implementation step of the invention is as follows：
The laying of 1 reference direction and tested point
The laying of reference direction and tested point should build according to project actual landform feature, and main principle is as follows：
1) lays tested point (observed object point) according to engineering demand, and datum mark is carried out on the basis of tested point determination
Laying, datum mark include be used for the datum mark of the direct observation of tested point and for determining Real-Time Atmospheric vertical refraction coefficient
Reference direction point (note：The reference direction proposed in text refers to the direction determined by datum mark to reference direction point, direction to be measured
Refer to the direction determined by datum mark to tested point)；
2) datum marks should have stability higher, it can be ensured that significantly change does not occur in one re-surveying cycle of datum mark
Shape, uses t methods of inspection to carry out each datum mark displacement significance test to determine whether significantly deformation here；
3) datum mark that is laid is to reference direction, the landform knot that should be passed through to tested point direction sight line with datum mark
Structure and close towards situation, it is ensured that both near-earth gas-bearing formation structures are similar, to ensure that it is similar that reference direction and direction to be measured have
Thermograde structure.
If 4) slip masses periphery does not meet the 2nd article and the 3rd article stable reference direction point of requirement of the above, can be different
Ground is independent to build auxiliary base point and reference direction, it is desirable to which the auxiliary base point that strange land is built should be with datum mark extremely with reference direction
Topographic structure and approached towards situation that tested point direction sight line is passed through, and should not be away from survey area, it is ensured that two places landform and court
To close, sunshine basic synchronization.A project is simulated below to introduce universal laying principle.
Fig. 2 is simulated experiment project schematic diagram.
It is slip mass in the range of white line in figure, according to monitoring plan, B1, B2, B3, B4 is built on deformable body, at this
On the basis of, observation datum mark H1 and H2 are laid, wherein H1 is observation datum mark, and H2 is auxiliary datum mark, reference direction H1 → H2
Topographic structure is similar to deformation point direction, is allowed to a refractive power relation and there is correlation.
The acquisition of 2 datum marks and point height to be measured
After the completion of datum mark and tested point are laid, elevation known to translocation datum mark and tested point, using the measurement of the level or
Data Processing in Rigorous Trigonometric Leveling method, Accurate Determining benchmark point height, certainty of measurement should be higher than that one grade of tested point.For obtaining
The project that the accurate elevation of tested point has difficulties, such as only needs relative deformation's (such as Slip moinitoring), can use one way
Measurement result, but the reference elevation that inverting refraction coefficient is used every time should be consistent, by estimation, as long as each inverting refractive power system
Several used reference elevations are consistent, and it influences value very little to the relative refraction coefficient change for being resolved.
3 obtain the sample data that refraction coefficient dependency relation determines
Reference direction and the foundation of the dependency relation in direction to be measured, should obtain the observation sample under multiple environment, by even
Continuous observation datum mark and tested point direction ranging triangulated height data, using the altitude data acquired in step 2, can synchronously calculate
Go out lasting refractive power delta data, Continuous Observation (after being set to the sun from before the rise of the morning sun) datum mark and tested point,
Lasting refractive power data are obtained, it is related to direction to be measured for setting up reference direction to these data statistics and noise reduction process
Relation.Observation time should avoid the cloudy day, it is ensured that complicated thermograde change, it is ensured that daily sight is obtained under this observation condition
The parameter for needing is surveyed, observation is encrypted in the case of air conversion acutely.
Before and after the sun rises and the sun sets, refractive power change is rapid, recommends measurement in 20 minutes once, and observation every time is no less than
4 survey time (this can flexibly determine according to precision), remaining time can be observed once 1 hour.
When tested point for being proposed in step 2 uses unidirectional Range finder triangle elevation, need to ensure in data acquisition
Rise, only tested point will not occur significantly deformation in the time period, for the point position for deforming, can by rising, only the time distinguish
Observation elevation, each moment point height to be measured is gone out using temporal interpolation.
In actual production, for the project for possessing many phase Range finder triangle elevation measurement data, can be directly to these data
After carrying out precision and certificate authenticity, calculating analysis is carried out as sample data.
The Range finder triangle elevation measurement sample data that either which kind of mode is obtained, is required to ensure every group of base for being gathered
Quasi- direction corresponds in time with direction ranging trigonometric levelling data to be measured.
The selection of observation instrument determines according to accuracy of observation requirement.
The determination of 4 Vertical atmosphere re- fraction coefficients
For the short distance Range finder triangle elevation commonly used in engineering, vertical angle refractive power angle can be exchanged into vertical refraction coefficient.
Point-to-point transmission Range finder triangle elevation measures unidirectional elevation fundamental formular：
H=STiltedly×Sinα+I-L+(1-K)×(STiltedly×Cosα)2/2R (1)
In formula (1)：STiltedlyIt is oblique distance, α is vertical angle, instrument height I, the observed quantity of absolute altitude L systems, and radius of curvature R is known.
The datum mark and tested point height value provided according to step 2, and the Range finder triangle elevation measurement that step 3 is obtained
Sample data, each group reference direction (direction containing auxiliary base) and Vertical atmosphere re- fraction system in direction to be measured are solved according to equation below
Number k values：
K=1- [(h-STiltedly×Sinα-I+L)2R/(STiltedly×cosα)2] (2)
Wherein, h is known difference high, STiltedlyIt is oblique distance, α is vertical angle, and I is instrument height, and L is absolute altitude, and R is bent reference ellipsoid
Rate radius.
The refraction coefficient of Each point in time preferential direction can be thus determined, due to vertical angle, the discharge observation such as the length of side
Still there is error, cause refraction coefficient inevitably to contain noise error, it is necessary in the case of need to carry out noise reduction process,
We have carried out noise reduction process to the refraction coefficient for calculating using small echo in the case of experimental stage.Or in regression equation
In parameter estimation procedure, parameter Estimation is carried out using Least Square method, this is accomplished by estimating the variance of refraction coefficient,
According to law of propagation of errors, refraction coefficient k variance estimation equations are released as follows：
In formulams 2、ma 2、mI 2、mL 2Respectively corresponding discrepancy in elevation h, oblique distance STiltedly, vertical angle α, instrument height I and
The variance yields of absolute altitude L.
When being calculated with tested point Continuous Observation, deformation point will not typically occur significantly deformation in a short time, such as become
Shape, can observing, only the time determine point height to be measured respectively, the deformation point height at specified moment is obtained by temporal interpolation.
The determination of 5 reference directions and Vertical atmosphere re- fraction coefficient dependency relation in direction to be measured
On the basis of the Vertical atmosphere re- fraction coefficient k and its variance that step 4 determines, it is established that reference direction and direction to be measured
The Correlation model of Vertical atmosphere re- fraction coefficient.Both correlations are set up two methods：
1 using Regression Equations reference direction and each directional correlation relation to be measured；
2 combine local near-earth gas-bearing formation distribution of temperature gradient, and any direction tested point is determined with orientation, elevation angle key element
Vertical atmosphere re- fraction coefficient computation model.
Using Regression Equations reference direction and each directional correlation relation to be measured, the air calculated using step 4
Vertical refraction coefficient k, by drawing scatter diagram, matches regression equation line style, then analyzes reference direction and each direction to be measured
The correlation of Vertical atmosphere re- fraction coefficient, the index of linear correlation is correlation coefficient ρ, is calculated with following formula here：
It is again to carry out coming and going survey at the same moment, then just can effectively cut if topographic structure is symmetrical between two stations
Weak Effect of Refraction, otherwise comes and goes and surveys limited to the weakening of refractive power.It is as follows using Regression Equations dependency relation method：
First by drawing scatter diagram, line style is matched according to scatter diagram, and set up regression equation, establishing equation should try one's best letter
It is single, otherwise can bring bigger difficulty to the reliability of the adjustment model evaluation.
Commonly referred to as
It is Gauss-markov linear model (k units linear regression model (LRM)), and is abbreviated as (Y, X β, σ2In)
We introduce its implementation process by taking the most frequently used equation of linear regression as an example below.
It is KH to set reference direction Vertical atmosphere re- fraction coefficient, and deformation point or point-refraction coefficient to be measured are KB, linear to close
System may be set to following form：
KBi=a+bKHi+ei (4)
Wherein：A, b are coefficient, eiIt is random error.KB and KH obeys Linear Regression Model in One Unknown.
The premise for seeking regression straight line is that variable KB and KH there must be linear correlation, and otherwise matched somebody with somebody straight line is just without actual meaning
Justice, the index of linear correlation is correlation coefficient ρ, is calculated with following formula here：
| ρ | is closer to 1, and the effect of linear regression analysis is better；Especially, when | ρ |=1,
(KB1,KH1),(KB2,KH2),…,(KBn,KHn) will fully fall on straight line KB=a+bKH.It is generally acknowledged that：
If ρ ∈ [0.75,1], then positive correlation is very strong；If ρ ∈ [- 1, -0.75], then negatively correlated very strong；If ρ
∈ (- 0.75, -0.30] or r ∈ [0.30,0.75), then as Relativity；If ρ ∈ [- 0.25,0.25], then correlation
It is weaker.
By after correlation test, making：
KB=KH β+e (6)
As effective KB more than 2, it is necessary to carry out optimal estimation of parameters.
According to the principle of least square, parameter estimation least square solution formula is directly given：
β=(KHTPKH)-1KHTPKB (7)
Solution normal equation system is obtained：
Below with the multiple correlation coefficient of model to Regression Model Simulator degree comprehensive measurement：
Wherein：It is Vertical atmosphere re- fraction coefficient average value in direction to be measured,It is Vertical atmosphere re- fraction system in direction to be measured
Number calculated value.R2Bigger (closer to 1), then models fitting effect is better, and the irrelevance of equation is smaller.
Then above formula parameter substitution formula (3) just be can determine that into reference direction and tested point direction refractive power relational expression.Then
Evaluation wherein error：
If residual values are V, then：
V=KH β-KB (10)
The estimate of variance σ of refraction coefficient KB in direction to be measured2For：
Variance item can more intuitively reflect the precise manner that model is calculated.
The F statistics of variance analysis are counted in addition
The significance probability of variance analysis
P=P (F (1, n-2) ＞ F) (13)
Data above is calculated and analysis can be realized in softwares such as Matlab.
If observation station is more, pointwise determination is not easy to, can be determined with orientation, elevation angle key element according to the 2nd kind of method
Any direction tested point Vertical atmosphere re- fraction coefficient computation model.Specifically chosen that method is special according to required precision and environment
Levy to determine.
In addition, the point position arrangement in step 1 of being had a talk again with reference to this step content, datum mark arrangement should be according to the fitting of primary election
Model, is assessed because datum mark original reference measurement of higher degree error is to the influence degree of fitting precision, and difference should be distinguished in use
Featured items are studied respectively.
The determination of 6 unidirectional Range finder triangle elevations
When tested point observation is carried out, as long as observing reference direction oblique distance STiltedly, vertical angle α, instrument height I and absolute altitude L, just
The reference direction Vertical atmosphere re- fraction coefficient without auxiliary base direction at measurement moment can be calculated by formula (14)：
KH=1- [(hH-STiltedly×Sinα-I+L)2R/(STiltedly×cosα)2] (14)
Due to having had confirmed the dependency relation of reference direction and refraction coefficient KH in direction to be measured in steps of 5.By formula
(14) the COEFFICIENT K H for calculatingiSubstitution formula (15)：
KBi=a+bKHi (15)
Just refraction coefficient KB in direction to be measured can be obtainedi, by KBiSubstitution formula (16), so that it may after calculating all directions amendment
Precise distance measurement triangle difference high：
hi=STiltedly×Sinαi+Ii-Li+(1-KBi)×(STiltedly×Cosαi)2/2R (16)
7 unidirectional Range finder triangle elevation nets determine power and adjustment
If measured to tested point by two or more survey stations, can be formed and conformed to or closed path, can be according to
Refraction coefficient is further corrected according to closure error of elevation.Calculating process is as follows：
If being respectively h to the tested point B1 discrepancy in elevation by what two datum marks were measured1And h2, two benchmark point heights are H1With
H2, then in the presence of following relation：
ω=H1+h1-h2-H2 (17)
ω in formula is exactly mis-tie misclosure, in theory ω=0, and then by ω, according to distance, really power is assigned to discrepancy in elevation h1And h2On,
By this numerical value, generation time formula (2) carries out the iterative calculation of shading factor again again.On the problem really weighed in adjustment, having herein must
Discuss：
According to law of propagation of errors, if the middle error of h, S, a, k, I and L is respectively mh、ms、ma、mk、mI、mL, according to formula (1)
According to law of propagation of errors：
Ignore derivation below, directly give unidirectional discrepancy in elevation accuracy formula：
Above formula in actual applications, due to range error influence be generally much smaller than vertical angle error influence, be
Simplified calculating, ignores length of side influence, and simplified formula is as follows：
Wherein ms 2、ma 2、mI 2、mL 2Variance can be calculated using nominal or estimation precision, tested point SEQUENCING VERTICAL folding in this patent
Backscatter extinction logarithmic ratio KB values primary concern is that relative accuracy level, thereforeDirectly using the variance evaluation of refraction coefficient KB in direction to be measured
ValueCalculated,
The accuracy of observation of all directions, adjustment is really expedient to be determined according to observation variance.In setting weight unit by mistake
Difference is σ0, determine that each weights for surveying section triangulated height is：
Discrepancy in elevation observation indirect adjustment model is then set up, so that it is determined that the optimal estimation value of each discrepancy in elevation.Model is as follows：
V is discrepancy in elevation observation correction；B is the coefficient matrix of adjustment Models；It is elevation unknown parameter；- f is adjustment mould
The constant term of type.
Thus the Posterior weight battle array for calculating, carries out vertical adjustment, and finally determines elevation parameter
It is demonstrated experimentally that after using above method, in the case of using unidirectional measurement, can still obtain survey higher
Amount achievement, when a point is using the Measurement results more than both direction, can further improve its reliability and precision.
Below the present invention is further illustrated with a case
One massif accumulation body of the monitoring project system, Contents for Monitoring includes sedimentation and plane displacement monitoring two parts, wherein
Settlement monitoring uses second-order levelling, and plane uses robot measurement forward intersection, according to three equal precision measurement, based on experiment
Existing some conditions of project, verify that planning of experiments is as follows to the patented method precision and reliability：
Station is set in datum mark H1, reference direction is H2, determine the tested points such as B1, B2, B3, B4.
Observation time avoids the cloudy day, it is ensured that there is a thermograde changing environment complicated and changeable, with to its reliability
Verified, since at 6 points in the morning (before the sun rises), cut-off at 8 points in evening (sun sets) continues 14 sights of hour
Survey.
When the sun rises, refractive power change is rapid, and once, every time 4 survey time, subsequent 1 small for 6 points to 9: 20 minutes measurements
When observation once, after 6 pm every 20 minutes once.
Observation instrument is used and comes card company's T M30 robot measurements.
Data analysis content after measurement：
1st, thermograph is drawn out.Calculate the Vertical atmosphere re- fraction coefficient of each point, and the refractive power that each is put
Journey line is drawn, and carries out wavelet de-noising treatment to Vertical atmosphere re- fraction coefficient if necessary.
2nd, Vertical atmosphere re- fraction coefficient scatter diagram is drawn, is determined that the type of curve must be matched somebody with somebody according to scatter diagram, letter is selected here
Single equation of linear regression, and all directions graph uniformity is tested analysis with correlation test method.
3rd, with reference direction Vertical atmosphere re- fraction coefficient as variable, regression equation is set up by related direction, sets up each and treat
Determine the relation function in direction and reference direction.
4th, the statistic such as digital simulation goodness and F.
5th, carry out determining power according to priori triangulated height precision, with to the multiple directions adjustment of trigonometric levelling
6th, the analysis and inspection of some other key element, the output of achievement and the comparing with Level Height, statistics of error etc.
Content.
By experiment, when reference direction selection is reasonable, the length of side is not more than 500 meters, and one way measurement can substitute Bidirectional observation.
Fig. 4 is the reference direction and Vertical atmosphere re- fraction index variation charting in direction to be measured after noise reduction.
Preliminary conclusion：The Vertical atmosphere re- fraction coefficient that the experimental data is counted exceedes conventional 0.14, and (earth curvature becomes
Change influence part), morning Vertical atmosphere re- fraction absolute coefficient progressively diminishes, and noon is in a situation for concussion, to afternoon
Vertical atmosphere re- fraction coefficient is presented the trend that absolute value becomes big before and after sunset, and this trend can be found out from left figure.Small echo goes
After making an uproar, Vertical atmosphere re- fraction coefficient is presented situation of change shown in upper figure, and all directions Vertical atmosphere re- fraction coefficient is primarily present often
Number difference, this part variation is measured caused by error high in addition to Effect of Refraction itself, mainly in measurement process, because this part side
Long universal in 150 meters to 200 meters scopes, influence amount is very small.
To sum up, the inventive method includes：1) (datum mark includes being used for for the laying of datum mark and tested point (observed object point)
Datum mark to the direct observation of tested point and the reference direction point for determining Real-Time Atmospheric vertical refraction coefficient)；2) benchmark
The determination of point and point height to be measured；3) reference direction for determining for Vertical atmosphere re- fraction coefficient dependency relation and direction sample to be measured
Notebook data obtains (note：Reference direction refers to the direction determined by datum mark to reference direction point, and direction to be measured refers to by datum mark extremely
Direction determined by tested point)；4) determination of each observed direction Vertical atmosphere re- fraction coefficient；5) reference direction is big with direction to be measured
The determination of gas vertical refraction coefficient dependency relation and refraction coefficient variance evaluation；6) determination of unidirectional Range finder triangle elevation；7) it is single
Determine power and adjustment to Range finder triangle elevation net.
The present invention preferably solution can never possess round bidirectional measurement condition, and need the project of High Accuracy Observation, Yi Jiwei
Improve Range finder triangle elevation certainty of measurement, it is thus necessary to determine that more accurately difference of refraction coefficient, or use for cost-effective unidirectionally
Instead of the project of bidirectional ranging trigonometric levelling, more show especially for the measurement of higher degree program result for needing to repeat
Write.
The method is to arrange some observation datum marks according to the tested point arranged, and by observing acquisition datum mark and treating
Measuring point elevation.Obtain each group reference direction and triangulated height simultaneous observation data in direction to be measured, and benchmark point and tested point
Grid DEM each group reference direction and Vertical atmosphere re- fraction coefficient in direction to be measured, and all directions Vertical atmosphere re- fraction to being calculated
Coefficient carries out noise reduction process.According to each group Vertical atmosphere re- fraction coefficient after noise reduction process, reference direction is set up with direction to be measured
Vertical atmosphere re- fraction coefficient Correlation model, and Vertical atmosphere re- fraction parameter variance can be estimated.In the application, when determining
The refraction coefficient of reference direction, just can obtain the refraction coefficient in each direction to be measured according to the model set up, by treating for obtaining
Survey in direction refraction coefficient substitution triangulated height computing formula, just can obtain datum mark to the tested point discrepancy in elevation and discrepancy in elevation variance yields.
Last foundation discrepancy in elevation variance carries out trigonometric levelling networks and really weighs, and carries out one way Range finder triangle elevation net or elevation mixed network adjustment.
The present invention gives on by setting certain observation rule, being measured by unidirectional Range finder triangle elevation and obtaining high
A series of thinkings and method of Cheng Chengguo.The criterion that datum mark, reference direction and tested point for the inventive method are laid,
It is included in tested point periphery and lays reference direction, and auxiliary base point and base is carried out in the similar landform in strange land and under the conditions of
The thinking of quasi- direction arrangement.Give datum mark and the initial height accuracy requirement of tested point and acquisition methods.Give for phase
The sample data acquisition methods that pass relation determines, including the thinking of data is obtained by Continuous Observation, and to data with existing
Using principle, Noise reducing of data processing method, the method for calculating each group reference direction and Vertical atmosphere re- fraction coefficient in direction to be measured is entered
Row k value variance evaluation methods, give the thinking that Correlation model is set up between reference direction and direction to be measured, including basis
Scatter diagram determines that regression model matches the method for line style, and determines any direction tested point air with orientation, elevation angle key element
The thinking of vertical refraction coefficient, and regression equation correlation test method, parametric solution method, and one way triangulated height side
Difference method of estimation, is really weighed and error compensation method present invention includes based on triangulated height prior uncertainty, including relative datum direction
Vertical atmosphere re- fraction parameter variance method of estimation, triangulated height variance evaluation method, and one way trigonometric levelling networks weigh really
Method.
Advantages of the present invention is as follows：
1st, it is suitable to the measurement of higher degree work under repetition and high-risk environment, such as Level monitoring project is provided for a set of
High efficiency, high-precision Range finder triangle elevation solution；
2nd, measurement efficiency is higher, due to using nonreciprocal observation, significantly reduces the field data collection time；
3rd, certainty of measurement is higher, such as measurement result and selection model reliability, can significantly attenuate due to coming and going survey environmental condition
Asymmetric, caused refraction coefficient is offset not thoroughly to the influence of result；
4th, measurement operation process is safer, because it need not carry out coming and going survey, after tested point can place prism, nobody
It is on duty, it is that continuously acquiring for danger zone Precision Elevation data provides possibility；
5th, measurement cost is lower, due to significantly improving for efficiency, more inexpensive solution is provided to repeat the measurement of higher degree
Scheme.
The method can be embodied by Practical Project, such as the settlement monitoring of certain slip mass, and landslide slip is larger, is
Its deformation dynamics is obtained, 50 monitoring points have been laid in a slip mass, its measurement of higher degree required precision is third, works as use
Triangulated height comes and goes to be surveyed, and limit by landslide transportation condition, and landslide body region climbs extremely difficult, at least needs the 4 day time could
The settlement monitoring work of a cycle is completed, when the method is used, because the traffic of datum mark layout area is facilitated relatively, Ke Yiyong
One time just can complete all of monitoring, carry out within one month 4 second periodicity monitorings, often assemble and put 7 staff, one
Year just can save 1008 working days, while the activity duration significantly shortens.
There is no the part for describing in detail to belong to the known conventional means of the industry in present embodiment, do not chat one by one here
State.It is exemplified as above be only to of the invention for example, do not constitute the limitation to protection scope of the present invention, it is every with this
The same or analogous design of invention is belonged within protection scope of the present invention.
Claims (4)
1. one-way precise Range finder triangle elevation measuring method, it is characterised in that comprise the following steps：
Step 1：Lay datum mark and tested point
This step is comprised the following specific steps that：
1) lays tested point according to engineering demand first, that is, lay observed object point；Carry out base on the basis of tested point determination
Laying on schedule, including laying for the datum mark to the direct observation of tested point and for determining Real-Time Atmospheric vertical refraction
The laying of the reference direction point of coefficient；
2) ensures that datum mark does not occur significantly deformation in a re-surveying cycle of datum mark, here using t methods of inspection to each base
Displacement significance test is carried out on schedule to determine whether significantly deformation；
3) reference direction that is laid, the topographic structure that should be passed through with direction sight line to be measured and close towards situation, it is ensured that two
Person's near-earth gas-bearing formation structure is similar, and wherein reference direction refers to the direction determined by datum mark to reference direction point, and direction to be measured refers to
The direction determined by datum mark to tested point；
If 4) slip masses periphery does not meet step 2) and step 3) require datum mark, independently build auxiliary in strange land
Datum mark and reference direction, it is desirable to which the auxiliary base point that strange land is built should be with datum mark to tested point direction sight line with reference direction
The topographic structure and direction for being passed through are consistent, it is ensured that two places landform and direction are consistent, and illumination condition is consistent；
Step 2：Obtain datum mark and point height to be measured
After the completion of datum mark, tested point are laid, elevation known to translocation datum mark and tested point, using level or precise distance measurement three
The mode translocation of the angle measurement of higher degree, benchmark point height wants Accurate Determining, and certainty of measurement is higher than one grade of tested point；At the beginning of tested point
Beginning height accuracy need to be higher than the required precision of design, and the project that the accurate elevation of tested point has difficulties is obtained for part, then adopt
With unidirectional Range finder triangle elevation measurement result, the reference elevation that each inverting Vertical atmosphere re- fraction coefficient is used should be consistent；
Step 3：Obtaining sample data is used to determine reference direction with Vertical atmosphere re- fraction coefficient dependency relation in direction to be measured
The measurement sample data of the Range finder triangle elevation under multiple environment is taken to set up the dependency relation of reference direction and direction to be measured；
It is synchronous using the altitude data acquired in step 2 by Continuous Observation datum mark and tested point direction ranging triangulated height data
Calculate lasting refraction coefficient；By the statistics to refraction coefficient, noise reduction process, the phase of reference direction and direction to be measured is set up
Pass relation；Observation time avoids the cloudy day, is changed with the thermograde for ensureing complexity, it is ensured that obtain daily under this observation condition
The parameter for needing is observed, is observed using unique step, observation is encrypted in the case of air conversion acutely；
For in step 2 propose tested point use unidirectional Range finder triangle elevation in the case of, need to ensure data acquisition rise, only
In time period tested point will not occur significantly deformation, for the point position for deforming, can by rise, only the time observe height respectively
Journey, according to each moment of temporal interpolation point height to be measured；
For the project for possessing many phase Range finder triangle elevation measurement data, precision and certificate authenticity directly are carried out to these data
Afterwards, calculating analysis is carried out as sample data；
The Range finder triangle elevation measurement sample data that either which kind of mode is obtained, is required to ensure every group of benchmark side for being gathered
Corresponded in time to direction ranging trigonometric levelling data to be measured；
Step 4：Determine each observed direction Vertical atmosphere re- fraction coefficient
The datum mark and tested point height value provided according to step 2, and the Range finder triangle elevation measurement sample that step 3 is obtained
Data, each group reference direction and Vertical atmosphere re- fraction coefficient k value in direction to be measured are solved according to equation below, wherein, each group benchmark
Direction direction containing auxiliary base：
K value computing formula are as follows：
K=1- [(h-STiltedly×Sinα-I+L)2R/(STiltedly×cosα)2] (2)
In above formula：H is known difference high, STiltedlyIt is oblique distance, α is vertical angle, and I is instrument height, and L is absolute altitude, and R is reference ellipsoid curvature
Radius；
Vertical atmosphere re- fraction coefficient to being calculated carries out noise reduction process using small echo, or in regression equation parameter estimation procedure
Middle use Least Square method carries out parameter Estimation, Vertical atmosphere re- fraction parameter variance mk 2Estimation equation is as follows：
M in formulah 2、ms 2、ma 2、mI 2、mL 2Respectively corresponding discrepancy in elevation h, oblique distance STiltedly, vertical angle α, instrument height I, the side of absolute altitude L
Difference；
When being calculated with tested point Continuous Observation, deformation point is then being observed, is stopping time difference in the event of deforming in a short time
Point height to be measured is determined, the deformation point height at specified moment is obtained by temporal interpolation；
Step 5：Determine the dependency relation and refraction coefficient variance evaluation of reference direction and Vertical atmosphere re- fraction coefficient in direction to be measured
On the basis of the Vertical atmosphere re- fraction coefficient k and its variance that step 4 determines, it is established that reference direction and direction SEQUENCING VERTICAL to be measured
The Correlation model of refraction coefficient；Both correlations are set up two methods：
Method one：Using Regression Equations reference direction and each directional correlation relation to be measured；
Method two：With reference to local near-earth gas-bearing formation distribution of temperature gradient, determine that any direction is to be measured with orientation, elevation angle key element
Point Vertical atmosphere re- fraction coefficient computation model；
Based on the Vertical atmosphere re- fraction coefficient k that step 4 is calculated, using Regression Equations reference direction and each direction to be measured
Dependency relation；First by drawing scatter diagram, determine that regression equation matches line style, then analyze reference direction to be measured with each
The correlation of direction Vertical atmosphere re- fraction coefficient, the direction to be measured sieve of related sexual satisfaction requirement is carried out according to project required precision
Choosing, the principle of screening is required precision more high then higher to correlation requirement；By after correlation test, set up reference direction with
The regression equation of each direction refraction coefficient to be measured, and carry out the calculating of regression equation parameter and the estimation of refraction coefficient variance；
If observation station is more, pointwise determination is not easy to, then according to method two, any direction is determined with orientation, elevation angle key element
Tested point Vertical atmosphere re- fraction coefficient computation model；
Step 6：The determination of unidirectional Range finder triangle elevation
Step 5 defines the dependency relation of reference direction and direction to be measured, and base is determined according to formula (2) in each measurement process
Quasi- direction Vertical atmosphere re- fraction coefficient, in order to represent difference, the reference direction refraction coefficient without auxiliary base direction uses KH
Represent：
KHi=1- [(hH-STiltedly×Sinα-I+L)2R/(STiltedly×cosα)2] (14)
In each monitoring process, by the discrepancy in elevation h for observing survey station point to datum markH, oblique distance STiltedly, vertical angle α, instrument height I and mark
L high, calculates Vertical atmosphere re- fraction coefficient；
The COEFFICIENT K H that will be calculatediSubstitute into following formula：
KBi=a+bKHi (15)
In each measurement process, by measuring KHi, it is possible to obtain KBi, by KBiFollowing formula is substituted into, repairing for all directions is determined
Positive Vee formation difference high：
hi=STiltedly×Sinαi+Ii-Li+(1-KBi)×(STiltedly×Cosαi)2/2R (16)
Step 7：Unidirectional Range finder triangle elevation net is weighed and adjustment really
Tested point is measured by two or more survey stations, can be formed and conformed to or closed path, then according to elevation
Mis-tie misclosure further corrects Vertical atmosphere re- fraction coefficient；Calculating process is as follows：
If measurement two datum marks to the discrepancy in elevation of tested point B1 is respectively h1And h2, two benchmark point heights are H1And H2, then exist
Following relation：
ω=H1+h1-h2-H2 (17)
ω in formula is exactly mis-tie misclosure, in theory ω=0, and then by ω, according to distance, really power is assigned to discrepancy in elevation h1And h2On, then will
Generation time formula (2) carries out the iterative calculation of k values to this numerical value again；
Discrepancy in elevation observation indirect adjustment model is then set up, the optimal estimation value of each discrepancy in elevation is determined, model is as follows：
V is discrepancy in elevation observation correction；B is the coefficient matrix of adjustment Models；It is elevation unknown parameter；- f is adjustment Models
Constant term；Thus model determines elevation parameter
Wherein vertical adjustment is really weighed according to Range finder triangle elevation variance.
2. one-way precise Range finder triangle elevation measuring method as claimed in claim 1, it is characterised in that described in step 1
Re-surveying cycle refer to due to the factors such as geological movement and engineering construction influence, the stability of datum mark may be influenced whether,
Need periodically to measure and control net measurement, to find the deformation of datum mark, and the datum mark imparting to deforming in time
New Measurement results；A re-surveying cycle mentioned here refers to just the time interval of duplicate measurements experience.
3. one-way precise Range finder triangle elevation measuring method as claimed in claim 1, it is characterised in that in the step 5, phase
Closing property determines that method is specifically to be realized with the most frequently used equation of linear regression, specific as follows：
First, the premise for seeking the tropic is variable tested point Vertical atmosphere re- fraction COEFFICIENT K B and reference direction Vertical atmosphere re- fraction system
Number KH there must be linear correlation, and the index of linear correlation is correlation coefficient ρ：
Secondly, order：
KB=KH β+e (6)
As effective KB more than 2, it is necessary to carry out optimal estimation of parameters；
According to the principle of least square, parameter estimation least square solution formula is directly given：
β=(KHTPKH)-1KHTPKB (7)
Solution normal equation system is obtained：
With the multiple correlation coefficient of model to Regression Model Simulator degree comprehensive measurement：
Wherein：It is Vertical atmosphere re- fraction coefficient average value in direction to be measured,It is Vertical atmosphere re- fraction coefficient meter in direction to be measured
Calculation value；R2Bigger, i.e., closer to 1, then models fitting effect is better, and the irrelevance of equation is smaller；
Finally, its variance is evaluated：
If residual values are V, then：
V=KH β-KB (10)
The estimate of variance σ of refraction coefficient KB in direction to be measured2For：
4. one-way precise Range finder triangle elevation measuring method as claimed in claim 1, it is characterised in that in the step 7, according to
The method for carrying out true power according to Range finder triangle elevation variance is as follows：
Unidirectionally Range finder triangle elevation variance evaluation formula is：
In formulams 2、ma 2、mI 2、mL 2Respectively corresponding discrepancy in elevation h, oblique distance STiltedly, vertical angle α, refraction coefficient k, instrument
The variance yields of I high and absolute altitude L, wherein ms 2、ma 2、mI 2、mL 2Variance is calculated using nominal or estimation precision,Directly using to be measured
The estimate of variance of direction refraction coefficient KBCalculated,Error is σ in setting weight unit0, determine that each is surveyed
Section triangulated height weights be：
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