CN110424201A - The calculation method of track unknown point is measured under high speed railway track not leveling state - Google Patents
The calculation method of track unknown point is measured under high speed railway track not leveling state Download PDFInfo
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- CN110424201A CN110424201A CN201910763916.5A CN201910763916A CN110424201A CN 110424201 A CN110424201 A CN 110424201A CN 201910763916 A CN201910763916 A CN 201910763916A CN 110424201 A CN110424201 A CN 110424201A
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- E—FIXED CONSTRUCTIONS
- E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
- E01B—PERMANENT WAY; PERMANENT-WAY TOOLS; MACHINES FOR MAKING RAILWAYS OF ALL KINDS
- E01B35/00—Applications of measuring apparatus or devices for track-building purposes
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- E—FIXED CONSTRUCTIONS
- E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
- E01B—PERMANENT WAY; PERMANENT-WAY TOOLS; MACHINES FOR MAKING RAILWAYS OF ALL KINDS
- E01B35/00—Applications of measuring apparatus or devices for track-building purposes
- E01B35/06—Applications of measuring apparatus or devices for track-building purposes for measuring irregularities in longitudinal direction
- E01B35/08—Applications of measuring apparatus or devices for track-building purposes for measuring irregularities in longitudinal direction for levelling
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Abstract
The invention discloses under a kind of high speed railway track not leveling state measure track unknown point calculation method, comprising steps of one, freely set up total station；Two, the observational equation group between the centre point of total station and the control point CPIII is established；Three, the error equation between the centre point of total station and the control point CPIII is determined；Four, three-dimensional coordinate of the centre point p of total station in CPIII coordinate system is calculated；Five, the coordinate of high speed railway track upper rail unknown point is calculated.The present invention is on the basis of the state coordinate at the control point CPIII, the centre point of total station is considered as phase center, by the error equation and Quan Zhen that construct space length, the CPIII coordinate of the centre point of total station is found out using the principle of least square, then can be obtained by the coordinate of track unknown point by method of polar coordinates.
Description
Technical field
The invention belongs to track unknown point computing technique fields, and in particular under a kind of high speed railway track not leveling state
Measure the calculation method of track unknown point.
Background technique
In high speed railway track accurate adjustment measurement process, coordinate system belonging to high speed railway track accurate adjustment is state coordinate
It is, as CPIII coordinate system mainly to flatten situation using instrument in the measurement process of existing trackage detection
Under Freedom Station, and it is station bulbus cordis coordinate system that Free Station with Total Station electronic Thacheometer method, which obtains, it is therefore desirable to be converted by coordinate
Coordinate in topocentric coordinate system is converted to CPIII coordinate system by method.The obtained point of total station in Freedom Station measurement
Coordinate is topocentric coordinate system, i.e., using total station phase center as origin, establishes left hand rectangular coordinate system in space system, Freedom Station
In every time survey station measurement range it is smaller, need repeatedly dispose leveling instrument, it is meant that measurement need repeatedly carry out instrument it is whole
It is flat, the progress and efficiency of track accurate adjustment can be seriously affected in this way.Therefore, it is direct in the case where not flattening nowadays to lack one kind
It disposes and measures track unknown point under high speed railway track not leveling state that instrument measures work and that operating efficiency is high
Calculation method.
Summary of the invention
In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is that providing a kind of high-speed railway
The calculation method that track unknown point is measured under track not leveling state, on the basis of the state coordinate at the control point CPIII, by whole station
The centre point of instrument is considered as phase center, by constructing the error equation and Quan Zhen of space length, utilizes the principle of least square
The CPIII coordinate of the centre point of total station is found out, then can be obtained by the coordinate of track unknown point by method of polar coordinates, just
In popularization and use.
In order to solve the above technical problems, the technical solution adopted by the present invention is that: it is surveyed under high speed railway track not leveling state
Measure the calculation method of track unknown point, which is characterized in that method includes the following steps:
Step 1: freely setting up total station: the I control point CPIII is chosen altogether in the two sides of high speed railway track, at I
Region between the control point CPIII freely sets up total station, wherein I is the positive integer not less than 3；
Step 2: establishing the observational equation group between the centre point of total station and the control point CPIII: according to formulaEstablish the observation between the centre point of total station and the control point CPIII
Equation group, wherein SiFor the distance at point p to i-th control point CPIII of centre of total station, as observed quantity, i is
The number and i=1 at the control point CPIII, 2 ..., I；VSiFor the seat at point p to i-th control point CPIII of centre of total station
Mark correction, (xp,yp,zp) it is three-dimensional coordinate of the centre point p of total station in CPIII coordinate system, (xi,yi,zi)
For three-dimensional coordinate of i-th of control point CPIII in CPIII coordinate system；
Step 3: determining the error equation between the centre point and the control point CPIII of total station: according to total station
Observational equation group between centre point and the control point CPIIIIt determines complete
The error equation stood between the centre point and the control point CPIII of instrumentWherein,Exist for the centre point p of total station
Three-dimensional coordinate estimated value in CPIII coordinate system；For in the instrument of total station
The initial value of the distance at point p to i-th control point CPIII of the heart；It is sat for the centre point p of total station in CPIII
The intermediate parameter of three-dimensional coordinate in mark system；
The matrix form of error equation between the centre point of total station and the control point CPIII isI.e.
Step 4: calculating three-dimensional coordinate of the centre point p of total station in CPIII coordinate system: utilizing minimum two
Multiply adjustment principle to resolve the error equation between the centre point of total station and the control point CPIII, obtains total station
The intermediate parameter of three-dimensional coordinate of the centre point p in CPIII coordinate systemWherein, H is to see
The power battle array of measurement andHiFor in the power battle array of observed quantity the i-th row i-th arrange element andA is the fixed error of total station, and b is the proportional error of total station；
According to formulaCalculate three-dimensional seat of the centre point p of total station in CPIII coordinate system
Mark (xp,yp,zp)；
Step 5: calculating the coordinate of high speed railway track upper rail unknown point: according to formulaCalculate the coordinate (x of high speed railway track upper rail unknown pointk,yk,zk),
In, SpkFor the distance between the centre point p of total station and track unknown point, αpiFor the centre point p to of total station
The azimuth at the i control point CPIII, ξpiFor the centre point p of total station and the line and whole station at i-th of control point CPIII
Angle between the centre point p and the line of track unknown point of instrument, βpkIt is unknown for the centre point p and track of total station
The line of point and the angle of horizontal plane, as vertical angle.
The calculation method of track unknown point is measured under above-mentioned high speed railway track not leveling state, it is characterised in that: step
The value range of I is 3~10 in rapid one.
The calculation method of track unknown point is measured under above-mentioned high speed railway track not leveling state, it is characterised in that: step
The I control point CPIII is separately positioned on the guardrails of both sides of high speed railway track in rapid one.
Compared with the prior art, the present invention has the following advantages:
1, the centre point of total station is considered as in phase by the present invention on the basis of the state coordinate at the control point CPIII
The heart, by constructing the error equation and Quan Zhen of space length, the columns of error equation is few and fixed, only 3 column, matrix element
Mainly unit vector, error equation are easy to establish, and are easy to carry out programming, because only resolving 3 unknown numbers, it is therefore desirable to
3 known control points CPIII can complete compensating computation, convenient for promoting the use of.
2, the centre point p of total station is considered as survey station point by the present invention, is considered as backsight point with any control point CPIII,
Track unknown point is preceding viewpoint, the azimuth at point p to i-th control point CPIII of centre by measuring total station, whole station
The company of centre the point p and track unknown point of the line and total station at the centre point p of instrument and i-th control point CPIII
The angle of the centre point p of angle and total station between line and the line of track unknown point and horizontal plane, are sat using pole
Mark method can be obtained by the state coordinate of track unknown point, reliable and stable, and using effect is good.
3, the method for the present invention step is simple, does not flatten measurement and carries out Free Station point CPIII measurement of coordinates with same
Precision and higher operating efficiency, when the superelevation of high speed railway track, which reaches, is up to 17cm, precision still is able to reach mm
Grade, improves the progress and efficiency of track accurate adjustment, convenient for promoting the use of.
In conclusion on the basis of the state coordinate at the control point CPIII, the centre point of total station is considered as by the present invention
Phase center is found out in the instrument of total station by constructing the error equation and Quan Zhen of space length using the principle of least square
The CPIII coordinate of heart point, then can be obtained by by method of polar coordinates the coordinate of track unknown point, convenient for promoting the use of.
Below by drawings and examples, technical scheme of the present invention will be described in further detail.
Detailed description of the invention
Fig. 1 is measuring principle schematic diagram of the present invention.
Fig. 2 is the method flow block diagram of the method for the present invention.
Description of symbols:
1-the control point CPIII；2-high speed railway tracks；3-track unknown points.
Specific embodiment
As depicted in figs. 1 and 2, the calculating side of track unknown point is measured under high speed railway track not leveling state of the invention
Method, comprising the following steps:
Step 1: freely setting up total station: the I control point CPIII 1 is chosen altogether in the two sides of high speed railway track 2, in I
Region between a control point CPIII 1 freely sets up total station, wherein I is the positive integer not less than 3；
In the present embodiment, the value range of I is 3~10 in step 1.
In the present embodiment, the I control point CPIII 1 is separately positioned on the guardrails of both sides of high speed railway track 2 in step 1
On.
In the present embodiment, not flattening measurement and carrying out Free Station point CPIII measurement of coordinates has same precision and higher
Operating efficiency, when the superelevation of high speed railway track, which reaches, is up to 17cm, precision still is able to reach mm grades, improves rail
The progress and efficiency of road accurate adjustment or detection.
Step 2: establishing the observational equation group between the centre point of total station and the control point CPIII: according to formulaEstablish the observation between the centre point of total station and the control point CPIII
Equation group, wherein SiFor the distance at point p to i-th control point CPIII 1 of centre of total station, as observed quantity, i is
The number and i=1 at the control point CPIII 1,2 ..., I；VSiFor centre point p to i-th control point CPIII 1 of total station
Coordinate corrective value, (xp,yp,zp) it is three-dimensional coordinate of the centre point p of total station in CPIII coordinate system, (xi,yi,
zi) it is three-dimensional coordinate of i-th of control point CPIII 1 in CPIII coordinate system；
Step 3: determining the error equation between the centre point and the control point CPIII of total station: according to total station
Observational equation group between centre point and the control point CPIIIIt determines complete
The error equation stood between the centre point and the control point CPIII of instrumentWherein,Exist for the centre point p of total station
Three-dimensional coordinate estimated value in CPIII coordinate system；For in the instrument of total station
The initial value of the distance at point p to i-th control point CPIII 1 of the heart；It is sat for the centre point p of total station in CPIII
The intermediate parameter of three-dimensional coordinate in mark system；
The matrix form of error equation between the centre point of total station and the control point CPIII isI.e.
Step 4: calculating three-dimensional coordinate of the centre point p of total station in CPIII coordinate system: utilizing minimum two
Multiply adjustment principle to resolve the error equation between the centre point of total station and the control point CPIII, obtains total station
The intermediate parameter of three-dimensional coordinate of the centre point p in CPIII coordinate systemWherein, H is to see
The power battle array of measurement andHiFor in the power battle array of observed quantity the i-th row i-th arrange element andA is the fixed error of total station, and b is the proportional error of total station；
According to formulaCalculate three-dimensional seat of the centre point p of total station in CPIII coordinate system
Mark (xp,yp,zp)；
In the present embodiment, on the basis of the state coordinate at the control point CPIII, the centre point of total station is considered as phase
Center, by constructing the error equation and Quan Zhen of space length, the columns of error equation is few and fixed, only 3 column, matrix element
Element is mainly unit vector, and error equation is easy to establish, and is easy to carry out programming, because only resolving 3 unknown numbers, is needed
Want 3 known control points CPIII that can complete compensating computation.
Step 5: calculating the coordinate of high speed railway track upper rail unknown point: according to formulaCalculate the coordinate (x of the upper rail unknown point 3 of high speed railway track 2k,yk,zk),
In, SpkFor the distance between the centre point p of total station and track unknown point 3, αpiFor total station centre point p extremely
The azimuth at i-th of control point CPIII 1, ξpiFor total station centre point p and i-th of control point CPIII 1 line with
Angle between the centre point p and the line of track unknown point 3 of total station, βpkFor the centre point p and rail of total station
The line of road unknown point 3 and the angle of horizontal plane, as vertical angle.
In the present embodiment, the centre point p of total station is considered as survey station point, backsight is considered as with any control point CPIII
Point, track unknown point are preceding viewpoint, the azimuth at point p to i-th control point CPIII of centre by measuring total station,
The centre point p and track unknown point of the line and total station at the centre point p of total station and i-th control point CPIII
Line between angle and total station centre point p and track unknown point line and horizontal plane angle, utilize
Method of polar coordinates can be obtained by the state coordinate of track unknown point, reliable and stable, and using effect is good.
The present invention in use, preferably, choose 7 control points CPIII 1 in the two sides of high speed railway track 2, at 7 altogether
Region between the control point CPIII 1 freely sets up total station, and measurement carries out leveling processing to total station for the first time, at this time high speed
Railroad track 2 has gone out 7 control points CPIII 1 using total station survey and has flattened space length when measuring without superelevation,
And the space length, angle and vertical angle of the centre point p to track unknown point k of total station, 7 control point CPIII tools
There are the coordinate and elevation in national coordinate system, observation data are as shown in table 1.
Table 1
| It calls the roll | Space length (m) | x(m) | y(m) | z(m) |
| CP1 | 45.196008 | 3455993.084570 | 480987.618630 | 10.024920 |
| CP2 | 37.521753 | 3456002.190080 | 480995.044560 | 10.022060 |
| CP3 | 17.742056 | 3455993.018760 | 481015.712490 | 10.074880 |
| CP4 | 17.598054 | 3456002.147290 | 481015.126140 | 10.020250 |
| CP5 | 24.507992 | 3455991.624870 | 481055.810330 | 10.043370 |
| CP6 | 24.300188 | 3456003.676120 | 481056.269670 | 10.007480 |
| CP7 | 111.049631 | 3455993.168280 | 481143.330930 | 10.069070 |
The distance between the centre point p of total station and track unknown point 3 are 108.620582m, the instrument of total station
Between the line at central point p and the 1st control point CPIII 1 and the centre point p and the line of track unknown point 3 of total station
Angle be 183.284507 °, the centre point p and the line of track unknown point 3 and the angle of horizontal plane of total station are
0.049220°；
Second of measurement, does not carry out leveling processing to total station, and high speed railway track 2 has inclination at this time, but is not most
Big inclination has gone out space length and whole station of 7 control points CPIII 1 when not flattening measurement using total station survey
There is country to sit for the space length, angle and vertical angle of the centre point p to track unknown point k of instrument, 7 control points CPIII
Coordinate and elevation in mark system, observation data are as shown in table 2.
Table 2
| It calls the roll | Space length (m) | x(m) | y(m) | z(m) |
| CP1 | 45.195606 | 3455993.084570 | 480987.618630 | 10.024920 |
| CP2 | 37.521953 | 3456002.190080 | 480995.044560 | 10.022060 |
| CP3 | 17.741357 | 3455993.018760 | 481015.712490 | 10.074880 |
| CP4 | 17.598353 | 3456002.147290 | 481015.126140 | 10.020250 |
| CP5 | 24.507092 | 3455991.624870 | 481055.810330 | 10.043370 |
| CP6 | 24.300889 | 3456003.676120 | 481056.269670 | 10.007480 |
| CP7 | 111.049936 | 3455993.168280 | 481143.330930 | 10.069070 |
The distance between the centre point p of total station and track unknown point 3 are 108.620989m, the instrument of total station
Between the line at central point p and the 1st control point CPIII 1 and the centre point p and the line of track unknown point 3 of total station
Angle be 183.288425 °, the centre point p and the line of track unknown point 3 and the angle of horizontal plane of total station are
0.085364°；
Third time measures, and does not carry out leveling processing to total station, and high speed railway track 2 has inclination and inclines for maximum at this time
Tiltedly, when maximum inclination, the superelevation of high speed railway track reaches maximum 17cm, has gone out 7 control points CPIII using total station survey
The space length of the centre point p to track unknown point k of 1 space length and total station when not flattening measurement,
Angle and vertical angle, 7 control points CPIII have coordinate and elevation in national coordinate system, and observation data are as shown in table 3.
Table 3
| It calls the roll | Space length (m) | x(m) | y(m) | z(m) |
| CP1 | 45.186708 | 3455993.084570 | 480987.618630 | 10.024920 |
| CP2 | 37.520255 | 3456002.190080 | 480995.044560 | 10.022060 |
| CP3 | 17.726556 | 3455993.018760 | 481015.712490 | 10.074880 |
| CP4 | 17.599954 | 3456002.147290 | 481015.126140 | 10.020250 |
| CP5 | 24.501891 | 3455991.624870 | 481055.810330 | 10.043370 |
| CP6 | 24.311788 | 3456003.676120 | 481056.269670 | 10.007480 |
| CP7 | 111.052322 | 3455993.168280 | 481143.330930 | 10.069070 |
The distance between the centre point p of total station and track unknown point 3 are 108.627076m, the instrument of total station
Between the line at central point p and the 1st control point CPIII 1 and the centre point p and the line of track unknown point 3 of total station
Angle be 183.227485 °, the centre point p and the line of track unknown point 3 and the angle of horizontal plane of total station are
0.068744°；Statistics measures the coordinate of middle orbit unknown point 3 three times, as shown in table 4.
Table 4
| State | Track unknown point | x(m) | y(m) | z(m) |
| Leveling state | Track unknown point k | 3456006.8971 | 481140.7624 | 9.9664 |
| Non- maximum inclination state | Track unknown point k | 3456006.8940 | 481140.7616 | 9.9630 |
| Maximum inclination state | Track unknown point k | 3456006.8924 | 481140.7603 | 9.9618 |
From table 4, it can be seen that the difference for not flattening coordinate under state and leveling state is up to 4.7mm, it is poor to be no more than limit
5mm (plane and high degree difference be 5mm), not flattening measurement and carrying out Free Station point CPIII measurement of coordinates has same precision
With higher operating efficiency, when the superelevation of high speed railway track, which reaches, is up to 17cm, precision still is able to reach mm grades, mentions
The high progress and efficiency of track accurate adjustment, is fully able to meet the requirement of high speed railway track detection.
The above is only presently preferred embodiments of the present invention, is not intended to limit the invention in any way, it is all according to the present invention
Technical spirit any simple modification to the above embodiments, change and equivalent structural changes, still fall within skill of the present invention
In the protection scope of art scheme.
Claims (3)
1. measuring the calculation method of track unknown point under high speed railway track not leveling state, which is characterized in that this method includes
Following steps:
Step 1: freely setting up total station: the I control point CPIII (1) is chosen altogether in the two sides of high speed railway track (2), in I
Region between a control point CPIII (1) freely sets up total station, wherein I is the positive integer not less than 3；
Step 2: establishing the observational equation group between the centre point of total station and the control point CPIII: according to formulaEstablish the observation between the centre point of total station and the control point CPIII
Equation group, wherein SiFor the distance of point p to i-th control point CPIII (1) of centre of total station, as observed quantity, i is
The number and i=1 at the control point CPIII (1), 2 ..., I；VSiFor point p to i-th control point CPIII of centre of total station
(1) coordinate corrective value, (xp,yp,zp) it is three-dimensional coordinate of the centre point p of total station in CPIII coordinate system,
(xi,yi,zi) it is three-dimensional coordinate of i-th of control point CPIII (1) in CPIII coordinate system；
Step 3: determining the error equation between the centre point and the control point CPIII of total station: according to the instrument of total station
Observational equation group between central point and the control point CPIIIDetermine total station
Centre point and the control point CPIII between error equationWherein,Exist for the centre point p of total station
Three-dimensional coordinate estimated value in CPIII coordinate system；For in the instrument of total station
The initial value of the distance of point p to i-th control point CPIII (1) of the heart；For total station centre point p in CPIII
The intermediate parameter of three-dimensional coordinate in coordinate system；
The matrix form of error equation between the centre point of total station and the control point CPIII isI.e.
Step 4: calculating three-dimensional coordinate of the centre point p of total station in CPIII coordinate system: flat using least square
Poor principle resolves the error equation between the centre point of total station and the control point CPIII, obtains the instrument of total station
The intermediate parameter of three-dimensional coordinate of the central point p in CPIII coordinate systemWherein, H is observed quantity
Power battle array andHiFor in the power battle array of observed quantity the i-th row i-th arrange element andA is the fixed error of total station, and b is the proportional error of total station；
According to formulaCalculate three-dimensional coordinate of the centre point p of total station in CPIII coordinate system
(xp,yp,zp)；
Step 5: calculating the coordinate of high speed railway track upper rail unknown point: according to formulaCalculate the coordinate (x of high speed railway track (2) upper rail unknown point (3)k,yk,
zk), wherein SpkFor the distance between the centre point p of total station and track unknown point (3), αpiFor in the instrument of total station
The azimuth of point p to i-th control point CPIII (1) of the heart, ξpiCentre point p and i-th of control point CPIII for total station
(1) the angle between the centre point p of line and total station and the line of track unknown point (3), βpkFor the instrument of total station
The angle of the line and horizontal plane of device central point p and track unknown point (3), as vertical angle.
2. the calculation method of track unknown point is measured under high speed railway track not leveling state described in accordance with the claim 1,
Be characterized in that: the value range of I is 3~10 in step 1.
3. the calculation method of track unknown point is measured under high speed railway track not leveling state described in accordance with the claim 1,
Be characterized in that: the I control point CPIII (1) is separately positioned on the guardrails of both sides of high speed railway track (2) in step 1.
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| CN113295149A (en) * | 2021-05-17 | 2021-08-24 | 中铁第四勘察设计院集团有限公司 | CP III coordinate calculation method and device based on joint observation quantity |
| CN113532305A (en) * | 2021-08-02 | 2021-10-22 | 上海浦江桥隧运营管理有限公司 | Urban tunnel horizontal displacement measurement method based on free station setting of total station |
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| CN110424201B (en) | 2020-10-30 |
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