CN112985348B - Method for realizing elevation measurement by utilizing gravity, GNSS-RTK and gravitational field model - Google Patents
Method for realizing elevation measurement by utilizing gravity, GNSS-RTK and gravitational field model Download PDFInfo
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Abstract
The invention discloses a method for realizing elevation measurement by utilizing gravity, GNSS-RTK and a gravitational field model, which comprises the following steps: firstly, acquiring geodetic coordinates of a measuring point; secondly, acquiring a gravity value of a measuring point; thirdly, acquiring elevation abnormity of the measuring point; fourthly, acquiring the gravity potential difference of the measuring point; and fifthly, acquiring the normal height of the point to be measured. The method has simple steps and reasonable design, obtains the geodetic height of the measuring points by utilizing the GNSS-RTK measuring technology, obtains the gravity potential difference between the measuring points by utilizing the flowing gravity observation, calculates the elevation abnormity of the measuring points by utilizing the gravity field model, and finally calculates the normal height of the points to be measured, thereby realizing the high-precision elevation measurement.
Description
Technical Field
The invention belongs to the technical field of engineering measurement, and particularly relates to a method for realizing elevation measurement by utilizing gravity, GNSS-RTK and a gravitational field model.
Background
Normal height and height difference measurement are always a basic task in the measurement field. The normal height has irreplaceable effect in engineering construction and even in daily economic life, and the most precise method for measuring the normal height is still leveling measurement. The leveling method adopts a leveling rod before and after the observation of a leveling instrument to read to obtain the height difference of the measuring station, and then the height differences measured station by station are accumulated to obtain the height difference of two control points. The error of leveling measurement can be less than +/-0.1 mm/km, and the method not only has the error increased sharply along with the increase of the length of the route, but also is time-consuming, labor-consuming and low in efficiency. The distance of each measuring station is not more than one hundred meters, and one operation group can measure the distance in a day and is not more than several kilometers in a flat area and can be shorter in a mountain area.
Since the advent of the GNSS (Global Navigation Satellite System) measurement technology, the GNSS measurement technology has surpassed the conventional measurement technology by virtue of its advantages of high measurement speed, high positioning accuracy, flexible network deployment, all weather, no need of communication between stations, and the like, and is widely applied to the production and life of people. However, in the GNSS elevation measurement, a reference ellipsoid is used as a datum plane, a geodetic height system is adopted, and a normal height system which is used in daily production and life and uses the geodetic height plane as a reference plane is adopted. The difference between the normal height and the ellipsoidal height is an elevation anomaly, and the elevation anomaly is not a unique value. Due to the uneven distribution of the earth mass, elevation abnormal values are different in different regions and different geological conditions. Therefore, if elevation fitting can be effectively carried out, the geodetic height of GNSS measurement is converted into the normal height of conventional leveling, the GNSS measurement technology is more widely applied to daily engineering, and the method has great significance to the surveying and mapping field.
The geodetic height measured by the GNSS is converted to a normal height. Namely, the difference value between the earth height and the elevation abnormity is the normal height, and the height difference between the two points is the difference between the normal heights of the two points. In order to solve the problem of difference between the normal altitude difference and the normal altitude, the existing methods for calculating the altitude difference by adopting the GNSS static technology mainly comprise:
(1) the principle of the method is that known common points (known geodetic height and normal height) in a measurement area are utilized to calculate elevation anomaly according to the geodetic height and the normal height, and an equation is established by utilizing the known elevation anomaly and corresponding point coordinates to calculate a fitting coefficient of the mathematical model. And calculating the elevation abnormality of each control point, finally calculating the normal height by using the known ground height and the calculated elevation abnormality, and directly calculating the height difference by using the difference of the normal heights. The method is greatly influenced by terrain, has low precision, cannot carry out recheck on an engineering first-level elevation control network, and has the defects that the existing three-dimensional control points in a measurement area have certain density and the network shape requirement of the control network is high. Time and labor are wasted, and the work process is slow.
(2) And calculating the elevation abnormity by using the gravity field model, converting the earth height into the normal height, and converting the earth height difference into the normal height difference. The method has the following defects: the different gravity field models lead to different calculated elevation abnormal accuracy, and the gravity field model accuracy can only obtain centimeter-grade to decimeter-grade elevation abnormal values; the accuracy of the elevation anomaly calculated in different areas is different, the accuracy in plain areas is higher, and the accuracy in mountain areas is poorer; the distance between adjacent points must be long enough (more than 5km or even longer) to meet the accuracy requirements of three, four, etc. leveling, and for engineering measurement, the distance between adjacent points is often only hundreds of meters, thus the practicability is poor. The gravity field model has a large difference between the place and the reality and a close place and the reality.
(3) And measuring the unknown elevation of each control point and the normal height difference between the two points by using the total station according to the elevation of the known gravity point. The method is time-consuming, labor-consuming and low in precision.
In order to solve the above defects, it is necessary to invent a method for realizing elevation measurement by using gravity, GNSS-RTK and a gravitational field model, so as to realize normal high calculation with high efficiency and guaranteed accuracy.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for realizing elevation measurement by utilizing gravity, a GNSS-RTK and a gravity field model, which has simple steps and reasonable design, obtains the geodetic height of measurement points by utilizing the GNSS-RTK measurement technology, obtains the gravity head between the measurement points by utilizing flowing gravity observation, calculates the elevation abnormity of the measurement points by utilizing the gravity field model, and finally calculates the normal height of the point to be measured, thereby realizing high-precision elevation measurement.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a method for realizing elevation measurement by utilizing gravity, GNSS-RTK and a gravitational field model is characterized by comprising the following steps:
step one, obtaining geodetic coordinates of a measuring point:
101, laying a starting point A and a point B to be measured in an area to be measured, and acquiring the normal height H of the starting point A A ；
102, setting e transition points between a starting point A and a point B to be measured; wherein e transition points are positioned on the line between the starting point A and the point B to be measured, and e is a natural number;
103, sequentially marking the starting point A, the multiple transition points and the point B to be measured as a 1 st measuring point, an ith measuring point, an nth measuring point from the starting point A to the point B to be measured; wherein i and n 'are positive integers, i is more than or equal to 1 and is more than or equal to n';
step 104, respectively measuring the n 'measuring points by adopting GNSS-RTK equipment to obtain geodetic coordinates of the n' measuring points; wherein the geodetic coordinates of the ith measurement point comprise the geodetic longitude L of the ith measurement point i Latitude of earth B i And ground height H i ；
Step two, obtaining the gravity value of the measuring point:
by relative weightThe force meter carries out closed route gravity measurement on n 'measuring points, the nearest known gravity point of the area to be measured is measured in parallel, and the gravity values of the n' measuring points are obtained through adjustment processing; wherein the gravity value of the ith measurement point is denoted as g i The gravity value of the i +1 th measuring point is recorded as g i+1 ；
Step three, acquiring elevation abnormity of the measuring points:
calculating the elevation anomaly of the n 'measuring points by using a gravity field model according to the geodetic coordinates of the n' measuring points obtained in the step 104; wherein, the elevation abnormity of the ith measuring point is recorded as xi i ；
Step four, acquiring the gravity potential difference of the measuring point:
step 401, according to the formula
Obtaining the approximate normal height of the ith measuring point
Step 402, acquiring a gravity potential difference between two adjacent measurement points according to the approximate normal height of each measurement point; wherein the gravity difference between the i +1 th measurement point and the i-th measurement point is denoted as Δ W i,i+1 ；
Step five, acquiring the normal height of the point to be measured:
step 501, according to the formula
Obtaining a normal gravity parameter k; wherein a 'represents the longer half axis of the earth, b' represents the shorter half axis of the earth, γ p Indicating normal gravity at both poles, gamma e Representing normal gravity on the equator;
according to the formula
Obtaining the normal gravity gamma of the point B to be measured on the ellipsoid 0 (ii) a Wherein e represents the first eccentricity of the ellipsoid, and B' represents the geodetic latitude and the waiting time of the starting point AThe arithmetic mean value of the geodetic latitude of the measuring point B;
502, according to a formula
Obtaining the average normal gravity between the starting point A and the point B to be measured
Wherein H B Representing the normal height of the point B to be measured;
step 503, according to the formula
Obtaining the gravity potential difference delta W between the point B to be measured and the starting point A AB ；
Step 504, when the starting point A and the point B to be measured are positioned in plain areas or hilly areas, according to a formula
Obtaining the normal height difference h between the point B to be measured and the initial point A AB ；
When the starting point A and the point B to be measured are positioned in the mountain area, the formula is used
Obtaining the normal height difference h between the point B to be measured and the initial point A AB (ii) a Wherein R represents the radius of the earth;
step 505, according to formula H B ＝H A +h AB To obtain the normal height H of the point B to be measured B (ii) a Wherein H A Indicating a normal high for the starting point a.
The method for realizing elevation measurement by using gravity, GNSS-RTK and gravitational field models is characterized by comprising the following steps: the gravity field model in the third step is an EIGEN6C4 gravity field model, and the EIGEN6C4 gravity field model is utilized to calculate the elevation anomaly xi of the ith measuring point i The specific process is as follows:
step 301, geodetic longitude L from the ith measurement point i And geodetic latitude B i To obtain the earth radial direction of the ith measuring pointρ i The geocentric latitude of the first measuring point
And geocentric longitude λ of ith measurement point i ；
Step 302, according to the formula
Obtaining the normal gravity value gamma of the ith measuring point i ；
303, according to the formula
Obtaining elevation abnormity of the ith measuring point; wherein G represents a gravitational constant, M represents the earth mass, a 'represents the earth's semi-major axis, N is a positive integer, N is more than or equal to 2 and less than or equal to N, M is a natural number, and M is more than or equal to 0 and less than or equal to N;
represents the fully normalized nth order mth order associative legendre function;
a bit coefficient representing the order n and m in the model of the gravitational field,
another one-bit coefficient representing the order N and the order m of the gravity field model, N representing the highest order of expansion of the gravity field model, and N being 2190.
The method for realizing elevation measurement by using gravity, GNSS-RTK and gravitational field models is characterized by comprising the following steps: in step 402, when i is located at 1-n' -1, the gravity potential difference Δ W between the i +1 th measurement point and the i th measurement point i,i+1 The acquisition process is as follows:
step 4021, according to the formula
Obtaining the approximate normal height difference delta h between the ith +1 measuring point and the ith measuring point i,i+1 (ii) a Wherein,
represents an approximate normal height for the (i + 1) th measurement point;
step 4022, according to the formula
Obtaining the measured gravity average value of the i +1 th measuring point and the i-th measuring point
Wherein, g i Representing the value of gravity, g, of the ith measurement point i+1 Representing the gravity value of the (i + 1) th measuring point;
step 4023, according to the formula
Obtaining the gravity difference delta W between the i +1 th measuring point and the ith measuring point i,i+1 。
The method for realizing elevation measurement by using gravity, GNSS-RTK and gravitational field models is characterized by comprising the following steps: the gravity value of the (i + 1) th measurement point in the second step is recorded as g i+1 The specific process of obtaining is as follows:
step 201, selecting a gravity control point closest to a starting point A as a known gravity point according to the distribution of gravity control points of an area to be measured, and performing joint measurement with the starting point A;
step 202, observing a known gravity point by using a relative gravimeter, and after the instrument is stabilized, carrying out interval measurement according to preset sampling time to obtain a measured value of each sampling time of the known gravity point;
step 203, recording the measured value of each sampling time on the known gravity point as the measured value vector G of the known gravity point y ＝[G y,1 ,G y,2 ,...,G y,j ,...,G y,l ](ii) a Wherein G is y,j The measured value of the jth sampling moment of the known gravity point is represented, j and l are positive integers, j is more than or equal to 1 and less than or equal to l, l represents the total number of samples, and l is more than 30;
step 204, when j is equal to 1, G' y,1 ＝G y,1 (ii) a When j is more than 1 and less than or equal to l-1, | G y,j -G y,j-1 When | ≧ 9 micro-gamma, G y,j If the value is abnormal, G is added y,j Is replaced by G' y,j And is and
otherwise, G y,j Is replaced by G' y,j And G' y,j ＝G y,j (ii) a When j ═ l, G' y,l ＝G y,l ；
Step 205, until the judgment of the l measured values is completed, obtaining a measured value vector G 'after the pretreatment of the known gravity point' y ＝[G′ y,1 ,G′ y,2 ,...,G′ y,j ,...,G′ y,l ](ii) a Wherein, G' y,j Representing the preprocessed measured value of the j sampling moment of the known gravity point;
step 206, observing the 1 st measuring point by using a relative gravimeter, measuring according to preset sampling time after the instrument is stabilized to obtain the measuring value of each sampling time of the 1 st measuring point, and obtaining the pre-processed measuring value vector G 'of the 1 st measuring point according to the method in the steps 203 to 205' 1 ＝[G′ 1,1 ,G′ 1,2 ,...,G′ 1,j ,...,G′ 1,l ](ii) a Wherein, G' 1,j Representing the preprocessed measuring value of the jth sampling moment of the 1 st measuring point;
step 207, according to the formula
Obtaining the relative gravity difference G between the 1 st measuring point and the known gravity point y,1 ；
According to the formula g 1 ＝G y +G y,1 Obtaining the gravity value g of the 1 st measuring point 1 (ii) a Wherein G is y An absolute gravity value representing a known point of gravity;
208, observing at the ith measuring point by using a relative gravimeter, measuring according to the preset sampling time after the instrument is stabilized to obtain the measured value of each sampling time of the ith measuring point, and performing steps 203 to 203The method in step 205 obtains a pre-processed measurement value vector G 'of the ith measurement point' i ＝[G′ i,1 ,G′ i,2 ,...,G′ i,j ,...,G′ i,l ](ii) a Wherein, G' i,j Representing the preprocessed measured value of the ith measuring point at the jth sampling moment;
step 209, repeating step 208 for multiple times to obtain a measurement value vector G ' preprocessed by the nth ' measurement point ' n′ ＝[G′ n′,1 ,G′ n′,2 ,...,G′ n′,j ,...,G′ n′,l ]And repeating the step 206 to obtain a measurement value vector G' after the preprocessing when the 1 st measurement point is in closed connection 1 ＝[G″ 1,1 ,G″ 1,2 ,...,G″ 1,j ,...,G″ 1,l ](ii) a Wherein, G ″) 1,j Representing the preprocessed measurement value at the jth sampling moment when the 1 st measurement point is closed and connected;
step 20A, according to the formula
Obtaining total error sigma of closed path gravity measurement z ；
Step 20B, setting the total time of the closed route gravity measurement of n' measuring points as T z Setting the time difference of gravity measurement between the (i + 1) th measurement point and the ith measurement point as T i,i+1 According to the formula
Obtaining the measurement error sigma of the i +1 th measurement point relative to the i-th measurement point i,i+1 ；
Step 20C, according to the formula
Obtaining the relative gravity difference G between the i +1 th measuring point and the i-th measuring point i,i+1 (ii) a And according to the formula g i+1 ＝g i +G i,i+1 -σ i,i+1 To obtain the gravity value g of the (i + 1) th measuring point i+1 。
The method for realizing height by using gravity, GNSS-RTK and gravity field modelThe program measuring method is characterized in that: the geodetic longitude L from the ith measurement point in step 301 i And geodetic latitude B i To obtain the earth radial rho of the ith measuring point i The geocentric latitude of the first measuring point
And geocentric longitude λ of ith measurement point i The specific process is as follows:
step 3011, according to the formula
Obtaining the X coordinate X of the ith measuring point under the geocentric rectangular coordinate system i And the Y coordinate Y of the ith measuring point under the geocentric rectangular coordinate system i And Z coordinate Z of the ith measuring point in the rectangular coordinate system of the earth center i (ii) a Wherein, N' represents the curvature radius of Mao unitary;
step 3012, according to the formula
Obtaining the earth radial rho of the ith measuring point i Geocentric latitude of the ith measurement point
And geocentric longitude λ of ith measurement point i 。
Compared with the prior art, the invention has the following advantages:
1. the method has simple steps and reasonable design, and obtains the normal height of the point B to be measured through the initial point A and each transition point, thereby realizing high-precision elevation measurement.
2. The invention only utilizes the GNSS-RTK equipment and the relative gravimeter to acquire the measurement data, is convenient for normal high-data processing, and has high measurement precision, time saving and labor saving compared with the geometric leveling method.
3. The geodetic coordinates of the measuring points are obtained by utilizing the GNSS-RTK measuring technology, so that the geocentric radial direction of the measuring points, the geocentric latitude of the measuring points and the geocentric longitude of the measuring points can be obtained subsequently; in addition, the gravity value of the measuring point is obtained through the relative gravimeter, and the measurement is convenient and fast.
4. The invention can replace the leveling work of four-level, three-level and two-level, the measurement precision reaches millimeter level and is irrelevant to the length of the measurement route.
5. The invention has no strict requirement on the distance between adjacent transition points, can be implemented for shorter distance and is particularly suitable for engineering construction measurement.
6. The invention has no special requirement on the net shape of the control net, and can be implemented in both strip-shaped nets (such as control nets of railway, highway, subway and other line projects) and planar nets (such as control nets of house buildings, municipal works and other projects).
7. The invention can carry out rechecking on the engineering first-level elevation control network.
8. The invention needs a gravimeter to measure the relative gravity value, and when the measuring distance is longer, a plurality of transition points (relief positions) need to be additionally measured so as to improve the precision.
9. The method for realizing elevation measurement by utilizing gravity, the GNSS-RTK and the gravity field model has the advantages of simple steps, convenient realization and simple and convenient operation, and ensures the accuracy of acquiring the normal height of the point to be measured.
10. The method for realizing elevation measurement by using gravity, GNSS-RTK and a gravitational field model is simple and convenient to operate and good in using effect, firstly, geodetic coordinates of a measurement point are obtained, secondly, a gravity value of the measurement point is obtained, secondly, elevation abnormity of the measurement point is obtained, the gravity potential difference of the measurement point is obtained according to the data, and finally, normal height of a point to be measured is obtained.
In conclusion, the method has simple steps and reasonable design, the geodetic height of the measuring points is obtained by utilizing the GNSS-RTK measuring technology, the gravity head between the measuring points is obtained by utilizing flowing gravity observation, the elevation abnormity of the measuring points is calculated by utilizing a gravity field model, and the normal height of the point to be measured is finally calculated, so that the high-precision elevation measurement is realized.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a block diagram of the process flow of the present invention.
Detailed Description
As shown in fig. 1, a method for implementing elevation measurement by using gravity, GNSS-RTK and gravitational field models includes the following steps:
step one, obtaining geodetic coordinates of a measuring point:
101, laying a starting point A and a point B to be measured in an area to be measured, and acquiring the normal height H of the starting point A A ；
102, setting e transition points between a starting point A and a point B to be measured; wherein e transition points are positioned on a line between the starting point A and the point B to be measured, and e is a natural number;
103, sequentially marking the starting point A, the plurality of transition points and the point B to be measured as a 1 st measuring point, an ith measuring point and an nth' measuring point from the starting point A to the point B to be measured; wherein i and n 'are positive integers, i is more than or equal to 1 and is more than or equal to n';
step 104, respectively measuring the n 'measuring points by adopting GNSS-RTK equipment to obtain geodetic coordinates of the n' measuring points; wherein the geodetic coordinates of the ith measurement point comprise the geodetic longitude L of the ith measurement point i Earth latitude B i And ground height H i ；
Step two, obtaining the gravity value of the measuring point:
carrying out closed route gravity measurement on n 'measuring points by using a relative gravimeter, measuring a nearest known gravity point of an area to be measured in parallel, and carrying out adjustment processing to obtain gravity values of the n' measuring points; wherein the gravity value of the ith measurement point is denoted as g i The gravity value of the i +1 th measuring point is recorded as g i+1 ；
Step three, acquiring elevation abnormity of the measuring points:
calculating elevation anomalies of the n 'measuring points by using a gravity field model according to the geodetic coordinates of the n' measuring points obtained in the step 104; wherein, the elevation abnormity of the ith measuring point is recorded as xi i ；
Step four, acquiring the gravity potential difference of the measuring point:
step 401, according to the formula
Obtaining the approximate normal height of the ith measuring point
Step 402, acquiring a gravity potential difference between two adjacent measurement points according to the approximate normal height of each measurement point; wherein the gravity difference between the i +1 th measurement point and the i-th measurement point is denoted as Δ W i,i+1 ；
Step five, acquiring the normal height of the point to be measured:
step 501, according to the formula
Obtaining a normal gravity parameter k; wherein a 'represents the longer half axis of the earth, b' represents the shorter half axis of the earth, γ p Indicating normal gravity at both poles, gamma e Representing normal gravity on the equator;
according to the formula
Obtaining the normal gravity gamma of the point B to be measured on the ellipsoid 0 (ii) a Wherein e represents the first eccentricity of the ellipsoid, and B' represents the arithmetic mean of the geodetic latitude of the starting point A and the geodetic latitude of the point B to be measured;
502, according to a formula
Obtaining the average normal gravity between the starting point A and the point B to be measured
Wherein H B Representing the normal height of the point B to be measured;
step 503, according to the formula
Obtaining a point B to be measured and a starting pointGravity head difference Δ W of A AB ；
Step 504, when the starting point A and the point B to be measured are positioned in plain areas or hilly areas, according to a formula
Obtaining the normal height difference h between the point B to be measured and the initial point A AB ；
When the starting point A and the point B to be measured are positioned in the mountain area, the formula is used
Obtaining the normal height difference h between the point B to be measured and the initial point A AB (ii) a Wherein R represents the radius of the earth;
step 505, according to formula H B ＝H A +h AB To obtain the normal height H of the point B to be measured B (ii) a Wherein H A Indicating a normal high for the starting point a.
The method for realizing elevation measurement by using gravity, GNSS-RTK and gravitational field models is characterized by comprising the following steps: the gravity field model in the third step is an EIGEN6C4 gravity field model, and the EIGEN6C4 gravity field model is used for calculating the elevation abnormity xi of the ith measuring point i The specific process is as follows:
step 301, geodetic longitude L from the ith measurement point i And geodetic latitude B i To obtain the earth radial rho of the ith measuring point i The geocentric latitude of the first measuring point
And geocentric longitude λ of the ith measurement point i ；
Step 302, according to the formula
Obtaining the normal gravity value gamma of the ith measuring point i ；
303, according to the formula
Get the height of the ith measurement pointA trip is abnormal; wherein G represents a gravitational constant, M represents the earth mass, a 'represents the earth's semi-major axis, N is a positive integer, N is more than or equal to 2 and less than or equal to N, M is a natural number, and M is more than or equal to 0 and less than or equal to N;
represents the fully normalized nth order mth order associative legendre function;
a bit coefficient representing the order n and m in the gravitational field model,
another one-bit coefficient representing the order N and the order m of the gravity field model, N representing the highest order of expansion of the gravity field model, and N being 2190.
The method for realizing elevation measurement by using gravity, GNSS-RTK and gravitational field models is characterized by comprising the following steps: when i is located at 1 to n' -1 in step 402, the gravity difference Δ W between the i +1 th measurement point and the i-th measurement point i,i+1 The acquisition process of (1) is as follows:
step 4021, according to the formula
Obtaining the approximate normal height difference delta h between the i +1 th measuring point and the ith measuring point i,i+1 (ii) a Wherein,
represents an approximately normal height for the i +1 th measurement point;
step 4022, according to the formula
Obtaining the measured gravity average value of the i +1 th measuring point and the i-th measuring point
Wherein, g i Representing the value of gravity, g, of the ith measurement point i+1 Representing the gravity value of the (i + 1) th measuring point;
step 4023, according to the formula
Obtaining the gravity potential difference delta W between the i +1 th measuring point and the i-th measuring point i,i+1 。
The method for realizing elevation measurement by using gravity, GNSS-RTK and gravitational field models is characterized by comprising the following steps: the gravity value of the (i + 1) th measurement point in the second step is recorded as g i+1 The specific process of obtaining is as follows:
step 201, selecting a gravity control point closest to a starting point A as a known gravity point according to the distribution of gravity control points of an area to be measured, and performing joint measurement with the starting point A;
step 202, observing a known gravity point by using a relative gravimeter, and after the instrument is stabilized, carrying out interval measurement according to preset sampling time to obtain a measured value of each sampling time of the known gravity point;
step 203, recording the measured value of each sampling time on the known gravity point as the measured value vector G of the known gravity point y ＝[G y,1 ,G y,2 ,...,G y,j ,...,G y,l ](ii) a Wherein G is y,j The measured value of the jth sampling moment of the known gravity point is represented, j and l are positive integers, j is more than or equal to 1 and less than or equal to l, l represents the total number of samples, and l is more than 30;
step 204, when j is equal to 1, G' y,1 ＝G y,1 (ii) a When j is more than 1 and less than or equal to l-1, | G y,j -G y,j-1 When | ≧ 9 micro-gamma, G y,j If the value is abnormal, G is added y,j Is replaced by G' y,j And is and
otherwise, G y,j Is replaced by G' y,j And G' y,j ＝G y,j (ii) a When j ═ l, G' y,l ＝G y,l ；
Step 205, obtaining a measurement vector G 'after preprocessing of the known gravity point until finishing the judgment of the l measurement values' y ＝[G′ y,1 ,G′ y,2 ,...,G′ y,j ,...,G′ y,l ](ii) a Wherein, G' y,j Representing the preprocessed measured value of the j sampling moment of the known gravity point;
step 206, observing the 1 st measuring point by using a relative gravimeter, measuring according to preset sampling time after the instrument is stabilized to obtain the measuring value of each sampling time of the 1 st measuring point, and obtaining the pre-processed measuring value vector G 'of the 1 st measuring point according to the method in the steps 203 to 205' 1 ＝[G′ 1,1 ,G′ 1,2 ,...,G′ 1,j ,...,G′ 1,l ](ii) a Wherein, G' 1,j Representing the preprocessed measured value of the jth sampling moment of the 1 st measuring point;
step 207, according to the formula
Obtaining the relative gravity difference G between the 1 st measuring point and the known gravity point y,1 ；
According to the formula g 1 ＝G y +G y,1 Obtaining the gravity value g of the 1 st measuring point 1 (ii) a Wherein G is y An absolute gravity value representing a known point of gravity;
step 208, observing the ith measurement point by using a relative gravimeter, measuring according to a preset sampling time after the instrument is stabilized to obtain a measurement value of each sampling time of the ith measurement point, and obtaining a preprocessed measurement value vector G 'of the ith measurement point according to the methods in steps 203 to 205' i ＝[G′ i,1 ,G′ i,2 ,...,G′ i,j ,...,G′ i,l ](ii) a Wherein, G' i,j Representing the preprocessed measured value of the ith measuring point at the jth sampling moment;
step 209, repeating step 208 for multiple times to obtain a measurement value vector G ' preprocessed by the nth ' measurement point ' n′ ＝[G′ n′,1 ,G′ n′,2 ,...,G′ n′,j ,...,G′ n′,l ]And repeating the step 206 to obtain a measurement value vector G' after the preprocessing when the 1 st measurement point is in closed connection 1 ＝[G″ 1,1 ,G″ 1,2 ,...,G″ 1,j ,...,G″ 1,l ](ii) a Wherein, G ″) 1,j Representing the preprocessed measurement value at the jth sampling moment when the 1 st measurement point is closed and connected;
step 20A, according to the formula
Obtaining total error sigma of closed path gravity measurement z ；
Step 20B, setting the total time of the closed route gravity measurement of n' measuring points as T z Setting the time difference of gravity measurement between the (i + 1) th measurement point and the ith measurement point as T i,i+1 According to the formula
Obtaining the measurement error sigma of the i +1 th measurement point relative to the i-th measurement point i,i+1 ；
Step 20C, according to the formula
Obtaining the relative gravity difference G between the i +1 th measuring point and the i-th measuring point i,i+1 (ii) a And according to the formula g i+1 ＝g i +G i,i+1 -σ i,i+1 Obtaining the gravity value g of the (i + 1) th measuring point i+1 。
The method for realizing elevation measurement by using gravity, GNSS-RTK and gravitational field models is characterized by comprising the following steps: the geodetic longitude L from the ith measurement point in step 301 i And geodetic latitude B i To obtain the earth radial rho of the ith measuring point i The geocentric latitude of the first measuring point
And geocentric longitude λ of ith measurement point i The specific process is as follows:
step 3011, according to the formula
Obtaining the X coordinate X of the ith measuring point under the geocentric rectangular coordinate system i Ith measurementY coordinate Y of point under rectangular coordinate system of geocentric i And Z coordinate Z of the ith measuring point in the rectangular coordinate system of the earth center i (ii) a Wherein, N' represents the curvature radius of Mao unitary;
step 3012, according to the formula
Obtaining the earth radial rho of the ith measuring point i Geocentric latitude of the ith measurement point
And geocentric longitude λ of ith measurement point i 。
In this embodiment, the preset sampling time is 8s, and the set measurement time is 5 min.
In the embodiment, the invention utilizes the measured gravity value to realize the physical principle of gravity potential difference of the measuring point so as to measure the normal height difference of the two points.
In this embodiment, the present invention can replace four-level, three-level, and two-level leveling operations.
In the embodiment, the accuracy of the existing elevation and height difference measuring method can only reach a centimeter level under a long distance condition, and the accuracy of the method can reach the millimeter level and is irrelevant to the length of a measuring route. The invention is simple to operate, saves time and labor.
In this embodiment, in actual use, when the starting point a and the point B to be measured are located in a mountain area, the number e of the transition points is not less than 2; and when the starting point A and the point B to be measured are positioned in a plain area, the number e of the transition points is 0.
In conclusion, the method has simple steps and reasonable design, the geodetic height of the measuring points is obtained by utilizing the GNSS-RTK measuring technology, the gravity head between the measuring points is obtained by utilizing flowing gravity observation, the elevation abnormity of the measuring points is calculated by utilizing a gravity field model, and the normal height of the point to be measured is finally calculated, so that the high-precision elevation measurement is realized.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and all simple modifications, changes and equivalent structural changes made to the above embodiment according to the technical spirit of the present invention still fall within the protection scope of the technical solution of the present invention.
Claims (5)
1. A method for realizing elevation measurement by utilizing gravity, GNSS-RTK and a gravitational field model is characterized by comprising the following steps:
step one, obtaining geodetic coordinates of a measuring point:
101, laying a starting point A and a point B to be measured in an area to be measured, and acquiring the normal height H of the starting point A A ；
102, setting e transition points between a starting point A and a point B to be measured; wherein e transition points are positioned on a line between the starting point A and the point B to be measured, and e is a natural number;
103, sequentially marking the starting point A, the plurality of transition points and the point B to be measured as a 1 st measuring point, an ith measuring point and an nth' measuring point from the starting point A to the point B to be measured; wherein i and n 'are positive integers, i is more than or equal to 1 and is more than or equal to n';
step 104, respectively measuring the n 'measuring points by adopting GNSS-RTK equipment to obtain geodetic coordinates of the n' measuring points; wherein the geodetic coordinates of the ith measurement point comprise the geodetic longitude L of the ith measurement point i Latitude of earth B i And ground height H i ；
Step two, obtaining the gravity value of the measuring point:
carrying out closed route gravity measurement on n 'measuring points by using a relative gravimeter, measuring a nearest known gravity point of an area to be measured in parallel, and carrying out adjustment processing to obtain gravity values of the n' measuring points; wherein the gravity value of the ith measurement point is denoted as g i The gravity value of the i +1 th measuring point is recorded as g i+1 ；
Step three, acquiring elevation abnormity of the measuring points:
calculating elevation anomalies of the n 'measuring points by using a gravity field model according to the geodetic coordinates of the n' measuring points obtained in the step 104; wherein, the elevation abnormity of the ith measuring point is recorded as xi i ；
Step four, acquiring the gravity potential difference of the measuring point:
step 401, according to the formula
Obtaining the approximate normal height of the ith measuring point
Step 402, acquiring a gravity potential difference between two adjacent measurement points according to the approximate normal height of each measurement point; wherein the gravity difference between the i +1 th measurement point and the i-th measurement point is denoted as Δ W i,i+1 ；
Step five, acquiring the normal height of the point to be measured:
step 501, according to the formula
Obtaining a normal gravity parameter k; wherein a 'represents the earth's major semi-axis, b 'represents the earth's minor semi-axis, γ p Indicating normal gravity at both poles, gamma e Representing normal gravity on the equator;
according to the formula
Obtaining the normal gravity gamma of the point B to be measured on the ellipsoid 0 (ii) a Wherein e represents the first eccentricity of the ellipsoid, and B' represents the arithmetic mean of the geodetic latitude of the starting point A and the geodetic latitude of the point B to be measured;
502, according to a formula
Obtaining the average normal gravity between the starting point A and the point B to be measured
Wherein H B Representing the normal height of the point B to be measured;
step 503, according to the formula
Obtaining the gravity potential difference delta W between the point B to be measured and the starting point A AB ；
Step 504, when the starting point A and the point B to be measured are positioned in plain areas or hilly areas, according to a formula
Obtaining the normal height difference h between the point B to be measured and the initial point A AB ；
When the starting point A and the point B to be measured are positioned in the mountain area, the formula is used
Obtaining the normal height difference h between the point B to be measured and the initial point A AB (ii) a Wherein R represents the radius of the earth;
step 505, according to formula H B ＝H A +h AB To obtain the normal height H of the point B to be measured B (ii) a Wherein H A Indicating a normal high for the starting point a.
2. The method for elevation measurement using gravity, GNSS-RTK and gravitational field models according to claim 1, wherein: the gravity field model in the third step is an EIGEN6C4 gravity field model, and the EIGEN6C4 gravity field model is utilized to calculate the elevation anomaly xi of the ith measuring point i The specific process is as follows:
step 301, geodetic longitude L from the ith measurement point i And geodetic latitude B i To obtain the earth radial rho of the ith measuring point i The geocentric latitude of the first measuring point
And geocentric longitude λ of ith measurement point i ；
Step 302, according to the formula
Get the ith measurementNormal gravity value of point gamma i ；
303, according to the formula
Obtaining elevation abnormity of the ith measuring point; wherein G represents a gravitational constant, M represents the earth mass, a 'represents the earth's semi-major axis, N is a positive integer, N is more than or equal to 2 and less than or equal to N, M is a natural number, and M is more than or equal to 0 and less than or equal to N;
represents the fully normalized nth order mth order associative legendre function;
a bit coefficient representing the order n and m in the model of the gravitational field,
another one-bit coefficient representing the order N and the order m of the gravity field model, N representing the highest order of expansion of the gravity field model, and N being 2190.
3. The method for elevation measurement using gravity, GNSS-RTK and gravitational field models according to claim 1, wherein: in step 402, when i is located at 1-n' -1, the gravity potential difference Δ W between the i +1 th measurement point and the i th measurement point i,i+1 The acquisition process is as follows:
step 4021, according to the formula
Obtaining the approximate normal height difference delta h between the i +1 th measuring point and the ith measuring point i,i+1 (ii) a Wherein,
represents an approximately normal height for the i +1 th measurement point;
step 4022, according to the formula
Obtaining the measured gravity average value of the i +1 th measuring point and the i-th measuring point
Wherein, g i Representing the value of gravity, g, of the ith measurement point i+1 Representing the gravity value of the (i + 1) th measuring point;
step 4023, according to the formula
Obtaining the gravity potential difference delta W between the i +1 th measuring point and the i-th measuring point i,i+1 。
4. The method for elevation measurement using gravity, GNSS-RTK and gravitational field models according to claim 1, wherein: the gravity value of the (i + 1) th measurement point in the second step is recorded as g i+1 The specific process of obtaining is as follows:
step 201, selecting a gravity control point closest to a starting point A as a known gravity point according to the distribution of gravity control points of an area to be measured, and performing joint measurement with the starting point A;
step 202, observing a known gravity point by using a relative gravimeter, and after the instrument is stabilized, carrying out interval measurement according to preset sampling time to obtain a measured value of each sampling time of the known gravity point;
step 203, recording the measured value of each sampling time on the known gravity point as the measured value vector G of the known gravity point y ＝[G y,1 ,G y,2 ,...,G y,j ,...,G y,l ](ii) a Wherein G is y,j The measured value of the jth sampling moment of the known gravity point is represented, j and l are positive integers, j is more than or equal to 1 and less than or equal to l, l represents the total number of samples, and l is more than 30;
step 204, when j is equal to 1, G' y,1 ＝G y,1 (ii) a When j is more than 1 and less than or equal to l-1, | G y,j -G y,j-1 When | ≧ 9 micro-gamma, G y,j If the value is abnormal, G is added y,j Is replaced by G' y,j And is and
otherwise, G y,j Is replaced by G' y,j And G' y,j ＝G y,j (ii) a When j ═ l, G' y,l ＝G y,l ；
Step 205, until the judgment of the l measured values is completed, obtaining a measured value vector G 'after the pretreatment of the known gravity point' y ＝[G′ y,1 ,G′ y,2 ,...,G′ y,j ,...,G′ y,l ](ii) a Wherein, G' y,j Representing the preprocessed measured value of the j sampling moment of the known gravity point;
step 206, observing the 1 st measuring point by using a relative gravimeter, measuring according to preset sampling time after the instrument is stabilized to obtain the measuring value of each sampling time of the 1 st measuring point, and obtaining the pre-processed measuring value vector G 'of the 1 st measuring point according to the method in the steps 203 to 205' 1 ＝[G′ 1,1 ,G′ 1,2 ,...,G′ 1,j ,...,G′ 1,l ](ii) a Wherein, G' 1,j Representing the preprocessed measured value of the jth sampling moment of the 1 st measuring point;
step 207, according to the formula
Obtaining the relative gravity difference G between the 1 st measuring point and the known gravity point y,1 ；
According to the formula g 1 ＝G y +G y,1 Obtaining the gravity value g of the 1 st measuring point 1 (ii) a Wherein G is y An absolute gravity value representing a known point of gravity;
step 208, observing the ith measurement point by using a relative gravimeter, measuring according to a preset sampling time after the instrument is stabilized to obtain a measurement value of each sampling time of the ith measurement point, and obtaining a preprocessed measurement value vector G 'of the ith measurement point according to the methods in steps 203 to 205' i ＝[G′ i,1 ,G′ i,2 ,...,G′ i,j ,...,G′ i,l ](ii) a Wherein, G' i,j Representing the preprocessed measured value of the ith measuring point at the jth sampling moment;
step 209, repeating step 208 for multiple times to obtain a measurement value vector G ' preprocessed by the nth ' measurement point ' n′ ＝[G′ n′,1 ,G′ n′,2 ,...,G′ n′,j ,...,G′ n′,l ]And repeating the step 206 to obtain a measurement value vector G' after the preprocessing when the 1 st measurement point is in closed connection 1 ＝[G″ 1,1 ,G″ 1,2 ,...,G″ 1,j ,...,G″ 1,l ](ii) a Wherein, G ″) 1,j Representing the preprocessed measurement value at the jth sampling moment when the 1 st measurement point is closed and connected;
step 20A, according to the formula
Obtaining total error sigma of closed path gravity measurement z ；
Step 20B, setting the total time of the closed route gravity measurement of n' measuring points as T z Setting the time difference of gravity measurement between the (i + 1) th measurement point and the ith measurement point as T i,i+1 According to the formula
Obtaining the measurement error sigma of the i +1 th measurement point relative to the i-th measurement point i,i+1 ；
Step 20C, according to the formula
Obtaining the relative gravity difference G between the i +1 th measuring point and the i-th measuring point i,i+1 (ii) a And according to the formula g i+1 ＝g i +G i,i+1 -σ i,i+1 Obtaining the gravity value g of the (i + 1) th measuring point i+1 。
5. The method for elevation measurement using gravity, GNSS-RTK and gravitational field models according to claim 2, wherein: geodetic from the ith measurement point in step 301Longitude L i And geodetic latitude B i To obtain the earth radial rho of the ith measuring point i The geocentric latitude of the first measuring point
And geocentric longitude λ of ith measurement point i The specific process is as follows:
step 3011, according to the formula
Obtaining the X coordinate X of the ith measuring point under the geocentric rectangular coordinate system i And the Y coordinate Y of the ith measuring point under the geocentric rectangular coordinate system i And Z coordinate Z of the ith measuring point in the rectangular coordinate system of the earth center i (ii) a Wherein, N' represents the curvature radius of Mao unitary;
step 3012, according to the formula
Obtaining the earth radial rho of the ith measuring point i Geocentric latitude of the ith measurement point
And geocentric longitude λ of ith measurement point i 。
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