CN109633723B - Single-epoch GNSS resolving method with horizontal constraint - Google Patents
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Abstract
The invention discloses a single epoch GNSS resolving method with horizontal constraint, which comprises the following steps: one key issue with dynamic single epoch positioning is the correct resolution of the ambiguity. By adding the constraint condition, the reliability of single epoch resolving ambiguity can be improved. And (3) acquiring a GNSS coordinate sequence of the monitoring point by using 15-30min observation data, determining a simple harmonic motion equation of the super high-rise building under the action of an external force load by using a wavelet analysis method, and constructing a constraint condition according to the motion rule of the super high-rise building. In order to solve the problem of rank deficiency in single epoch solution, a pseudo range observation value is introduced, and the ambiguity is easy to determine due to the fact that the wide-lane combination wavelength is long. Therefore, by adding constraint conditions of motion states of the super high-rise building, firstly, the widelane ambiguity is fixed, and secondly, the state constraints are added to determine the L1 and L2 ambiguities, so that the ambiguity can be resolved quickly.
Description
Technical Field
The invention belongs to the technical field of deformation monitoring of super high-rise buildings, and relates to a single-epoch GNSS resolving method with horizontal constraint.
Background
The general rules of civil building design (GB 50352-2005) in China divides residential buildings into the following according to the number of floors: one to three floors are low-rise houses, four to six floors are multi-rise houses, seven to nine floors are medium-high-rise houses, and ten or more floors are high-rise houses. Civil buildings with the height not more than 24m except the residential buildings are single-storey and multi-storey buildings, and buildings with the height more than 24m are high-storey buildings (excluding single-storey public buildings with the building height more than 24 m); the civil buildings with the building height more than 100m are super high-rise buildings. According to statistics: by 9 months end in 2018, the number of constructed super high-rise buildings in China (including the Hongkong and Australian area) is about 260, wherein 100-; 200 and 300 meters are about 80, and more than 300 meters are about 80. At present, the highest-rise building in China is a Shanghai central building, and is about 632 meters. For buildings, due to the influence of environmental loads (such as wind load and earthquake load), fatigue effect, corrosion and material aging of self structures, even artificial factors, the buildings gradually deform with the lapse of time, and the structural bearing capacity of the buildings also gradually reduces. Usually, the construction shows uniform or non-uniform settlement, or some phenomena of crack, inclination, torsion and displacement, when the deformation value exceeds the allowable value of the construction design, the construction is damaged to a certain extent. The formation of construction accidents is not a trivial matter, and the accidents go through a deformation process. Super high-rise buildings are more dangerous and complex in construction, operation and management than ordinary buildings due to their height characteristics. Compared with the common type of buildings, the super high-rise structure can generate more obvious dynamic deformation under the influence of factors such as wind load, sunlight action, earthquake and the like. In the construction stage and the normal use stage of the super high-rise building, a plurality of dynamic deformation quantities needing important monitoring exist, such as vibration amplitude, inclination angle, vibration track, speed, acceleration and the like under the action of wind load. Wind load is a complex non-steady random process, which causes the wind to act intermittently and dynamically on the building structure, and the discussion of the relation between wind speed and dynamic deformation of a super high-rise building has very important significance on the safety evaluation of the structure.
The traditional measuring system mainly adopts equipment such as a total station, an accelerometer, a laser interferometer, a displacement sensor and the like, and has the following defects: when the height is over 300m, the laser divergence angle is increased, the elevation angle of the total station is large, and observation cannot be met; the device is not suitable for monitoring under severe conditions such as strong wind, heavy rain and the like, and the climate condition is just a key monitoring time period; multi-point real-time and synchronous measurement cannot be carried out, and long-time continuous measurement cannot be carried out; the angle measurement and distance measurement precision becomes low under the influence of atmospheric turbulence and atmospheric refraction. The GNSS technology has unique advantages in the aspect of monitoring deformation of the super high-rise building: the sampling rate is high, and the current GNSS receiver sampling rate reaches 20Hz, even 100 Hz; the degree of automation is high, and the data acquisition work of the GNSS receiver is automatically carried out; four-dimensional monitoring, high-precision three-dimensional displacement measurement and time information with the precision reaching 30 ns; the GNSS receiver can receive working satellite signals at any time period, can normally work in severe weather such as wind, snow, rain and fog, and is easy to realize long-term continuous monitoring. For high-precision dynamic positioning, a GNSS relative positioning method is mainly adopted, as shown in fig. 1, and particularly, in a short baseline, an error with strong correlation can be well eliminated or weakened. Therefore, the GNSS-RTK technology is widely applied to deformation monitoring of super high-rise buildings. Under good environmental conditions, the time required for RTK initialization is typically a few seconds. However, under poor environmental conditions, a receiver with advanced technology also needs several minutes to more than ten minutes, and a receiver with poor technical performance has difficulty in completing initialization. Compared with multi-epoch dynamic positioning, the real-time dynamic single-epoch positioning technology is a development trend of future GNSS positioning technology. The single epoch positioning based on the current epoch observation data has the advantages of no need of detecting cycle slip, full utilization of observation data, high positioning precision and the like, and improves the reliability of the ambiguity of the calculation by adding constraint conditions.
Disclosure of Invention
The technical problem is as follows: the current common GNSS-RTK technology needs cycle slip detection and repair and has the problems of long initialization time and the like, but the method has the advantages of no need of cycle slip detection, full utilization of observation data, high positioning precision and the like, and improves the ambiguity resolution reliability by increasing the motion law constraint conditions of super high-rise buildings.
The technical scheme is as follows:
a single epoch GNSS resolving method with horizontal constraint specifically comprises the following steps;
step 1, utilizing early-stage GNSS observation data to solve static coordinates (X) of monitoring points 0 ,Y 0 ,Z 0 )；；
Step 2, separating and observing signals with different frequencies in GNSS three-dimensional coordinate value data for 15-30min through wavelet analysis, establishing a simple harmonic motion equation of the super high-rise building, and solving the displacement y of the super high-rise building;
step 3, approximate coordinates (X) of the current monitoring point are utilized 0 ,Y 0 ,Z 0 ) Static coordinate (X) 0 ,Y 0 ,Z 0 ) Calculating the displacement y with simple harmonic motion, and establishing a constraint equation
Wherein C is a matrix of coefficients, where,
is a three-dimensional coordinate correction number, and W is a residual error;
step 4, constructing an observation equation by using the carrier phase observation value, wherein the observation equation is rank-deficient, and introducing a pseudo-range observation value to solve the equation rank-deficient problem; simultaneously solving a wide lane carrier double-difference ambiguity floating solution and a variance-covariance matrix through a pseudo-range double-difference observation equation, a wide lane carrier double-difference observation equation and a constraint equation, and searching for a fixed wide lane carrier double-difference ambiguity through LAMBDA;
and 5, after the double-difference ambiguity of the wide lane carrier is fixed, when an error equation of observed values of the L1 and the L2 is listed, the double-difference ambiguity N of the wide lane carrier is determined W Carrier L1 double difference ambiguity N L1 Sum L2 double difference ambiguity N L2 Relation N of W ＝N L1 -N L2 Expressing the error equation as containing only L1 ambiguity N L1 The method comprises the following steps of solving an L1 carrier double-difference ambiguity floating solution and a variance-covariance matrix by combining constraint conditions, and searching fixed L1 carrier double-difference ambiguity through LAMBDA;
step 6, substituting the fixed L1 carrier double-difference ambiguity back into an error equation, and recombining a normal equation to obtain a final coordinate;
and 7, selecting a proper moving window for the coordinates without the gross error, separating signals with different frequencies in the observed data through wavelet analysis, updating the motion state of the super high-rise building, and reestablishing a constraint equation
And repeating the steps 3 to 6.
As a further preferable scheme of the single epoch GNSS solution method with horizontal constraint of the present invention, the steps specifically include: utilizing early-stage GNSS observation data to search a time period when the wind speed is zero, performing static calculation once per hour through GAMIT software, and then taking the average value of all calculation results as the initial position coordinate (X) of the monitoring point 0 ,Y 0 ,Z 0 )。
As a further preferable scheme of the single epoch GNSS solution method with horizontal constraint of the present invention, in step 2, the simple harmonic motion equation is specifically as follows:
wherein: y is the displacement, f is the frequency, t is the time, A is the amplitude,
is the initial value of the phase.
As a further preferable scheme of the single epoch GNSS solution method with horizontal constraint, the establishment of a constraint equation comprises the following steps: by using the displacement y obtained in step 2, the following can be obtained:
(X-X 0 ) 2 +(Y-Y 0 ) 2 +(Z-Z 0 ) 2 ＝y 2
let the GNSS approximate coordinate of the monitoring station be (X) 0 ,Y 0 ,Z 0 ) In (X) 0 ,Y 0 Z0) is developed by taylor's formula:
therefore, we get the constraint equation:
wherein: c ═ 2 (X) 0 -X 0 )2(Y 0 -Y 0 )2(Z 0 -Z 0 )]；W＝y 2 -(X 0 -X 0 ) 2 -(Y 0 -Y 0 ) 2 -(Z 0 -Z 0 ) 2 。
As a further preferable scheme of the single epoch GNSS solution method with horizontal constraint of the present invention, the step 4 is specifically as follows: according to phase observation data of one epoch, the rank deficiency of the normal equation is 3, and the unknown number cannot be solved. Therefore, the pseudo-range observation equation, the constraint condition and the wide-lane double-difference phase observation equation are combined to form the following mathematical model:
wherein: v is residual error, A is a coordinate parameter coefficient array, B is a coefficient array of carrier double-difference ambiguity N, l is an OMC value, and P is weight.
Applying least squares criterion, equation of law:
wherein: k is a joint coefficient vector of the constraint equation.
Resolving a floating solution of the widelane ambiguity through the above normal equation, extracting a variance-covariance matrix of the floating solution, and fixing the widelane ambiguity by using an LAMBDA method.
As a further preferable scheme of the single epoch GNSS solution method with horizontal constraint of the present invention, the step 5 is specifically as follows:
after the widelane ambiguity is fixed, according to N in the error equation of observed values of columns L1 and L2 W ＝N L1 -N L2 Expressing the error equation as containing only L1 ambiguity N L1 In combination with constraints, the following mathematical model is obtained:
the equation of the method can be obtained:
ambiguity fixing was performed using the Lambda method L1.
As a further preferable scheme of the single epoch GNSS solution method with horizontal constraint of the present invention, the step 6 is specifically as follows:
the fixed L1 ambiguity is substituted back into the error equation, and the normal equation is recomposed:
the current epoch coordinate of the available monitoring point is as follows:
wherein, (X, Y, Z) is the current coordinate of the GNSS monitoring point, (X) 0 ,Y 0 ,Z 0 ) Approximate coordinates for GNSS monitoring points, (dX, dY, dZ) are three-dimensional coordinate corrections.
Has the advantages that:
1. one key problem of GNSS high-precision positioning is the correct resolution of ambiguity, and by adding constraint conditions, the reliability of resolving ambiguity can be improved;
2. the invention utilizes the coordinate values of the monitoring points obtained in the early stage, determines the simple harmonic motion equation of the super high-rise building under the action of the external force load to solve the displacement through a wavelet analysis method, constructs the constraint condition according to the motion rule of the super high-rise building, and has easier determination of the ambiguity due to longer wavelength of the wide roadway combination;
3. by adding constraint conditions of motion states of super high-rise buildings, the widelane ambiguity is firstly fixed, and after the widelane ambiguity is fixed, the L1 and L2 ambiguities are determined through the constraint conditions again.
Drawings
FIG. 1 is a schematic view of GNSS monitoring of a super high-rise building according to the present invention;
fig. 2 is a flow chart of monitoring horizontal swinging of a super high-rise building under the action of strong wind based on GNSS multi-frequency difference.
Detailed Description
Illustrating according to what is contained in the claims
Example 1: static coordinates (X) of monitoring points 0 ,Y 0 ,Z 0 ) Obtained by
In the deformation measurement of the super high-rise building under the action of strong wind, the initial position of the super high-rise building in a static state needs to be determined firstly. In order to measure the initial position, a time point with good weather condition is selected to perform static observation on the super high-rise building for about two to three weeks, GAMIT software is used for performing static calculation once per hour, and then the average value of all the calculation results is taken as the static coordinate (X) of the monitoring point 0 ,Y 0 ,Z 0 )。
Example 2: the displacement y is obtained.
Firstly, a GNSS-RTK technology is utilized to carry out coordinate resolving on a monitoring point for 15-30min, a wavelet filtering method is adopted to carry out multi-scale decomposition on a GNSS coordinate (displacement) sequence, and a proper wavelet filter (Daubechies four-coefficient wavelet is adopted to carry out orthogonal decomposition, ten scale results are taken for analysis) is selected, so that structural vibration and various influence items can be effectively separated. Establishing a simple harmonic motion equation of the super high-rise building under the action of strong wind:
example 3: establishment of constraint equations
(X-X 0 ) 2 +(Y-Y 0 ) 2 +(Z-Z 0 ) 2 ＝y 2
Let the GNSS approximate coordinate of the monitoring station be (X) 0 ,Y 0 ,Z 0 ) The formula (11) is represented by (X) 0 ,Y 0 ,Z 0 ) And (3) performing Taylor formula expansion to obtain:
therefore, a constraint equation can be derived:
wherein: c ═ 2 (X) 0 -X 0 )2(Y 0 -Y 0 )2(Z 0 -Z 0 )]；W＝y 2 -(X 0 -X 0 ) 2 -(Y 0 -Y 0 ) 2 -(Z 0 -Z 0 ) 2
Example 4: wide lane carrier double-difference ambiguity fixing
The observation equation is built by utilizing the carrier phase observation value, and the pseudo-range observation value can be introduced to solve the equation rank deficiency problem. Simultaneously solving a wide-lane carrier double-difference ambiguity floating-point solution and a variance-covariance matrix through a pseudo-range double-difference observation equation, a wide-lane carrier double-difference observation equation and a constraint equation, wherein the normal equation is as follows:
according to the least square criterion, obtaining:
wherein:
searching double-difference ambiguity of fixed wide-lane carrier through LAMBDA, and judging
Whether the threshold value is larger than the threshold value (generally set to be 3) or not, if so, carrying out the next step; otherwise, return to example 2.
Example 5: l1 Carrier double Difference ambiguity fixing
After the double-difference ambiguity of the wide lane carrier is fixed, when an error equation of observed values of columns L1 and L2 is obtained, the double-difference ambiguity of the wide lane carrier is determined according to N W ＝N L1 -N L2 Expressing the error equation as containing only L1 ambiguity N L1 In combination with constraint conditions to solve the L1 carrier double-difference ambiguity floating pointThe solution and variance-covariance matrix, the normal equation is:
according to the least square criterion, obtaining:
wherein:
searching fixed L1 carrier double-difference ambiguity through LAMBDA to judge
Whether the threshold value is larger than the threshold value (the same as the above), if so, carrying out the next step; otherwise, return to example 2.
Example 6: calculation of current epoch coordinate of monitoring point
And (3) substituting the solved result back into an error equation, and recombining a normal equation:
according to the least square criterion, obtaining:
wherein:
therefore, the current epoch coordinates of the monitoring point are as follows:
example 7: constraint equation updating
Selecting a proper moving window (the latest 20min data) for the coordinates without the gross error, separating signals with different frequencies in the observed data through wavelet analysis, updating the motion state of the super high-rise building, and reestablishing a constraint equation
Examples 3, 4, 5, 6 were repeated.
Claims (7)
1. A single epoch GNSS resolving method with horizontal constraint is characterized in that: the method specifically comprises the following steps;
step 1, utilizing early-stage GNSS observation data to solve static coordinates (X) of monitoring points 0 ,Y 0 ,Z 0 )；
Step 2, separating and observing signals with different frequencies in GNSS three-dimensional coordinate value data for 15-30min through wavelet analysis, establishing a simple harmonic motion equation of the super high-rise building, and solving the displacement y of the super high-rise building;
step 3, approximate coordinates (X) of the current monitoring point are utilized 0 ,Y 0 ,Z 0 ) Static coordinate (X) 0 ,Y 0 ,Z 0 ) And obtaining the displacement y by simple harmonic motion, and establishing a constraint equation
Wherein C is a matrix of coefficients, where,
is a three-dimensional coordinate correction number, and W is a residual error;
step 4, constructing an observation equation by using the carrier phase observation value, wherein the observation equation is rank-deficient, and introducing a pseudo-range observation value to solve the equation rank-deficient problem; simultaneously solving a wide lane carrier double-difference ambiguity floating solution and a variance-covariance matrix through a pseudo-range double-difference observation equation, a wide lane carrier double-difference observation equation and a constraint equation, and searching for a fixed wide lane carrier double-difference ambiguity through LAMBDA;
step 5, after the wide lane carrier double-difference ambiguity (WL) is fixed, when the error equation of the observed values of the train carriers L1 and L2 is carried out, the double-difference ambiguity N of the wide lane carrier is determined W Carrier L1 double difference ambiguity N L1 Sum L2 double difference ambiguity N L2 Relation N of W ＝N L1 -N L2 Expressing the error equation as containing only L1 ambiguity N L1 The method comprises the following steps of solving an L1 carrier double-difference ambiguity floating solution and a variance-covariance matrix by combining constraint conditions, and searching fixed L1 carrier double-difference ambiguity through LAMBDA;
step 6, substituting the fixed L1 carrier double-difference ambiguity back into an error equation, and recombining a normal equation to obtain a final coordinate;
and 7, selecting a proper moving window for the coordinates without the gross error, separating signals with different frequencies in the observed data through wavelet analysis, updating the motion state of the super high-rise building, and reestablishing a constraint equation
And repeating the steps 3 to 6.
2. The single-epoch GNSS solution with horizontal constraints according to claim 1, wherein: the steps are as follows: utilizing early-stage GNSS observation data to search a time period when the wind speed is zero, performing static calculation once per hour through GAMIT software, and then taking the average value of all calculation results as the initial position coordinate (X) of the monitoring point 0 ,Y 0 ,Z 0 )。
3. The single-epoch GNSS solution with horizontal constraints according to claim 1, wherein: in step 2, the simple harmonic motion equation is specifically as follows:
wherein: y is the displacement, f is the frequency, t is the time, A is the amplitude,
is the initial value of the phase.
4. The single-epoch GNSS solution with horizontal constraints according to claim 1, wherein: and (3) establishing a constraint equation: by using the displacement y obtained in step 2, the following can be obtained:
(X-X 0 ) 2 +(Y-Y 0 ) 2 +(Z-Z 0 ) 2 ＝y 2
let the GNSS approximate coordinate of the monitoring station be (X) 0 ,Y 0 ,Z 0 ) In (X) 0 ,Y 0 ,Z 0 ) And (3) performing Taylor formula expansion to obtain:
wherein: (dX, dY, dZ) is a three-dimensional coordinate correction number;
therefore, we get the constraint equation:
wherein: c ═ 2 (X) 0 -X 0 ) 2(Y 0 -Y 0 ) 2(Z 0 -Z 0 )]；W＝y 2 -(X 0 -X 0 ) 2 -(Y 0 -Y 0 ) 2 -(Z 0 -Z 0 ) 2 。
5. The single-epoch GNSS solution with horizontal constraints according to claim 1, wherein: the step 4 is specifically as follows: according to phase observation data of an epoch, the rank deficiency of a normal equation is 3, and an unknown number cannot be solved; therefore, the pseudo-range observation equation, the constraint condition and the wide-lane double-difference phase observation equation are combined to form the following mathematical model:
wherein: v is residual error, A is a coordinate parameter coefficient array, B is a coefficient array of double-difference ambiguity N, l is an OMC value, and P is weight;
applying least squares criterion, equation of law:
wherein: k is a joint coefficient vector of a constraint equation;
resolving a floating solution of the widelane ambiguity through the above normal equation, extracting a variance-covariance matrix of the floating solution, and fixing the widelane ambiguity by using an LAMBDA method.
6. The single-epoch GNSS solution with horizontal constraints according to claim 1, wherein: the step 5 is specifically as follows:
after the widelane ambiguity is fixed, according to N in the error equation of observed values of columns L1 and L2 W ＝N L1 -N L2 Expressing the error equation as containing only L1 ambiguity N L1 In combination with constraints, the following mathematical model is obtained:
the equation of the method can be obtained:
ambiguity fixing was performed using the Lambda method L1.
7. The single-epoch GNSS solution with horizontal constraints according to claim 1, wherein: the step 6 is specifically as follows:
the fixed L1 ambiguity is substituted back into the error equation, and the normal equation is recomposed:
the current epoch coordinate of the available monitoring point is as follows:
wherein, (X, Y, Z) is the current coordinate of the GNSS monitoring point, (X) 0 ,Y 0 ,Z 0 ) And (dX, dY and dZ) are three-dimensional coordinate correction numbers for approximate coordinates of the GNSS monitoring points.
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