CN112146557A - GNSS-based real-time bridge deformation monitoring system and method - Google Patents

GNSS-based real-time bridge deformation monitoring system and method Download PDF

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CN112146557A
CN112146557A CN202010823286.9A CN202010823286A CN112146557A CN 112146557 A CN112146557 A CN 112146557A CN 202010823286 A CN202010823286 A CN 202010823286A CN 112146557 A CN112146557 A CN 112146557A
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屈樊
张践
朱红巍
王�华
段准
马骏
易飞
艾文
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Wuhan Cangqiong Electronic Instrument Co ltd
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    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
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Abstract

The invention relates to a real-time bridge deformation monitoring system and method based on GNSS, which uses a reference station GNSS A device and a plurality of GNSS B devices of a mobile station to obtain real-time observation data, and the deformation monitoring system calculates the obtained observation data to obtain the three-dimensional coordinate offset of a bridge monitoring point, accurately knows the real-time displacement information of the bridge, provides analysis data for the safe operation of the bridge, and is convenient for the operation, maintenance and management of the bridge.

Description

GNSS-based real-time bridge deformation monitoring system and method
Technical Field
The invention relates to the field of surveying and mapping, in particular to a GNSS-based real-time bridge deformation monitoring system and method.
Background
GNSS generally refers to global navigation satellite system, and positioning of global navigation satellite system is based on observations of pseudoranges, ephemeris, satellite transmission time, etc. of a set of satellites, and also requires knowledge of user clock error. The global navigation satellite system is a space-based radio navigation positioning system that can provide users with all-weather three-dimensional coordinates and speed and time information at any location on the earth's surface or in near-earth space. In the prior art, a plurality of GNSS devices are used for data fusion and simultaneously participate in resolving, so that the problem of large data calculation amount and low calculation speed can occur.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a real-time bridge deformation monitoring system and method based on GNSS, which utilize mutually independent data calculation between a reference station GNSS A device and N mobile station GNSS B devices to directly extract deformation information from the variation of double-difference observation values of a reference point and a deformation monitoring point, so that the cost of the whole monitoring system is greatly reduced.
The invention discloses a real-time bridge deformation monitoring system based on a GNSS, which comprises a data receiving module, a data preprocessing module, a baseline initialization resolving module, a baseline real-time resolving module and a result output module, wherein the data receiving module is used for receiving data;
the data receiving module 1 comprises a device GNSS A for receiving first observation data of a reference station and N device GNSS B for receiving second observation data of a rover station, wherein N is an integer greater than or equal to 1, and the first observation data and the second observation data are transmitted to the data preprocessing module through a communication system in a wired, wireless or wired and wireless mixed mode;
the data preprocessing module 2 comprises a data synchronization module 2a for synchronizing the first observation data of the reference station and the second observation data of the rover station; the data processing module 2b is used for correcting various error sources; a positioning module 2c for pseudo-range point positioning to obtain satellite position, receiver clock error and altitude; a composition module 2d for composing pseudo-range and phase double-difference observed values;
the baseline initialization resolving module 3 is used for receiving the data processed by each module of the data preprocessing module, thereby obtaining the baseline vector and the initial value of the related information of various errors thereof and providing high-precision prior information for the error processing module 2 b;
the baseline real-time calculating module 4 is used for receiving the initialization data processed by the baseline initialization calculating module to carry out baseline calculation so as to obtain the latest baseline vector filtering calculating result;
and the result output module 5 is used for outputting a final calculation result calculated by the baseline real-time calculation module.
In the above technical solution, the data of the device GNSS a and the data of the N device GNSS B in the data receiving module 1 are resolved in parallel and independently.
In the above technical solution, the error processing module 2b further includes a deformation monitoring error processing submodule 2b a, a cycle slip detection and repair submodule 2bb, and an integer ambiguity fixing and confirming submodule 2 bc.
In the above technical solution, the deformation monitoring error processing submodule 2ba is configured to process various error sources in observation and analyze an influence on monitoring precision, so as to ensure that an accurate baseline component is obtained.
In the above technical solution, the cycle slip detection and repair submodule 2bb is configured to detect a lost observation value in the deformation monitoring data processing, correct the lost observation value, and restore the lost observation value to a correct observation value.
In the above technical solution, the integer ambiguity fixing and confirming submodule 2bc is configured to confirm the integer ambiguity in each phase observation value by using an LAMBDA method, which is a least square ambiguity reduction correlation adjustment method, to prepare for subsequent baseline solution.
In the technical scheme, the baseline initialization resolving module 3 initializes by using an OTF multi-epoch method, forms a double-difference observation equation according to the double-difference observation data and satellite information, calculates a floating point solution according to least square filtering, fixes an integer ambiguity by an LAMBDA method, and combines quality control indexes to obtain an initialization resolving result.
In the above technical solution, the baseline real-time calculating module 4 performs baseline calculation with the second observation data according to the initialized calculation result, and obtains a latest baseline vector filtering result by combining the baseline prior information and the first observation data according to a least square filtering method.
In the above technical solution, the final solution result includes time information, a baseline vector, covariance matrix information, precision evaluation information, satellite information, coordinate information, and an observation residual.
The invention also discloses a real-time bridge deformation monitoring method based on the GNSS, which comprises the following steps:
1) receiving first observation data of a reference station and second observation data of a mobile station in real time through a data receiving module, and transmitting the first observation data and the second observation data to a data preprocessing module;
2) the data preprocessing module receives the first observation data and the second observation data, performs preprocessing, and transmits the preprocessed observation data to the baseline initialization resolving module;
3) the baseline initialization resolving module receives the preprocessed observation data, resolves and obtains a baseline vector, and transmits the obtained baseline vector to the baseline real-time resolving module;
4) the baseline real-time resolving module performs baseline resolution on the obtained baseline vector and the related information to obtain a latest resolving result;
5) and outputting a resolving result and determining the real-time displacement information of the bridge.
The invention relates to a GNSS-based real-time bridge deformation monitoring system and method, which have the following beneficial effects:
1) data resolving which is independent of each other before a reference station GNSS A device and N mobile station GNSS B devices is applied, and theoretically, an infinite observation station device can participate in the data resolving;
2) automatically resolving the observed single-frequency or double-frequency, single-system or multi-system fusion GNSS data in a time period mode according to the resolving time period length set by a user, wherein the minimum time can reach 0.2 second for resolving once, and can be set from 0.2 second to other intervals, and other monitoring systems are generally more than 1 second;
3) both real-time and post-event solution support;
4) simultaneously, single-frequency/double-frequency data processing of GPS/BDS/GLONASS is supported;
5) real-time filtering resolving can be carried out on the observed GNSS data;
6) the device has the functions of selecting and setting a navigation satellite system and the carrier frequency thereof;
7) the real-time modeling and real-time estimation functions of troposphere delay errors are realized;
8) the function of eliminating the observation data of the specified satellite is realized;
9) the function of resisting the gross error of the observed value is provided;
10) the method has the resolving function of self-adapting to the deformation of the monitoring points;
11) the method has the function of evaluating the internal coincidence precision.
Drawings
FIG. 1 is a GNSS device connection diagram of a GNSS-based real-time bridge deformation monitoring system of the present invention;
FIG. 2 is a block diagram of a GNSS-based real-time bridge deformation monitoring system according to the present invention;
FIG. 3 is a data processing flow chart of a GNSS-based real-time bridge deformation monitoring system according to the present invention;
Detailed Description
The invention is described in further detail below with reference to the attached drawing
The invention discloses a real-time bridge deformation monitoring system based on GNSS, which comprises a data receiving module, a data preprocessing module, a baseline initialization resolving module, a baseline real-time resolving module and a result output module, wherein the data receiving module, the data preprocessing module, the baseline initialization resolving module, the baseline real-time resolving module and the result output module are shown in figure 2;
a data receiving module 1, including a device GNSS a for receiving first observation data of a reference station, N devices GNSS B or GNSS C for receiving second observation data of a rover station, where N is an integer greater than or equal to 1, and the first observation data and the second observation data are transmitted to a data preprocessing module through a wired, wireless, or wired and wireless hybrid communication system, as shown in fig. 1;
the data receiving module 1 is configured to receive the GNSS a data and the GNSS B data of N devices, and to perform parallel and independent solution processing.
The data preprocessing module 2 comprises a data synchronization module 2a for synchronizing the first observation data of the reference station and the second observation data of the rover station; the error processing module 2b is used for correcting various error sources; a positioning module 2c for pseudo-range point positioning to obtain satellite position, receiver clock error and altitude; a component module 2d for composing pseudo-range and phase double-difference observed values, as shown in fig. 2;
the error processing module 2b further comprises a deformation monitoring error processing submodule 2ba, a cycle slip detection and repair submodule 2bb and an integer ambiguity fixing and confirming submodule 2 bc;
and the deformation monitoring error processing submodule 2ba is used for processing various error sources in observation and analyzing the influence on monitoring precision, so as to ensure that accurate baseline components are obtained.
Specifically, the deformation monitoring system analyzes various error sources in the GPS/BeiD ou observation and the influence of the error sources on the monitoring precision aiming at the specific application scene of deformation monitoring, and provides corresponding countermeasures aiming at different characteristics of the error sources. The method comprises the following steps: 1) ephemeris error, 2) satellite clock error, 3) relativistic effect, 4) troposphere delay error, 5) ionosphere delay error, 6) multipath effect, 7) earth rotation correction, 8) receiver clock error, 9) antenna phase center error, 10) starting point coordinate error, and the like. The deformation monitoring system can reasonably process various errors (model correction or parameter estimation is adopted), and accurate and reliable baseline vectors are ensured to be obtained.
The cycle slip detection and restoration submodule 2bb is configured to detect a lost observation value in the deformation monitoring data processing, correct the observation value, and restore the observation value to a correct observation value.
Specifically, in the GNSS carrier phase measurement, to achieve high-precision positioning, it is necessary to ensure that there is no cycle slip in the carrier phase observation data, and therefore, correct detection and cycle slip repair are a key problem in the GNSS carrier phase data processing. Cycle slip detection is the discovery of cycle slip using observed information. After the cycle slip is detected, the carrier phase observed value after the cycle slip is corrected by estimating the number of cycles lost using the observation information, which is called cycle slip repair. If one can detect when and where a cycle slip has occurred and determine an accurate value for the number of whole cycles lost, subsequent observations can be corrected one by one to restore them to the correct observations, a task known as cycle slip detection and remediation. Generally, the cycle slip detection and repair firstly preliminarily detect some obvious cycle slips and repair, then detect some smaller cycle slips by using residual information O-c (observation Minus calculation), repair the cycle slips under the condition of cycle slip confirmation, and estimate the cycle slips which cannot be confirmed as unknown parameters (blend with the integer ambiguity parameters).
In the pre-solution module for GNSS deformation monitoring, the double-difference observation value of a certain epoch can be represented as follows:
Figure BDA0002635098050000051
in the above formula, the first and second carbon atoms are,
Figure BDA0002635098050000052
for the purpose of the double-difference phase data,
Figure BDA0002635098050000053
the distance between the two different stations is the star distance,
Figure BDA0002635098050000054
in order to be a double-difference ambiguity,
Figure BDA0002635098050000055
the residual error after double difference, such as observation error, multipath, etc., f is the carrier frequency, and c is the speed of light. It can be seen that the effects of orbit error, satellite clock error, troposphere, ionosphere, receiver clock error, etc. are eliminated by double differences, whose phase can be expressed as a polynomial of the above three terms, the first term for the static baseline
Figure BDA0002635098050000056
The change with time is very smooth, the value of the third term is very small, and the second term, i.e. the cycle slip, does not occur
Figure BDA0002635098050000057
No change, so that the observed value of double difference phases
Figure BDA0002635098050000058
Should also be smooth over time. Once a cycle slip has occurred, i.e.
Figure BDA0002635098050000059
When sudden change occurs, the observed value of double differences
Figure BDA00026350980500000510
And no longer smooth but abrupt. Therefore, the cycle slip can be detected by time series using the double-difference observation value as a detection quantity.
The method only uses one frequency observation data, thereby being suitable for a single-frequency/double-frequency receiver. The method can only detect the cycle slip of the double-difference observed quantity, and can not determine the non-difference data position of the cycle slip, thereby being not beneficial to cycle slip analysis. Also, the method is by analysis
Figure BDA00026350980500000511
The cycle slip is detected and analyzed over a time series, and if the observed sampling rate is higher,
Figure BDA00026350980500000512
and
Figure BDA00026350980500000513
the smaller the variation of (A), the observed value
Figure BDA00026350980500000514
The more gradual the change of (A), the easier it is to detect
Figure BDA00026350980500000515
Cycle slip present in (1).
And the integer ambiguity fixing and confirming submodule 2bc is used for confirming the integer ambiguity in each phase observation value through an L AMBDA method and preparing for subsequent baseline solution, and the LAMBDA method is a least square ambiguity reduction correlation adjustment method.
In particular, the GPS receiver can only measure a less than integer portion of the carrier phase and a portion that changes over a period of time. Thus, in each phase observation, there is a constant unknown, called initial integer ambiguity (integer ambiguity for short). This ambiguity parameter must be resolved before the carrier phase measurements can be converted into precise geometric distances between the satellite and the receiver. Once all ambiguities are correctly resolved, a positioning result with centimeter-level accuracy can be easily obtained using four satellites. The determination of the integer ambiguity is a very critical issue when using the double-difference least squares algorithm for baseline solution. At present, relevant scholars propose a series of integer ambiguity determination methods, in a deformation monitoring system, an lamb da method is adopted to determine integer ambiguity in an initialization stage, and after the initialization is completed, a known baseline method is adopted to determine integer ambiguity in a coordinate domain in a single epoch mode.
Among them, the Lambda method, which is the Least-squares Ambiguity resolution Adjustment (Lambda), was proposed in 1993 by the Tennissen of Delft university, the Netherlands. The method is the most successful ambiguity searching method in the current rapid static positioning, can shorten the searching range and accelerate the searching process, and is widely adopted. The method comprises the following basic steps: z transformation; searching algorithm.
A single epoch integer ambiguity determination method based on prior coordinate information;
for the short edge monitoring network, influence of various system errors is ignored, and then the double-difference carrier phase observation equation can be abbreviated as the following form:
Figure BDA0002635098050000061
when the coordinate of the reference station is in the meter-level range, the influence of the coordinate error on the baseline component is small, the error is ignored, the coordinate of the reference station is determined to be accurately known and fixed, the approximate value of the rover coordinate is given, the approximate value of the geometric distance of the double-difference observation value can be calculated, the approximate value is linearized based on the initial value of the coordinate, and the method can be obtained:
Figure BDA0002635098050000062
wherein
Figure BDA0002635098050000063
As an approximation of the geometric distance of the dual diff-star,
Figure BDA0002635098050000064
cosine of direction from rover to reference star and delta of direction from rover to rover star, respectively2Is the rover coordinate error amount, and therefore, the error of the ambiguity parameter floating solution caused by the rover coordinate error does not exceed the error of the rover coordinate based on the observation data of one epoch. Meanwhile, the precision of the double-difference phase observed value is considered to be high, so that if high-precision prior information of a baseline vector can be obtained, a high-precision floating solution result of an ambiguity parameter can be obtained by using observation data of one or a few epochs, the deviation between the high-precision floating solution result and an accurate fixed solution is small, and an integer method or other ambiguity fixing methods are adopted, so that an ambiguity fixed solution can be very easily obtained, and the ambiguity fixing is realized.
In the deformation monitoring, because the variation among the epochs of the coordinate of the measuring station is small, a baseline vector with high precision of the current epoch can be quickly obtained by combining the coordinate result of the measuring station of the previous epoch, and the double-difference ambiguity parameter can be directly calculated by adopting a single epoch mode by substituting the coordinate of the measuring station.
After the fixed solution of the ambiguity parameter is obtained, it needs to be verified to confirm the reliability of the fixed solution, otherwise, a serious error result may be generated. The self-developed deformation monitoring software adopts Ratio test and double-frequency related constraint test.
The Ratio test is to fix the ambiguity based on the LAMBDA method, to obtain multiple sets of alternative solutions of the ambiguity parameter, and usually to confirm with the Ratio test, which means that the ambiguity parameter is fixed to the Ratio of the error in the residual error of the parameter estimation after the suboptimal solution and the optimal solution obtained based on the LAMBDA method, and can be expressed as:
ratio=ssub-optimal/sOptimization of
The index reflects the reliability of the integer ambiguity parameter, and the greater the value, the higher the reliability of the ambiguity fixing solution. It should be noted that the above-mentioned indexes are related to various factors, including the quality of the observed data, the quality of the observed conditions (the distribution and variation of the geometric figures of the satellite constellation), and the like. Therefore, in the actual data processing, the corresponding adjustment is needed, and in the self-developed deformation monitoring software, the tolerance is directly fixed to 3 according to experience and relevant documents.
The double-frequency correlation constraint test is that the ambiguity fixed solutions of different frequencies can be seen according to an observation equation, and the following relations are satisfied:
Figure BDA0002635098050000071
wherein,
Figure BDA0002635098050000072
and fixing a solution and double-difference phase observed values for ambiguity parameters at different frequencies. From the error propagation rate, one can obtain:
Figure BDA0002635098050000073
thus, for a set of ambiguity parameter alternative solutions, it is assumed
Figure BDA0002635098050000074
Calculated for the possible correct ambiguity result
Figure BDA0002635098050000075
In error
Figure BDA0002635098050000076
Should be an integer, if the requirement is met, the set of alternative solutions is considered as candidates, otherwise it is discarded, as shown in fig. 3.
The baseline initialization resolving module 3 is used for receiving the data processed by each module of the data preprocessing module, thereby obtaining the baseline vector and the initial value of the related information of various errors thereof and providing high-precision prior information for the error processing module 2 b;
the baseline initialization resolving module is initialized by using an OTF multi-epoch mode, a double-difference observation equation is formed according to double-difference observation data and satellite information, a floating point solution is calculated according to least square filtering, an integer ambiguity is fixed by an LAMBDA method, and an initialization resolving result is obtained by combining quality control indexes. Due to the short baseline, the result of the rapid static solution (less than 30 minutes) is generally better than 2cm, and the precision requirement of subsequent treatment can be met.
The baseline real-time calculating module 4 is used for receiving the initialization data processed by the baseline initialization calculating module to carry out baseline calculation so as to obtain the latest baseline vector filtering calculating result;
and performing baseline calculation with the second observation data according to the initialization calculation result, and obtaining a latest baseline vector filtering result by combining baseline prior information and the first observation data according to a least square filtering method.
And the result output module 5 is used for outputting a final calculation result calculated by the baseline real-time calculation module.
The final calculation result comprises time information, a base line vector, covariance matrix information, precision evaluation information, satellite information, coordinate information and an observation value residual error.
The invention also discloses a real-time bridge deformation monitoring method based on the GNSS, which comprises the following steps:
1) receiving first observation data of a reference station and second observation data of a mobile station in real time through a data receiving module, and transmitting the first observation data and the second observation data to a data preprocessing module;
2) the data preprocessing module receives the first observation data and the second observation data, performs preprocessing, and transmits the preprocessed observation data to the baseline initialization resolving module;
3) the baseline initialization resolving module receives the preprocessed observation data, resolves and obtains a baseline vector, and transmits the obtained baseline vector to the baseline real-time resolving module;
4) the baseline real-time resolving module performs baseline resolution on the obtained baseline vector and the related information to obtain a latest resolving result;
5) and outputting a resolving result and determining the real-time displacement information of the bridge.
The invention relates to a real-time bridge deformation monitoring system and method based on GNSS, which directly extracts deformation information from the variation of double-difference observation values of a reference point and a deformation monitoring point, and provides a new method without solving the deformation value through the original complicated two-stage GP S positioning result, establishes a new model and a new method, and compiles a new system. Therefore, the problems of detection and repair of cycle slip, integer ambiguity determination and the like are avoided. And the new model can only use a single-frequency observation value, thereby providing possibility for using a single-frequency receiver in short-distance high-precision deformation monitoring and greatly reducing the cost of the whole GPS monitoring system.
The above method embodiments correspond to the system embodiments one to one, and reference may be made to the system embodiments for a brief point of the method embodiments.
The parts not described in the specification are prior art or common general knowledge. The present embodiments are to be considered as illustrative and not restrictive, and all changes coming within the meaning and equivalency range of the appended claims are intended to be embraced therein.

Claims (10)

1. The utility model provides a real-time bridge deformation monitoring system based on GNSS which characterized in that: the system comprises a data receiving module, a data preprocessing module, a baseline initialization resolving module, a baseline real-time resolving module and a result output module;
the data receiving module (1) comprises a device GNSS A for receiving first observation data of a reference station and N device GNSS B for receiving second observation data of a rover station, wherein N is an integer greater than or equal to 1, and the first observation data and the second observation data are transmitted to the data preprocessing module through a communication system in a wired, wireless or wired and wireless mixed mode;
a data pre-processing module (2) comprising a data synchronization module (2a) for synchronizing the reference station first observation and the rover second observation; the error processing module (2b) is used for correcting various error sources; a positioning module (2c) for pseudo-range point positioning and obtaining satellite position, receiver clock error and altitude; a composition module (2d) for composing pseudo-range and phase double-difference observed values;
the baseline initialization resolving module (3) is used for receiving the data processed by each module of the data preprocessing module so as to obtain the baseline vector and the initial value of the related information of various errors of the baseline vector, and provide high-precision prior information for the error processing module (2 b);
the baseline real-time calculating module (4) is used for receiving the initialization data processed by the baseline initialization calculating module to carry out baseline calculation so as to obtain the latest baseline vector filtering calculating result;
and the result output module (5) is used for outputting the final calculation result calculated by the baseline real-time calculation module.
2. The GNSS-based real-time bridge deformation monitoring system of claim 1, wherein: and the data of the equipment GNSS A and the data of the N equipment GNSS B in the data receiving module (1) are resolved in parallel and independently.
3. The GNSS-based real-time bridge deformation monitoring system of claim 1, wherein: the error processing module (2b) further comprises a deformation monitoring error processing submodule (2ba), a cycle slip detection and repair submodule (2bb) and an integer ambiguity fixing and confirming submodule (2 bc).
4. The GNSS-based real-time bridge deformation monitoring system of claim 3, wherein: and the deformation monitoring error processing submodule (2ba) is used for processing various error sources in observation and analyzing the influence on monitoring precision, so as to ensure that accurate baseline components are obtained.
5. The GNSS-based real-time bridge deformation monitoring system of claim 3, wherein: and the cycle slip detection and repair submodule (2bb) is used for detecting a lost observation value in the deformation monitoring data processing, correcting the lost observation value and recovering the lost observation value to a correct observation value.
6. The GNSS-based real-time bridge deformation monitoring system of claim 3, wherein: and the integer ambiguity fixing and confirming submodule (2bc) is used for confirming the integer ambiguity in each phase observation value by using a LAMBDA (least squares ambiguity reduction) method, and preparing for subsequent baseline solution, wherein the LAMBDA method is a least square ambiguity reduction correlation adjustment method.
7. The GNSS-based real-time bridge deformation monitoring system according to claims 1-6, wherein: the baseline initialization resolving module (3) is initialized by using an OTF multi-epoch mode, a double-difference observation equation is formed according to the double-difference observation data and satellite information, a floating point solution is calculated according to least square filtering, the integer ambiguity is fixed by an LAMBDA method, and an initialization resolving result is obtained by combining quality control indexes.
8. The GNSS-based real-time bridge deformation monitoring system of claim 7, wherein: and the baseline real-time calculating module (4) carries out baseline calculation with the second observation data according to the initialized calculation result, and combines baseline prior information and the first observation data according to a least square filtering method to obtain a latest baseline vector filtering result.
9. The GNSS-based real-time bridge deformation monitoring system of claim 1, wherein: the final resolving result comprises time information, a base line vector, covariance matrix information, precision evaluation information, satellite information, coordinate information and an observed value residual error.
10. A real-time bridge deformation monitoring method based on GNSS is characterized by comprising the following steps:
1) receiving first observation data of a reference station and second observation data of a mobile station in real time through a data receiving module, and transmitting the first observation data and the second observation data to a data preprocessing module;
2) the data preprocessing module receives the first observation data and the second observation data, performs preprocessing, and transmits the preprocessed observation data to the baseline initialization resolving module;
3) the baseline initialization resolving module receives the preprocessed observation data, resolves and obtains a baseline vector, and transmits the obtained baseline vector to the baseline real-time resolving module;
4) the baseline real-time resolving module performs baseline resolution on the obtained baseline vector and the related information to obtain a latest resolving result;
5) and outputting a resolving result and determining the real-time displacement information of the bridge.
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CN113916179A (en) * 2021-12-15 2022-01-11 北京讯腾智慧科技股份有限公司 Highway and railway dual-purpose bridge line shape automatic measurement system and method
CN114200854A (en) * 2021-11-05 2022-03-18 中铁大桥勘测设计院集团有限公司 Precision design method for first-level GNSS control network of sea-crossing bridge
CN117055069A (en) * 2023-08-16 2023-11-14 无锡卡尔曼导航技术有限公司南京技术中心 Mapping GNSS deformation monitoring method, device and medium
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