Inversion cross-water-area bridge deformation solving method based on Beidou No.3 / GNSS (Global Navigation Satellite System)

Abstract

The invention discloses a cross-water-area bridge deformation solving method based on Beidou No.3 / GNSS inversion, and particularly relates to the technical field of bridge monitoring. The method comprises the following steps: establishing an observation equation by combining all satellites based on satellites which can be observed by a bridge structure monitoring station; solving the observation equation by using a matrix method to obtain a prediction state vector of the deformation quantity of the bridge structure and a covariance matrix of the state vector; in consideration of the influence of gross error of a Beidou No.3 / GNSS observation value, a self-adaptive factor is provided to correct a predicted value of a state vector; obtaining a vector K and an updated state vector covariance; introducing a robust factor M to determine the weight of each type of observation values in consideration of gross errors in the Beidou No.3 / GNSS carrier phase observation values; updating the matrix K and the state covariance matrix by using the corrected measurement covariance matrix R; and calculating the updated state vector. According to the technical scheme, the problem that a conventional Beidou / GNSS data processing method is low in precision is solved, and the precision of bridge deformation calculation is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge monitoring, and in particular to a method for solving deformation of a cross-water bridge based on BeiDou-3 / GNSS inversion. Background Art

[0002] my country has a large number of bridges. By the end of 2023, the total number of highway bridges in my country will reach 1.0793 million. Moreover, the performance of bridges built earlier has seriously degraded with the increasing traffic load, which will seriously affect the normal use of bridges and even cause damage to people's lives and property. In bridge structure health monitoring BSHM (Bridge Structure Health Monitoring), deformation response is an important basis for judging structural safety. Deformation response is the response of the structure to performance degradation and damage under load. Accurately capturing the deformation of the bridge structure can timely grasp the dynamic response and health status of the bridge under load, which can ensure the service life of the bridge and improve the toughness of the bridge structure. It has certain reference significance for managers to formulate bridge maintenance policies.

[0003] Traditional bridge structure deformation monitoring methods use measuring instruments such as total stations and levels. While these methods offer high precision, they also suffer from labor-intensiveness, low efficiency, and high costs. BeiDou-3 / GNSS technology enables real-time, all-weather, automated measurement regardless of weather conditions. This significantly reduces labor intensity and improves efficiency, offering broad application in bridge construction control, intelligent construction, and information-based maintenance.

[0004] like Figure 1 As shown in the figure, the current conventional BeiDou-3 / GNSS data processing method first calculates the coordinate sequence of the bridge structure monitoring station and then obtains the deformation value through differential coordinates. This method has problems such as error accumulation and the introduction of absolute coordinate errors. Furthermore, based on the principle of resection between the BeiDou-3 / GNSS satellite and the bridge structure monitoring station, it does not consider the inherent characteristics of bridge structure deformation, which limits the accuracy of BeiDou-3 / GNSS in sensing the transient deformation of bridges. Summary of the Invention

[0005] The present invention aims to provide a method for solving the deformation of cross-water bridges based on BeiDou-3 / GNSS inversion, which solves the problem of low accuracy in conventional BeiDou / GNSS data processing methods.

[0006] In order to achieve the above object, the technical solution of the present invention is as follows: a method for solving the deformation of a bridge across waters based on BeiDou-3 / GNSS inversion, comprising the following steps:

[0007] S1. Based on the satellites that can be observed by the bridge structure monitoring station, the observation equation of the BeiDou-3 / GNSS monitoring station to satellite carrier phase observation value is established by combining all satellites;

[0008] S2. Using the matrix method to solve the observation equation, we can obtain the predicted state vector of the bridge structure deformation and the covariance matrix of the state vector considering different satellite observation accuracy.

[0009] S3. Considering the influence of the gross error of BeiDou-3 / GNSS observations, an adaptive factor is proposed to correct the predicted value of the state vector in step S2.

[0010] S4. Obtain the vector K and the updated state vector covariance through step S3;

[0011] S5. Considering that there are still gross errors in the BeiDou-3 / GNSS carrier phase observations, the robustness factor M is introduced to determine the weight of each type of observation;

[0012] S6. Use the corrected measurement covariance matrix Update the K matrix and state covariance matrix;

[0013] S7. Calculate the updated state vector.

[0014] Furthermore, the observation equation of step S1 is:

[0015] y=Agx+ε y , ε y :N(0,Q yy ).

[0016] Furthermore, the calculation formula of step S2 is as follows:

[0017]

[0018] Where δx is the state vector, - represents the predicted value, + represents the updated value, k and k-1 represent two adjacent epochs, Φ represents the transfer matrix, P represents the state vector covariance matrix, and Q represents the process noise of the covariance matrix.

[0019] Furthermore, the calculation formula of step S3 is as follows:

[0020]

[0021] Where c0 and c1 are empirical values, c0 = 2, c1 = 3.5;

[0022] is an intermediate calculated value, expressed as:

[0023]

[0024] in is the estimated value of the state vector calculated using the new observations;

[0025] tr represents the trace of the matrix.

[0026] Furthermore, the calculation formula of step S4 is as follows:

[0027]

[0028] Furthermore, the calculation formula of step S5 is as follows:

[0029]

[0030] Among them F i j represents the F test statistic, and is the F test value at the significance level α0 and α1, with the significance level α0 = 0.05 and α1 = 0.1;

[0031] v j represents the degrees of freedom;

[0032] Covariance matrix of the corrected observations Elements

[0033]

[0034] in, and Represent the pseudorange and carrier phase value noise of each satellite respectively;

[0035] Obtained by solving the original covariance matrix;

[0036] R is the classification factor of GPS and BeiDou satellites,

[0037]

[0038] Furthermore, the calculation formula of step S6 is as follows:

[0039]

[0040] Furthermore, the calculation formula of step S7 is as follows:

[0041]

[0042] Where δz represents the linear combination observation value of BeiDou and GPS.

[0043] Compared with the existing technology, this solution has the following beneficial effects:

[0044] 1. The traditional solution treats the station coordinates as unknowns. After solving for the station coordinates, the deformation is obtained by differentially calculating the station coordinates. This presents a problem of gradual error accumulation. The disadvantage is that the accuracy is at the centimeter level, and the errors gradually accumulate. Furthermore, the traditional method first solves the monitoring station coordinates based on the BeiDou-3 / GNSS satellite range intersection method, and then obtains the deformation by differentially calculating the two coordinates, resulting in a two-step solution. However, this solution treats the bridge structure deformation as an unknown parameter and takes into account the gross error caused by the carrier phase observation from the monitoring station to the BeiDou-3 / GNSS satellite, thus calculating the bridge structure deformation using a one-step solution.

[0045] 2. This solution uses the deformation values ​​of bridge structure monitoring stations as the error source of carrier phase observations. The influence of the bridge structure deformation values ​​on the carrier phase observations is analyzed. Using the bridge structure deformation values ​​as unknown parameters, a one-step solution is used to directly calculate the deformation values ​​without error accumulation. Furthermore, considering that BeiDou-3 / GNSS carrier phase observations are subject to gross errors due to the influence of the ionosphere and troposphere when the bridge structure is obscured, an adaptive factor robust solution algorithm is derived. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a schematic diagram of the traditional bridge deformation monitoring based on the North technology in the background art;

[0047] Figure 2 This is a schematic diagram of the change in carrier phase observation caused by the deformation of the measuring station in this embodiment;

[0048] Figure 3 This is the deformation monitoring point of the bridge across water area inverted by BeiDou-3 / GNSS in this embodiment;

[0049] Figure 4 : is a comparison diagram of the deformation variables calculated by the solution method adopted in this embodiment and the traditional method;

[0050] Figure 5 3 is a comparison chart of the errors between the solution method adopted in this embodiment and the traditional solution method. DETAILED DESCRIPTION

[0051] The present invention will be further described in detail below through specific embodiments:

[0052] Example

[0053] The deformation value of the bridge monitoring station causes the distance between the station and the satellite to change, which has a great impact on the high-precision data processing of BeiDou-3. The schematic diagram of the change of carrier phase observation caused by station deformation is shown in Figure 2 shown.

[0054] exist Figure 2In the equation, S(i) represents the satellite observed at the same time, R is the station coordinate without considering the bridge deformation, and γ i is the distance between the satellite and the station R, R′ is the station coordinate considering the bridge deformation, γ′ i is the distance between the satellite and the station R′. R is the origin of the station coordinate system, (X i ,Y i ,Z i ) are satellite coordinates, and the station coordinates R′(x,y,z) take into account the bridge deformation. RR′ is the station coordinate displacement caused by the bridge deformation. (x,y,z) represents the north, east, and vertical components, respectively. δT is the estimated value of the receiver clock error taking into account the bridge deformation, and δT′ is the estimated value without taking into account the receiver clock error. The RR′ distance is very small compared to the satellite orbit altitude of more than 20,000 km, so the satellite elevation angle θ is calculated. i and azimuth angle α i When , the station coordinate change RR′ caused by the bridge deformation can be ignored.

[0055]

[0056] The change in the distance between the satellite and the station caused by the bridge deformation is expressed as:

[0057]

[0058] where δ εi =ε i -ε′ i , δt=δT-δT′, δt is the receiver clock error caused by bridge deformation.

[0059] In the bridge deformation calculation precision single point positioning PPP (Precise Point Positioning), the traditional data processing is to treat the measuring station coordinates as unknowns, and then calculate the measuring station coordinates and obtain the deformation by differential, which has the problem of error propagation and accumulation. DOB It is an unknown parameter. The solution model is shown in the formula below. The deformation value is directly obtained by one-step solution.

[0060]

[0061] Among them, P i is the pseudorange observation value, Φ i is the carrier phase observation value, f i is the signal frequency, ρ is the geometric distance between the satellite and the station, l DOB is the bridge deformation value, d t is the receiver clock error, d trop is the tropospheric delay error, λ is the wavelength, N is the combined phase ambiguity value, modelse Indicates that all other errors, including Earth rotation, solid tide, relativity, antenna phase center correction, etc., are corrected by the corresponding model.

[0062] like Figure 3 As shown in the figure, the deformation solution method of bridges across water areas based on BeiDou-3 / GNSS inversion includes the following steps:

[0063] S1. Assuming that the observation station r can observe m satellites at a certain epoch, the observation equation of the BeiDou-3 / GNSS monitoring station to satellite carrier phase observation value is established by combining all satellites. When constructing the observation equation, the bridge deformation is regarded as an error source of the bridge structure monitoring station to satellite carrier phase observation value and listed as an unknown parameter. The observation equation is expressed as:

[0064] y=Agx+ε y , ε y :N(0,Q yy ).

[0065] S2. Use the matrix method to solve the observation equation to obtain the predicted vector of the bridge structure deformation and the covariance matrix of the state vector considering different satellite observation accuracy. The calculation formula is as follows:

[0066]

[0067] Where δx is the state vector, - represents the predicted value, + represents the updated value, k and k-1 represent two adjacent epochs, Φ represents the transfer matrix, P represents the state vector covariance matrix, and Q represents the process noise of the covariance matrix.

[0068] S3. Considering the influence of gross errors of BeiDou-3 / GNSS observation values, an adaptive factor is proposed to correct the predicted value of the state vector in step S2. The calculation formula is as follows:

[0069]

[0070] Where c0 and c1 are empirical values, c0 = 2, c1 = 3.5;

[0071] is an intermediate calculated value, expressed as:

[0072]

[0073] in is the estimated value of the state vector calculated using the new observations;

[0074] tr represents the trace of the matrix.

[0075] S4. Obtain the covariance of the vector K and the updated state vector through step S3; the calculation formula is as follows:

[0076]

[0077] S5. Considering that there are still gross errors in the BeiDou-3 / GNSS carrier phase observations, the robustness factor M is introduced to determine the weight of each type of observation; the calculation formula is as follows:

[0078]

[0079] Among them F i j represents the F test statistic, and is the F test value at the significance level α0 and α1, with the significance level α0 = 0.05 and α1 = 0.1;

[0080] v j represents the degrees of freedom;

[0081] Covariance matrix of the corrected observations Elements

[0082]

[0083] in, and Represent the pseudorange and carrier phase value noise of each satellite respectively;

[0084] Obtained by solving the original covariance matrix;

[0085] R is the classification factor of GPS and BeiDou satellites,

[0086]

[0087] S6. Use the corrected measurement covariance matrix Update the K matrix and state covariance matrix; the calculation formula is as follows:

[0088]

[0089] S7, the updated state vector, is calculated as follows:

[0090]

[0091] Where δz represents the linear combination observation value of BeiDou and GPS.

[0092] Case comparison:

[0093] like Figure 4 As shown in the figure, the data was measured on a bridge across waters in Chongqing from 8:00 am to 2:00 pm Beijing time on August 12, 2024. Figure 4 The midpoint represents the deformation variable of the traditional two-step solution, and the line represents the deformation variable solved by the method adopted in this embodiment.

[0094] like Figure 5 As shown, the traditional method uses the geometric distance resection method based on the Beidou / GNSS satellite to the bridge structure monitoring station, using the least squares method to calculate the coordinates of the bridge structure monitoring station, and then obtains the bridge structure deformation through a second-phase coordinate difference. The method of this embodiment treats the bridge structure deformation as an unknown parameter in the precise single-point positioning model, directly solving for the unknown deformation variable while taking into account gross errors, without errors such as spatial coordinate datum conversion.

[0095] Taking the measurement value of the measuring robot as the true value, the root mean square error of the traditional two-step solution is calculated to be 1.9 cm, and the root mean square error of the method described in this embodiment is 0.8 cm, achieving a breakthrough from the centimeter-level deformation accuracy of the traditional method to the millimeter-level deformation accuracy.

[0096] The above are only embodiments of the present invention, and common knowledge such as the specific structure and / or characteristics of the scheme are not described in detail here. It should be pointed out that for those skilled in the art, without departing from the structure of the present invention, several variations and improvements can be made, which should also be regarded as the scope of protection of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A method for solving deformation of bridges across waters based on BeiDou-3 / GNSS inversion, characterized by: The steps include: S1. Based on the satellites that can be observed by the bridge structure monitoring station, the observation equation of the BeiDou-3 / GNSS monitoring station to satellite carrier phase observation value is established by combining all satellites; S2. Using the matrix method to solve the observation equation, we can obtain the predicted state vector of the bridge structure deformation and the covariance matrix of the state vector considering different satellite observation accuracy. S3. Considering the influence of the gross error of BeiDou-3 / GNSS observations, an adaptive factor is proposed to correct the predicted value of the state vector in step S2. S4. Obtain the vector K and the updated state vector covariance through step S3; S5. Considering that there are still gross errors in the BeiDou-3 / GNSS carrier phase observations, the robustness factor M is introduced to determine the weight of each type of observation; S6. Use the corrected measurement covariance matrix Update the K matrix and state covariance matrix; S7. Calculate the updated state vector.

2. The method for solving deformation of a cross-water bridge based on BeiDou-3 / GNSS inversion according to claim 1 is characterized by: The observation equation of step S1 is: y=Agx+ε y ,ε y :N(0,Q yy )。 3. The method for solving deformation of a cross-water bridge based on BeiDou-3 / GNSS inversion according to claim 2 is characterized by: The calculation formula of step S2 is as follows: Where δx is the state vector, - represents the predicted value, + represents the updated value, k and k-1 represent two adjacent epochs, Φ represents the transfer matrix, P represents the state vector covariance matrix, and Q represents the process noise of the covariance matrix.

4. The method for solving deformation of a cross-water bridge based on BeiDou-3 / GNSS inversion according to claim 3 is characterized by: The calculation formula of step S3 is as follows: Where c0 and c1 are empirical values, c0 = 2, c1 = 3.5; is an intermediate calculated value, expressed as: in is the estimated value of the state vector calculated using the new observations; tr represents the trace of the matrix.

5. The method for solving deformation of a bridge across waters based on BeiDou-3 / GNSS inversion according to claim 4 is characterized by: The calculation formula of step S4 is as follows:

6. The method for solving deformation of a bridge across waters based on BeiDou-3 / GNSS inversion according to claim 5 is characterized by: The calculation formula of step S5 is as follows: Among them F i j represents the F test statistic, and is the F test value at the significance level α0 and α1, with the significance level α0 = 0.05 and α1 = 0.1; v j represents the degrees of freedom; Covariance matrix of the corrected observations Elements in, and Represent the pseudorange and carrier phase value noise of each satellite respectively; Obtained by solving the original covariance matrix; R is the classification factor of GPS and BeiDou satellites, 7. The method for solving deformation of a bridge across waters based on BeiDou-3 / GNSS inversion according to claim 6 is characterized by: The calculation formula of step S6 is as follows:

8. The method for solving deformation of a bridge across waters based on BeiDou-3 / GNSS inversion according to claim 7 is characterized by: The calculation formula of step S7 is as follows: Where δz represents the linear combination observation value of BeiDou and GPS.

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