A GNSS-IMU-based method for monitoring the deformation and attitude of cableway supports

Abstract

A GNSS-IMU-based method for monitoring the deformation and attitude of cableway supports involves installing GNSS receivers 1 and 2 parallel to each other on both sides of the cableway crossbar. GNSS receiver 3 is placed perpendicular to receiver 1, forming two mutually perpendicular baselines. The IMU is positioned between receivers 1 and 2. GNSS receivers 1, 2, and 3 synchronously measure the cableway crossbar. The pseudorange signal from receiver 1 is corrected. The corrected pseudorange data from receiver 1 is then subtracted from the pseudorange signals from receivers 2 and 3 using a double-difference solution model. The baseline coordinate data is then transformed using the Euler angle transformation formula to obtain three-axis Euler angle attitude data. The IMU measures the three-axis acceleration data of the cableway crossbar. The three-axis Euler angle attitude data and the three-axis acceleration data are fused, and a covariance matrix is ​​constructed. This invention enables more effective, accurate, and timely monitoring of the deformation of the cableway crossbar.

Description

Technical Field

[0001] This invention relates to a method for monitoring the deformation of cableway supports, specifically a method for monitoring the deformation and attitude of cableway supports based on GNSS-IMU, belonging to the field of cableway support monitoring and positioning technology. Background Technology

[0002] Deformation monitoring involves using specialized instruments and methods to continuously observe the deformation phenomena of a deformable body, analyze its deformation morphology, and predict its future development. Deformation monitoring includes establishing a deformation detection network to monitor horizontal displacement, settlement, tilt, cracks, deflection, swaying, and vibration.

[0003] Currently, conventional deformation monitoring methods typically refer to methods that use conventional surveying instruments to measure direction, angle, side length, and elevation difference to determine deformation. These methods include setting up a perimeter-angle grid, various intersection methods, polar coordinate methods, geometric leveling, and trigonometric leveling. Conventional geodetic instruments include optical theodolites, optical levels, electromagnetic distance measuring instruments, electronic theodolites, electronic total stations, and surveying robots.

[0004] The GNSS method, currently available, is an emerging deformation monitoring approach that can be used for high-precision monitoring and forecasting of bridges, dams, and other structures. Existing research, through short-baseline tests, has demonstrated that the accuracy and characteristics of GNSS receivers can meet the potential high-frequency data rate requirements for applications such as bridge deformation monitoring. Meanwhile, researchers in the UK have conducted GPS monitoring, deploying two reference stations and five monitoring stations. Studies show that GNSS can identify changes in bridge vibration frequencies caused by structural variations, providing easily obtainable and useful data for bridge structure monitoring. Experiments have monitored the Nottingham Wilford Suspension Bridge in the UK using GNSS receivers and accelerometers. Research indicates that the dynamic displacements identified by the two sensors are largely consistent, with both the standard deviation and average deviation of the difference being less than 1 mm. The combination of GNSS and accelerometers for deformation monitoring can accurately and effectively identify dynamic displacement changes in bridges, achieving millimeter-level positioning accuracy. However, current cableway support deformation monitoring faces limitations such as high alignment accuracy, stringent attitude requirements, and complex environments. At present, GNSS alone is insufficient to meet the deformation monitoring requirements of cableways. Summary of the Invention

[0005] The purpose of this invention is to provide a method for monitoring the deformation and attitude of cableway supports based on GNSS-IMU. By combining GNSS and IMU for high-precision attitude deformation monitoring, the deformation of the cableway can be monitored more effectively, accurately, and in a timely manner.

[0006] To achieve the above objectives, the present invention provides a method for monitoring the deformation and attitude of a cableway support based on GNSS-IMU. The device for implementing this monitoring method includes a GNSS receiver No. 1, a GNSS receiver No. 2, a GNSS receiver No. 3, and an IMU inertial measurement unit. The GNSS receiver No. 1 and the GNSS receiver No. 2 are respectively installed on both sides of the cableway crossbar and arranged parallel to the cableway crossbar. With the GNSS receiver No. 1 as the origin, the GNSS receiver No. 3 is placed perpendicular to the GNSS receiver No. 1 to form two mutually perpendicular baselines. The IMU inertial measurement unit is placed between the GNSS receiver No. 1 and the GNSS receiver No. 2. The monitoring method includes the following steps: Step 1: Synchronously measure the cableway crossbar using GNSS receivers 1, 2, and 3 to obtain pseudorange signals from these receivers. Perform single-point positioning calculations on the pseudorange signal data from receiver 1 to obtain corrected pseudorange data. Then, combine the corrected pseudorange data from receiver 1 with the pseudorange signals from receivers 2 and 3 using a double-difference solution model, respectively, to correct the pseudorange signals from receivers 2 and 3. Next, use the Euler angle transformation formula to obtain two baseline coordinate data. Convert the obtained baseline coordinate data to obtain the three-axis Euler angle attitude data of the cableway crossbar. The IMU (Inertial Measurement Unit) can measure the three-axis acceleration data of the cableway crossbar. Step 2: Use the EKF fusion algorithm to fuse the three-axis Euler angle attitude data of the cableway crossbar in Step 1 with the three-axis acceleration data of the cableway crossbar, so as to obtain the corrected three-axis Euler angle attitude data, in order to solve the problem that GNSS cannot provide stable and high-precision attitude angles when the signal quality deteriorates. Step 3: Construct a covariance matrix to correct the location information of the static GNSS-IMU combined positioning and solve the problem of data divergence.

[0007] This invention performs error correction on the pseudorange signal measured by GNSS receiver No. 1 in step one to obtain corrected pseudorange data. The details are as follows: GNSS receiver No. 1 single-point positioning calculation Single-point positioning is used to obtain the coordinates of GNSS receiver No. 1. It utilizes orbital, clock error, and pseudorange observations provided by the broadcast ephemeris for calculation. The single-point positioning observation equation is shown below. The pseudorange observation equation is: The pseudorange observations obtained by GNSS receiver 1 through receiving and processing satellite ephemeris signals will be subject to varying degrees of refraction due to the influence of the ionosphere and troposphere during satellite signal propagation, as well as errors between the satellite clock and the clock of GNSS receiver 1. The final result is a pseudorange containing errors. In the formula: It is a pseudo-range; This represents the actual geometric distance between GNSS receiver #1 and the satellite. Clock bias for GNSS receiver #1; For satellite clock bias; Indicates ionospheric delay; Indicates tropospheric delay; Indicates pseudorange measurement error; set up The corrected pseudorange data is represented as follows: Set the coordinate vector of GNSS receiver No. 1 as follows: The coordinate vector of the satellite is represented as , This indicates the observed satellite number. The geometric distance from this satellite to GNSS receiver #1 is: When to give up After that, only four unknowns remain, namely the three coordinate vectors of GNSS receiver No. 1. Clock difference with GNSS receiver No. 1 When there are four unknowns, at least four observation equations are needed to solve the problem, which requires at least four satellites for positioning. The system of linear equations is shown below: Before solving for the coordinates and clock error of GNSS receiver #1, the nonlinear equations first need to be linearized. Satellite No. The linearization formula for the direction is shown below: Will Linearization of direction means that the unit observation vector is in The directional component is denoted as The linearized equation in matrix form is: To simplify the representation of the least squares formula calculation process, some matrices are simplified as follows: The simplified matrix equation is: The solution obtained using the least squares method is as follows: Finally, the pseudorange data after error correction is obtained. .

[0008] The specific double-difference solution model in step one of this invention is as follows: The formula for the double-difference solution model is: In the formula: , respectively , Station carrier wave measurement values; The speed of light; For receiver frequency; For the corrected GNSS receiver No. 1 , Pseudorange measurements from satellite No. 1; For GNSS receiver No. 2 , Pseudorange measurements from satellite No. 1; For integer ambiguity; By subtracting data between stations, clock errors between satellites and receivers can be offset, while reducing the impact of orbital deviations. via satellite , If we continue to subtract the values, the above equation can be transformed into: In the formula: These are double-difference phase observations; The coordinate equation in a linearized form; This refers to coordinate error; For ambiguity function; make Thus, the observation error equation can be obtained: Finally, the baseline coordinate data of the combination of GNSS receiver No. 1 and GNSS receiver No. 2 were calculated. ; Baseline coordinate data composed of GNSS receiver No. 1 and GNSS receiver No. 3 The solution method and the baseline coordinate data composed of GNSS receiver No. 1 and GNSS receiver No. 2 same.

[0009] The Euler angle transformation in step one of this invention is as follows: Let the coordinates of the two obtained baselines be... , , The baseline is parallel to the cableway crossbar. The baseline is perpendicular to the crossbar. , The intersection point is GNSS receiver number 1, determined by the corresponding formula: Heading angle: ; Heading angle: The angle between the projection of the x-axis of the vehicle coordinate system onto the horizontal plane and the x-axis of the ground coordinate system; Pitch angle: ; Pitch angle: The angle between the x-axis of the carrier coordinate system and the horizontal plane; Roll angle: Roll angle: The angle between the horizontal axis of the carrier and the horizontal line is called the roll angle.

[0010] The EKF fusion algorithm in step two of this invention is as follows: Based on the triaxial Euler angle attitude data and triaxial acceleration data of the cableway crossbar, Kalman filtering is performed and updated using the extended Kalman state equation and the EKF observation equation. The state prediction matrix and covariance matrix prediction matrix of the extended Kalman filter are: In the formula: This is the state prediction vector; This is the state transition matrix; This refers to process noise in the state equations. The covariance matrix of the previous time step; The covariance prediction matrix at the current moment; For process noise related to covariance; The Kalman filter gain matrix at the current time is In the formula: This represents the Kalman filter gain. It is a Jacobian matrix; Then you can get State estimates and covariance matrix after time-time updates In the formula: For observation vectors; This is the updated state estimation vector; This is the state prediction vector; It is the covariance matrix; It is the identity matrix; The extended Kalman filter estimates the quaternion corresponding to the optimal attitude angle, and the discrete-time model of updating the attitude using the rotation quaternion is used as the state equation: In the formula: State quantities composed of quaternions; for The angular rate of rotation of the carrier at any given time; for The quaternion corresponding to the optimal attitude angle estimate at any given time; for The antisymmetric matrix; The sampling interval for sensor data; This is system noise; Attitude angles obtained from GNSS three antennas Expressed using quaternions as Then, based on the accelerometer measurements from the IMU... and Establish the EKF observation equation: In the formula: The attitude rotation matrix is ​​updated using quaternions; In the formula: This is the normalized vector of local gravitational acceleration. In the formula: It is a 4×4 identity matrix; The covariance matrix of the measurement noise; and For adaptive covariance; Linearizing the EKF observation equation yields the Jacobian matrix. , represented as: .

[0011] The specific steps for constructing the covariance parameters in step three of this invention are as follows: (1) Construct the acceleration covariance. When the carrier is in a static state and its acceleration is equal to the acceleration due to gravity, its acceleration is: In the formula: For modulo operation; ; However, when the carrier accelerates, its resultant acceleration is no longer equal to the sum of its initial values. Considering the variance of the acceleration magnitude and the acceleration meter magnitude over a time window as observations, a covariance is constructed. , In the formula: and As a weighting factor; To solve for the variance function; Calculate the window size for variance; , and The values ​​of are all obtained experimentally; (2) Constructing quaternion covariance The formula for adaptive covariance of quaternions is: In the formula: As obtained from the experiment, here ; The ratio value is an important parameter for ambiguity testing and confirmation. Therefore, it is necessary to select the Ratio value based on the fuzzy floating-point solution, when hour, It will increase rapidly after being solved, when At that time, it was considered that the attitude angles calculated by BD were unreliable. As a weighting factor, it will be combined with Finish The adjustments, in practice This requires multiple experiments; here we choose... ; Based on quaternion theory, the formula for calculating the attitude angle (Euler angle) corresponding to the optimal quaternion estimated by extended Kalman filter is obtained, and the cableway vibration is observed by the change in the attitude angle of the cableway crossbar. In the formula: The heading angle of the combined cableway crossbar; The pitch angle of the combined cableway crossbar; This refers to the roll angle of the combined cableway crossbar.

[0012] In the Kalman filter update process, this invention encounters a Kalman filter divergence phenomenon. This divergence leads to data that becomes difficult to solve. Ideally, Kalman filtering is a linear, unbiased, minimum variance estimate, but in practical applications, the estimate obtained by the filter is biased, and the variance of the estimation error may tend towards infinity. This is because Kalman filtering is a recursive process; as the number of filtering iterations increases, rounding errors gradually accumulate. This accumulated error can potentially affect the estimation error covariance matrix. and If the nonnegative definiteness is lost during calculation... Loss of nonnegativity leads to Transform it into a singular matrix or near-singular matrix, so that the gain matrix value The filter gradually loses its appropriate weighting effect, leading to filter divergence.

[0013] The solution is: Calculated during the filtering process and The square root is used instead of the calculation, that is... Decomposed into a lower triangular matrix according to Cholesky's method During the transmission process in filtering, square root filtering not only ensures... and The nonnegativity definiteness of the equation, under the premise of achieving the same accuracy, is used to calculate... The word length is calculated Half the length of the character; Initially, the square root filter is first... Perform Cholesky decomposition, and then proceed in each subsequent step with... Time-filtered Substitute calculation And then Perform Cholesky decomposition to obtain Participate in the Potter algorithm; for Widley measurement vector, let the measurement noise matrix be... ; First Perform Cholesky decomposition for diagonal transformation: ; Multiply both sides of the observation equation by the left side. The transformed formula is obtained as follows: in And so on, we have: The above transformation can convert the noise array into a diagonal array, thereby avoiding filter divergence. One method to prevent mean square error convergence is to set a certain lower limit boundary for the mean square error based on the actual physical meaning of the state or experience. Constraints (usually a diagonal matrix) are applied when the filter measurements update the mean square error matrix. The diagonal elements are less than When dealing with the lower limit value, it is manually and directly forced to be taken as the lower limit value; For i=1,2,...n If end end.

[0014] Compared with existing technologies, this invention installs two parallel GNSS receivers, GNSS receiver 1 and GNSS receiver 2, on both sides of the cableway crossbar. Using GNSS receiver 1 as the origin, GNSS receiver 3 is placed perpendicular to GNSS receiver 1, forming two mutually perpendicular baselines. An inertial measurement unit (IMU) is placed between GNSS receivers 1 and 2. The cableway crossbar is simultaneously measured by GNSS receivers 1, 2, and 3, ensuring the simultaneity of the measurement data. Single-point positioning is used to correct the pseudorange signal from GNSS receiver 1, obtaining corrected pseudorange data. This corrected pseudorange data from GNSS receiver 1 is then combined with a double-difference solution model and compared with GNSS receiver 2... The pseudorange signals from receivers 2 and 3 are subtracted to correct the pseudorange signals from receivers 2 and 3, resulting in two baseline coordinate data. These baseline coordinate data are then transformed using the Euler angle transformation formula to obtain the three-axis Euler angle attitude data of the cableway crossbar. Simultaneously, the IMU (Inertial Measurement Unit) measures the three-axis acceleration data of the cableway crossbar. The EKF fusion algorithm is used to fuse the three-axis Euler angle attitude data and the three-axis acceleration data of the cableway crossbar, thus obtaining the corrected three-axis Euler angle attitude data. This addresses the issue of GNSS failing to provide stable and high-precision attitude angles when signal quality deteriorates. Furthermore, a covariance matrix is ​​constructed to correct the position information of the static GNSS-IMU combined positioning and resolve data divergence issues. This invention utilizes integrated navigation for high-precision cableway attitude monitoring, offering significant advantages over traditional methods such as total stations. It employs ambiguity function and extended Kalman filtering for high-precision cableway attitude monitoring, resulting in high computational efficiency and fully considering the fixed ambiguity error generated by BDS alone. This invention is applicable to any Kalman-filter-based GNSS / IMU system, enabling more effective, accurate, and timely monitoring of cableway crossbar deformation through the combination of GNSS and IMU. Attached Figure Description

[0015] Figure 1 This is a schematic diagram showing the locations of the GNSS and IMU in this invention; Figure 2 This is a schematic diagram of the GNSS and IMU hardware installation of the present invention. Detailed Implementation

[0016] The invention will now be further described with reference to the accompanying drawings.

[0017] like Figures 1-2As shown, a method for monitoring the deformation and attitude of a cableway support based on GNSS-IMU is described. The device for implementing this monitoring method includes a GNSS receiver (number 1), a GNSS receiver (number 2), a GNSS receiver (number 3), and an IMU (Inertial Measurement Unit). GNSS receivers 1 and 2 are installed on opposite sides of the cableway crossbar, arranged parallel to it. With GNSS receiver 1 as the origin, GNSS receiver 3 is placed perpendicular to GNSS receiver 1, forming two mutually perpendicular baselines. The IMU is placed between GNSS receivers 1 and 2. Figure 1 As shown: with GNSS receiver No. 1 as the origin, the horizontal bar as the y-axis, GNSS receiver No. 2 is placed on the y-axis, GNSS receiver No. 3 is placed on the z-axis, and the IMU is placed between receivers No. 1 and No. 2. The monitoring method includes the following steps: Step 1: Simultaneously measure the cableway crossbar using GNSS receivers 1, 2, and 3 to obtain pseudorange signals from these receivers. Perform single-point positioning calculations on the pseudorange signal data from receiver 1 to obtain corrected pseudorange data. Then, combine the corrected pseudorange data from receiver 1 with the pseudorange signals from receivers 2 and 3 using a double-difference solution model, respectively, to correct the pseudorange signals from receivers 2 and 3, resulting in two baseline coordinate data. , Then, the obtained baseline coordinate data is transformed using the Euler angle transformation formula to obtain the three-axis Euler angle attitude data of the cableway crossbar; the IMU inertial measurement unit can measure the three-axis acceleration data of the cableway crossbar; Step 2: Use the EKF fusion algorithm to fuse the three-axis Euler angle attitude data of the cableway crossbar in Step 1 with the three-axis acceleration data of the cableway crossbar, so as to obtain the corrected three-axis Euler angle attitude data, in order to solve the problem that GNSS cannot provide stable and high-precision attitude angles when the signal quality deteriorates. Step 3: Construct a covariance matrix to correct the location information of the static GNSS-IMU combined positioning and solve the problem of data divergence.

[0018] Error correction is performed on the pseudorange signal data measured by GNSS receiver No. 1 in step one to obtain the corrected pseudorange data. The specific steps are as follows: Step 1.1: Single-point positioning calculation for GNSS receiver No. 1 Single-point positioning is used to obtain the coordinates of GNSS receiver No. 1. It utilizes orbital, clock error, and pseudorange observations provided by the broadcast ephemeris for calculation. The single-point positioning observation equation is shown below. The pseudorange observation equation is: The pseudorange observations obtained by GNSS receiver 1 through receiving and processing satellite ephemeris signals will be subject to varying degrees of refraction due to the influence of the ionosphere and troposphere during satellite signal propagation, as well as errors between the satellite clock and the clock of GNSS receiver 1. The final result is a pseudorange containing errors. In the formula: It is a pseudo-range; This represents the actual geometric distance between GNSS receiver #1 and the satellite. Clock bias for GNSS receiver #1; For satellite clock bias; Indicates ionospheric delay; Indicates tropospheric delay; Indicates pseudorange measurement error; set up The corrected pseudorange data is represented as follows: Set the coordinate vector of GNSS receiver No. 1 as follows: The coordinate vector of the satellite is represented as , This indicates the observed satellite number. The geometric distance from this satellite to GNSS receiver #1 is: When to give up After that, only four unknowns remain, namely the three coordinate vectors of GNSS receiver No. 1. Clock difference with GNSS receiver No. 1 When there are four unknowns, at least four observation equations are needed to solve the problem, which requires at least four satellites for positioning. The system of linear equations is shown below: Before solving for the coordinates and clock error of GNSS receiver #1, the nonlinear equations first need to be linearized. Satellite No. The linearization formula for the direction is shown below: Will Linearization of direction means that the unit observation vector is in The directional component is denoted as The linearized equation in matrix form is: To simplify the representation of the least squares formula calculation process, some matrices are simplified as follows: The simplified matrix equation is: The solution obtained using the least squares method is as follows: Finally, the pseudorange data after error correction is obtained. .

[0019] In step one, the pseudorange data corrected by GNSS receiver 1 and the pseudorange signal from GNSS receiver 2 are subtracted using a double-difference solution model, as detailed below: The formula for the double-difference solution model is: In the formula: , respectively , Station carrier wave measurement values; The speed of light; For receiver frequency; For the corrected GNSS receiver No. 1 , Pseudorange measurements from satellite No. 1; For GNSS receiver No. 2 , Pseudorange measurements from satellite No. 1; For integer ambiguity; By subtracting data between stations, clock errors between satellites and receivers can be offset, while reducing the impact of orbital deviations. via satellite , If we continue to subtract the values, the above equation can be transformed into: In the formula: These are double-difference phase observations; The coordinate equation in a linearized form; This refers to coordinate error; For ambiguity function; make Thus, the observation error equation can be obtained: Finally, the baseline coordinate data of the combination of GNSS receiver No. 1 and GNSS receiver No. 2 were calculated. ; Baseline coordinate data composed of GNSS receiver No. 1 and GNSS receiver No. 3 The solution method and the baseline coordinate data composed of GNSS receiver No. 1 and GNSS receiver No. 2 They are the same, as follows: In step one, the pseudorange data corrected by GNSS receiver 1 and the pseudorange signal from GNSS receiver 3 are subtracted using a double-difference solution model, as detailed below: The formula for the double-difference solution model is: In the formula: , respectively , Station carrier wave measurement values; The speed of light; For receiver frequency; For the corrected GNSS receiver No. 1 , Pseudorange measurements from satellite No. 1; For GNSS receiver No. 3 , Pseudorange measurements from satellite No. 1; For integer ambiguity; By subtracting data between stations, clock errors between satellites and receivers can be offset, while reducing the impact of orbital deviations. via satellite , If we continue to subtract the values, the above equation can be transformed into: In the formula: These are double-difference phase observations; The coordinate equation in a linearized form; This refers to coordinate error; For ambiguity function; make Thus, the error equation can be obtained: Finally, the baseline coordinate data of the combination of GNSS receiver No. 1 and GNSS receiver No. 3 were calculated. .

[0020] The Euler angle transformation in step one of this invention is as follows: Let the coordinates of the two obtained baselines be... , , The baseline is parallel to the cableway crossbar. The baseline is perpendicular to the crossbar. , The intersection point is GNSS receiver number 1, determined by the corresponding formula: Heading angle: ; Heading angle: The angle between the projection of the x-axis of the vehicle coordinate system onto the horizontal plane and the x-axis of the ground coordinate system; Pitch angle: ; Pitch angle: The angle between the x-axis of the carrier coordinate system and the horizontal plane; Roll angle: Roll angle: The angle between the horizontal axis of the carrier and the horizontal line is called the roll angle; The above heading angle Pitch angle Roll angle The initial attitude of the cableway crossbar is obtained.

[0021] The EKF fusion algorithm in step two of this invention is as follows: Based on the triaxial Euler angle attitude data and triaxial acceleration data of the cableway crossbar, Kalman filtering is performed and updated using the extended Kalman state equation and the EKF observation equation. The state prediction matrix and covariance matrix prediction matrix of the extended Kalman filter are: In the formula: This is the state prediction vector; This is the state transition matrix; This refers to process noise in the state equations. The covariance matrix of the previous time step; The covariance prediction matrix at the current moment; For process noise related to covariance; The Kalman filter gain matrix at the current time is In the formula: This represents the Kalman filter gain. It is a Jacobian matrix; Then you can get State estimates and covariance matrix after time-time updates In the formula: For observation vectors; This is the updated state estimation vector; This is the state prediction vector; It is the covariance matrix; It is the identity matrix; The extended Kalman filter estimates the quaternion corresponding to the optimal attitude angle, and the discrete-time model of updating the attitude using the rotation quaternion is used as the state equation: In the formula: State quantities composed of quaternions; for The angular rate of rotation of the carrier at any given time; for The quaternion corresponding to the optimal attitude angle estimate at any given time; for The antisymmetric matrix; The sampling interval for sensor data; This is system noise; Attitude angles obtained from GNSS three antennas Expressed using quaternions as Then, based on the accelerometer measurements from the IMU... and Establish the EKF observation equation: In the formula: The attitude rotation matrix is ​​updated using quaternions; In the formula: This is the normalized vector of local gravitational acceleration. In the formula: It is a 4×4 identity matrix; The covariance matrix of the measurement noise; and For adaptive covariance; Linearizing the EKF observation equation yields the Jacobian matrix. , represented as: .

[0022] The specific steps for constructing the covariance parameters in step three of this invention are as follows: (1) Construct the acceleration covariance. When the carrier is in a static state and its acceleration is equal to the acceleration due to gravity, its acceleration is: In the formula: For modulo operation; ; However, when the carrier accelerates, its resultant acceleration is no longer equal to the sum of its initial values. Considering the variance of the acceleration magnitude and the acceleration meter magnitude over a time window as observations, a covariance is constructed. , In the formula: and As a weighting factor; To solve for the variance function; Calculate the window size for variance; , and The values ​​of are all obtained experimentally; (2) Constructing quaternion covariance The formula for adaptive covariance of quaternions is: In the formula: As obtained from the experiment, here ; The ratio value is an important parameter for ambiguity testing and confirmation. Therefore, it is necessary to select the Ratio value based on the fuzzy floating-point solution, when hour, It will increase rapidly after being solved, when At that time, it was considered that the attitude angles calculated by BD were unreliable. As a weighting factor, it will be combined with Finish The adjustments, in practice This requires multiple experiments; here we choose... ; Based on quaternion theory, the formula for calculating the attitude angle (Euler angle) corresponding to the optimal quaternion estimated by extended Kalman filter is obtained, and the cableway vibration is observed by the change in the attitude angle of the cableway crossbar. In the formula: The heading angle of the combined cableway crossbar; The pitch angle of the combined cableway crossbar; This refers to the roll angle of the combined cableway crossbar.

[0023] During the Kalman filter update process, Kalman filter divergence can occur, leading to unsolvable data. Ideally, Kalman filtering should be a linear, unbiased, minimum variance estimate, but in practice, the estimate obtained by the filter is biased, and the variance of the estimation error may approach infinity. This is because Kalman filtering is a recursive process; as the number of filtering iterations increases, rounding errors gradually accumulate, potentially affecting the variance matrix of the estimation error. and If the nonnegative definiteness is lost during calculation... Loss of nonnegativity leads to Transform it into a singular matrix or near-singular matrix, so that the gain matrix value The filter gradually loses its appropriate weighting effect, leading to filter divergence.

[0024] The solution is: Calculated during the filtering process and The square root is used instead of the calculation, that is... Decomposed into a lower triangular matrix according to Cholesky's method During the transmission process in filtering, square root filtering not only ensures... and The nonnegativity definiteness of the equation, under the premise of achieving the same accuracy, is used to calculate... The word length is calculated Half the length of the character; Initially, the square root filter is first... Perform Cholesky decomposition, and then proceed in each subsequent step with... Time-filtered Substitute calculation And then Perform Cholesky decomposition to obtain Participate in the Potter algorithm; for Widley measurement vector, let the measurement noise matrix be... ; First Perform Cholesky decomposition for diagonal transformation: ; Multiply both sides of the observation equation by the left side. The transformed formula is obtained as follows: in And so on, we have: The above transformation can convert the noise array into a diagonal array, thereby avoiding filter divergence. One method to prevent mean square error convergence is to set a certain lower limit boundary for the mean square error based on the actual physical meaning of the state or experience. Constraints (usually a diagonal matrix) are applied when the filter measurements update the mean square error matrix. The diagonal elements are less than When dealing with the lower limit value, it is manually and directly forced to be taken as the lower limit value; For i=1,2,...n If end end.

Claims

1. A method for monitoring the deformation and attitude of cableway supports based on GNSS-IMU, characterized in that, The device for implementing this monitoring method includes GNSS receiver No. 1, GNSS receiver No. 2, GNSS receiver No. 3, and IMU inertial measurement unit. GNSS receiver No. 1 and GNSS receiver No. 2 are respectively installed on both sides of the cableway crossbar and arranged parallel to the cableway crossbar. With GNSS receiver No. 1 as the origin and the crossbar as the y-axis, GNSS receiver No. 2 is placed on the y-axis, GNSS receiver No. 3 is placed on the z-axis, and IMU is placed between receivers No. 1 and No.

2. The monitoring method includes the following steps: Step 1: Synchronously measure the cableway crossbar using GNSS receivers 1, 2, and 3 to obtain pseudorange signals from these receivers. Perform single-point positioning calculations on the pseudorange signal data from GNSS receiver 1 to obtain corrected pseudorange data. Then, use a double-difference solution model to subtract the pseudorange signals from GNSS receivers 2 and 3 to obtain two baseline coordinate data. Finally, use the Euler angle transformation formula to transform the obtained baseline coordinate data to obtain the three-axis Euler angle attitude data of the cableway crossbar. The IMU (Inertial Measurement Unit) can measure the three-axis acceleration data of the cableway crossbar. Step 2: Use the EKF fusion algorithm to fuse the three-axis Euler angle attitude data of the cableway crossbar in Step 1 with the three-axis acceleration data of the cableway crossbar to obtain the corrected three-axis Euler angle attitude data. Step 3: Construct a covariance matrix to correct the location information of static GNSS-IMU combined positioning and solve the problem of data divergence; Step three is as follows: (1) Construct the covariance. When the carrier is in a static state, its acceleration is equal to the acceleration due to gravity. ; However, when the carrier accelerates, its resultant acceleration is no longer equal to the sum of its initial values. Using the acceleration magnitude and the variance of the accelerometer magnitude within a time window as observations, a covariance is constructed. , In the formula: For monitoring time Accelerometer measurements from the IMU (Inertial Measurement Unit); This represents the acceleration magnitude at the corresponding moment. To use the current sampling time Centered on the left boundary of the window, at time The corresponding accelerometer measurement value of the IMU inertial measurement unit; To use the current sampling time Centered on the left boundary of the window, at time The corresponding accelerometer measurement value of the IMU inertial measurement unit; From arrive The sequence of acceleration magnitude values ​​of all sampling points within the entire time window; and As a weighting factor; To solve for the variance function; Calculate the window size for variance; , and The values ​​of are all obtained experimentally; (2) Constructing quaternion covariance The formula for adaptive covariance of quaternions is: In the formula: As obtained from the experiment, here ; The ratio value is an important parameter for ambiguity testing and confirmation. when hour, It will increase rapidly after being solved, when At that time, it was considered that the attitude angles calculated by BD were unreliable. As a weighting factor, it will be combined with Finish Adjustments; Based on quaternion theory, the formula for calculating the attitude angle corresponding to the optimal quaternion estimated by extended Kalman filtering is derived, and the cableway vibration is observed by the change in the attitude angle of the cableway crossbar.

2. The method for monitoring the deformation and attitude of cableway supports based on GNSS-IMU according to claim 1, characterized in that, Error correction is performed on the pseudorange signal measured by GNSS receiver No. 1 in step one to obtain the corrected pseudorange data. The specific steps are as follows: Step 1.1: Single-point positioning calculation for GNSS receiver No. 1 Single-point positioning is used to obtain the coordinates of GNSS receiver No.

1. It utilizes orbital, clock error, and pseudorange observations provided by the broadcast ephemeris for calculation. The single-point positioning observation equation is shown below. The pseudorange observation equation is: The pseudorange observations obtained by GNSS receiver 1 through receiving and processing satellite ephemeris signals will be subject to varying degrees of refraction due to the influence of the ionosphere and troposphere during satellite signal propagation, as well as errors between the satellite clock and the clock of GNSS receiver 1. The final result is a pseudorange containing errors. In the formula: It is a pseudo-range; This represents the actual geometric distance between GNSS receiver #1 and the satellite. Clock bias for GNSS receiver #1; For satellite clock bias; Indicates ionospheric delay; Indicates tropospheric delay; Indicates pseudorange measurement error; set up The corrected pseudorange data is represented as follows: Set the coordinate vector of GNSS receiver No. 1 as follows: The coordinate vector of the satellite is represented as , This indicates the observed satellite number. The geometric distance from this satellite to GNSS receiver #1 is: For the first, without considering errors The actual geometric distance between the satellite and GNSS receiver No. 1; When to give up After that, four unknowns remain, which are the three coordinate vectors of GNSS receiver No.

1. Clock difference with GNSS receiver No. 1 Solving this system requires four observation equations, necessitating at least four satellites for positioning. The system of linear equations is shown below: Before solving for the coordinates and clock error of GNSS receiver #1, the nonlinear equations first need to be linearized. Satellite No. The linearization formula for the direction is shown below: Will Linearization of direction means that the unit observation vector is in The directional component is denoted as The linearized equation in matrix form is: To simplify the representation of the least squares formula calculation process, some matrices are simplified as follows: The simplified matrix equation is: The solution obtained using the least squares method is as follows: Finally, the pseudorange data after error correction is obtained. .

3. The method for monitoring the deformation and attitude of cableway supports based on GNSS-IMU according to claim 2, characterized in that, The specific double-difference solution model in step one is as follows: The formula for the double-difference solution model is: In the formula: , respectively , Station carrier wave measurement values; The speed of light; For receiver frequency; For the corrected GNSS receiver No. 1 , Pseudorange measurements from satellite No. 1; For GNSS receiver No. 2 , Pseudorange measurements from satellite No. 1; For integer ambiguity; via satellite , If we continue to subtract the values, the above equation becomes: In the formula: These are double-difference phase observations; The coordinate equation in a linearized form; This refers to coordinate error; For ambiguity function; make Thus, the observation error can be obtained: Finally, the baseline coordinate data of the combination of GNSS receiver No. 1 and GNSS receiver No. 2 were calculated. ; Baseline coordinate data composed of GNSS receiver No. 1 and GNSS receiver No. 3 The solution method and the baseline coordinate data composed of GNSS receiver No. 1 and GNSS receiver No. 2 same.

4. The method for monitoring the deformation and attitude of cableway supports based on GNSS-IMU according to claim 3, characterized in that, The Euler angle transformation in step one is as follows: Let the coordinates of the two obtained baselines be... , , The baseline is parallel to the cableway crossbar. The baseline is perpendicular to the crossbar. , The intersection point is GNSS receiver number 1, determined by the corresponding formula: Heading angle: ; Heading angle: The angle between the projection of the x-axis of the vehicle coordinate system onto the horizontal plane and the x-axis of the ground coordinate system; Pitch angle: ; Pitch angle: The angle between the x-axis of the carrier coordinate system and the horizontal plane; Roll angle: Roll angle: The angle between the horizontal axis of the carrier and the horizontal line is called the roll angle.

5. The method for monitoring the deformation and attitude of a cableway support based on GNSS-IMU as described in claim 3, characterized in that, The EKF fusion algorithm in step two is as follows: Based on the triaxial Euler angle attitude data and triaxial acceleration data of the cableway crossbar, Kalman filtering is performed and updated using the extended Kalman state equation and the EKF observation equation. The state prediction matrix and covariance matrix prediction matrix of the extended Kalman filter are: In the formula: This is the state prediction vector; This is the state transition matrix; This refers to process noise in the state equations. The covariance matrix of the previous time step; The covariance prediction matrix at the current moment; For process noise related to covariance; The Kalman filter gain matrix at the current time is In the formula: This represents the Kalman filter gain. It is a Jacobian matrix; Then we get State estimates and covariance matrix after time-time updates In the formula: For observation vectors; This is the updated state estimation vector; This is the state estimation vector; It is the covariance matrix; It is the identity matrix; The extended Kalman filter estimates the quaternion corresponding to the optimal attitude angle, and the discrete-time model of updating the attitude using the rotation quaternion is used as the state equation: In the formula: State quantities composed of quaternions; for The angular rate of rotation of the carrier at any given time; for The quaternion corresponding to the optimal attitude angle estimate at any given time; for The antisymmetric matrix; The sampling interval for sensor data; This is system noise; Attitude angles obtained from GNSS three antennas Expressed using quaternions as Then, based on the accelerometer measurements from the IMU... and Establish the EKF observation equation: In the formula: The attitude rotation matrix is ​​updated using quaternions; In the formula: This is the normalized vector of local gravitational acceleration. In the formula: It is a 4×4 identity matrix; The covariance matrix of the measurement noise; and For adaptive covariance; Linearizing the EKF observation equation yields the Jacobian matrix. , represented as: 。 6. The method for monitoring the deformation and attitude of a cableway support based on GNSS-IMU as described in claim 5, characterized in that, The formula for calculating the attitude angle in step three is as follows: In the formula: The heading angle of the combined cableway crossbar; The pitch angle of the combined cableway crossbar; This refers to the roll angle of the combined cableway crossbar.

7. The method for monitoring the deformation and attitude of a cableway support based on GNSS-IMU as described in claim 5, characterized in that, In the Kalman filter update process, the method to solve filter divergence is: calculate and The square root of, is about to Decomposed into a lower triangular matrix according to Cholesky's method The transmission is performed during filtering, and calculations are performed while maintaining the same level of accuracy. The word length is calculated Half the length of the character; Initially, the square root filter is first... Perform Cholesky decomposition, and then proceed in each subsequent step with... Time-filtered Substitute calculation And then Perform Cholesky decomposition to obtain Participate in the Potter algorithm; for Widley measurement vector, let the measurement noise matrix be... ; First Perform Cholesky decomposition for diagonal transformation: ; Multiply both sides of the observation equation by the left. The transformed formula is obtained as follows: in And so on, we have: The above transformation can convert the noise array into a diagonal array, thereby avoiding filter divergence. Set the lower limit boundary of mean square error. When the filter measurement updates the covariance matrix When the diagonal element is less than the corresponding lower limit value, that is Injunction .

Images