High-altitude tunnel GPS correction method based on gyro lead

Abstract

The invention discloses a high-altitude tunnel GPS correction method based on a gyro wire, and belongs to the technical field of communication, and the method comprises the steps: S1, constructing an initial GPS baseline network, and obtaining an initial coordinate solution; s2, measuring a TEC gradient value, and collecting an azimuth angle observation value and a pitch angle observation value; s3, constructing a GPS baseline network correction model, and calculating an optimized coordinate solution; s4, carrying out network adjustment calculation on the initial GPS baseline network, and identifying abnormal node coordinates; and S5, reducing the baseline observation weights of all abnormal node coordinates, and updating the coordinate correction to the node coordinates of the initial GPS baseline network. According to the method, the gyro wire is combined with the GPS signal, the disturbance intensity is quantified through the TEC gradient, fusion modeling is carried out based on the TEC gradient data and the GPS observation value, the influence of the ionized layer in the high-altitude area is avoided, and the method has the advantages that the defect that conventional repairing is insufficient in ionized layer disturbance processing is overcome, and systematic deviation is effectively corrected.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and specifically to a GPS correction method for high-altitude tunnels based on gyroscope wires. Background Technology

[0002] In the construction of long, high-altitude tunnels in regions such as the Qinghai-Tibet Plateau and the Andes Mountains, establishing a high-precision, unified spatial reference is crucial for ensuring the accurate connection of multiple working faces within the tunnel. The Global Positioning System (GPS) technology, due to its all-weather, high-efficiency, and high-precision characteristics, has become the core means of establishing ground control networks and transferring references. However, the unique spatial physical environment of high-altitude regions, especially the intense disturbances in the ionosphere, can easily lead to delays in higher-order ionospheric terms.

[0003] As a diffuse medium, the ionosphere's effect on GPS signal delay is not simply linearly inversely proportional to the signal frequency. The first-order term, inversely proportional to the square of the frequency, can be perfectly eliminated through dual-frequency observation. However, due to the presence of second-order (inversely proportional to the cube of the frequency) and third-order terms, the effects are typically only at the millimeter level in typical low- and mid-latitude regions and are often ignored as noise in data processing. In high-altitude regions, especially plateaus near the equator, solar radiation is stronger, and ionospheric activity is more intense. This leads to large variations in the total electron content (TEC), steep gradients, and significant spatial inhomogeneity. The magnitude of the delay caused by higher-order terms is strongly correlated with TEC and its gradient; therefore, its impact is significantly amplified in this environment, resulting in increased GPS signal deviation during tunnel excavation. Current conventional GPS signal correction and repair methods employ a dual-frequency, ionospheric-free combination method. This method lacks correction for ionospheric effects and is prone to introducing unmodeled systematic errors in active regions such as high altitudes. More sophisticated methods combining three or more frequencies and geomagnetic field modeling methods can relatively improve the accuracy of GPS signal repair, but they suffer from low popularity and low data availability. Summary of the Invention

[0004] This invention provides a GPS correction method for high-altitude tunnels based on gyro-guided wires, which solves the problem that conventional repair techniques lack effective handling of ionospheric disturbances when GPS signals deviate significantly due to ionospheric disturbances in high-altitude tunnels.

[0005] This invention is achieved through the following technical solution: A GPS correction method for high-altitude tunnels based on gyro-guided lines, the method comprising: Step S1: Obtain GPS observations and use them to construct the initial GPS baseline network for the target tunnel. Perform initial calculations on the GPS observations using a dual-frequency ionosphere-free combination method to obtain the initial coordinate solutions for the node coordinates on the initial GPS baseline network. Step S2: Measure and obtain the TEC gradient value of the target tunnel, lay out a number of gyro wires along the tunnel excavation direction, and collect all the azimuth and pitch angle observations obtained using the gyro wires. Step S3: Based on the azimuth and elevation observations, set the azimuth and elevation parameters respectively. Based on the initial coordinate solution, TEC gradient value, azimuth and elevation parameters, construct a GPS baseline network correction model. Use the GPS baseline network correction model to calculate the optimized coordinate solution representing the corrected initial coordinate solution. Step S4: Perform network adjustment on the initial GPS baseline network based on GPS observations, and use the optimized coordinate solution to participate in the network adjustment solution to identify the coordinates of anomalous nodes on the initial GPS baseline network that have higher-order ionospheric anomalies. Step S5: Reduce the baseline observation weights of all abnormal node coordinates in the network adjustment solution, and then update the coordinate corrections obtained from the network adjustment solution to the node coordinates of the initial GPS baseline network to complete the network layer correction of the GPS signal.

[0006] Furthermore, the excavation cycle of the target tunnel is set, and the time interval between every two excavation cycles is marked as the correction period; step S1 is completed before the target tunnel is excavated, and steps S2, S3, S4 and S5 are all completed sequentially within each correction period.

[0007] Furthermore, the settings of the GPS baseline network correction model include: Let X0 be the initial coordinate solution of each node on the GPS baseline network, and let Xop be the optimized coordinate solution corresponding to each initial coordinate solution; let Gtec be the TEC gradient value; let α be the azimuth parameter and β be the elevation parameter; let d(α,β) be set based on the azimuth and elevation parameters; let k1 be the direction modulation coefficient and k2 be the ionospheric disturbance coefficient. The calculation formula for the GPS baseline network correction model is expressed as follows: .

[0008] Furthermore, the process of setting the directional modulation coefficient includes: All azimuth observations are organized into an azimuth sequence according to the tunneling direction, and the difference between adjacent observations is calculated based on the azimuth sequence. An azimuth difference threshold is set for the difference between adjacent observations. The standard deviation of the azimuth sequence is calculated and denoted as σ, and the azimuth difference threshold is denoted as σv. The baseline scaling factor is set to k0. The formula for obtaining the directional modulation coefficient is expressed as: .

[0009] Furthermore, an ionospheric activity level is set, including a first ionospheric level and a second ionospheric level with activity levels ranging from low to high, and the ionospheric perturbation coefficient includes a first perturbation term, a second perturbation term, and a third perturbation term with values ​​ranging from small to large; When the TEC gradient value is lower than the first ionospheric level, the ionospheric perturbation coefficient is the first perturbation term; when the TEC gradient value is between the first and second ionospheric levels, the ionospheric perturbation coefficient is the second perturbation term; when the TEC gradient value is higher than the second ionospheric level, the ionospheric perturbation coefficient is the third perturbation term.

[0010] Furthermore, the specific form of the direction correction vector is set as follows: , Where ω1 represents the horizontal weight component and ω2 represents the vertical weight component.

[0011] Furthermore, the network adjustment solution process includes: Based on GPS observations and optimized coordinate solutions, a matrix-style baseline observation equation is constructed for the initial GPS baseline network. The variables of the baseline observation equation include coordinate corrections and observation residuals. The least squares method is used to perform network adjustment on the baseline observation equation to obtain a weighted least squares closed-form solution, and the coordinate corrections of the target node coordinates are calculated. The coordinate corrections are then substituted into the baseline observation equation to obtain the observation residuals. Update all calculated coordinate corrections for each node coordinate to the corresponding node coordinate; use observation residuals to screen out abnormal node coordinates and reduce the baseline observation weights of abnormal node coordinates in the baseline observation equation for all baselines.

[0012] Furthermore, the baseline observation equation is set as follows: Let the observation residual be represented by v, and the GPS observation value by I; let the optimized coordinate solution be represented by Xop, and let the vector form of the optimized coordinate solution be f(Xop); let the coordinate correction be represented by δ. The baseline observation equation, expressed in terms of observation residuals, is: v = If(Xop) - Aδ. Where A represents the design matrix used to characterize the sensitivity of each baseline to the target node coordinates.

[0013] Furthermore, the least squares method is set as follows: the objective function for network adjustment is constructed using the least squares method. Let the objective function be denoted as Φ, then the calculation formula for the objective function is: Φ(δ) = min δ v T Pv, Where P represents the baseline observation weight matrix preset for the coordinates of each node in the initial GPS baseline network.

[0014] Furthermore, the network adjustment solution process includes: Substitute the baseline observation equation, expressed in terms of observation residuals, into the objective function constructed using the least squares method: Φ(δ)=min δ v T Pv=min δ {[If(Xop)-Aδ] T P[If(Xop)-Aδ]}; Differentiating δ and setting the gradient of Φ(δ) to zero, we express it using the coordinate correction δ as: δ = (A T PA) -1 A T P[If(Xop)].

[0015] Furthermore, let the node coordinates be represented as X1, and let the ordinal number of the node coordinates be j, then the coordinates of the j-th node are represented as X1j; The update formula for setting the node coordinates is: X1j = Xopj + δj. Where Xopj represents the optimized coordinate solution corresponding to the coordinates of the j-th node, and δj represents the coordinate correction amount corresponding to the coordinates of the j-th node.

[0016] Furthermore, the process of using observation residuals to screen out the coordinates of outlier nodes includes: Let the baseline residual norm of the node coordinates be r, and let r = ||v||; let the number of baselines connected to the node coordinates be m, and let the associated baseline residual of the node coordinates be R. Then the associated baseline residual of the j-th node coordinate is denoted as Rj. The formula for calculating the associated baseline residual of the j-th node coordinate is as follows: ; A baseline residual threshold is set for the associated baseline residual. When the associated baseline residual exceeds the baseline residual threshold, the current node coordinates are identified as abnormal node coordinates.

[0017] Furthermore, the method for reducing the baseline observation weights is set as follows: The baseline observation weight matrix of the abnormal node coordinates is labeled as the low-amplitude observation weight matrix Pr. The calculation formula of the low-amplitude observation weight matrix is ​​set as: Pr=λ∙P, where λ represents the weight attenuation coefficient, and the value of λ is set to be in the range of (0,1).

[0018] Furthermore, the process of deploying the gyro conductors is set as follows: when the absolute value of the difference between adjacent observations is higher than the azimuth difference threshold, the gyro conductor segments involved in the calculation of the difference between adjacent observations are marked as abnormal observation conductor segments, and the conductors are re-adjusted and deployed for the abnormal observation conductor segments; the azimuth difference threshold is positively correlated with the deployment distance between adjacent gyro conductors, and the threshold change rate of the azimuth difference threshold does not exceed the preset direction change rate value inside the target tunnel.

[0019] Further, let the set of azimuth sequence be represented by Q, and θ represent the observed azimuth value. i Let represent the azimuth angle observation value obtained for the i-th segment of the gyroscope conductor; let Δθi represent the difference between adjacent observations. The set form of the azimuth sequence Q is: Q = {θ1, θ2, ..., θ n}, The formula for calculating the difference between adjacent observations Δθi is set as follows: Δθ i =θ i+1 -θ i , Where i represents the ordinal number of the gyroscope wire, and i = 1, 2, ..., n-1; n represents the total number of segments of the gyroscope wire.

[0020] Compared with the prior art, the present invention has the following advantages and beneficial effects: By combining gyro-guided lines with GPS signals and quantifying disturbance intensity using TEC gradients, the influence of the ionosphere in high-altitude areas was completely avoided. A spatial orientation reference independent of GPS was established, and fusion modeling based on TEC gradient data and GPS observations was performed, effectively compensating for the shortcomings of conventional repair methods in handling ionospheric disturbances. At the same time, the high-precision orientation and elevation observations provided by the gyro-guided lines were fused with the GPS initial solution and TEC gradient data to accurately locate nodes affecting ionospheric anomalies, effectively correcting systematic deviations. This allowed the correction process to incorporate real-time spatial environment characteristics, while maintaining high stability of the control network even under severe ionospheric disturbances. Attached Figure Description

[0021] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings: Figure 1 This is a structural block diagram of the present invention; Figure 2 This is a schematic diagram of the gyroscope's wire layout. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of this invention are only for explaining this invention and are not intended to limit this invention.

[0023] Examples, such as Figure 1 As shown, this embodiment is a GPS correction method for high-altitude tunnels based on gyro-guided lines. The method includes: Step S1: Obtain GPS observations and use them to construct the initial GPS baseline network for the target tunnel. Perform initial calculations on the GPS observations using a dual-frequency ionosphere-free combination method to obtain the initial coordinate solutions for the node coordinates on the initial GPS baseline network. Step S2: Measure and obtain the TEC gradient value of the target tunnel, lay out a number of gyro wires along the tunnel excavation direction, and collect all the azimuth and pitch angle observations obtained using the gyro wires. Step S3: Based on the azimuth and elevation observations, set the azimuth and elevation parameters respectively. Based on the initial coordinate solution, TEC gradient value, azimuth and elevation parameters, construct a GPS baseline network correction model. Use the GPS baseline network correction model to calculate the optimized coordinate solution representing the corrected initial coordinate solution. Step S4: Perform network adjustment on the initial GPS baseline network based on GPS observations, and use the optimized coordinate solution to participate in the network adjustment solution to identify the coordinates of anomalous nodes on the initial GPS baseline network that have higher-order ionospheric anomalies. Step S5: Reduce the baseline observation weights of all abnormal node coordinates in the network adjustment solution, and then update the coordinate corrections obtained from the network adjustment solution to the node coordinates of the initial GPS baseline network to complete the network layer correction of the GPS signal.

[0024] The construction of the initial GPS baseline network refers to establishing a spatial control network composed of multiple station nodes and their interconnected baseline vectors using conventional baseline calculation methods based on acquired GPS observation data. This network serves as the initial data basis for subsequent corrections and network adjustment. Network adjustment is a commonly used technique in spatial positioning and surveying science, widely applied in GPS, geological surveying, Geographic Information Systems (GIS), and geodesy. It involves optimizing the measurement data of multiple measurement points to obtain the most accurate point coordinates. The GPS observations refer to satellite signal information received by existing GPS receivers within the target tunnel area. Each GPS observation reflects the propagation time and spatial relationship between the receiver and the satellite at a specific moment. Without limitation, the GPS observations may include: dual-frequency carrier phase observations, dual-frequency pseudorange observations, multi-epoch continuous observation data, and observation data from interconnected stations within the tunnel. The initial GPS baseline network refers to a GPS reference measurement network composed of multiple fixed base stations and at least one mobile station within a certain geographical area. This baseline network calculates the relative positions between base stations by acquiring GPS observations from each base station and mobile station, thereby establishing a preliminary spatial coordinate framework. Each baseline corresponds to the distance between two measurement points and their spatial positioning relationship. By solving multiple baselines, a complete set of preliminary calculated node coordinates can be obtained. The observations acquired by the GPS receiver are the key input data for establishing the initial GPS baseline network. Based on the GPS observations, the coordinates of each node are preliminarily determined by calculating and solving the relative positions between different base stations. This preliminary coordinate solution constitutes the initial GPS baseline network. The initial GPS baseline network is typically one of the following: a radial baseline network, radiating outwards from the external base station to various stations at the tunnel entrance or inside the tunnel; a chain baseline network, connecting adjacent stations segment by segment along the tunnel axis, commonly used in long tunnel projects; or a hybrid baseline network, forming a closed or semi-closed network outside the tunnel, and using a chain or segmented network inside the tunnel. The dual-frequency ionospheric-free combination method is a widely used technique in GNSS global navigation satellite system data processing, aiming to eliminate the impact of ionospheric delay on positioning accuracy. The ionosphere, part of Earth's atmosphere, introduces a delay to satellite signals, and this delay is inversely proportional to the square of the signal frequency. Combining observations from two different frequencies can effectively eliminate primary ionospheric errors. A dual-frequency ionospheric-free combination method is used for initial processing, actively accepting and retaining higher-order ionospheric errors that cannot be eliminated through conventional combinations in high-altitude environments. This yields node coordinate results that serve as the benchmark for subsequent corrections, making this initial coordinate solution the carrier for subsequent anomaly identification and network correction. The initial coordinate solution is obtained after removing the first-order ionospheric delay effect; it still contains higher-order ionospheric errors and other systematic errors.The initial coordinate solution represents the coordinate solution of each node obtained by solving the initial GPS baseline network of the target tunnel based on the acquired raw GPS observations and using the dual-frequency ionosphere-free combination method, without introducing gyro-guided observation constraints or specifically suppressing higher-order terms of the ionosphere.

[0025] It should be noted that in high-altitude, long tunnel projects, the surrounding rock of the tunnel completely blocks satellite signals, preventing measuring points inside the tunnel from directly receiving GPS signals. This means that the spatial coordinates inside the tunnel cannot be directly calculated as they are outside. Therefore, the establishment of the spatial reference inside the tunnel is not based on real-time satellite positioning, but rather relies on an initial GPS control network established outside the tunnel. Spatial coordinates are then gradually introduced into the tunnel through geometric transfer. Specifically, GPS observation stations are first deployed in the area outside the tunnel, and an initial GPS baseline network is constructed using dual-frequency or multi-frequency GPS observations. This initial GPS baseline network constitutes the unified spatial reference for the entire tunnel project. Subsequently, using the control points at the tunnel entrance as the starting points for coordinate transfer, a control traverse network is established segment by segment along the tunnel excavation direction using traverse surveying or other underground control surveying methods. The spatial positions of each measuring station inside the tunnel are not obtained by directly receiving GPS signals, but rather by observing the distance and elevation difference between adjacent control points and combining this with the known GPS coordinates at the tunnel entrance, calculating the coordinates step by step according to the spatial coordinate transfer and geometric constraints. Therefore, the three-dimensional coordinates of each control point inside the tunnel are essentially derived from the ground-based GPS baseline network through coordinate extension and spatial inversion calculations. This can be understood as an indirect mapping or reverse calculation of the ground-based GPS spatial reference in underground space. This process achieves the continuation of the GPS spatial coordinate system in the absence of satellite signals, ensuring that the control network inside the tunnel maintains consistency with the ground-based GPS baseline network in terms of coordinate framework. Currently, methods for obtaining GPS signals through inversion calculations inside tunnels are very common. In practical applications, a common method is to use a total station to measure angles and distances, and then use the measured data to calculate the precise position of the tunnel's current excavation axis.

[0026] In this embodiment, as a specific example, the method for obtaining the GPS observations and the initial GPS baseline network inside the tunnel can be set as follows: an independent control network is used at the tunnel entrance, where leveling is conducted according to second-order leveling, and a second-order GPS network is used for horizontal control; using the tunnel entrance control point as the starting point for coordinate transfer, several total station traverse survey stations are set up inside the tunnel along the excavation direction. The total station is used to sequentially conduct slope distance observations, horizontal angle observations, and vertical angle observations between adjacent stations to obtain the spatial geometric observations of the total station's traverse lines. The traverse survey stations represent underground horizontal and vertical control points set up along the tunnel axis, which are spatial control points formed by station-by-station observations using the total station to create the traverse network structure. Based on the above observation data, the three-dimensional coordinates of the traverse points inside the tunnel relative to the tunnel entrance control point can be obtained through inversion calculation using the total station. Since the tunnel entrance control point is already within the GPS coordinate framework, the coordinates of each traverse point inside the tunnel are essentially a spatial extension of the ground GPS reference. Based on this, the traverse points inside the tunnel can be regarded as control nodes under a unified GPS coordinate system, and equivalent baseline vectors can be constructed according to the spatial coordinate differences between adjacent points, thereby forming an initial GPS baseline network that includes the GPS baseline outside the tunnel and the equivalent baseline of the traverse inside the tunnel. Therefore, although no satellite signals are actually received inside the tunnel, the coordinates of the nodes inside the tunnel and the equivalent baseline information consistent with the GPS coordinate system can still be obtained through total station traverse surveying and coordinate transfer calculations. That is, in this embodiment, GPS observations and the initial GPS baseline network can be obtained inside the tunnel. It should be noted that the enumerated application method of obtaining GPS signals through inversion calculation inside the tunnel is a conventional technical means in tunnel control surveying in this field, and is only used for illustrative purposes here.

[0027] The gyroguide is a measuring device based on the principle of a gyroscope, primarily used for accurately measuring direction and position in tunnels or other underground engineering projects. It monitors changes in the tunnel's excavation direction and position. Its working principle is as follows: the gyroguide utilizes the inertial characteristics of a gyroscope to measure angular changes during movement; the gyroscope maintains its rotation axis direction unchanged, thus sensing changes in direction through its measurements. The azimuth angle is measured by the gyroguide's direction sensor, reflecting changes in the tunnel's excavation direction. The gyroguide determines whether the tunnel is excavating in the predetermined direction by accurately measuring azimuth angle changes. The pitch angle is measured by the gyroguide's pitch sensor, reflecting changes in the tunnel's verticality, ensuring that tunnel design and construction are carried out in the correct vertical direction.

[0028] It should be noted that in this embodiment, the number of gyro orientation edges used to provide absolute azimuth constraints in the gyro traverse lines laid along the tunnel axis is not fixed, but can be configured according to engineering accuracy requirements and implementation conditions. The function of the gyro orientation edges is to provide a spatial direction reference for the propagation path of the GPS baseline network. With the increase of the number of orientation edges, higher precision azimuth and pitch angle control information can be obtained at different spatial locations along the tunnel axis, making the spatial attitude constraints between nodes along the line denser and more uniform, thereby more fully revealing the directional system deviation caused by the delay of higher-order terms of the ionosphere. At the same time, each additional gyro orientation edge requires an increase in the corresponding instrument setup, observation time, personnel input, and data processing workload. Gyro orientation operations usually have high requirements for the operating environment, observation time, and the proficiency of technicians; therefore, increasing the number of orientation edges will directly lead to an increase in field observation costs and office processing costs. Therefore, in practical implementation, the number of gyro directional edges needs to be comprehensively balanced between the accuracy improvement effect and the engineering implementation cost. The number of gyro directional edges can be configured in stages according to the tunnel length, expected breakthrough accuracy level, and construction conditions to achieve cost-controllable engineering implementation while meeting accuracy requirements. In this embodiment, the parameters obtained from gyro traverse observations are mainly used to assist in correcting the GPS signals inside the tunnel obtained in high-altitude areas, reducing GPS signal deviations caused by severe ionospheric disturbances at high altitudes. Therefore, even if only a single gyro directional edge is used, the basic needs of signal correction calculation in this embodiment can be met, and GPS correction can still be achieved.

[0029] As a feasible implementation example, the method for laying out the gyro traverse is as follows: Using a total station inside the target tunnel, traverse control points are marked symmetrically on both sides of the tunnel inner wall along the tunnel excavation direction; the two ends of each gyro traverse are laid out on two traverse control points in asymmetrical positions on the left and right sides of the tunnel inner wall, and the laying directions of adjacent gyro traverses are opposite. To ensure cost-effective engineering implementation, the average adjacent spacing between each gyro traverse is set to 5 km. In specific implementation examples, such as... Figure 2 As shown in the figure, the transverse penetration surface of the target tunnel is represented by traverse control points GPS01 and GPS02 outside the target tunnel. Traverse control points on both sides inside the target tunnel are denoted by D-xx, where xx represents the ordinal number of the traverse control point. In the figure, GPS01→GPS02, D-04→D07, and D-13→D-14 correspond to gyro-guide wires AB, DC, and EF, respectively. The spacing between adjacent traverse control points on the same inner wall of the tunnel, as well as the spacing between adjacent gyro-guide wires, can be adjusted adaptively according to specific application requirements.

[0030] The TEC gradient value represents the rate or intensity of change of the total electron content (TEC) of the ionosphere within a unit spatial scale. In specific implementations, it can be expressed as the spatial rate of change of TEC along the tunnel's direction, or the degree of non-uniformity of TEC change in the horizontal or oblique direction within the tunnel area. In practical applications, it can be obtained through various existing methods. For example, multiple spatially distributed dual-frequency GNSS receivers can be used to invert the ionospheric TEC and calculate the TEC gradient value based on inter-station differential calculations; alternatively, TEC values ​​in different spatial directions can be inverted based on multi-satellite observations from a single GNSS station, and the TEC gradient can be calculated according to their spatial distribution relationship. Along the tunnel's excavation axis, multiple gyro traverse stations are sequentially deployed at predetermined intervals. Gyroscopes are used to observe the traverse segments between adjacent stations, obtaining the corresponding azimuth and elevation angle observations for each traverse segment. The azimuth angle refers to the angle from a reference direction (usually geographic north as the baseline) to the target object or measurement direction. It is typically measured on a horizontal plane and describes the horizontal rotation angle of the object relative to the reference direction. The azimuth angle observation value is an angle value, usually expressed in degrees or radians. The pitch angle refers to the vertical rotation angle of the object relative to the horizontal direction, i.e., the degree of tilt of the object relative to the horizontal plane (such as the ground). The pitch angle observation value is an angle value, usually expressed in degrees or radians. The azimuth angle observation value represents the offset angle of the tunnel excavation direction relative to north, helping to determine the horizontal direction of excavation; the pitch angle observation value represents the inclination of the tunnel relative to the horizontal plane during excavation, helping to control the tunnel slope. The TEC gradient value is used to characterize the spatial variation trend of the total electron content of the ionosphere. The magnitude of the delay of higher-order ionospheric terms is not only related to the absolute value of TEC but also closely related to the spatial gradient variation of TEC. When GPS signals propagate through the ionosphere, variations in TEC (Temperature Effort Capacity) in different spatial directions lead to different projections of higher-order term delays onto each baseline direction, resulting in directionally correlated system coordinate deviations in the GPS baseline network. This embodiment introduces the spatial variation characteristics of the ionospheric higher-order term delays into the correction model by acquiring the TEC gradient value along the target tunnel axis. This gives the inherent directional errors in the GPS baseline network a modelable physical indicator, providing a weighting basis and correction trend constraint corresponding to the intensity of ionospheric disturbances for subsequent coordinate correction.

[0031] The azimuth and elevation angle observations obtained from the gyro-guided observations provide an independent spatial attitude reference unaffected by ionospheric propagation delay. Gyro-guided orientation is based on inertial orientation principles, and its observation results are independent of the satellite signal propagation path, thus accurately reflecting the tunnel axis's extension direction in three-dimensional space. When the GPS baseline network node coordinates undergo systematic shifts due to ionospheric higher-order term delays, the baseline spatial direction calculated from these coordinates will deviate from the gyro-guided observation direction. This directional difference exhibits spatial continuity and structure, revealing the overall geometric distortion trend caused by ionospheric higher-order terms. By introducing the gyro-guided observation parameters as directional constraints into the GPS baseline network correction model, the baseline direction error can be reversed, thereby suppressing spatial attitude distortion caused by ionospheric higher-order terms.

[0032] The TEC gradient value and the gyro-conductor observation parameters complement each other in the modified model: the TEC gradient value is used to describe the spatial source and trend of the error field, and the gyro-conductor observation parameters are used to provide the true geometric direction reference. The two work together to transform the hidden system error caused by the delay of higher-order terms of the ionosphere from "inseparable coordinate noise" into "identifiable directional structural error", which is then effectively weakened in the process of network adjustment and weight adjustment.

[0033] By constructing one or more spatial orientation reference chains measured by gyroscopes along the tunnel's excavation direction inside the tunnel, three-dimensional orientation information unaffected by the ionosphere is introduced into the initial GPS baseline network correction process. This is used to constrain and correct GPS coordinate solutions affected by higher-order ionospheric terms in high-altitude environments. The optimized coordinate solution refers to the initial coordinate solution, incorporating TEC gradient information of the target tunnel and azimuth and elevation angle observations obtained from gyroscope traverses laid along the tunnel. Based on these azimuth and elevation angle observations, azimuth and elevation angle parameters representing the parameters used in the model construction are obtained. A GPS baseline network correction model is constructed using these azimuth and elevation angle parameters, and the initial coordinate solution is then collaboratively constrained and corrected to obtain the final coordinate solution.

[0034] In this embodiment, the azimuth and elevation parameters are obtained by adjusting the azimuth and elevation observation values. Alternatively, the azimuth and elevation observation values ​​can be used directly as the corresponding parameters without adjustment. The adjustment method is not unique in this embodiment. As the simplest adjustment method, the azimuth and elevation parameters are set as follows: the azimuth observation value is set as the azimuth parameter, and the elevation observation value is set as the elevation parameter. The initial coordinate solution and the optimized coordinate solution form a progressively corrected and optimized relationship. The optimized coordinate solution is not a simple replacement of the initial coordinate solution, but an improved solution obtained by specifically suppressing the systematic errors introduced by higher-order terms of the ionosphere in the initial coordinate solution after introducing gyro-guided observation constraints and TEC gradient information that are insensitive to the ionosphere.

[0035] As a feasible special application, the construction process of the GPS baseline network correction model is set as follows: The azimuth and elevation angle observations obtained from the gyro traverse observations are labeled as the first azimuth and the first elevation angle, respectively; the azimuth and elevation angle observations at the observation points of each gyro traverse are obtained using a total station and labeled as the second azimuth and the second elevation angle, respectively; the difference between the first and second azimuth angle values ​​is calculated and labeled as the azimuth parameter, and the difference between the first and second elevation angle values ​​is calculated and labeled as the elevation parameter; based on the initial coordinate solution, TEC gradient value, azimuth parameter, and elevation parameter, the GPS baseline network correction model is constructed.

[0036] The azimuth and elevation parameters, calculated by the difference between azimuth measurements obtained through two methods, replace the original single azimuth and elevation observations. These angle differences can be considered as a net signal reflecting abnormal changes in the traverse direction, providing error direction information for the model. By introducing dual-source angle observations from a gyro traverse and a total station, and utilizing their azimuth and elevation differences in the GPS baseline network correction model construction, the model achieves a distinguishable expression of the actual direction changes in underground space and instrument system errors. This enables the model to acquire direction-selective modulation capabilities, thus correcting only spatial distortions with consistent direction under TEC gradient drive. This suppresses the misleading effects of instrument drift and local construction disturbances on GPS network calculations, improving the stability and reliability of baseline calculations under high-altitude, strong ionospheric disturbance environments.

[0037] In a specific implementation, as an example, the method for measuring and obtaining the TEC gradient value is set as follows: several GNSS receivers are deployed inside and outside the tunnel, and the TEC value of each GNSS receiver point is obtained by inverting the carrier phase observation values ​​of the GNSS receivers. Let the set of TEC values ​​be represented as {TEC1, TEC2, ..., TEC...} LLet L represent the total number of GNSS receivers; let y be the ordinal number of the GNSS receiver, and y > 1; let Gtec be the TEC gradient value; and let Df be the distance between adjacent GNSS receivers. The formula for calculating the TEC gradient value can be expressed as: , Among them TEC y The y-th GNSS receiver, TEC y-1 The (y-1)th GNSS receiver, Df (y,y-1) This represents the point distance between the y-th GNSS receiver and the (y-1)-th GNSS receiver.

[0038] The calculation formula is the arithmetic mean of multiple adjacent spatial differential gradients. The GNSS receivers are numbered according to the tunnel direction. The TEC values ​​of each GNSS receiver location within the same observation epoch are obtained through carrier phase observation inversion. Local TEC gradients are calculated based on the TEC differences between adjacent GNSS receivers and the distance between locations. These local TEC gradients are then averaged to obtain the TEC gradient value of the target tunnel. The TEC value is the equivalent vertical TEC value processed by a unified mapping function and obtained within the same observation epoch or time window. Obtaining TEC values ​​through carrier phase observation inversion of GNSS receivers is a mature method in ionospheric monitoring. It is based on the characteristic of the difference in ionospheric influence on different frequency signals in dual-frequency GNSS observations, constructing an ionospheric observation combination, and inverting to obtain the total electron content parameters of the ionosphere corresponding to each station in the target tunnel area. The above calculation method is only one implementation method and is not the only limitation of this embodiment.

[0039] A GPS baseline network correction model is constructed, and an optimized coordinate solution representing the corrected initial coordinate solution is calculated using this model. This means that, based on the initial GPS coordinates and combined with tunnel orientation information and ionospheric variation characteristics, a set of coordinates closer to the actual tunnel geometry is generated through mathematical optimization or adjustment models. The GPS baseline network correction model refers to a mathematical model that, based on the initial GPS baseline network and its initial coordinate solution, introduces azimuth and elevation angle constraints obtained from gyrocompass observations and incorporates the ionospheric total electron content gradient information of the target tunnel region to collaboratively correct the node coordinates in the initial GPS baseline network. In practical applications, the GPS baseline network correction model can set a baseline component model and a node coordinate parameter model, obtaining the optimized quantity by directly adding the initial quantity and the difference. The optimized coordinate solution is introduced into the network adjustment calculation as the starting coordinate, and a unified network adjustment solution is performed on the initial GPS baseline network without changing the GPS observation values. The optimized coordinate solution represents a highly reliable coordinate solution for network layer correction calculated under the multi-source constraint collaborative optimization mechanism of the GPS baseline network correction model. However, it should be noted that the optimized coordinate solution is not the final coordinate. The optimized coordinate solution is used as a reliable initial value for network adjustment calculation, which is used to correct the initial GPS baseline network. The purpose is to reduce the coordinate deviation in the system affected by the ionosphere.

[0040] The anomalous node coordinates refer to node coordinates whose coordinate residuals or corrections significantly deviate from the overall network consistency during network adjustment, and whose deviation cannot be explained by the first-order ionospheric model. Identifying anomalous node coordinates with anomalies in higher-order ionospheric terms on the initial GPS baseline network refers to identifying, during network adjustment, node coordinates whose coordinate solution deviations are mainly caused by the unmodeled effects of higher-order ionospheric delays, through residual analysis, direction consistency constraints, and TEC gradient information. In specific implementations, a single-point residual threshold method can be used to identify anomalous node coordinates: calculate the observation residuals of each node's coordinate components, set a threshold, and determine the current node coordinates as anomalous when the observation residuals exceed the set threshold. Reducing the baseline observation weights of anomalous node coordinates in network adjustment refers to assigning lower weights to baseline observations connected to at least one anomalous node during network adjustment to reduce the impact of the anomalous node on the overall baseline network solution results. Reducing the baseline observation weights of all anomalous node coordinates in the network adjustment solution means, without removing the original GPS observations, weakening the control of nodes and their related baselines that are greatly affected by higher-order terms of the ionosphere on the adjustment results by adjusting the weights or variances, thereby achieving network layer correction of the initial GPS baseline network.

[0041] As a feasible implementation method, a tunneling cycle for the target tunnel is set, and the time interval between every two tunneling cycles is marked as a correction period; step S1 is completed before the target tunnel is tunneled, and steps S2, S3, S4 and S5 are all completed sequentially within each correction period.

[0042] The GPS correction process is decoupled and synchronized with the tunnel excavation rhythm in time. Without interfering with continuous excavation, the baseline correction under the influence of higher-order ionospheric terms is periodically completed during relatively stable periods between excavations. Setting excavation cycles and correction periods clarifies that the target tunnel has several excavation cycles, conforming to actual construction organization patterns. In practical applications, excavation cycles typically include excavation, muck removal, support, and equipment adjustment, with implementation gaps between cycles. Due to strong environmental disturbances during excavation, processing the detection and calculation correction process during cycle gaps provides a stable time window for observation and calculation. Limiting step S1 to completion before excavation ensures that the initial GPS baseline network and initial coordinate solution are prerequisites based on conventional techniques. Setting steps S2-S5 to be completed sequentially within each correction period allows for tracking changes in TEC gradient values ​​over time and the degree of observational changes due to spatial extension of the gyro traverse as excavation progresses, ensuring the timeliness and relevance of the input data. By introducing a time organization mechanism of "tunneling cycle - correction period", GPS correction is transformed from a one-time static process into a phased network correction process synchronized with the tunnel construction rhythm, which effectively suppresses the time accumulation effect of higher-order terms of ionospheric errors in high-altitude areas.

[0043] Furthermore, as a feasible implementation method, the settings of the GPS baseline network correction model include: Let X0 be the initial coordinate solution of each node on the GPS baseline network, and let Xop be the optimized coordinate solution corresponding to each initial coordinate solution; let Gtec be the TEC gradient value; let α be the azimuth parameter and β be the elevation parameter; let d(α,β) be set based on the azimuth and elevation parameters; let k1 be the direction modulation coefficient and k2 be the ionospheric disturbance coefficient. The calculation formula for the GPS baseline network correction model is expressed as follows: .

[0044] The conventional dual-frequency ionospheric combination method assumes that the two frequency signals travel along the same propagation path. However, in the strong TEC gradient region, the curvature and actual paths of different frequency signals differ, leading to the emergence of higher-order residual terms. The larger the TEC gradient difference, the more pronounced the path difference. The higher-order ionospheric error is related to the total electron content along the signal path and is closely related to the spatial variation of electron density. When the TEC gradient value increases, the difference in propagation paths of different frequency signals in the ionosphere significantly increases, resulting in second-order and higher-order ionospheric delay terms that cannot be completely eliminated by the conventional dual-frequency ionospheric combination method. Their residual error amplifies nonlinearly with increasing TEC gradient. That is, TEC determines the cardinality of the ionospheric error, while the TEC gradient value determines whether higher-order ionospheric errors are excited and to what extent they are amplified. When the TEC distribution is uniform, the electron density change along the signal path is gradual, and the contribution of higher-order expansion terms is small. When the TEC gradient increases, the refraction and phase rotation on different path segments are inconsistent, and higher-order terms cannot be canceled by the dual-frequency combination. The azimuth and elevation parameters, by describing the spatial orientation of the tunnel, serve as correction vectors for higher-order ionospheric errors. These higher-order ionospheric errors are not uniformly distributed but rather vary with the inhomogeneity of ionospheric electron density, affecting positioning deviations in specific directions.

[0045] Directional corrections to signals can be obtained using azimuth and elevation parameters. In GPS correction, these angle data are converted into a direction correction vector to correct coordinates in the GPS baseline network, reducing errors caused by ionospheric interference. Higher-order ionospheric errors are closely related to the propagation direction and path of GPS signals. Changes in the electron content of the ionosphere typically exhibit strong gradients in space, especially at high altitudes. These gradient changes can cause varying degrees of delay in GPS signals in different directions. For example, if the TEC gradient is large in a certain direction, the GPS signal in that direction may experience a greater delay. The azimuth parameter can determine the directionality of this delay, and errors can be reduced by correcting the coordinate values ​​in that direction. The directional information provided by the azimuth and elevation parameters, together with the TEC gradient, constitutes a direction correction model. In the formula, the direction correction vector d(α,β) is calculated based on the azimuth and elevation angles and is used to guide how to correct GPS coordinates. As a specific implementation example, the direction correction vector is set in the following form: The expression denoted by α(cosβ∙cosα) describes the horizontal component, representing the change in position in the horizontal direction; cosβ∙sinα is also a horizontal component, representing the change in position in the horizontal direction, but with the direction α; sinβ represents the vertical component, describing the change in position in the vertical direction. The enumerated formulas, based on the azimuth and pitch parameters, describe the tunnel's corresponding excavation direction in three-dimensional space, i.e., the direction for ionospheric error correction. The direction correction vector d(α,β) is a three-dimensional direction vector calculated based on the azimuth and pitch parameters, used to describe the tunnel excavation direction and playing a directional correction role in GPS coordinate correction. This vector effectively corrects errors caused by higher-order ionospheric terms, ensuring high accuracy and stability of GPS measurements in high-altitude, complex ionospheric environments.

[0046] The GPS baseline network correction model is used to optimize and correct the initial GPS coordinate solution in a direction-controlled, amplitude-adaptive manner, with a suppression mechanism, by utilizing the TEC gradient value and stable direction information provided by the gyroconductor, without explicitly modeling higher-order ionospheric terms. The fractional part in the formula represents a small-amplitude directional correction for known systematic deviations. Since the GPS deviation in the target tunnel is relatively small, the model calculation formula is designed as an addition of the initial coordinate solution and the correction, rather than a multiplication or independent variable reconstruction formula, to avoid changes in the overall coordinate scale or recalculation of coordinates, thus preventing new calculation deviations and disruption of network geometry. The k1∙Gtec∙d(α,β) part in the numerator represents the initial correction, whose direction is determined by the gyroconductor and whose amplitude varies with the TEC gradient value; when the ionospheric environment is stable, the correction naturally decreases; when ionospheric disturbances increase, the correction is activated. In the formula, the 1+k2∙|Gtec| part of the denominator is used as a nonlinear suppression factor, serving as a normalization and suppression term. When |Gtec| is small, the denominator is close to 1, and the correction is approximately linear; when |Gtec| is large, the denominator increases, and the correction amount is compressed. This denominator term is used to suppress over-correction under strong perturbation conditions, improving the robustness and engineering safety of the model. The directional modulation coefficient k1 represents the scaling factor used to adjust the correction amplitude, and the ionospheric perturbation coefficient k2 represents the parameter used to characterize the degree of correction suppression under strong ionospheric perturbation conditions. The directional modulation coefficient k1 and the ionospheric perturbation coefficient k2 can be determined from historical engineering data or empirical data from simulation experiments.

[0047] Furthermore, as a feasible implementation method, the process of setting the directional modulation coefficient includes: All azimuth observations are organized into an azimuth sequence according to the tunneling direction, and the difference between adjacent observations is calculated based on the azimuth sequence. An azimuth difference threshold is set for the difference between adjacent observations. The standard deviation of the azimuth sequence is calculated and denoted as σ, and the azimuth difference threshold is denoted as σv. The baseline scaling factor is set to k0. The formula for obtaining the directional modulation coefficient is expressed as: .

[0048] The directional modulation coefficient k1 is calculated based on the standard deviation σ of the azimuth sequence observed by the gyro traverse and a preset azimuth difference threshold σv. Specifically, when the azimuth change is small during tunneling (i.e., σ < σv), the system relies heavily on directional information for correction, and the directional modulation coefficient k1 remains high. However, when the azimuth change is large (i.e., σ > σv), the directional modulation coefficient k1 decreases, reducing the reliance on azimuth information and thus avoiding the impact of unstable directional observations on GPS signal correction.

[0049] To analyze the stability of directional changes during tunneling, the azimuth data for each instance are arranged into a time series according to the tunneling direction and time sequence. This azimuth series reflects directional fluctuations during tunneling. Statistical analysis of the stability of the gyro-guided azimuth observation series is performed, and the standard deviation of the azimuth series is used to apply exponential decay modulation to the direction modulation coefficient. This enhances the direction correction effect when the azimuth observation stability is high, while automatically weakening the direction correction intensity when the azimuth observation fluctuation is large, thus avoiding the adverse impact of unreliable direction information on the GPS higher-order ionospheric error correction results. The difference between adjacent observations reflects the magnitude of the tunneling direction change between two observations. A large difference indicates a significant change in direction, possibly due to equipment disturbance or external influences; a small difference indicates a relatively stable tunneling direction. In the formula... The exponential decay factor is used to adjust the correction coefficient based on the standard deviation and threshold of the azimuth sequence. As σ increases, the exponential part decreases, leading to a decrease in k1. This exponential decay factor determines the impact of azimuth stability on the correction coefficient: when σ is small, the decay factor is close to 1, indicating good directional stability and a high correction coefficient; when σ is large, the decay factor approaches 0, the correction coefficient drops significantly, indicating unreliable directional information and reduced correction strength.

[0050] Furthermore, as a feasible implementation method, an ionospheric activity level is set, including a first ionospheric level and a second ionospheric level with activity levels ranging from low to high, and the ionospheric perturbation coefficient includes a first perturbation term, a second perturbation term, and a third perturbation term with values ​​ranging from small to large; When the TEC gradient value is lower than the first ionospheric level, the ionospheric perturbation coefficient is the first perturbation term; when the TEC gradient value is between the first and second ionospheric levels, the ionospheric perturbation coefficient is the second perturbation term; when the TEC gradient value is higher than the second ionospheric level, the ionospheric perturbation coefficient is the third perturbation term.

[0051] The first perturbation term applies to cases of low ionospheric activity, meaning a smaller impact on GPS signals; therefore, a lower perturbation coefficient is chosen. The second perturbation term applies to cases of moderate ionospheric activity, with a moderate perturbation coefficient, requiring stronger perturbation compensation for signal correction. The third perturbation term applies to cases of high ionospheric activity, indicating a stronger influence of the ionosphere on the signal; therefore, a higher perturbation coefficient is needed to correct the signal. As ionospheric activity increases, the TEC gradient value increases, and its impact on GPS signals becomes more significant. Therefore, different ionospheric perturbation coefficients are selected to adjust the correction strength according to different ionospheric activity levels. To adapt to the impact of different ionospheric activity levels on GPS signals, the method sets ionospheric activity levels, including a first ionospheric level, a second ionospheric level, and corresponding ionospheric perturbation coefficients. When ionospheric activity is low, the TEC gradient value is lower than the first ionospheric level, and a smaller perturbation coefficient is used. When ionospheric activity is moderate, the TEC gradient value is between the first and second ionospheric levels, and a medium perturbation coefficient is used. When ionospheric activity is strong, the TEC gradient value is higher than the second ionospheric level, and a larger perturbation coefficient is used. This effectively adjusts the GPS signal correction, ensuring correction accuracy and stability. The value of the perturbation term can be determined based on actual engineering data or simulation results. To ensure effective correction without overcorrection, as a feasible specific application example, the value of the perturbation term can refer to the following principles: First perturbation term: smaller values ​​(0.1 to 0.5), suitable for situations with low ionospheric activity.

[0052] The second perturbation term: a moderate value (0.5 to 1.0), suitable for moderate ionospheric activity.

[0053] The third perturbation term: a larger value (1.0 to 2.0), is suitable for situations with strong ionospheric activity.

[0054] Furthermore, as a feasible implementation method, in this embodiment, the specific form of the direction correction vector is set as follows: , Where ω1 represents the horizontal weight component and ω2 represents the vertical weight component.

[0055] This embodiment, based on the aforementioned implementations, adds a horizontal weight component ω1 and a vertical weight component ω2. The horizontal weight component ω1 is used to adjust the influence intensity of the horizontal component in the direction correction, and the vertical weight component ω2 is used to adjust the influence intensity of the vertical component in the direction correction. If the direction change during tunnel excavation is significant and its impact on the horizontal direction is important, the horizontal weight component ω1 may need to be increased; conversely, if the impact of the pitch angle is significant and the vertical correction amount is large, the vertical weight component ω2 needs to be appropriately increased. The reasonable values ​​of the horizontal weight component ω1 and the vertical weight component ω2 can be determined through field testing, simulation, or empirical formulas. Generally, their values ​​should ensure that the direction correction vector is neither too large nor too small, ensuring the reliability and stability of the correction results. In the horizontal direction, the direction correction vector is influenced by the combination of the azimuth parameter α and the pitch angle parameter β. The horizontal weight component ω1 adjusts the intensity of the correction on the horizontal plane, meaning that the correction of the azimuth and pitch angle parameters will proportionally affect the correction of the horizontal component. In the vertical direction, the orientation correction vector is adjusted by the pitch angle β and the vertical weighted component ω2; the correction of the vertical component is not affected by the azimuth parameter α, but only by the pitch angle. By decomposing the orientation correction vector into horizontal and vertical components and flexibly adjusting the correction intensity using weighting coefficients, it is possible to accurately adapt to changes in azimuth and pitch angles during tunnel excavation, providing an efficient orientation correction method.

[0056] Furthermore, the network adjustment solution process includes: Based on GPS observations and optimized coordinate solutions, a matrix-style baseline observation equation is constructed for the initial GPS baseline network. The variables of the baseline observation equation include coordinate corrections and observation residuals. The least squares method is used to perform network adjustment on the baseline observation equation to obtain a weighted least squares closed-form solution, and the coordinate corrections of the target node coordinates are calculated. The coordinate corrections are then substituted into the baseline observation equation to obtain the observation residuals. Update all calculated coordinate corrections for each node coordinate to the corresponding node coordinate; use observation residuals to screen out abnormal node coordinates and reduce the baseline observation weights of abnormal node coordinates in the baseline observation equation for all baselines.

[0057] Least squares is the most commonly used fitting algorithm, obtaining the optimal solution by minimizing the sum of squared errors. Specifically, in GPS network adjustment, it optimizes node coordinates by minimizing the errors in the baseline observation equations. Weighted least squares, on the other hand, assigns different weights based on the accuracy of different baselines. Higher-precision observation data is given larger weights to dominate the solution, while lower-precision observation data is given smaller weights to reduce its impact on the results. The network adjustment process includes: constructing a matrix-like baseline observation equation for the initial GPS baseline network based on GPS observations and optimized coordinate solutions, where the variables include coordinate corrections and observation residuals. The weighted least squares method is used to perform network adjustment on the baseline observation equations to obtain the coordinate corrections for the target nodes, and the observation residuals are calculated based on these corrections. Then, outlier nodes are identified, and their weights in the baseline observation equations are reduced, thereby improving the accuracy and stability of the network solution. This method can effectively address GPS measurement errors and external interference in special environments such as high altitudes. Anomaly node coordinates are screened out using observation residuals. In specific implementations, a preset threshold method can be used for screening. After obtaining the observation residuals, a screening threshold is directly set for the calculated observation residuals using conventional empirical rules. When the observation residuals are greater than the screening threshold, the node coordinates calculated for the current target are determined to be anomaly node coordinates. By using weighted least squares network adjustment and anomaly node processing methods, the accuracy and robustness of GPS measurements in high-altitude areas are improved, effectively reducing the impact of measurement errors and external interference, and ensuring the smooth progress of high-precision tasks such as tunnel excavation. The baseline observation equation can be constructed in multiple ways. As a basic example, the calculation formula of the baseline observation equation can be expressed as: I = A∙δ + v, where I represents the GPS observation value, A represents the design matrix, v represents the observation residual, and δ represents the coordinate correction amount.

[0058] Furthermore, as a feasible implementation method, the baseline observation equation is set as follows: Let the observation residual be represented by v, and the GPS observation value by I; let the optimized coordinate solution be represented by Xop, and let the vector form of the optimized coordinate solution be f(Xop); let the coordinate correction be represented by δ. The baseline observation equation, expressed in terms of observation residuals, is: v = If(Xop) - Aδ. Where A represents the design matrix used to characterize the sensitivity of each baseline to the target node coordinates.

[0059] The observation residual represents the error between the actual observed values ​​and the model predictions. For GPS baseline measurements, errors can be caused by various factors, such as equipment errors, changes in the measurement environment, and ionospheric disturbances. The smaller the observation residual, the more accurate the corrected coordinates. The optimized coordinate solution is a coarse optimization solution obtained from the initial calculation of dual-frequency GPS data. A more accurate initial GPS baseline network coordinate is obtained through subsequent least-squares optimization methods. The coordinate correction is the target quantity to be calculated, obtained through adjustment algorithms, and represents the change in node coordinates relative to the initial estimate. Finally, through optimization of the coordinate correction, more accurate target node coordinates are obtained. The design matrix describes the sensitivity of each baseline to the target node coordinates and is the basis for network adjustment, used to correlate the coordinate correction with the actual observations.

[0060] The least squares method is defined as follows: The objective function for network adjustment is constructed using the least squares method. Let the objective function be denoted as Φ, then the calculation formula for the objective function is: Φ(δ) = min δ v T Pv, Where P represents the baseline observation weight matrix preset for the coordinates of each node in the initial GPS baseline network.

[0061] The baseline observation weight matrix P is a diagonal matrix, where each diagonal element represents the weight of the corresponding baseline observation. Typically, the baseline observation matrix is ​​preset based on the observation accuracy of the baseline. Specifically, the baseline observation weight matrix is ​​used to represent the importance and accuracy of each observation in network adjustment solutions within surveying systems such as geodesy, GPS positioning, and spatial benchmarks. In this embodiment, the preset of the baseline observation matrix is ​​performed simultaneously with the construction of the initial GPS baseline network. The purpose of presetting the baseline observation weight matrix is ​​to ensure that high-quality observation data has a significant impact on the solution results in subsequent network adjustment solutions, while the influence of low-quality observation data is appropriately suppressed. The size of its diagonal elements reflects the accuracy and reliability of the observations. The objective function represents the quantity to be minimized, and the minimization objective is the product of the observation residual vector v and the weight matrix P. δ This represents the coordinate correction δ that minimizes the objective function Φ(δ), which is the final result to be solved in this embodiment. T Pv represents the weighted sum of squares of the observation residuals, and represents the weighted total error of all observation errors. The goal of minimizing the weighted error is to reduce the difference between all observed values ​​and the calculated values ​​from the model as much as possible, while ensuring that high-precision observations contribute significantly to the final solution. The objective function optimizes the coordinate solution by minimizing the sum of squares of the weighted observation residuals. The participation of the weight matrix ensures that observations of different precisions receive different influence weights during the optimization process.

[0062] Furthermore, the network adjustment solution process includes: Substitute the baseline observation equation, expressed in terms of observation residuals, into the objective function constructed using the least squares method: Φ(δ)=min δ v T Pv=min δ {[If(Xop)-Aδ] T P[If(Xop)-Aδ]}; Taking the derivative of δ and setting the gradient of Φ(δ) to zero, we can express it using the coordinate correction δ as: δ=(A T PA) -1 A T P[If(Xop)].

[0063] The least squares method for solving coordinate corrections can significantly improve the accuracy of measurement results, especially in complex geometric relationships between multiple benchmarks and measurement points. By optimizing residuals, errors and systematic biases can be reduced, ensuring the accuracy of engineering measurements. The weight matrix can adjust its influence according to the precision of different data; high-precision data contributes more, while low-precision data has a smaller impact, thus effectively improving the reliability of the solution results. Substituting the residual expression of the baseline observation equation into the least squares objective function essentially embeds the functional relationship between node coordinate corrections and observation errors into the network adjustment optimization model, thereby achieving optimal absorption of observation bias by coordinate corrections. This provides quantifiable criteria for anomaly identification and weight adjustment, and improves the stability and accuracy of GPS network solutions in complex ionospheric environments at high altitudes without increasing the cost of high-precision ionospheric modeling.

[0064] In this embodiment, the specific process of finding the derivative of δ using the substitution of the objective function is explained as follows: Regarding [If(Xop)-Aδ] T For clarity, we differentiate the part P[If(Xop)-Aδ] and let If(Xop)=b. Then, in this embodiment, Φ=(b-Aδ). T P(b-Aδ), expanding the transpose matrix terms: Φ=(b T -δ T A T )P(b-Aδ); Expanding further, the calculation after removing the parentheses is: Φ=b T Pb-b T PAδ-δ T A T Pb+δ T A T PAδ.

[0065] Because matrix bT PAδ is a scalar matrix, therefore b T PAδ=δ T PA T b; Therefore, -b in the formula can be... T PAδ-δ T A T The Pb portions are merged, and the merged result is expressed as: -2δ T A T Pb; The calculation formula can then be simplified to: Φ=b T Pb-2δ T A T Pb+δ T A T PAδ.

[0066] Substituting If(Xop)=b into the simplified expression, the objective function can be expressed as: Φ=δ T A T PAδ-2δ T A T P[If(Xop)]+[If(Xop)] T P[If(Xop)].

[0067] δ in the formula T A T The PAδ part represents the impact of node coordinate corrections on the consistency of the entire GPS baseline network under the current baseline observation weighting system. It indicates "the network cost of calculating the coordinate changes," and in practical applications, it can be used to constrain the coordinate correction magnitude, preventing over-adjustment under high-weight baseline constraints. The -2δ part in the formula... T A T The P[If(Xop)] part characterizes the driving force exerted on the nodal coordinate correction under the influence of inconsistencies in baseline observations at the current coordinate solution, through weight modulation and geometric mapping. It represents the correction method required to drive the coordinates due to errors. [If(Xop)] in the formula... T The P[If(Xop)] part is a measure of the overall error level of the current GPS baseline network, reflecting the degree of weighted mismatch between the network and the observations under the existing coordinate conditions; it represents the sum of squares of the weighted observation difference between the GPS baseline observations and the theoretical model under the current node coordinate conditions, and is used to quantify the overall inconsistency caused by unmodeled errors such as higher-order ionospheric terms in the initial network.

[0068] More specifically, the process of finding the derivative with respect to δ is as follows: Regarding δ in the objective function T AT PAδ, -2δ T A T P[If(Xop)]、[If(Xop)] T Differentiate each of the three terms in P[If(Xop)].

[0069] The simplification process of the first term with respect to δ is as follows: Given the simplified forms of matrix differentiation and least squares: Furthermore, when A is symmetric, the right side of the equation can be simplified to 2Ax. Because A T Since PA is a symmetric matrix, the derivative of the first term with respect to δ can be directly derived as: 2A T PAδ.

[0070] The simplification process of differentiating the second term with respect to δ is as follows: Because in -2δ T A T In P[If(Xop)], A T P[If(Xop)] are constant vectors independent of the nodal coordinate corrections, equivalent to coefficients that do not participate in differentiation. Therefore, the derivative of the second term with respect to δ can be directly derived as: -2A T P[If(Xop)].

[0071] The simplification process of differentiating the third term with respect to δ is as follows: Because of [If(Xop)] T P[If(Xop)] are constant vectors that are independent of the node coordinate corrections, which are equivalent to coefficients that do not participate in the differentiation. Therefore, it can be directly concluded that the derivative of the third term with respect to δ is 0.

[0072] Therefore, the objective function constructed by the least squares method, after differentiating with respect to δ and setting the gradient of Φ(δ) to 0, is expressed as: 2A T PAδ-2A T P[If(Xop)]=0.

[0073] Further simplified to: A T PAδ=A T P[If(Xop)], Therefore, the simplified coordinate correction δ is expressed as: δ=(A T PA) -1 A T P[If(Xop)].

[0074] The simplified formula for calculating coordinate correction can be used to calculate the coordinate correction for the corresponding target node.

[0075] It should be noted that the mathematical simplification process to satisfy the coordinate correction δ must ensure that A T PA is an invertible matrix, therefore, in this embodiment, it is specifically defined that the design matrix A is a full-rank matrix. In this embodiment, because the node coordinates on the GPS baseline network have weights for each baseline, i.e., the eigenvalues ​​of P are all greater than 0, P satisfies the positive definiteness matrix condition; at the same time, setting the design matrix A as a full-rank matrix in the specific implementation ensures that A... T PA is an invertible matrix. The design matrix may be incomplete in rank due to: baseline degradation, where all baselines lie on the same straight line or plane, resulting in unconstrained translation or normals; missing baseline observations; or low node coordinate weights. Therefore, in practical applications, ensuring the design matrix A is full rank can be achieved by adding constrained observations or fixing observation benchmarks. Even in the rare case of the design matrix A being incomplete in rank, leading to non-invertible or rank-deficient coefficient matrices in the normal equations, the generalized inverse method can be used to solve the matrix invertibly, obtaining the node coordinate correction δ. This ensures that even with network degrees of freedom or observation degradation, the optimal solution with the minimum norm can still be obtained, thus achieving stable correction of the GPS baseline network.

[0076] Furthermore, it is necessary to add some explanation during the expansion and simplification of the objective function, specifically regarding matrix b. T The derivation process for PAδ as a scalar matrix is ​​as follows: In this embodiment, let m be the number of baselines for each node coordinate and q be the number of target node coordinates to be processed.

[0077] The If(Xop) part physically represents the observation difference vector, that is, the difference between the GPS observation value on the baseline and the optimized coordinate solution. The If(Xop) vector is a single column vector with a dimension of m×1. Therefore, the vector b has a dimension of m×1, and the transpose matrix b... T The dimension is 1×m. The dimension of the baseline observation weight matrix is ​​m×m; the dimension of the design matrix is ​​m×q; the dimension of the coordinate correction is q×1, which is also a single column vector.

[0078] matrix b T PAδ is decomposed successively using dimension multiplication: Matrix b T P→(1×m)(m×m)=1×m; Matrix b T PA→(1×m)(m×m)(m×q)=1×q; Matrix b T PAδ→(1×m)(m×m)(m×q)(q×1)=1×1.

[0079] Therefore, the discriminant matrix b T PAδ is a scalar matrix such that bT PAδ=(b T PAδ) T Established.

[0080] Because (b) T PAδ) T =δ T P T A T b, while P T =P, therefore we get the equation: b T PAδ=δ T PA T b.

[0081] It should be noted that the design matrix is ​​a core tool in statistics for constructing linear models, presenting the relationship between observed data and model parameters in matrix form. Typically, the rows of the design matrix correspond to the observed data, and the columns correspond to the unknown data in the target study. In this embodiment, the dimension of the design matrix A is derived from the number of observation baselines and the number of unknown parameters to be determined; its number of rows equals the number of observation baselines, and its number of columns equals the number of unknown parameters. In this embodiment, the unknown parameters to be determined are the coordinate correction and the observation residuals, both of which are equal in quantity, representing the number of target node coordinates to be processed.

[0082] Furthermore, as a feasible implementation method, the node coordinates are represented as X1, and the ordinal number of the node coordinates is represented as j, then the coordinates of the j-th node are represented as X1j; The update formula for setting the node coordinates is: X1j = Xopj + δj. Where Xopj represents the optimized coordinate solution corresponding to the coordinates of the j-th node, and δj represents the coordinate correction amount corresponding to the coordinates of the j-th node.

[0083] X1j represents the updated coordinates of the j-th node, which are the node coordinates after adjustment by the coordinate correction amount, i.e., the final node coordinate state. Xopj represents the optimized coordinate solution of the j-th node, which is the coordinate value obtained by adjusting the initial coordinate solution, representing the estimated coordinates obtained based on the initial data. δj is the coordinate correction amount of the j-th node, representing the part that corrects the initial coordinates; this correction amount is obtained by the least squares method, which is the coordinate adjustment amount calculated by the optimization objective function during the network adjustment process.

[0084] Furthermore, as a feasible implementation method, the process of using observation residuals to screen out the coordinates of outlier nodes includes: Let the baseline residual norm of the node coordinates be r, and let r = ||v||; let the number of baselines connected to the node coordinates be m, and let the associated baseline residual of the node coordinates be R. Then the associated baseline residual of the j-th node coordinate is denoted as Rj. The formula for calculating the associated baseline residual of the j-th node coordinate is as follows: ; A baseline residual threshold is set for the associated baseline residual. When the associated baseline residual exceeds the baseline residual threshold, the current node coordinates are identified as abnormal node coordinates.

[0085] r = ||v|| represents the magnitude of the residual vector, calculated by taking the Euclidean norm of the residual vector v. The baseline residual norm r quantifies the error magnitude of each node. A larger r indicates a larger observation error at that node, potentially indicating a more severe bias. r is a single value representing the combined performance of all observation errors at a node, used to assess the observation quality of that node. The associated baseline residual represents the weighted average of all baseline residuals related to that node, used to quantify the overall error or bias of the j-th node. This value indicates the reliability of the node coordinates; a larger Rj indicates a larger error at that node, which may need to be excluded. m is the number of baselines associated with the j-th node, representing the number of observations from node j to other nodes or reference points. For example, in GPS measurements, each node typically has multiple associated baselines connecting the observations of that node to those of other nodes. The baseline residual threshold can be set based on engineering project rules of thumb or recommended values ​​in standardized literature. For example, some high-precision engineering projects may specify a maximum tolerance error of 1 mm, while the standard baseline residual threshold may be 0.5 mm. Thresholds can be set based on such standard values. In practical applications, if there are no readily available standard values, historical data can be referenced to examine the residual values ​​of abnormal nodes in past projects, and appropriate thresholds can be set accordingly.

[0086] Furthermore, as a feasible implementation method, the reduction adjustment method of the baseline observation weights is set as follows: The baseline observation weight matrix of the abnormal node coordinates is labeled as the low-amplitude observation weight matrix Pr. The calculation formula of the low-amplitude observation weight matrix is ​​set as: Pr=λ∙P, where λ represents the weight attenuation coefficient, and the value of λ is set to be in the range of (0,1).

[0087] P is the initial baseline observation weight matrix, reflecting the degree of influence of each baseline observation on the target node coordinate estimation. Pr is the adjusted baseline observation weight matrix, used to identify the low weights of outlier nodes in network adjustment, serving as the new observation weight matrix obtained after reducing the weights of outlier nodes. λ is the weight decay coefficient, controlling the degree of decay of the baseline observation weights; λ acts on the baseline observation weight matrix P, reducing it and thus minimizing the impact of outlier nodes on the results. In practice, for each baseline, the decay coefficient λ can be selected based on the degree of node anomalousness. For example, the λ value for some outlier nodes may be smaller than that for other nodes to reflect the significance of their errors.

[0088] Furthermore, as a feasible implementation method, the process of deploying gyro traverses is set as follows: when the absolute value of the difference between adjacent observations is higher than the azimuth difference threshold, the gyro traverse segments involved in the calculation of the difference between adjacent observations are marked as abnormal observation traverse segments, and the traverses are readjusted and deployed again for the abnormal observation traverse segments; the azimuth difference threshold is positively correlated with the deployment distance between adjacent gyro traverses, and the threshold change rate of the azimuth difference threshold does not exceed the preset direction change rate value inside the target tunnel.

[0089] The azimuth difference threshold is a standard used to determine whether observation differences are normal. If the azimuth parameter difference between adjacent traverses exceeds the preset azimuth difference threshold, the traverse segment is considered abnormal. This azimuth difference threshold can be set based on the tunnel's structural characteristics and the excavation process. Large-scale azimuth deviations may indicate problems with the measurement system or external environmental interference. When the difference between adjacent observations exceeds the threshold, the gyro-guided traverse segment is marked as an abnormal traverse segment and needs to be readjusted. This calibration method effectively eliminates abnormal observation data caused by errors, equipment problems, or external interference, thereby improving the accuracy of positioning during tunnel excavation. Correcting abnormal traverses helps avoid systematic errors introduced by measurement errors in network adjustment, thus improving the correction accuracy of the GPS positioning system.

[0090] In one feasible implementation, let the azimuth sequence set be represented as Q, and θ represent the azimuth observation value. i Let represent the azimuth angle observation value obtained for the i-th segment of the gyroscope conductor; let Δθi represent the difference between adjacent observations. The set form of the azimuth sequence Q is: Q = {θ1, θ2, ..., θ n}, The formula for calculating the difference between adjacent observations Δθi is set as follows: Δθ i =θ i+1 -θ i , Where i represents the ordinal number of the gyroscope wire, and i = 1, 2, ..., n-1; n represents the total number of segments of the gyroscope wire.

[0091] The azimuth sequence Q is used to store the observation data for each segment of the gyroconductor. It can be viewed as a list or array, where each element represents the azimuth angle measured at a specific location for a gyroconductor. θ i+1 Δθ represents the azimuth angle observation value obtained from the latest tunnel section. i This represents the angle difference between the azimuth angle observations obtained from two gyroscope wires. The difference between adjacent observations is Δθ. iThis reflects the change in azimuth angle between two adjacent gyroscope conductors. During tunnel excavation, the azimuth angle should change smoothly, with a large Δθ... i Abnormalities or sudden changes in values ​​may indicate significant deviations or observational malfunctions. By monitoring and analyzing the differences between all adjacent observations, measurement errors that may require correction can be detected, allowing for timely adjustments. Collecting the azimuth sequence set Q allows for real-time updates of the azimuth values ​​for each traverse segment during tunnel excavation. Analyzing these values ​​reveals directional changes along the entire excavation path, improving positioning accuracy during tunnel excavation, preventing the impact of abnormal data on network adjustment calculations, and ultimately ensuring the accurate completion of the tunnel.

[0092] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A GPS correction method for high-altitude tunnels based on gyro-guided wires, characterized in that, The method includes: Step S1: Obtain GPS observations and use them to construct the initial GPS baseline network for the target tunnel. Perform initial calculations on the GPS observations using a dual-frequency ionosphere-free combination method to obtain the initial coordinate solutions for the node coordinates on the initial GPS baseline network. Step S2: Measure and obtain the TEC gradient value of the target tunnel, lay out a number of gyro wires along the tunnel excavation direction, and collect all the azimuth and pitch angle observations obtained using the gyro wires. Step S3: Based on the azimuth and elevation observations, set the azimuth and elevation parameters respectively. Based on the initial coordinate solution, TEC gradient value, azimuth and elevation parameters, construct a GPS baseline network correction model. Use the GPS baseline network correction model to calculate the optimized coordinate solution representing the corrected initial coordinate solution. Step S4: Perform network adjustment on the initial GPS baseline network based on GPS observations, and use the optimized coordinate solution to participate in the network adjustment solution to identify the coordinates of anomalous nodes on the initial GPS baseline network that have higher-order ionospheric anomalies. Step S5: Reduce the baseline observation weights of all abnormal node coordinates in the network adjustment solution, and then update the coordinate corrections obtained from the network adjustment solution to the node coordinates of the initial GPS baseline network to complete the network layer correction of the GPS signal.

2. The GPS correction method for high-altitude tunnels based on gyro-guided wires according to claim 1, characterized in that, Set the tunneling cycle for the target tunnel, and mark the time interval between every two tunneling cycles as the correction period; step S1 is completed before the target tunnel is tunneled, and steps S2, S3, S4 and S5 are all completed sequentially within each correction period.

3. The GPS correction method for high-altitude tunnels based on gyro-guided wires according to claim 1, characterized in that, The settings of the GPS baseline network correction model include: Let X0 be the initial coordinate solution of each node on the GPS baseline network, and let Xop be the optimized coordinate solution corresponding to each initial coordinate solution; let Gtec be the TEC gradient value; let α be the azimuth parameter and β be the elevation parameter; let d(α,β) be set based on the azimuth and elevation parameters; let k1 be the direction modulation coefficient and k2 be the ionospheric disturbance coefficient. The calculation formula for the GPS baseline network correction model is expressed as follows: .

4. The GPS correction method for high-altitude tunnels based on gyro-guided wires according to claim 3, characterized in that, The process of setting the directional modulation coefficient includes: All azimuth observations are organized into an azimuth sequence according to the tunneling direction, and the difference between adjacent observations is calculated based on the azimuth sequence. An azimuth difference threshold is set for the difference between adjacent observations. The standard deviation of the azimuth sequence is calculated and denoted as σ, and the azimuth difference threshold is denoted as σv. The baseline scaling factor is set to k0. The formula for obtaining the directional modulation coefficient is expressed as: .

5. The GPS correction method for high-altitude tunnels based on gyro-guided wires according to claim 3, characterized in that, The ionospheric activity level is set, including a first ionospheric level and a second ionospheric level with activity levels from low to high, and the ionospheric perturbation coefficient includes a first perturbation term, a second perturbation term and a third perturbation term with values ​​from small to large. When the TEC gradient value is lower than the first ionospheric level, the ionospheric perturbation coefficient is the first perturbation term; when the TEC gradient value is between the first and second ionospheric levels, the ionospheric perturbation coefficient is the second perturbation term; when the TEC gradient value is higher than the second ionospheric level, the ionospheric perturbation coefficient is the third perturbation term.

6. The GPS correction method for high-altitude tunnels based on gyro-guided wires according to claim 3, characterized in that, The specific form of the direction correction vector is set as follows: , Where ω1 represents the horizontal weight component and ω2 represents the vertical weight component.

7. The GPS correction method for high-altitude tunnels based on gyro-guided wires according to claim 1, characterized in that, The network adjustment solution process includes: Based on GPS observations and optimized coordinate solutions, a matrix-style baseline observation equation is constructed for the initial GPS baseline network. The variables of the baseline observation equation include coordinate corrections and observation residuals. The least squares method is used to perform network adjustment on the baseline observation equation to obtain a weighted least squares closed-form solution, and the coordinate corrections of the target node coordinates are calculated. The coordinate corrections are then substituted into the baseline observation equation to obtain the observation residuals. Update all calculated coordinate corrections for each node coordinate to the corresponding node coordinate; use observation residuals to screen out abnormal node coordinates and reduce the baseline observation weights of abnormal node coordinates in the baseline observation equation for all baselines.

8. A GPS correction method for high-altitude tunnels based on gyro-guided wires according to claim 7, characterized in that, The baseline observation equation is set as follows: Let the observation residual be represented by v, and the GPS observation value by I; let the optimized coordinate solution be represented by Xop, and let the vector form of the optimized coordinate solution be f(Xop); let the coordinate correction be represented by δ. The baseline observation equation, expressed in terms of observation residuals, is: v = If(Xop) - Aδ. Where A represents the design matrix used to characterize the sensitivity of each baseline to the target node coordinates.

9. A GPS correction method for high-altitude tunnels based on gyro-guided wires according to claim 8, characterized in that, The least squares method is set as follows: The objective function for network adjustment is constructed using the least squares method. Let the objective function be denoted as Φ, then the calculation formula for the objective function is: Φ(δ) = min δ v T Pv, Where P represents the baseline observation weight matrix preset for the coordinates of each node in the initial GPS baseline network.

10. A GPS correction method for high-altitude tunnels based on gyro-guided wires according to claim 9, characterized in that, The network adjustment solution process includes: Substitute the baseline observation equation, expressed in terms of observation residuals, into the objective function constructed using the least squares method: Φ(δ)=min δ v T Pv=min δ {[If(Xop)-Aδ] T P[If(Xop)-Aδ]}; Differentiating δ and setting the gradient of Φ(δ) to zero, we express it using the coordinate correction δ as: δ = (A T PA) -1 A T P[If(Xop)].

11. A GPS correction method for high-altitude tunnels based on gyro-guided wires according to claim 9, characterized in that, Let the node coordinates be represented as X1, and let the ordinal number of the node coordinates be represented as j. Then the coordinates of the j-th node are represented as X1j. The update formula for setting the node coordinates is: X1j = Xopj + δj. Where Xopj represents the optimized coordinate solution corresponding to the coordinates of the j-th node, and δj represents the coordinate correction amount corresponding to the coordinates of the j-th node.

12. A GPS correction method for high-altitude tunnels based on gyro-guided wires according to claim 11, characterized in that, The process of using observation residuals to screen out the coordinates of outlier nodes includes: Let the baseline residual norm of the node coordinates be r, and let r = ||v||; let the number of baselines connected to the node coordinates be m, and let the associated baseline residual of the node coordinates be R. Then the associated baseline residual of the j-th node coordinate is denoted as Rj. The formula for calculating the associated baseline residual of the j-th node coordinate is as follows: ; A baseline residual threshold is set for the associated baseline residual. When the associated baseline residual exceeds the baseline residual threshold, the current node coordinates are identified as abnormal node coordinates.

13. A GPS correction method for high-altitude tunnels based on gyro-guided wires according to claim 12, characterized in that, The method for reducing the baseline observation weights is set as follows: The baseline observation weight matrix of the abnormal node coordinates is labeled as the low-amplitude observation weight matrix Pr. The calculation formula of the low-amplitude observation weight matrix is ​​set as: Pr=λ∙P, where λ represents the weight attenuation coefficient, and the value of λ is set to be in the range of (0,1).

14. The GPS correction method for high-altitude tunnels based on gyro-guided wires according to claim 4, characterized in that, The process of setting up the gyro traverse is set as follows: when the absolute value of the difference between adjacent observations is higher than the azimuth difference threshold, the gyro traverse segment involved in the calculation of the difference between adjacent observations is marked as an abnormal observation traverse segment, and the traverse is readjusted and set up again for the abnormal observation traverse segment; the azimuth difference threshold is positively correlated with the setting distance between adjacent gyro traverses, and the threshold change rate of the azimuth difference threshold does not exceed the preset direction change rate value inside the target tunnel.

15. A GPS correction method for high-altitude tunnels based on gyro-guided wires according to claim 13, characterized in that, ... The azimuth sequence set is denoted as Q, where θ represents the observed azimuth value. i Let represent the azimuth angle observation value obtained for the i-th segment of the gyroscope conductor; let Δθi represent the difference between adjacent observations. The set form of the azimuth sequence Q is: Q = {θ1, θ2, ..., θ n }, The formula for calculating the difference between adjacent observations Δθi is set as follows: Δθ i =θ i+1 -θ i , Where i represents the ordinal number of the gyroscope wire, and i = 1, 2, ..., n-1; n represents the total number of segments of the gyroscope wire.

Images