Astronomical coordinate determination method and system fusing laser tracking and gravity gradient correction

Abstract

The invention discloses an astronomical coordinate determination method and system fusing laser tracking and gravity gradient correction, and relates to the technical field of astronomical coordinate determination. According to the method, a trajectory observation equation is established by dynamically tracking a target doing parabolic motion. And solving the trajectory observation equation by adopting a least square iteration method in which a damping factor is introduced to obtain a gravity vector in a local terrestrial coordinate system (LTCS). And then the gravity vectors are converted into a ground Cartesian coordinate system by using a direction conversion method based on a common baseline. The geodetic coordinates of the measurement point are used to determine an astronomical geodetic plumb deviation (DOV), and finally the astronomical coordinates of the measurement point are derived from the DOV component. According to the invention, continuous real-time coordinate determination without being influenced by weather is realized, and the key limitation of the traditional astronomical technology is overcome.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of astronomical coordinate determination, in particular to an astronomical coordinate determination method and system fusing laser tracking and gravity gradient correction. BACKGROUND

[0002] The traditional method for determining astronomical coordinates relies heavily on night sky observation, and each method has its own advantages and limitations. The star altitude-time method, although simple and historical, is greatly affected by weather and lighting conditions and requires manual operation, making it unsuitable for continuous all-weather applications. The zenith telescope method observes the near-zenith trajectory of stars to determine astronomical latitude, providing sub-arcsecond accuracy. This method is highly accurate and less sensitive to atmospheric refraction, but it can only measure latitude and requires expensive specialized equipment. The theodolite clock method measures astronomical coordinates and azimuth angles with arcsecond-level accuracy, but it has operator-related errors and weather limitations. Astronomical photography relies on visible stars and requires repeated observations on cloudless nights. SUMMARY

[0003] The purpose of the present application is to provide an astronomical coordinate determination method and system fusing laser tracking and gravity gradient correction to realize continuous, weather-independent real-time astronomical coordinate determination and overcome the key limitations of traditional astronomical technology.

[0004] To achieve the above-mentioned purpose, the present application provides the following solutions.

[0005] In a first aspect, the present application provides an astronomical coordinate determination method fusing laser tracking and gravity gradient correction, comprising: obtaining a three-dimensional LTCS coordinate time series of a target in a parabolic motion process and a geodetic Cartesian coordinate of a measurement point; the parabolic motion process takes the measurement point as the starting point According to the three-dimensional LTCS coordinate time series of the target in the parabolic motion process, a least squares iteration method with a damping factor is used to solve the trajectory observation equation to obtain the gravity vector in the LTCS coordinate system; the trajectory observation equation has a gravity gradient; Converting the gravity vector in the LTCS coordinate system into a gravity vector in the geodetic Cartesian system; According to the gravity vector in the geodetic Cartesian system and the geodetic Cartesian coordinate of the measurement point, the astronomical geodetic vertical deviation is determined; According to the astronomical geodetic vertical deviation and the geodetic Cartesian coordinate of the measurement point, the astronomical coordinate of the measurement point is calculated.

[0006] In a second aspect, the present application provides an astronomical coordinate determination system fusing laser tracking and gravity gradient correction, comprising an astronomical coordinate determination device and an upper computer. The astronomical coordinate determination device includes: a measuring cylinder, a laser tracker, a time acquisition device, and multiple GNSS antennas; The laser tracker is mounted on top of the measuring cylinder, and multiple GNSS antennas are distributed around the measuring cylinder; The time acquisition device is connected to the laser tracker and the multiple GNSS antennas respectively; The measuring cylinder provides a vacuum environment, during which the target undergoes parabolic motion within the cylinder. The laser tracker and the time acquisition unit capture the three-dimensional LTCS coordinate time series of the target during its parabolic motion. The GNSS antenna acquires the geodetic coordinates of the measurement point. The host computer is used to obtain the astronomical coordinates at the measurement point by employing the above-mentioned astronomical coordinate determination method that combines laser tracking and gravity gradient correction.

[0007] According to the specific embodiments provided in this application, this application has the following technical effects.

[0008] This application provides a method and system for determining astronomical coordinates by integrating laser tracking and gravity gradient correction. The application dynamically tracks a target undergoing parabolic motion and establishes a trajectory observation equation. A least-squares iterative method incorporating a damping factor is used to solve the trajectory observation equation, obtaining the gravity vector in the Local Tangent Plane Coordinate System (LTCS). Then, a direction transformation method based on a common baseline is used to transform these gravity vectors to a geodetic Cartesian coordinate system. Using the geodetic coordinates of the measurement point, the Astrometric-Geodetic Deflection of the Vertical (DOV) is determined. Finally, the astronomical coordinates of the measurement point are derived from the DOV components. This application achieves continuous, weather-independent, real-time coordinate determination, overcoming key limitations of traditional astronomical techniques. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a flowchart illustrating an astronomical coordinate determination method that integrates laser tracking and gravity gradient correction, provided as an embodiment of this application.

[0011] Figure 2This is a schematic diagram of an astronomical coordinate determination method that integrates laser tracking and gravity gradient correction, provided as an embodiment of this application.

[0012] Figure 3 This is a target falling trajectory diagram provided in one embodiment of this application.

[0013] Figure 4 This is a schematic diagram of the structure of an astronomical coordinate measuring device provided in an embodiment of this application.

[0014] Figure 5 This is a schematic diagram of a simulation experiment provided for one embodiment of this application.

[0015] Explanation of reference numerals in the attached diagram: 1. Base; 2. Time acquisition device; 3. Measuring cylinder; 4. Laser tracker; 5. GNSS antenna; 6. Target; 7. Electronic level; 8. Altitude adjuster. Detailed Implementation

[0016] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0017] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] To address the technical issues mentioned in the background section, a method and system for determining astronomical coordinates that integrates laser tracking and gravity gradient correction is proposed. This is a real-time, all-weather solution that utilizes the high precision and dynamic tracking capabilities of three-dimensional laser tracking technology to combine it with GNSS measurements to obtain high-precision astronomical coordinates.

[0019] In one exemplary embodiment, a method for determining astronomical coordinates that integrates laser tracking and gravity gradient correction is provided, such as... Figure 1 and Figure 2 As shown, it includes the following steps 101-105.

[0020] Step 101: Obtain the three-dimensional LTCS coordinate time series of the target during its parabolic motion and the geodetic Cartesian coordinates of the measurement point; the parabolic motion process starts from the measurement point.

[0021] Step 102: Based on the three-dimensional LTCS coordinate time series of the target during its parabolic motion, the trajectory observation equation is solved using the least squares iterative method with damping factor introduced, and the gravity vector in the LTCS coordinate system is obtained; the trajectory observation equation contains the gravity gradient.

[0022] Step 103: Convert the gravity vector in the LTCS coordinate system to the gravity vector in the Earth Cartesian coordinate system.

[0023] Step 104: Determine the astronomical geodetic vertical deviation based on the gravity vector of the geodetic Cartesian system and the geodetic Cartesian coordinates of the measurement point.

[0024] Step 105: Calculate the astronomical coordinates of the measurement point based on the astronomical geodetic vertical deviation and the geodetic Cartesian coordinates of the measurement point.

[0025] Implementing steps 101-105 above enables continuous, weather-independent real-time coordinate determination, overcoming key limitations of traditional astronomical techniques. Its adaptability and accuracy provide a powerful and efficient solution for modern geodetic applications in different environments.

[0026] In another exemplary embodiment, step 101 above is the process of acquiring and preprocessing high-frequency three-dimensional spatial trajectories, which can be implemented by the following steps 201-202.

[0027] Step 201: Prepare a small ball as the target and make it move in a parabolic motion on the platform.

[0028] Step 202: Use a laser tracker to capture the trajectory and use a time acquisition device to record the ball's movement time at the corresponding position.

[0029] The measurement process is based on an astronomical coordinate measuring device.

[0030] The astronomical coordinate measuring device is set up as follows: the measuring cylinder is vertically mounted on the base, with the center of the cylinder aligned with the center of the base. A laser tracker is mounted on the upper part of the measuring cylinder. A Leica AT960 laser tracker is used, measuring approximately 30 cm × 30 cm × 40 cm and weighing approximately 14 kg, ensuring high-precision coordinate measurements. The time acquisition unit and electronic level are located on the outside of the measuring cylinder and mounted on the base. Four GNSS antennas are fixed on separate brackets above the measuring cylinder. The GNSS antennas used in this embodiment are standard geodetic grade equipment, each with a diameter of approximately 20 cm and a height of approximately 10 cm, which facilitates stable and accurate baseline measurements. The time acquisition unit is connected to the laser tracker and each GNSS antenna via cables to ensure consistent time acquisition. During measurement, the electronic level is used to keep the base horizontally aligned.

[0031] In another exemplary embodiment, step 102 above is the process of calculating the gravity vector in the LTCS coordinate system, which can be implemented by the following steps 301-303.

[0032] Step 301: Based on the parabolic trajectory data, derive the trajectory observation equation of the target.

[0033] Laser trackers and time loggers dynamically monitor parabolic motion targets in a vacuum environment and capture their three-dimensional coordinate time series in LTCS. The trajectory data of falling targets tracked by 3D laser tracking technology typically exhibits a parabolic motion with an initial velocity, such as... Figure 3 As shown. Based on the parabolic trajectory data, the trajectory observation equation of the target is derived. To solve for the Gravity Direction Vector (GDV) in the LTCS, the damping factor μ is incorporated into the iterative equation, and the solution is obtained through the least squares iterative method. It is worth noting that the experimental environment in this embodiment is assumed to be a vacuum, which serves as the theoretical reference framework for the proposed method. The vacuum condition eliminates the influence of air resistance on parabolic motion, thus enabling a clearer simulation of the trajectory caused by gravity. The observation equation is as follows: in, , , The starting time of the target during parabolic motion 3D LTCS coordinates , , For the target during parabolic motion, time 3D LTCS coordinates , , Let the initial three-dimensional velocity of the target be during its parabolic motion. The acceleration due to gravity at the measurement point. Gravity gradient The distance of the fall. , , These are the angles between the direction of the gravitational acceleration at the measurement point and the x-axis, y-axis, and z-axis of the LTCS coordinate system, respectively. , and These represent the initial velocities of the target in the x, y, and z axes of the LTCS coordinate system, respectively.

[0034] Step 302: Construct constraint equations, incorporating the damping factor μ into the constraint equations. In time The constraint equations are: In the observation equation, , , , All values ​​are observed, and the remaining variables are solved as unknown parameters. The error equation and constraint equations can then be expressed in matrix form as follows: in, It is a correction number. For state vectors, , A The coefficients of the error equation are... For the observation constant term, C For the constraint coefficient matrix, For the constraint constant term, It is an identity matrix.

[0035] The constraint equations are as follows: in, The coefficient matrix of the normal equations, and These represent the connection number vector and weight matrix, respectively, which represent the constraints.

[0036] To improve solution efficiency and prevent ill-conditioned equations, a damping factor μ is added to the equations, resulting in the following iterative equation: in, and These are the state vectors for the (n+1)th and nth iterations, respectively. The coefficient matrix of the normal equations, , The damping factor, It is the identity matrix. For the constraint coefficient matrix, For the constraint constant term, , The coefficient matrix of the error equation, The weight matrix of the constraint equations, For the observation constant term, The matrix of normal equations corresponding to the constraints. subscript For measuring stations.

[0037] Step 303: Solve for the gravity vector using the least squares iterative method. Solving the above iterative equation using the least squares iterative method yields the iterative result of the state vector X. The gravity vector in the LTCS coordinate system is then: ; in, The gravity vector in the LTCS coordinate system. , , The angle between the direction of the gravitational acceleration at the measurement point obtained by iterative solution and the x-axis, y-axis and z-axis of the LTCS coordinate system.

[0038] In another exemplary embodiment, step 103 above is the process of converting gravity vector coordinates to the Earth Cartesian system. In this embodiment, a direction conversion method based on a common baseline is used for the conversion, specifically including the following steps 401-405.

[0039] Step 401, Coordinate Transformation Method: Seven-parameter nonlinear transformation, the transformation model is: in, and These represent common points in the LTCS and GCCS coordinate systems, respectively. i The coordinates. As a scaling factor, The translation factor is... R It is a rotation matrix.

[0040] In the formula, These are the rotation parameters.

[0041] Step 402, determine the initial value. Taylor series expansion, retaining only first-order terms in, It is the baseline Scale factor; , , For public points GNSS baseline vector; , and It is a common point in the LTCS coordinate system The baseline vector, superscript " " indicates the initial value.

[0042] Step 403, the error equation is obtained from the Taylor expansion as follows: in, This is the GNSS baseline correction matrix. for The elements in Indicates GNSS baseline The correction value, Represents the error coefficient matrix. Indicates the parameter correction amount. Represents the constant term of the observed values. , , , and These are all intermediate matrices used to express the error coefficient matrix; Step 404, based on indirect adjustment, least squares iterative calculation: Step a. Determine the initial values ​​of the parameters: ; Step b. Based on the error equation, solve for the parameter correction using the indirect adjustment method. ; Step c. Utilize parameter correction amount Update the unknown parameter estimates and iterate; Step d. Determine the parameter correction amount Check if the convergence condition is met. If not, repeat steps b-c until the convergence condition is met.

[0043] Step 405: The rotation matrix R obtained through iteration is used to convert the gravity vector in the LTCS coordinate system into the gravity vector in the Earth Cartesian coordinate system.

[0044] In another exemplary embodiment, step 104 above is the process of calculating the meridional and lateral components of the line deviation, which can be implemented using the following steps 501-503.

[0045] Step 501: Determine the reference coordinate system and calculate the first-order partial derivatives with respect to X, Y, and Z.

[0046] Taking the WGS84 ellipsoid as an example, the results of taking the first-order partial derivatives with respect to X, Y, and Z are as follows: in, , These are the major and minor axes of the WGS84 ellipsoid, respectively.

[0047] Step 502: Obtain the ellipsoid normal vector and calculate the astro-geodetic vertical deviation.

[0048] Normal vector of the ellipsoid at the measurement point for: ;in, , , Let p be the Cartesian coordinates of the measurement point.

[0049] like Figure 4 As shown, the astronomical geodetic vertical deviation is: ;in, This is the gravity vector of the Earth's Cartesian system.

[0050] Step 503: Project the astronomical geodetic plumb line deviation onto the north-south and east-west directions to obtain the north-south and east-west components of the astronomical geodetic plumb line deviation. in, This represents the north-south component of the astronomical geodetic perpendicular deviation. It represents the east-west component of the deviation of the astronomical geodetic plumb line. and They represent The north-south and east-west components.

[0051] In another exemplary embodiment, step 105 above is the process of inverting astronomical geodetic coordinates, which can be implemented using the following steps 601-602.

[0052] Step 601, measure the Cartesian coordinates of point p. Convert to geodetic coordinates of the measurement point; ;in, These represent the geodetic longitude, geodetic latitude, and geodetic altitude at measurement point p, respectively.

[0053] Step 602: Calculate the astronomical coordinates using the north-south and east-west components of the DOV at the observation point.

[0054] Using measurement point p Astronomical longitude and latitude can be obtained by combining the coordinates with the geodetic coordinates.

[0055] in, To measure the astronomical longitude at point p, To measure the astronomical latitude at point p, To measure the geodetic longitude at point p, To measure the geodetic latitude at point p, This represents the north-south component of the astronomical geodetic perpendicular deviation. It represents the east-west component of the deviation of the astronomical geodetic plumb line.

[0056] Based on the same inventive concept, this application also provides an astronomical coordinate determination system for implementing the aforementioned method of fusion laser tracking and gravity gradient correction for determining astronomical coordinates. The solution provided by this system is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the astronomical coordinate determination system for fusion laser tracking and gravity gradient correction provided below can be found in the limitations of the astronomical coordinate determination method for fusion laser tracking and gravity gradient correction described above, and will not be repeated here.

[0057] In one exemplary embodiment, an astronomical coordinate determination system integrating laser tracking and gravity gradient correction is provided, comprising: an astronomical coordinate measuring device and a host computer.

[0058] like Figure 4 As shown, the aforementioned astronomical coordinate determination device includes: a measuring cylinder 3, a laser tracker 4, a time acquisition device 2, and multiple GNSS antennas 5; the laser tracker 4 is installed on top of the measuring cylinder 3, and the multiple GNSS antennas 5 are distributed around the measuring cylinder 3; the time acquisition device 2 is connected to the laser tracker 4 and the multiple GNSS antennas 5 respectively; the measuring cylinder 3 is used to provide a vacuum environment, and during measurement, the target 6 undergoes parabolic motion inside the measuring cylinder 3; the laser tracker 4 and the time acquisition device 2 are used to capture the three-dimensional LTCS coordinate time series of the target during parabolic motion; the GNSS antennas 5 are used to obtain the geodetic coordinates of the measurement point; The host computer is used to obtain the astronomical coordinates at the measurement point by employing the above-mentioned astronomical coordinate determination method that combines laser tracking and gravity gradient correction.

[0059] In another exemplary embodiment, such as Figure 4 As shown, the aforementioned astronomical coordinate measuring device also includes a base 1, an electronic level 7, and a height adjuster 8; the measuring cylinder 3 is mounted on the base 1, and the center of the measuring cylinder 3 is aligned with the center of the base 1; the electronic level 7 is mounted on the base 1; and the height adjuster 8 is mounted between the legs of the base 1 and the ground.

[0060] In another exemplary embodiment, the above-described method and system can achieve all-day, all-weather observation of astronomical coordinates, unaffected by environmental factors, and with high observation accuracy. After the subsequent development of the observation model, it can be deployed on a large scale for astronomical coordinate observation. To verify this effect, an experiment considering the gravity gradient error analysis of astronomical coordinates is provided.

[0061] 1. Experimental Design like Figure 5As shown, laser tracker 4 and time measurement errors were added to the theoretical coordinate system to obtain simulated observation results in the LTCS. Based on the theoretical transformation parameters between the LTCS and GCCS, the theoretical coordinates of the GNSS antenna in the GCCS were obtained, and the theoretical GNSS baseline was calculated. Similarly, simulated observation results of the GNSS baseline including errors were obtained. Simulated observations of the common baseline vector between the LTCS and GCCS were used to calculate the direction transformation. The transformation method of the medium GDV was used to calculate the parameters of the two coordinate systems affected by laser tracking errors, time errors, and GNSS baseline errors. The direction transformation parameters with errors between the two coordinate systems were used to calculate the GDV with errors in the GCCS. The astronomical latitude and longitude with errors were calculated by combining the ellipsoidal normal vector passing through the measurement point p.

[0062] During the experiment, the vertical gravitational gradient causes a small but not negligible deviation from the ideal parabolic motion. This deviation occurs because the gravitational acceleration acting on the object is not constant with the falling height, but decreases slightly with increasing height.

[0063] Ignoring this gradient introduces systematic errors into the trajectory fitting model, which in turn affects the estimation of the gravity vector (GDV). Since the accuracy of the GDV directly determines the reliability of the derived astronomical coordinates, the influence of the gravity gradient needs to be considered when establishing the observation equations for parabolic motion.

[0064] 2. Experimental Procedure A laser tracker 4 is used to predict the coordinates of a fixed GNSS antenna 5 in the LTCS to determine its accuracy of 10 μm. It is assumed that four GNSS devices are uniformly distributed on a circle with a radius of 3 m centered on the laser tracker. Since the accuracy of the three-dimensional point position m is 10 μm, according to error propagation theory... Therefore, it is assumed that the range constraint accuracy based on laser tracker 4 is 10 µm. Since a 10 µm range constraint is incorporated into GNSS data processing, the relative accuracy of the GNSS baseline is set to 100 µm. In actual GNSS measurements, the influence of near-field and phase center variations makes it difficult to achieve a measurement accuracy of 0.1 mm. Furthermore, to explore the theoretical accuracy of astronomical coordinates under the influence of gravity gradient, a gravity gradient is incorporated into the simulation. To investigate the influence of gravity gradient, the astronomical coordinate measurement accuracy considering the influence of gravity gradient is studied by extracting GDV using the derived observation equation.

[0065] Other experimental conditions were the same as before. The average of every 30 observations was taken and recorded as one observation. The experiment was repeated 1000 times, and the statistical results are shown in Table 1.

[0066] Table 1. Statistics on the accuracy of astronomical coordinates considering the influence of gravity gradient (")

[0067] In Table 1, MAX represents the maximum value, MIN the minimum value, MEAN the average value, STD the standard deviation, and RMS the root mean square. As can be seen from Table 1, the RMS and STD values ​​of astronomical coordinates considering the gravity gradient are close to 0, indicating that the extracted GDV is more stable when considering the gravity gradient. The accuracy of astronomical coordinates considering the gravity gradient also meets the accuracy requirements of China's first-order geodetic surveying. By combining high-frequency three-dimensional laser tracking with GNSS measurements and employing robust least-squares adjustment enhanced by damping and gravity gradient correction, this method can accurately estimate the gravity vector and the astronomical geodetic deviation (DOV), and derive astronomical coordinates from them. Simulation experiments confirm the theoretical feasibility of this method, achieving an accuracy of approximately 0.2 inches. This method is designed to operate under various environmental conditions, offering potential for continuous, real-time astronomical coordinate determination.

[0068] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0069] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method of determining an astronomical coordinate by fusing laser tracking and gravity gradient correction, characterized in that, The method comprises the following steps: acquiring a time sequence of three-dimensional LTCS coordinates of a target in a parabolic motion process and geodetic Cartesian coordinates of a measuring point; the parabolic motion process starts from the measuring point; solving a trajectory observation equation by using a least square iteration method with a damping factor to obtain a gravity vector in the LTCS coordinate system according to the time sequence of three-dimensional LTCS coordinates of the target in the parabolic motion process; the trajectory observation equation contains a gravity gradient; converting the gravity vector in the LTCS coordinate system into a gravity vector in the geodetic Cartesian coordinate system; determining an astronomical geodetic vertical deviation according to the gravity vector in the geodetic Cartesian coordinate system and the geodetic Cartesian coordinates of the measuring point; calculating astronomical coordinates of the measuring point according to the astronomical geodetic vertical deviation and the geodetic Cartesian coordinates of the measuring point.

2. The method of claim 1, wherein the method is characterized by, The trajectory observation equation is as follows: ； wherein, 、 、 three-dimensional LTCS coordinates of the target at the initial time during the parabolic motion, three-dimensional LTCS coordinates of the target at the time during the parabolic motion, initial three-dimensional velocity of the target during the parabolic motion, gravity acceleration at the measuring point, gravity gradient, falling distance, respectively, the angles between the direction of the gravity acceleration at the measuring point and the x-axis, y-axis and z-axis of the LTCS coordinate system.​​​​​​​​ 3. The method of claim 1, wherein the method is implemented by a fusion laser tracking and gravity gradient corrected astrogeodetic coordinate determination method, characterized by, solving a trajectory observation equation by using a least square iteration method with a damping factor to obtain a gravity vector in the LTCS coordinate system according to the time sequence of three-dimensional LTCS coordinates of the target in the parabolic motion process, and the solving specifically comprises the following steps: converting the trajectory observation equation into an iteration equation containing a damping factor; solving the iteration equation by using a least square iteration method to obtain an iteration result of a state vector; calculating the gravity vector in the LTCS coordinate system according to the iteration result.

4. The method of claim 3, wherein the method is characterized by, The iteration equation is as follows: ； wherein, and are the state vectors of the (n+1)th and nth iteration, respectively, is the normal equation coefficient matrix, , is the damping factor, is the identity matrix, is the constraint condition coefficient matrix, is the constraint condition constant term, , is the error equation coefficient matrix, is the constraint equation weight matrix, is the observation constant term, is the normal equation matrix corresponding to the constraint condition, , subscript is the station.

5. The method of claim 3, wherein the method is characterized by, The state vector is: ; wherein is the state vector, , , is the three-dimensional LTCS coordinate of the target at the start time of the parabolic motion, , , is the initial three-dimensional velocity of the target during the parabolic motion, is the gravitational acceleration at the measurement point, , , are the angles between the direction of the gravitational acceleration at the measurement point and the x-axis, y-axis and z-axis of the LTCS coordinate system, respectively. The gravity vector in the LTCS coordinate system is: ; wherein, is the gravity vector in the LTCS coordinate system, , , are the angles between the direction of the gravity acceleration at the measurement point obtained by the iterative solution and the x-axis, y-axis and z-axis of the LTCS coordinate system.

6. The method of claim 1, wherein the method is a fusion laser tracking and gravity gradient corrected astrogeodetic determination method. The algorithm for converting the gravity vector in the LTCS coordinate system into a gravity vector in the geodetic Cartesian coordinate system is a direction conversion method based on a common baseline.

7. The method of claim 1, wherein the method is a fusion laser tracking and gravity gradient corrected astrogeodetic determination method. determining an astronomical geodetic vertical deviation according to the gravity vector in the geodetic Cartesian coordinate system and the geodetic Cartesian coordinates of the measuring point, and the determining specifically comprises the following steps: determining a normal vector of an ellipsoid at the measuring point according to the geodetic Cartesian coordinates of the measuring point; The astronomical geodetic deflection is determined from the normal vector of the ellipsoid at the measuring point and the gravity vector in the geodetic Cartesian system ; ； wherein, is the gravity vector in the terrestrial Cartesian system, is the normal vector of the ellipsoid at the measurement point.

8. The method of claim 1, wherein the method is a fusion laser tracking and gravity gradient corrected astrogeodetic determination method. calculating astronomical coordinates of the measuring point according to the astronomical geodetic vertical deviation and the geodetic Cartesian coordinates of the measuring point, and the calculating specifically comprises the following steps: converting the geodetic Cartesian coordinates of the measuring point into geodetic coordinates of the measuring point; determining the astronomical coordinates of the measuring point by using the following formula according to the geodetic coordinates of the measuring point and the astronomical geodetic vertical deviation; ； wherein is the astronomical longitude at the point of measurement p, is the astronomical latitude at the point of measurement p, is the geodetic longitude at the point of measurement p, is the geodetic latitude at the point of measurement p, is the north-south component of the astronomic geodetic deflection of the vertical, is the east-west component of the astronomic geodetic deflection of the vertical.

9. An astrometric coordinate determination system that fuses laser tracking and gravity gradient corrections, characterized by, The astronomical coordinate determination device comprises a measuring cylinder, a laser tracker, a time collector and a plurality of GNSS antennas. The laser tracker is installed at the top of the measuring cylinder, and the plurality of GNSS antennas are distributed around the measuring cylinder. The time collector is connected with the laser tracker and the plurality of GNSS antennas respectively. The measuring cylinder is used to provide a vacuum environment, and the target performs a parabolic motion in the measuring cylinder during measurement; the laser tracker and the time collector are used to capture a time sequence of three-dimensional LTCS coordinates of the target in the parabolic motion process; and the GNSS antennas are used to acquire geodetic coordinates of the measuring point. The upper computer is used to obtain astronomical coordinates at the measuring point by using the astronomical coordinate determination method of claim 1-8. The astronomical coordinate determination device further comprises a base, an electronic level and a height adjuster.

10. The integrated laser tracking and gravity gradient corrected astrogeodetic positioning system of claim 9, wherein, The measuring cylinder is arranged on the base, and the center of the measuring cylinder is aligned with the center of the base. The electronic level is arranged on the base. ​ The height adjuster is disposed between the legs of the base and the ground.

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