Gradient-based Method, Device and Equipment for Solving Asteroid Gravity Field

Abstract

The present disclosure provides a gradient-based method, device, and equipment for solving the gravity field of an asteroid. The method includes: obtaining the initial orbital parameters of a detector flying around a target asteroid and the observation data transmitted back when the detector flies around the target asteroid; wherein the observation data is divided into multiple batches based on the time dimension; determining the single-arc normal equation of the detector corresponding to each batch of observation data based on each batch of observation data; fusing the single-arc normal equations corresponding to each batch of observation data based on a preset fusion rule to obtain a multi-arc normal equation; and solving the multi-arc normal equation using a preset solution rule to obtain the precise orbit determination parameters of the detector flying around the target asteroid and the gravity field model coefficients of the target asteroid. Using the method of the present disclosure, the solution accuracy of the gravity field model coefficients of the asteroid can be improved.

Description

Technical Field

[0001] The present disclosure relates to the technical field of asteroid gravitational field inversion and deep space exploration, and particularly relates to a method, apparatus, electronic device, non-transitory computer-readable storage medium, and computer program product for calculating an asteroid gravitational field based on gradients. Background Art

[0002] Deep space exploration generally refers to space exploration activities carried out on the moon and other more distant celestial bodies (such as asteroids). The exploration means can include ground-based observations, space telescope observations, and launching detectors for close-range remote sensing. The asteroids are small celestial bodies belonging to the solar system, orbiting the sun like planets, but much smaller in volume and mass. Broadly speaking, asteroids range in size between meteoroids and dwarf planets, with diameters ranging from a few meters to 1,000 kilometers, including all small non-cometary celestial bodies in the solar system within this size range. However, most asteroids are distributed in the inner solar system, and the physical characteristics of small outer solar system celestial bodies (such as centaurs and trans-Neptunian objects) are different from those of small inner solar system celestial bodies. Therefore, asteroids are more commonly used to specifically refer to small non-cometary celestial bodies in the inner solar system.

[0003] The gravitational field of the asteroid can provide important information about its internal structure, material composition, and early evolution. At the same time, the asteroid gravitational field is of great significance for the landing and orbit design of the detector. Therefore, calculating the gravitational field coefficients of the asteroid has become one of the necessary steps in deep space exploration. To calculate the gravitational field coefficients of the asteroid, the relevant technical solution is to launch a detector from the earth to the asteroid, and at the same time, the radio telescope of the ground deep space station communicates with the detector and conducts Doppler tracking and velocity measurement.

[0004] However, the current existing technology only uses Doppler data to calculate the asteroid gravitational field, and there is a problem that the accuracy of the calculation result is not high enough. Summary of the Invention

[0005] The present disclosure provides a method, apparatus, electronic device, non-transitory computer-readable storage medium, and computer program product for calculating an asteroid gravitational field based on gradients, so as to at least solve one of the defects existing in the prior art.

[0006] The present disclosure provides a method for calculating an asteroid gravitational field based on gradients, including:

[0007] Obtaining initial orbital parameters of a detector flying around a target asteroid and observation data transmitted back when the detector flies around the target asteroid; wherein, the observation data is divided into multiple batches based on the time dimension, and each batch of observation data includes the position and velocity of the detector itself, the ground Doppler data fed back by the detector to the ground Doppler detection signal, and the gravity gradient data collected by the detector;

[0008] Based on the observation data of each batch, determine the single-arc normal equation of the detector corresponding to the observation data of each batch;

[0009] Based on a preset fusion rule, fuse the single-arc normal equations corresponding to the observation data of each batch to obtain a multi-arc normal equation;

[0010] Using a preset solution rule, solve the multi-arc normal equation to obtain the precise orbit determination parameters of the detector flying around the target asteroid and the gravity field model coefficients of the target asteroid.

[0011] The present disclosure also provides a gradient-based asteroid gravity field solution device, including:

[0012] A data acquisition module, configured to: acquire the initial orbit parameters of the detector flying around the target asteroid and the observation data transmitted back when the detector flies around the target asteroid; wherein, the observation data is divided into multiple batches based on the time dimension, and the observation data of each batch includes the position and velocity of the detector itself, the ground Doppler data fed back by the detector to the ground Doppler detection signal, and the gravity gradient data collected by the detector;

[0013] A single-arc normal equation determination module, configured to: based on the observation data of each batch, determine the single-arc normal equation of the detector corresponding to the observation data of each batch;

[0014] A fusion module, configured to: based on a preset fusion rule, fuse the single-arc normal equations corresponding to the observation data of each batch to obtain a multi-arc normal equation;

[0015] A solution module, configured to: using a preset solution rule, solve the multi-arc normal equation to obtain the precise orbit determination parameters of the detector flying around the target asteroid and the gravity field model coefficients of the target asteroid.

[0016] The present disclosure also provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, and when the processor executes the program, it implements the gradient-based asteroid gravity field solution method as described in any one of the above.

[0017] The present disclosure also provides a non-transitory computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the gradient-based asteroid gravity field solution method as described in any one of the above.

[0018] The present disclosure also provides a computer program product, including a computer program, and when the computer program is executed by a processor, it implements the gradient-based asteroid gravity field solution method as described in any one of the above.

[0019] As described above, the gradient-based method for solving the asteroid gravity field provided by the embodiments of the present disclosure can reduce the standard deviation of the solution results in the solution of the asteroid gravity field based on multi-arc orbit determination by adding gravity gradient data, thereby improving the solution accuracy of the asteroid gravity field model coefficients. In addition, even in the application of single-arc orbit determination, it can also be used to solve the gravity field model coefficients of higher orders, and at the same time, it can avoid the situation where the standard deviation cannot be calculated due to too little data volume in single-arc orbit determination. Description of the Drawings

[0020] In order to more clearly illustrate the technical solutions in the present disclosure or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present disclosure. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0021] Figure 1 is one of the schematic flowcharts of the gradient-based method for solving the asteroid gravity field provided by the embodiments of the present disclosure;

[0022] Figure 2 is the second schematic flowchart of the gradient-based method for solving the asteroid gravity field provided by the embodiments of the present disclosure;

[0023] Figure 3 is the relationship diagram between the body-fixed coordinate system, the spherical coordinate system and the local north-pointing coordinate system provided by the embodiments of the present disclosure;

[0024] Figure 4 is the third schematic flowchart of the gradient-based method for solving the asteroid gravity field provided by the embodiments of the present disclosure;

[0025] Figure 5 is the schematic structural diagram of the gradient-based asteroid gravity field solving device provided by the embodiments of the present disclosure;

[0026] Figure 6 is the schematic structural diagram of the electronic device provided by the present disclosure. Detailed Embodiments

[0027] To make the objectives, technical solutions, and advantages of the present disclosure clearer, the following will clearly and completely describe the technical solutions in the present disclosure with reference to the drawings in the present disclosure. Obviously, the described embodiments are some, but not all, of the embodiments of the present disclosure. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present disclosure without creative efforts fall within the scope of protection of the present disclosure.

[0028] Overview of the Invention Concept:

[0029] The inventors of the present disclosure have found through research that the reasons for the problems in the prior art may be as follows: First, there is a time delay in the transmission of radio signals between the ground deep space station and the detector (usually reaching several hours); Second, radio signals are also affected by the Earth's troposphere, ionosphere, and the plasma in the interplanetary space; the above two points will make the observed data unable to meet the requirements of real-time and effectiveness (due to the influence of the "troposphere, ionosphere, and the plasma in the interplanetary space"), so the solution for calculating the asteroid gravity field using only Doppler data has the problem of low accuracy of the calculation results.

[0030] In view of this, to solve the above problems in the prior art, the inventors of the present disclosure have proposed the gradient-based asteroid gravity field solution scheme described in the following embodiments through research.

[0031] Embodiment:

[0032] The following will describe the implementation details of the gradient-based asteroid gravity field solution scheme of the present disclosure in conjunction with the accompanying drawings.

[0033] Figure 1 FIG. is a schematic flow chart of a gradient-based asteroid gravity field solution method provided by an exemplary embodiment of the present disclosure. This embodiment can be applied to an electronic device (such as a server or a cloud computing platform), as Figure 1 shown, the gradient-based asteroid gravity field solution method includes the following steps:

[0034] S110. Obtain the initial orbital parameters of the detector orbiting the target asteroid and the observation data transmitted back when the detector orbits the target asteroid.

[0035] S120. Based on each batch of the observation data, determine the single-arc normal equation of the detector corresponding to each batch of the observation data.

[0036] The specific implementation details will be described below and will not be elaborated here.

[0037] S130. Based on a preset fusion rule, fuse the single-arc normal equations corresponding to each batch of the observation data to obtain a multi-arc normal equation.

[0038] The specific implementation details will be described below and will not be elaborated here.

[0039] S140. Use a preset solution rule to solve the multi-arc normal equation to obtain the precise orbit determination parameters of the detector orbiting the target asteroid and the gravity field model coefficients of the target asteroid.

[0040] In step S110, the observation data is divided into multiple batches based on the time dimension. Each batch of observation data includes the position and velocity of the detector itself, the ground Doppler data fed back by the detector for the ground Doppler detection signal, and the gravity gradient data collected by the detector.

[0041] In step S110, the present disclosure does not limit the manner of "acquiring". For example, the observation data may be stored in a data storage server, and an electronic device (such as a server or a cloud computing platform) serving as the execution subject of step S110 may communicate with the data storage server to acquire the observation data.

[0042] In steps S120 to S140, the specific implementation manners are described below and will not be elaborated here.

[0043] As described above, the gradient-based asteroid gravity field solution method provided by the embodiments of the present disclosure can reduce the standard deviation of the solution result in the asteroid gravity field solution based on multi-arc orbit determination by adding gravity gradient data, thereby improving the accuracy of the asteroid gravity field solution coefficients. In addition, even in the application of single-arc orbit determination, it can also be used to solve the gravity field model coefficients of higher orders, and at the same time, it can avoid the situation where the standard deviation cannot be calculated due to too little data volume in single-arc orbit determination.

[0044] In Figure 1 On the basis of the embodiment, as an optional implementation manner, referring to Figure 2 , step S120 "Based on each batch of observation data, determine the single-arc normal equation of the detector corresponding to each batch of observation data" may include:

[0045] S1210. Based on each batch of observation data, establish the observation motion equation of the detector.

[0046] As an optional example, step S1210 may be implemented in the following manner:

[0047] 11) Use the position and velocity of the detector itself in each batch of observation data to determine the observation acceleration equation of the detector corresponding to each batch of observation data.

[0048] Optionally, first, the acceleration of the detector in the inertial system of the central celestial body may be determined by using the position and velocity of the detector itself in each batch of observation data. Then, based on the acceleration in the inertial system of the central celestial body, the observation acceleration equation is established.

[0049] Specifically, the observation acceleration equation may be represented by the following calculation formula (1):

[0050] (1)

[0051] Among them, represents the acceleration of the detector in the inertial system of the central celestial body; represents the gravitational acceleration of the central celestial body on the detector; represents the gravitational acceleration of other celestial bodies on the detector; represents the acceleration caused by the influence of general relativity on the detector; represents the acceleration caused by the pressure of solar radiation on the detector; represents the acceleration caused by the change part of the gravitational force of the central celestial body on the detector due to the solid tide of the central celestial body.

[0052] It should be noted that the central celestial body refers to the celestial body around which the target asteroid revolves. Assuming that the target asteroid is Phobos, then the central celestial body here refers to Mars.

[0053] 12) Based on the observation acceleration equation, determine the matching first-order ordinary differential equation.

[0054] Optionally, the observation acceleration equation shown in formula (1) can be rewritten as two first-order ordinary differential equations shown in formula (2);

[0055] (2)

[0056] Among them, represents the position of the detector in the inertial system of the central celestial body, represents the velocity vector of the detector in the inertial system of the central celestial body, represents the initial epoch time, represents the derivative of the position vector with respect to time, represents the derivative of the velocity vector with respect to time.

[0057] 13) Use the first-order ordinary differential equation to determine the observed motion equation of the detector.

[0058] Optionally, based on the first-order ordinary differential equation in 12), performing an integration can obtain the observed motion equation of the detector.

[0059] Optionally, step S120 may further include: continuously observing the detector to continuously refine the reference value, and then obtaining a high-precision initial state vector.

[0060] It should be noted that generally, the initial state vector of the detector cannot be accurately known in advance, and only their reference values can be obtained Meanwhile, there are also many uncertain parameters in the mathematical model for calculating acceleration, such as the gravitational field coefficient and solar radiation pressure coefficient of the asteroids to be solved. Therefore, in the subsequent precise orbit determination (i.e., solving the multi-arc normal equations), these parameters are generally involved in the calculation together with the state variables to be solved for the detector, in order to obtain the best estimate.

[0061] S1220. Use the observation motion equation, ground Doppler data, and gravity gradient data to establish the state error equation for the detector corresponding to each batch of observation data, as the single-arc normal equation.

[0062] As an optional example, step S1220 can be implemented in the following manner:

[0063] 21) Calculate the residuals based on the observation motion equation.

[0064] Among them, the observed values can be determined based on the observation motion equation, and then the expression of the residuals can be constructed by using the observed values and the true ideal observed values.

[0065] 22) Calculate the first-order partial derivatives of the ground Doppler data and the gravity gradient data respectively, as the coefficient matrix of the state error equation.

[0066] The first-order partial derivative of the ground Doppler data can be expressed by the following calculation formula (3).

[0067] (3)

[0068] Among them, represents the distance vector from the ground deep space station to the detector in the geocentric inertial coordinate system; represents the relative velocity vector of; represents the scalar of the velocity; represents the distance scalar from the ground deep space station to the detector in the geocentric inertial coordinate system.

[0069] The first-order partial derivative of the gravity gradient data can be expressed by the following calculation formula (4).

[0070] (4)

[0071] Among them, referring to Figure 3 the relationship diagram between the body-fixed coordinate system, spherical coordinate system, and local north-pointing coordinate system shown; represents the second-order derivative of the potential function of the gravitational force received by the detector with respect to the body-fixed coordinates, and is also the gravitational gradient tensor in the body-fixed coordinate system; represents the position vector of the detector in the inertial reference system; represents the transformation matrix from the body-fixed coordinate system of the target asteroid to the inertial system; Denote the radial vector, latitude, and longitude of the detector in the spherical coordinates of the target asteroid with respect to the center of the sphere; Denote the rectangular coordinates of the detector.

[0072] 23) Based on the coefficient matrix and the residuals, establish the state error equation of the detector corresponding to each batch of observation data.

[0073] Optionally, the state error equation of the detector corresponding to each batch of observation data can be established by using the following calculation formula (5):

[0074] (5)

[0075] where denotes the difference between the observed value (i.e., the observation data, the same below) and the true observed value (i.e., the true value of the observation data), that is, the residual; denotes the partial derivative of the observed value with respect to the state quantity at the initial time ; denotes the partial derivative of the observed value with respect to the state quantity at the observation time t; denotes the design matrix, which is the transformation matrix for transforming to ; denotes the random noise of the observed value.

[0076] where the above and include the coefficient matrix described in step 22).

[0077] Based on the above embodiments, as an optional implementation manner, step S130 "Based on a preset fusion rule, fuse the single-arc normal equations corresponding to each batch of observation data to obtain a multi-arc normal equation" may include:

[0078] A1) According to a preset partitioning rule, determine the local state quantities to be solved and the global state quantities to be solved in the single-arc normal equations of the single-arc normal equations corresponding to each batch of observation data.

[0079] As an optional example, the orbital parameters to be solved for each single arc can be used as the local state quantities to be solved; the gravity field model coefficients of the target asteroid to be solved can be used as the global state quantities to be solved.

[0080] A2) Based on the local state quantities to be solved and the global state quantities to be solved, determine the matrix equation of the single-arc normal equation.

[0081] As an optional example, the single-arc normal equation shown in the above calculation formula (5) can be rewritten into the matrix equation form shown in the following calculation formula (6);

[0082] (6)

[0083] Among them, x 1 represents the local state quantity to be solved; x 2 represents the global state quantity to be solved; A 11 , A 12 , A 21 , A 22 represent each sub-block of the coefficient matrix; among them, A 11 corresponds to the local state quantity to be solved, A 22 corresponds to the global state quantity to be solved; B 1 is the constant term matrix sub-block corresponding to the local state quantity to be solved; B 2 is the constant term matrix sub-block corresponding to the global state quantity to be solved.

[0084] A3) Superimpose each of the matrix equations to obtain the multi-arc segment method equation.

[0085] As an optional example, superimposing multiple matrix equations as shown in the calculation formula (6) can obtain the multi-arc segment method equation as shown in the following calculation formula (7).

[0086] (7)

[0087] Among them, the meanings of each letter in the formula can be referred to in A2). It should be noted that here, that is, in the calculation formula (7), the superscripts (1), (2),..., (n) of each letter symbol represent the corresponding serial numbers of single arc segments. Specifically, for example, represents the local state quantity to be solved corresponding to the 1st single arc segment; represents corresponding to a sub-block of the coefficient matrix.

[0088] It should also be explained that the reason for adopting the above "multi-arc segment" implementation method in this embodiment is as follows: In actual tasks, the observation data (or measurement data) transmitted back by the detector may not be continuous, and there may be a time interval of two or three years between some of them. If orbital integration is relied on to fill in the difference in time, it will lead to the accumulation of errors in the detector dynamics model, and further lead to an increase in errors in the orbit determination solution. In the face of this situation, we should first classify the parameters to be estimated (i.e., the state quantities to be solved), into local parameters and global parameters. For example, the orbital parameters of each arc segment are local parameters, and the gravity field model coefficients of the celestial body to be solved are global parameters. Then, the normal equations constructed from the data of each arc segment are combined to perform orbit determination and parameter solution, which is called multi-arc segment orbit determination.

[0089] Based on the above embodiment, as an optional implementation method, referring to Figure 4 , step S140 "Using a preset solution rule, solve the multi-arc segment normal equation to obtain the precise orbit determination parameters for the detector to fly around the target asteroid and the gravity field model coefficients of the target asteroid" can be implemented in the following manner:

[0090] S1410. Use a preset matrix decomposition method to decompose the coefficient matrix of the multi-arc segment normal equation to obtain the decomposed form of the multi-arc segment normal equation.

[0091] As an optional example, the QR decomposition method is used to process the coefficient matrix of the error equation (i.e., the decomposed form of the multi-arc segment normal equation) to improve the operation efficiency. Specifically,

[0092] When processing the measured data, the coefficient matrix of the error equation usually becomes larger as the amount of observation data and the number of parameters to be solved increase. If some methods are not used to process this matrix, the orbit determination program will occupy a large amount of unnecessary memory during operation. At the same time, for the least squares problem, we need a large amount of observation data to provide the information required to estimate all parameters, otherwise the above matrix may become singular. Therefore, we generally use the QR decomposition method to process this matrix. Suppose there are a total of n observation values, l parameters to be estimated, then this matrix is a matrix of size . After QR decomposition transformation, it becomes a matrix of size , thus improving the operation efficiency of the program.

[0093] S1420. Use the least squares method to iteratively solve the decomposed form of the multi-arc segment normal equation to obtain the precise orbit determination parameters and the gravity field model coefficients of the target asteroid.

[0094] As an alternative example, the variable to be solved in the multi-arc segment method equation is the state quantity to be solved of the detector, where the state quantity to be solved includes the position, velocity, and measurement parameters of the detector, and the measurement parameter is the gravity field model parameter of the target asteroid.

[0095] As an alternative example, step S1420 may include the following steps:

[0096] Step 1: Solve the correction amount of the state quantity to be solved of the detector.

[0097] Among them, since the types, observation times, and observation devices of the observation data returned by the detector are different, the accuracies of the respective observation data are also different, and it is necessary to perform weighted processing on the observation data.

[0098] Step 1: Generally assume that the observations (i.e., the above-mentioned observation data) are independent of each other, and the weight of the observation is the reciprocal of the observation noise. Therefore, the weight matrix can be expressed in the form of a diagonal matrix as the following calculation formula (8):

[0099] (8)

[0100] In the formula, represents the weight matrix, represents the noise level of the observation; n represents the number of observations.

[0101] Step 2: Considering that the state quantity to be solved generally has prior information, which are the prior covariance matrix of the state quantity to be solved and the prior value of the state quantity to be solved, the correction amount of the state quantity to be solved can be expressed by the following calculation formula (9):

[0102] (9)

[0103] In the formula, represents the partial derivative of the observation (i.e., the observation data) with respect to the state quantity to be solved at the initial time , represents the weight matrix of the observation, represents the prior covariance matrix of the state quantity to be solved, represents the prior value of the state quantity to be solved.

[0104] Step 2: Use the correction amount of the state quantity to be solved to solve the measurement parameter.

[0105] Step 3: Use the correction amount of the state quantity to be solved to correct the initial orbit parameters to obtain the first corrected orbit parameters.

[0106] Step 4: Calculate the correction difference between the correction of the state quantity to be solved in the current iteration round and the correction of the state quantity to be solved in the previous iteration round.

[0107] Step 5: In response to the correction difference satisfying a preset convergence condition, use the measurement parameters in the current iteration round to determine the gravity field model coefficients of the target asteroid, and use the first corrected orbit parameters as the precise orbit determination parameters.

[0108] Step 6: In response to the correction difference not satisfying the preset convergence condition, use the correction of the state quantity to be solved in the current iteration round to adjust each batch of observation data, and iterate Steps 1 to 4 based on the adjusted each batch of observation data until the correction difference satisfies the preset convergence condition.

[0109] Optionally, the preset convergence condition is that the correction difference is less than a preset error threshold. The preset error threshold can be determined according to actual situations or requirements.

[0110] As another optional example, in Step 4, the root mean square of the residuals in the current iteration round and the root mean square of the residuals in the previous iteration round can also be calculated; then calculate the difference between the two root mean squares of the residuals; then determine whether the difference between the root mean squares of the residuals is less than a preset relative error threshold. If so, "use the measurement parameters in the current iteration round to determine the gravity field model coefficients of the target asteroid, and use the first corrected orbit parameters as the precise orbit determination parameters". If not, "use the correction of the state quantity to be solved in the current iteration round to adjust each batch of observation data, and iterate Steps 1 to 4 based on the adjusted each batch of observation data until the correction difference satisfies the preset convergence condition".

[0111] It should be noted that since the error equation (i.e., the multi-arc method equation in this embodiment) is obtained by Taylor expansion and the high-order terms are discarded, the final result obtained by calculation contains truncation error, and the truncation error needs to be reduced by the above method of iteratively solving the correction (i.e., the correction to be solved of the state quantity).

[0112] In Figure 4 Based on the implementation manner, as an optional example, after the above Step 5, the planetary gravity field solution method further includes:

[0113] I1. Determine the covariance matrix of the state quantity to be solved based on the prior covariance matrix of the state quantity to be solved.

[0114] Optionally, use the following calculation formula (10) to determine the covariance matrix of the state quantity to be solved.

[0115] (10)

[0116] Among them, represents the partial derivative of the observed value (i.e., the observed data) with respect to the state quantity to be solved at the initial moment ; represents the weight matrix of the observed value; represents the prior covariance matrix of the state quantity to be solved; represents the covariance matrix of the state quantity to be solved.

[0117] I2. Using the covariance matrix of the state quantity to be solved, determine the standard deviation of the best estimate of the state quantity to be solved.

[0118] Optionally, calculate the standard deviation of the best estimate of the state quantity to be solved through the diagonal elements of the covariance matrix. This standard deviation can be used to evaluate the accuracy of precise orbit determination and the solution of asteroid gravity field model coefficients. For the off-diagonal elements, they represent a measure of the correlation between the parameter errors. The standard deviation calculation formula (11) is as follows:

[0119]

[0120] Among them, represents the standard deviation of the state quantity to be solved; represents the covariance matrix of the state quantity to be solved.

[0121] Next, the gradient-based asteroid gravity field solution device provided by the present disclosure will be described. The gradient-based asteroid gravity field solution device described below can be correspondingly referred to the gradient-based asteroid gravity field solution method described above.

[0122] Figure 5 is a schematic structural diagram of a gradient-based asteroid gravity field solution device provided by an exemplary embodiment of the present disclosure. As Figure 5 shown, the gradient-based asteroid gravity field solution device includes:

[0123] A data acquisition module 510, configured to: acquire initial orbital parameters of a detector orbiting a target asteroid and observation data transmitted back when the detector orbits the target asteroid; wherein the observation data is divided into multiple batches based on the time dimension, and each batch of observation data includes the position and velocity of the detector itself, ground Doppler data fed back by the detector for a ground Doppler detection signal, and gravity gradient data collected by the detector; A single-arc normal equation determination module 520, configured to: determine a single-arc normal equation of the detector corresponding to each batch of observation data based on each batch of observation data; A fusion module 530, configured to: fuse the single-arc normal equations corresponding to each batch of observation data based on a preset fusion rule to obtain a multi-arc normal equation; A solution module 540, configured to: solve the multi-arc normal equation using a preset solution rule to obtain precise orbit determination parameters of the detector orbiting the target asteroid and gravity field model coefficients of the target asteroid.

[0124] Figure 6 An example of a schematic physical structure of an electronic device is shown in Figure 6 As shown, the electronic device may include: a processor 610, a communication interface 620, a memory 630, and a communication bus 640. Among them, the processor 610, the communication interface 620, and the memory 630 complete communication with each other through the communication bus 640. The processor 610 can call logic instructions in the memory 630 to execute a gradient-based asteroid gravity field solution method, which includes: acquiring initial orbital parameters of a detector orbiting a target asteroid and observation data transmitted back when the detector orbits the target asteroid; wherein the observation data is divided into multiple batches based on the time dimension, and each batch of observation data includes the position and velocity of the detector itself, ground Doppler data fed back by the detector for a ground Doppler detection signal, and gravity gradient data collected by the detector; determining a single-arc normal equation of the detector corresponding to each batch of observation data based on each batch of observation data; fusing the single-arc normal equations corresponding to each batch of observation data based on a preset fusion rule to obtain a multi-arc normal equation; solving the multi-arc normal equation using a preset solution rule to obtain precise orbit determination parameters of the detector orbiting the target asteroid and gravity field model coefficients of the target asteroid.

[0125] In addition, when the logical instructions in the above-mentioned memory 630 are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present disclosure, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present disclosure. The aforementioned storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs.

[0126] On the other hand, the present disclosure also provides a computer program product. The computer program product includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the gradient-based asteroid gravity field solution method provided by the above-mentioned various methods. The method includes: obtaining the initial orbital parameters of the detector flying around the target asteroid and the observation data transmitted back when the detector flies around the target asteroid; wherein, the observation data is divided into multiple batches based on the time dimension, and each batch of observation data includes the position and velocity of the detector itself, the ground Doppler data fed back by the detector to the ground Doppler detection signal, and the gravity gradient data collected by the detector; based on each batch of observation data, determining the single-arc normal equation of the detector corresponding to each batch of observation data; based on a preset fusion rule, fusing the single-arc normal equations corresponding to each batch of observation data to obtain a multi-arc normal equation; using a preset solution rule to solve the multi-arc normal equation to obtain the precise orbit determination parameters of the detector flying around the target asteroid and the gravity field model coefficients of the target asteroid.

[0127] In another aspect, the present disclosure also provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the gradient-based method for solving the asteroid gravity field provided by the above-mentioned various methods. The method includes: obtaining the initial orbital parameters of the detector flying around the target asteroid and the observation data transmitted back when the detector flies around the target asteroid; wherein, the observation data is divided into multiple batches based on the time dimension, and each batch of observation data includes the position and velocity of the detector itself, the ground Doppler data fed back by the detector to the ground Doppler detection signal, and the gravity gradient data collected by the detector; based on each batch of observation data, determining the single-arc normal equation of the detector corresponding to each batch of observation data; based on a preset fusion rule, fusing the single-arc normal equations corresponding to each batch of observation data to obtain a multi-arc normal equation; using a preset solution rule to solve the multi-arc normal equation to obtain the precise orbit determination parameters of the detector flying around the target asteroid and the gravity field model coefficients of the target asteroid.

[0128] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art can understand and implement it without creative labor.

[0129] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on this understanding, the essence of the above technical solution, or the part that contributes to the prior art, can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0130] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present disclosure, rather than to limit them; although the present disclosure has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present disclosure.

Claims

1. A gradient-based asteroid gravity field solution method, comprising: Acquire the initial orbital parameters of the probe flying around the target asteroid, and the observation data sent back by the probe when flying around the target asteroid; wherein the observation data is divided into multiple batches based on the time dimension, and each batch of observation data includes the position and velocity of the probe itself, the ground Doppler data fed back by the probe to the ground Doppler detection signal, and the gravity gradient data collected by the probe; Based on each batch of observation data, determining a single arc segment normal equation of the detector corresponding to each batch of observation data; Based on the preset fusion rules, the single arc segment normal equations corresponding to each batch of observation data are fused to obtain the multi-arc segment normal equations; The multi-arc segment normal equation is solved by using a preset solution rule to obtain precise orbit determination parameters of the probe flying around the target asteroid and gravity field model coefficients of the target asteroid; and the single arc segment normal equation corresponding to each batch of observation data of the probe is determined based on each batch of observation data, including: Based on each batch of observation data, establishing an observation motion equation of the detector; Using the observed motion equation, ground Doppler data and gravity gradient data, a state error equation of the detector corresponding to each batch of observed data is established as the single arc segment normal equation; The state error equation of the detector corresponding to each batch of observation data is established by using the observed motion equation, ground Doppler data and gravity gradient data as the single arc segment normal equation, including: Based on the observed motion equation, calculating a residual; Calculating the first-order partial derivatives of the ground Doppler data and the gravity gradient data respectively as coefficient matrices of the state error equation; Based on the coefficient matrix and the residual, a state error equation of the detector corresponding to each batch of observation data is established.

2. The planetary gravity field calculation method according to claim 1, characterized in that: The step of establishing the observation motion equation of the detector based on each batch of observation data includes: Determine the observed acceleration equation of the detector corresponding to each batch of observation data by using the position and velocity of the detector itself in each batch of observation data; Based on the observed acceleration equation, determining a matching first-order ordinary differential equation; The observed motion equation of the detector is determined using the first-order ordinary differential equation.

3. The planetary gravity field calculation method according to claim 1, characterized in that: Based on the preset fusion rule, the single arc segment normal equation corresponding to each batch of observation data is fused to obtain the multi-arc segment normal equation, including: According to a preset division rule, determining the local state quantities to be solved and the global state quantities to be solved in the state quantities to be solved of the single arc segment normal equation corresponding to each batch of observation data; Determine the matrix equation of the single arc segment normal equation based on the local state quantity to be solved and the global state quantity to be solved; The matrix equations are superimposed to obtain the multi-arc segment normal equation.

4. The planetary gravity field calculation method according to claim 1, characterized in that: The method of solving the multi-arc segment normal equation by using a preset solution rule to obtain precise orbit determination parameters of the probe flying around the target asteroid and gravity field model coefficients of the target asteroid includes: Decomposing the coefficient matrix of the multi-arc-segment normal equation by using a preset matrix decomposition method to obtain the multi-arc-segment normal equation in a decomposed form; The multi-arc segment normal equation in the decomposed form is iteratively solved by using the least squares method to obtain the precise orbit determination parameters and the gravity field model coefficients of the target asteroid.

5. The planetary gravity field calculation method according to claim 4, characterized in that: The variables to be solved of the multi-arc segment normal equation are the state quantities to be solved of the probe, wherein the state quantities to be solved include the position, velocity and measurement parameters of the probe, wherein the measurement parameters are the gravity field model parameters of the target asteroid; The method of iteratively solving the decomposed multi-arc segment normal equation by the least square method to obtain the precise orbit determination parameters and the gravity field model coefficients of the target asteroid includes: Step 1, solving the correction amount of the state quantity to be solved of the detector; Step 2, solving the measurement parameters using the correction amount of the state quantity to be solved; Step 3: Using the correction amount of the state quantity to be solved, the initial orbit parameter is corrected to obtain the first corrected orbit parameter; Step 4, calculating the difference between the correction amount of the state quantity to be solved in the current iteration round and the correction amount of the state quantity to be solved in the previous iteration round; Step 5: In response to the correction difference satisfying a preset convergence condition, the gravity field model coefficients of the target asteroid are determined using the measurement parameters in the current iteration round, and the first corrected orbit parameters are used as the precise orbit determination parameters; Step 6: In response to the correction difference not satisfying the preset convergence condition, each batch of observation data is adjusted using the correction of the state quantity to be solved in the current iteration round, and steps 1 to 4 are iterated based on the adjusted batches of observation data until the correction difference satisfies the preset convergence condition.

6. The planetary gravity field calculation method according to claim 5, characterized in that: In response to the correction difference satisfying a preset convergence condition, the gravity field model coefficients of the target asteroid are determined using the measurement parameters in the current iteration round, and the first corrected orbit parameters are used as the precise orbit determination parameters, the planetary gravity field solution method further includes: Determine the covariance matrix of the state quantity to be solved based on the prior covariance matrix of the state quantity to be solved; The covariance matrix of the state quantity to be solved is used to determine the standard deviation of the best estimate of the state quantity to be solved.

7. A gradient-based asteroid gravity field solver, comprising: The data acquisition module is configured to: acquire the initial orbital parameters of the probe flying around the target asteroid, and the observation data sent back by the probe when flying around the target asteroid; wherein the observation data is divided into multiple batches based on the time dimension, and each batch of observation data includes the position and speed of the probe itself, the ground Doppler data fed back by the probe to the ground Doppler detection signal, and the gravity gradient data collected by the probe; The single arc segment normal equation determination module is configured to: determine the single arc segment normal equation of the detector corresponding to each batch of observation data based on each batch of observation data; The fusion module is configured to: fuse the single arc segment normal equations corresponding to each batch of observation data based on a preset fusion rule to obtain a multi-arc segment normal equation; A solution module is configured to: solve the multi-arc segment normal equation using a preset solution rule to obtain precise orbit determination parameters of the probe flying around the target asteroid and gravity field model coefficients of the target asteroid; The single arc segment normal equation determination module is specifically: Based on each batch of observation data, establishing an observation motion equation of the detector; Using the observed motion equation, ground Doppler data and gravity gradient data, a state error equation of the detector corresponding to each batch of observed data is established as the single arc segment normal equation; The state error equation of the detector corresponding to each batch of observation data is established by using the observed motion equation, ground Doppler data and gravity gradient data as the single arc segment normal equation, including: Based on the observed motion equation, calculating a residual; Calculating the first-order partial derivatives of the ground Doppler data and the gravity gradient data respectively as coefficient matrices of the state error equation; Based on the coefficient matrix and the residual, a state error equation of the detector corresponding to each batch of observation data is established.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the gradient-based asteroid gravity field solution method as described in any one of claims 1 to 6 is implemented.

Images