Method and system for improving precision orbit determination of Mars probe by using image data

Abstract

The invention discloses a method and system for improving precision orbit determination of a Mars probe by using image data, and the method comprises the steps: constructing a Mars image data set, including image preprocessing and image feature point extraction; converting the image feature points from an image coordinate system to a Mars fixed coordinate system, and performing Mars surface feature point interpolation; constructing an image observation model, linearizing the constructed image observation model, and calculating a partial derivative matrix and a state transition matrix; and according to the image feature points, the surface feature points and the calculated model and partial derivative information, combining Doppler data, and carrying out iterative calculation by adopting an iterative weighted batch processing least square method to determine an orbit. The method focuses on image data acquired by the Mars detector in the Mars detection process, and through a series of data processing and calculation methods, the precision of precise orbit determination of the detector is improved, and the accuracy and reliability of orbit determination are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of aerospace orbit measurement and control, and particularly to a method for improving the precise orbit determination of the Tianwen-1 Mars probe by using Mars image data. Background Art

[0002] In deep space exploration missions, the precise orbit determination of spacecraft is crucial for the successful execution of missions and the effective acquisition of scientific data. As the probe for China's first Mars exploration mission, the accurate determination of the orbit of Tianwen-1 is directly related to the smooth implementation of mission links such as Mars orbiting, landing, and roving.

[0003] The Tianwen-1 Mars exploration mission includes multiple key links such as orbiting, landing, and roving, and each link has extremely high requirements for the orbit accuracy of the probe. In the orbiting stage, accurate orbit determination helps the probe stably conduct scientific observations of Mars, obtaining high-quality Mars surface images, geological data, etc.; in the landing and roving stages, accurate orbit information is the basis for ensuring the safe landing of the probe on the Mars surface and carrying out roving exploration work according to the predetermined path. If the orbit accuracy is insufficient, it may cause the probe to fail to reach the predetermined position, or even lead to mission failure, resulting in huge waste of resources.

[0004] Currently, the precise orbit determination of spacecraft usually relies on the radiometric measurement data of ground tracking stations, such as Doppler and range measurements. However, this traditional method has many defects.

[0005] 1. When the angle between the sun, the earth, and the spacecraft approaches 180°, the spacecraft will be blocked by the sun, and the ground station cannot receive the measurement signal; when the angle approaches 0°, the solar plasma will seriously interfere with the radio tracking data of the spacecraft, reducing the orbit determination accuracy.

[0006] 2. The radiometric measurement data is also restricted by the scheduling of ground tracking stations. Multiple missions may share the tracking station resources, resulting in the timeliness and integrity of data acquisition being affected.

[0007] Compared with traditional radiometric measurement data, the image data obtained by the cameras carried by the probe has unique advantages. The image data is not interfered by the propagation medium, and its accuracy mainly depends on the flight altitude, the accuracy of camera parameters, and the accuracy of camera attitude.

[0008] In other deep space exploration missions, such as NEAR, Dawn, OSIRIS-Rex, and Hayabusa2, etc., the image data has been successfully used for spacecraft orbit determination and the solution of relevant parameters of target celestial bodies, achieving good results.

[0009] For example, in the Near Earth Asteroid Rendezvous (NEAR) mission and the Dawn mission, researchers successfully jointly determined multiple key parameters of the target celestial body, including the gravitational field, mass, heliocentric orbit, its own orientation and rotation state, and the positions of surface optical landmarks, by means of ground-based tracking data and optical landmark tracking data through a global estimation program. At the same time, the orbit of the spacecraft was also accurately determined. Among them, the optical landmark tracking data played a key role in the parameter solution process, significantly improving the accuracy and reliability of orbit determination.

[0010] However, in the Mars exploration mission, the Mars image data has not been fully utilized for precise orbit determination. Although a large amount of image data has been obtained during the Mars exploration process, due to the lack of effective processing methods and technical means, the potential of these data in precise orbit determination has not been explored.

[0011] In summary, the existing orbit determination technologies are difficult to meet the requirements of the Tianwen-1 Mars exploration mission for high-precision orbit determination, while the image data has great potential in precise orbit determination but has not been effectively applied. Therefore, there is an urgent need for a method to improve the precise orbit determination of the Tianwen-1 Mars probe using Mars image data, so as to improve the accuracy and reliability of orbit determination, ensure the smooth progress of the Mars exploration mission, and provide technical support for subsequent deep space exploration missions. Summary of the Invention

[0012] Aiming at the problems of traditional orbit determination methods in Mars exploration, such as being affected by solar interference and limited by ground tracking stations, the present invention focuses on using the image data obtained by the Mars probe during the Mars exploration process, and through a series of data processing and calculation methods, improves the accuracy of the precise orbit determination of the probe, significantly enhancing the accuracy and reliability of orbit determination.

[0013] According to one aspect of the specification of the present invention, there is provided a method for improving the precise orbit determination of a Mars probe using image data, including:

[0014] Constructing a Mars image data set, including image preprocessing and extraction of image feature points;

[0015] Converting the image feature points from the image coordinate system to the Mars fixed coordinate system, and performing interpolation of the Mars surface feature points;

[0016] Constructing an image observation model, linearizing the constructed image observation module, and calculating the partial derivative matrix and the state transition matrix;

[0017] According to the image feature points, surface feature points, and the calculated model and partial derivative information, combined with Doppler data, using the iterative weighted batch least squares method to iteratively calculate and determine the orbit.

[0018] As a further technical solution, the method further includes:

[0019] Calculate the errors of the orbital position and velocity in the radial, tangential, and normal directions, and compare the initial spacecraft states calculated using only Doppler data and the initial spacecraft states calculated using Doppler and image combination data with the initial spacecraft state respectively to evaluate the orbit determination performance;

[0020] Calculate the root mean square of the orbital position and velocity differences under different data combinations and analyze the orbit determination performance under different parameters;

[0021] According to the evaluation results, adjust the weight coefficients in the iterative weighted batch least squares method to optimize the orbit determination algorithm and parameters.

[0022] As a further technical solution, construct a Mars image dataset, including:

[0023] Use the image acquisition equipment carried by the Mars probe to take pictures of Mars during the Mars exploration mission to obtain image data under different angles and different lighting conditions;

[0024] Collect the Mars probe orbit data corresponding to the image data acquisition time, including the position and velocity information of the Mars probe in the Mars J2000 coordinate system, and the geometric attribute data of the image acquisition equipment;

[0025] Collect high-precision Mars shape model data.

[0026] As a further technical solution, after preprocessing the constructed Mars image dataset, it also includes:

[0027] Adopt an algorithm based on corner detection to extract stable and significant image feature points from the preprocessed images, and record the coordinates of each image feature point in the image coordinate system.

[0028] As a further technical solution, perform interpolation of Mars surface feature points, including:

[0029] According to the coordinates of the projection center and the image feature points in the fixed coordinate system of Mars, construct a straight line connecting the image feature points and the corresponding surface feature points;

[0030] Intersect the straight line with the approximate spherical model of Mars to obtain a local area point set containing the feature points;

[0031] Calculate the average elevation plane of the local area point set, and interpolate through the Mars shape model to calculate the elevation of the intersection point of the straight line and the average elevation plane;

[0032] Set the calculated intersection elevation as the new elevation, calculate the difference between the new elevation plane and the previous elevation plane. If the difference is less than the preset value, the currently calculated point is the surface feature point and stop the calculation; otherwise, repeat the calculation process with the new elevation until the condition is met.

[0033] As a further technical solution, construct an image observation model, including:

[0034] Construct an image observation model based on the collinear relationship among the projection center, image feature points, and surface feature points.

[0035] As a further technical solution, linearize the constructed image observation module and calculate the partial derivative matrix and state transition matrix, including:

[0036] Perform a Taylor expansion on the state vector of the linearized image observation model at time t to obtain the partial derivative matrix and state transition matrix.

[0037] As a further technical solution, based on the image feature points, surface feature points, and the calculated model and partial derivative information, combined with Doppler data, use the iterative weighted batch least squares method to iteratively calculate and determine the orbit, including:

[0038] Combine the image feature points, surface feature points, and the calculated model and partial derivative information with Doppler data to obtain the total measurement vector formula, the total model calculation value vector formula, and the total measurement error vector formula;

[0039] Use the iterative weighted batch least squares method to find the initial state solution of the spacecraft that minimizes the residual variance, and output the final state vector as the determined orbit.

[0040] According to one aspect of the specification of the present invention, provide a system for improving the precise orbit determination of a Mars probe using image data, including:

[0041] The first main module is used to construct a Mars image data set, including image preprocessing and image feature point extraction;

[0042] The second main module is used to convert the image feature points from the image coordinate system to the Mars fixed coordinate system and perform interpolation of Mars surface feature points;

[0043] The third main module is used to construct an image observation model, linearize the constructed image observation module, and calculate the partial derivative matrix and state transition matrix;

[0044] The fourth main module is used to iteratively calculate and determine the orbit according to the image feature points, surface feature points, and the calculated model and partial derivative information, combined with Doppler data, using the iterative weighted batch least squares method.

[0045] According to one aspect of the specification of the present invention, there is provided a non-transitory computer-readable storage medium storing computer instructions that cause a computer to perform the steps of the method for improving the precise orbit determination of a Mars probe using image data as described above.

[0046] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0047] The present invention utilizes the real Mars image data captured by the Mars probe during the Mars exploration process, combines the Mars shape model, the probe orbit data, and the camera geometric attribute data to extract image feature points and calculate surface feature points. Coordinate transformation is used to establish the geometric connection between the image and the Mars surface, an image observation model is constructed and partial derivatives are calculated to realize the fusion of image data and Doppler data, and the orbit determination algorithm is used to accurately calculate the probe orbit parameters. The orbit position accuracy is significantly improved in the tangential and normal directions, providing more accurate orbit data support for the Mars exploration mission. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings used in the description of the embodiments or the prior art. Obviously, the following-described drawings are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0049] Figure 1 It is a schematic flowchart of the method for improving the precise orbit determination of a Mars probe using image data provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0050] Taking "Tianwen-1" as an example, the present invention proposes a method for improving the precise orbit determination of the "Tianwen-1" Mars probe using image data. By using the image data obtained by the "Tianwen-1" Mars probe to participate in precise orbit determination and combining Doppler data and image data, the orbit determination accuracy in the tangential and normal directions is significantly improved. The present invention is particularly applicable to multiple fields such as deep space exploration missions, planetary science research, and aerospace engineering technology optimization. By constructing a higher-precision orbit determination system, it provides autonomous and controllable navigation guarantees for major national projects such as the Tianwen series of missions. The Mars gravity field model constructed based on high-precision orbit data will provide key support for revealing the internal structure and evolution law of Mars. The application of this method will effectively enhance the systematic ability of China's deep space exploration and serve the strategic needs of national space security.

[0051] Specifically, this method first obtains the real image data of Mars taken during the Mars exploration process of Tianwen-1, combines the Mars shape model, the detector orbit data, and the camera geometric attribute data, and extracts image feature points and calculates surface feature points. Secondly, it uses coordinate transformation to establish the geometric connection between the image and the Mars surface, constructs an image observation model and calculates the partial derivatives, realizes the fusion of image data with other measurement data (such as Doppler data), and uses the orbit determination algorithm to accurately calculate the detector orbit parameters. After a large number of simulations and experimental verifications, the present invention effectively improves the orbit determination accuracy of Tianwen-1 when orbiting Mars, significantly improves the orbit position accuracy in the tangential and normal directions, provides more accurate orbit data support for the Mars exploration mission, is of great significance for in-depth scientific exploration of Mars, and also provides an innovative method and technical reference for orbit determination of subsequent deep space exploration missions.

[0052] The technical solution of the present invention can improve the orbit determination accuracy of the Tianwen-1 Mars detector, provide efficient and accurate orbit determination support for the Tianwen-1 Mars exploration mission, and has broad application prospects and good market prospects.

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention. In addition, the technical features in each embodiment or a single embodiment provided by the present invention can be combined with each other arbitrarily to form a new technical solution. This combination is not restricted by the order of steps and / or the structural composition mode, but must be based on what can be achieved by those of ordinary skill in the art. When the combination of technical solutions conflicts with each other or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the protection scope required by the present invention.

[0054] The present invention provides a method for improving the precise orbit determination of the Tianwen-1 Mars detector using image data, as Figure 1 shown, including the following steps:

[0055] Step 1: Construct an image data set of Mars, including image preprocessing and extraction of image feature point coordinates.

[0056] In step 1, to construct the Mars image dataset, first, use the camera carried by Tianwen-1 to take pictures of Mars during the Mars exploration mission to obtain image data under different angles and lighting conditions. At the same time, collect the orbital data of Tianwen-1 corresponding to the image data acquisition time, including the position and velocity information of the detector in the Mars J2000 coordinate system, as well as the geometric attribute data of the camera. In addition, collect high-precision Mars shape model data.

[0057] Furthermore, in step 1, perform preprocessing operations on the obtained image data. First, use a filtering algorithm, such as Gaussian filtering, to remove noise in the image, reducing the interference of noise on subsequent feature point extraction. Then, apply image enhancement techniques, such as histogram equalization, to improve the contrast of the image, making the features in the image clearer and facilitating subsequent feature point extraction.

[0058] Furthermore, the extraction of the coordinates of the image feature points in step 1 is specifically as follows: Use an advanced feature extraction algorithm, such as an algorithm based on corner detection (such as an improved version of the Harris corner detection algorithm), to extract stable and significant image feature points from the preprocessed image. During the extraction process, considering the characteristics of the Mars image, optimize the algorithm parameters to ensure that representative feature points can be accurately extracted. For each extracted image feature point, record its coordinates (x, y) in the image coordinate system.

[0059] Step 2: Convert the image feature points from the image coordinate system to the Mars fixed coordinate system and perform interpolation of the feature points on the Mars surface.

[0060] The conversion of the image feature points from the image coordinate system to the Mars fixed coordinate system in step 2 is specifically as follows: Since the image coordinates (x, y) in the photo coordinate system always correspond to the image coordinates (x, y, -f) in the image space coordinate system, where f is the camera focal length. Therefore, the image space coordinate is used as an intermediate coordinate system to help convert from the photo coordinate system to the Mars fixed coordinate system. The image space coordinate system can be converted to the Mars fixed coordinate system using formula (1):

[0061]

[0062] where X, Y, and Z are the image coordinates in the Mars fixed coordinate system, and x, y, and z are the image coordinates in the image space coordinate system. R r is the rotation parameter matrix, and R0 is the displacement parameter matrix. The derivation of R r and R0 is as follows: Assume that the coordinates of the projection center in the Mars fixed coordinate system are (X S , Y S , Z S)。The coordinates of the projection center in the image space coordinate system are (0, 0, 0). Therefore, considering that the z-axis direction of the image space coordinate system is from the origin of the Mars-fixed coordinate system to the projection center, the rotation parameter matrix R r and the displacement parameter matrix R0 can be derived as shown in Formulas (2) and (3).

[0063]

[0064] where r ij (i = 1, 2, 3; j = 1, 2, 3) are the nine components corresponding to the rotation matrix. In addition, in the initial data, the orbital coordinates of Tianwen-1 are in the Mars J2000 coordinate system, and this orbit needs to be converted to the Mars-fixed coordinate system.

[0065] Furthermore, the interpolation of the Mars surface feature points described in Step 2 is specifically as follows:

[0066] 1. Construct a straight line

[0067] At the photography moment, the projection center S, the image feature point m, and the corresponding Mars surface feature point A are collinear. According to the coordinates (X S , Y S , Z S ) of the projection center S and the coordinates (X m , Y m , Z m ) of the image feature point in the Mars-fixed coordinate system, construct a straight line L connecting the image feature point m and the corresponding surface feature point A.

[0068] 2. Obtain the intersection point set

[0069] Intersect the straight line L with the approximate spherical model of Mars to obtain a point set of the local area containing the feature point A.

[0070] 3. Calculate the average elevation plane and the elevation of the intersection point

[0071] Calculate the average elevation plane h mean of the local area point set, and this average elevation plane represents the approximate elevation level of the local area. The straight line L intersects the average elevation plane at point a1, and through interpolation calculation from the Mars shape model, the elevation h1 of point a1 can be obtained. The interpolation calculation here is based on the mathematical expression of the Mars shape model and combines the position information of the point set to obtain an accurate elevation value.

[0072] 4. Iterative calculation

[0073] Set h1 as the new elevation, calculate the difference Δh = h1 - h mean between the new elevation plane and the previous elevation plane (i.e., the average elevation plane h meanIf Δh is less than 0.1 m, it is considered that the currently calculated point is the surface feature point and the calculation stops; otherwise, using the elevation h1 of a1 as the new elevation, repeat the above calculation steps until the condition of being less than is met. The intersection point that meets the condition finally obtained is the surface feature point.

[0074] Step 3: Construct an image observation model and perform linearization processing, and calculate the partial derivative matrix and the state transition matrix.

[0075] The construction of the image observation model described in Step 3 is specifically as follows: Assume that there are m image feature points in each image, and the coordinates of the nth image feature point in the ith image are (x, y). According to the collinearity relationship of the three points of the projection center (X S , Y S , Z S ), the image feature point (x, y), and the surface feature point (X A , Y A , Z A ), the geometric relationship between the image feature point and the Martian surface feature point can be constructed. The image observation model is as shown in (4):

[0076]

[0077] where f is the camera focal length. r ij (i = 1, 2, 3; j = 1, 2, 3) are the nine components of the inverse matrix of the rotation matrix R r . Assume that the position of the spacecraft is consistent with the projection center coordinates. When the spacecraft position (i.e., (X S , Y S , Z S ), the camera focal length f, and the surface feature point coordinates (X A , Y A , Z A ) are known, through the above image observation model formula (4), the surface feature point can be projected onto the focal plane to obtain the coordinates (x, y) in the phase plane coordinate system. Then, according to the pixel scale parameter of the camera, the pixel coordinates (r, c) of the image feature point in the image can be calculated.

[0078] Furthermore, the linearization of the image observation model and the calculation of the partial derivative and the state transition matrix described in Step 3 are specifically as follows:

[0079] Assume that at time t, the measured image feature point (x', y') is the observation Obs, then the image observation model (4) can be simplified as:

[0080] Obs = G(X S , t) - ε (5)

[0081] where G is the calculated value corresponding to Obs and is also the right part of Equation (4), which is a non - linear function of X S and t, is the state vector of Tianwen - 1 probe at time t, and ε corresponds to Obs.

[0082] For the state vector X of Tianwen - 1 at time t S * Perform the Taylor expansion of Equation (5). Therefore, Equation (6) will be obtained by linearization without considering the high - order terms:

[0083]

[0084] where the H matrix is the partial matrix of the calculated value G with respect to the state vector X S of the partial derivative, is the state transition matrix. H and are calculated by Formulas (7) and (8) respectively.

[0085]

[0086]

[0087] where

[0088]

[0089] X0(t0) is the state vector at t0.

[0090] Step 4: Fuse the image feature points, surface feature point data, and the calculated model and partial derivative information, together with the Doppler data, and use the iterative weighted batch least - squares method to iteratively calculate and determine the orbit.

[0091] The combined orbit determination of the image observation data and Doppler data in Step 4 is specifically as follows:

[0092] After the above processing, combine the image data (i.e., image feature points, surface feature point data, and the calculated model and partial derivative information) and the Doppler data to obtain the total measurement vector l in Formula (9), the total model calculated value vector G(X S ) in Formula (10), and the total measurement error vector ε in Formula (11) as:

[0093]

[0094] Thereafter, use the iterative weighted batch least - squares method to find the initial state solution of the spacecraft that can minimize the residual variance. Specifically as follows:

[0095] 1. Initialization: Set the initial state vector Set the weight matrix W, set the convergence threshold ∈ and the maximum number of iterations N max .

[0096] 2. Calculate the radio tracking data residuals respectively:

[0097]

[0098] 3. Then perform linearization processing:

[0099]

[0100] Among them, H is the partial derivative of the observation matrix, is the state transition matrix.

[0101] 4. Construct the normal equation:

[0102] Construct the normal equation of the weighted least squares method

[0103]

[0104] Among them, is the update amount of the state vector, and k represents the state vector after k iterations. V (k) refers to the residual vector calculated in the k-th iteration. The residual vector represents the difference between the observed value and the model predicted value. Specifically, V (k) is a vector composed of the residuals of the image data and the Doppler data, and the form is as follows:

[0105]

[0106] 5. Solve for the update amount:

[0107] Solve the normal equation to obtain the update amount of the state vector

[0108]

[0109] 6. Update the state vector:

[0110]

[0111] 7. Check the convergence:

[0112] In the k-th iteration, calculate the norm of the state vector update amount of the norm The norm is used to measure the magnitude of the update amount, and usually the L2 norm (Euclidean norm) is used for calculation:

[0113]

[0114] Among them, Represents the \(i\)-th component of the state vector update amount. If this norm is less than the convergence threshold \(\epsilon\) or reaches the maximum number of iterations \(N\) max , the iteration stops; otherwise, return to step 2 to continue the iteration.

[0115] Finally, output the final state vector and the corresponding residuals.

[0116] Step Five: Evaluate the orbit determination result, and optimize the algorithm and parameters according to the evaluation to improve the accuracy and reliability of orbit determination.

[0117] The evaluation of the orbit determination result described in step five is specifically as follows: First, calculate the errors of the orbit position and velocity in the radial (R), tangential (T), and normal (N) directions, and compare the initial spacecraft states calculated using only Doppler data and the initial spacecraft states calculated using combined Doppler and image data with the initial spacecraft state respectively to evaluate the orbit determination performance. Second, analyze the orbit determination performance under different parameters by calculating the root mean square (RMS) of the differences in orbit position and velocity under different data combinations. According to the evaluation results, further optimize the orbit determination algorithm and parameters. Adjust the weight coefficient in the iterative weighted batch least squares (WBLS) method to change the weight ratio of image data and Doppler data in the calculation to improve the accuracy and reliability of orbit determination.

[0118] In the embodiment of the present invention, taking Tianwen-1 as an example, the technical solution of the present invention is described in detail in combination with a specific embodiment simulating the relevant situation of MEX flying by Phobos.

[0119] Step One: Construct and preprocess the image data set

[0120] 1. Orbit simulation: Based on the initial MEX state, high-precision force model, and orbit integration, generate high-precision MEX ephemeris through a 5s integration step.

[0121] 2. Necessary data collection: Collect the shape model of Phobos. In this simulation, a spherical harmonic function model up to 45 orders is used. At the same time, determine the geometric properties of the SRC camera carried by MEX;

[0122] 3. Image feature point simulation: Directly simulate image feature points according to the geometric characteristics of the SRC camera. We assume that there are 150 randomly distributed image feature points in each image to increase the number of image feature points. For 35 orbit points in the 2013 flyby simulation, 5250 image feature points are generated. Noise is also added to approximate real image feature points. Record the coordinates of each image feature point in the image coordinate system.

[0123] Step Two: Coordinate system conversion and interpolation of Mars surface feature points.

[0124] 1. First, convert the above image feature points from the image coordinate system to the Mars-fixed coordinate system. For an image feature point with photo coordinates (x, y), use the formula to convert it to the Mars-fixed coordinate system. In addition, for the previously generated ephemeris data, the orbital coordinates of MEX are in the Mars J2000 coordinate system, and this orbit needs to be converted to the Mars-fixed coordinate system.

[0125] 2. Perform interpolation of the Mars surface feature points: At the photography moment, according to the coordinates (X S , Y S , Z S ) of the projection center S and the coordinates (X m , Y m , Z m ) of the image feature point in the Phobos-fixed coordinate system, construct a straight line L connecting the image feature point m and the corresponding surface feature point A. Intersect the straight line L with the approximate spherical model of Phobos to obtain a point set of the local area containing the feature point A. Calculate the average elevation plane h mean . The straight line L intersects the average elevation plane at point a1. By interpolating and calculating from the Phobos shape model, the elevation h1 of point a1 can be obtained. Set h1 as the new elevation, and calculate the difference Δh = h1 - h between the new elevation plane and the previous elevation plane mean . If Δh is less than 0.1 m, it is considered that the currently calculated point is the surface feature point, and the calculation stops; otherwise, take the elevation h1 of a1 as the new elevation and repeat the above calculation steps until the condition of being less than is satisfied. The finally obtained intersection point that meets the condition is the surface feature point.

[0126] Step 3: Linearize the image observation model and calculate the partial derivative matrix and the state transition matrix.

[0127] 1. Assume that the coordinates of the nth image feature point in the ith image are (x, y). According to the collinear relationship of the projection center, the image feature point, and the surface feature point, the geometric relationship between the image feature point and the Phobos surface feature point can be constructed to obtain the image observation model

[0128] where f is the camera focal length. r ij (i = 1, 2, 3; j = 1, 2, 3) are the nine components of the inverse matrix of the rotation matrix R r in Step 2. Assume that the position of the spacecraft is the same as the projection center coordinates. For the coordinates (X A , Y A , Z A), the surface feature points can be projected onto the focal plane through the above image observation model to obtain the coordinates (x, y) in the phase plane coordinate system. Then, according to the pixel scale parameter of the camera, the pixel coordinates (r, c) of the image feature points in the image can be calculated.

[0129] 2. Calculate its partial derivatives and state transition matrix. Assume that at time t, the image feature points (x', y') are measured as the observation Obs. Then the image observation model can be simplified as: Obs = G(X S , t) - ε, and its linearized form is The H matrix is the partial matrix of the calculated value G with respect to the state vector X S for the partial derivatives, i.e., the state transition matrix.

[0130] Step 4: Fuse the image and Doppler data, and use the iterative weighted batch least squares method to iteratively calculate and determine the orbit.

[0131] After the above processing is completed, the image data and Doppler data are combined to obtain the total measurement formula The formula for the total model calculated value vector The formula for the total measurement error vector ε After that, use the iterative weighted batch least squares (WBLS) estimator to find the initial state solution of the spacecraft that can minimize the residual variance under a given set of measurement data, and complete the precise orbit determination.

[0132] First, set the initial state vector The weight matrix W convergence threshold ∈ and the maximum number of iterations N max . Calculate the radio tracking data residuals respectively:

[0133] V img = G img (X S ) - l img

[0134] V doppler = G doppler (X S ) - l doppler ,

[0135] After linearization processing, we get

[0136] Then construct the normal equation of the weighted least squares method:

[0137] Solve the normal equation to obtain the update amount of the state vector

[0138] Update the state vector

[0139] In the k-th iteration, calculate the update amount of the state vector of the norm

[0140]

[0141] If this norm is less than the convergence threshold ∈ or reaches the maximum number of iterations N max , stop the iteration; otherwise, return to step 2 to continue the iteration. Finally, output the final state vector and the corresponding residual.

[0142] Step Five: Result evaluation and parameter optimization

[0143] 1. First, calculate the errors of the orbital position and velocity in the radial (R), tangential (T), and normal (N) directions. Compare the initial spacecraft states calculated using only Doppler data and the initial spacecraft states calculated using combined Doppler and image data with the initial spacecraft state (which can be preset in advance) to evaluate the orbit determination performance.

[0144] 2. Analyze the orbit determination performance under different parameters by calculating the root mean square (RMS) of the differences in orbital position and velocity under different data combinations.

[0145] 3. According to the evaluation results, further optimize the orbit determination algorithm and parameters. Adjust the weight coefficient in the iterative weighted batch least squares (WBLS) method to change the weight ratio of image data and Doppler data in the calculation, so as to improve the accuracy and reliability of orbit determination.

[0146] Through the above steps, the present invention proves that image data is feasible as a new orbital constraint and can effectively improve the orbit determination accuracy. Compared with Doppler data, image data can provide stronger constraints on the tangential and normal orbits. After including image data, the orbit position accuracy has been significantly improved in both the tangential and normal directions.

[0147] In the embodiments of the present invention, the joint orbit determination of the image data and Doppler data of the MEX flying over Phobos is simulated, and the Monte Carlo method is used to verify the ability of the image data during the MEX flyby of Phobos to accurately determine the orbit of MEX. We added random noises of 300 m and 0.1 m / s to the initial position and velocity respectively, and conducted 100 experiments for each strategy. A total of eight parameters were estimated; including the initial spacecraft state, solar radiation scale factor, and Mars atmospheric drag scale factor. The orbit determination performance was evaluated by directly comparing the initial spacecraft state calculated from different data with the initial spacecraft state given in the ephemeris. The initial spacecraft state calculated using only Doppler data and the initial spacecraft state calculated using the combined Doppler and image data were respectively compared with the initial spacecraft state, and the errors of the orbit position and velocity in the radial (R), tangential (T), and normal (N) directions were calculated to measure the accuracy of orbit determination. Secondly, we calculated the root mean square (RMS) of the differences in orbit position and velocity under different data combinations to comprehensively reflect the deviation degree between the orbit determination result and the true state. In the experiment of simulating the MEX flyby of Phobos, when only using Doppler data, the RMS values of the orbit position in the radial, tangential, and normal directions were 0.4715 m, 33.5680 m, and 294.4105 m respectively; when using the combined Doppler and image data, the corresponding RMS values in the respective directions were 0.2497 m, 0.6971 m, and 5.1336 m. By analyzing the correlation of the estimated parameters, it was found that when only using Doppler data, except for the radial position parameter, the other parameters had high correlations; when using the combined data, the parameter correlations decreased, indicating that the image data improved the sensitivity of parameter estimation and contributed to improving the orbit determination accuracy.

[0148] The implementation basis of each embodiment of the present invention is achieved through programmed processing by a device with a processor function. Therefore, in engineering practice, the technical solutions and their functions of each embodiment of the present invention are encapsulated into various modules. Based on this actual situation, on the basis of the above embodiments, an embodiment of the present invention provides a system for improving the precise orbit determination of a Mars probe using image data, and this system is used to execute the method for improving the precise orbit determination of a Mars probe using image data in the above method embodiments.

[0149] The system includes: a first main module for constructing a Mars image data set, including image preprocessing and extraction of image feature points; a second main module for converting the image feature points from the image coordinate system to the Mars fixed coordinate system and interpolating the surface feature points of Mars; a third main module for constructing an image observation model, linearizing the constructed image observation module, and calculating the partial derivative matrix and state transition matrix; a fourth main module for iteratively calculating and determining the orbit using the iterative weighted batch least squares method in combination with Doppler data based on the image feature points, surface feature points, and the calculated model and partial derivative information.

[0150] The system for improving the precise orbit determination of a Mars probe using image data provided by an embodiment of the present invention addresses issues such as solar interference and ground tracking station limitations in traditional orbit determination methods for Mars exploration. By adopting several of the aforementioned modules and using the image data obtained by the Mars probe to participate in precise orbit determination, combining Doppler data and image data significantly improves the orbit determination accuracy in the tangent and normal directions.

[0151] It should be noted that the system embodiment provided by the present invention, in addition to being used to implement the method in the above method embodiment, is also used to implement the methods in other method embodiments provided by the present invention. The difference lies only in setting corresponding functional modules, and its principle is basically the same as that of the above system embodiment provided by the present invention. As long as those skilled in the art, based on the above system embodiment, refer to the specific technical solutions in other method embodiments, obtain corresponding technical means by combining technical features, and the technical solutions constituted by these technical means, and on the premise of ensuring the practicality of the technical solution, improve the modules in the above system embodiment to obtain corresponding system-like embodiments for implementing the methods in other method-like embodiments.

[0152] Based on the same inventive concept as the foregoing embodiments, an embodiment of the present invention also provides a non-transitory computer-readable storage medium. The non-transitory computer-readable storage medium stores computer instructions, and the computer instructions cause the computer to execute the steps of the method for improving the precise orbit determination of a Mars probe using image data.

[0153] In summary of the above embodiments, through the above innovative multi-level technical path, the present invention expects to make significant progress in the following aspects: enabling the image data obtained by the "Tianwen-1" Mars probe to participate in precise orbit determination, combining Doppler data and image data, and significantly improving the orbit determination accuracy in the tangent and normal directions.

[0154] The main innovative points and advantages of the present invention are embodied in the following aspects:

[0155] 1. Data acquisition and preprocessing: Use the camera carried by "Tianwen-1" to obtain image data of Mars, and at the same time collect high-precision Mars shape model data, probe orbit data, and geometric attribute data of the camera. Perform preprocessing operations such as denoising and enhancement on the image data to remove noise interference, improve the clarity and contrast of the image, and highlight the feature information in the image, providing a high-quality data basis for subsequent feature point extraction.

[0156] 2. Image Feature Point and Surface Feature Point Processing: Adopt advanced feature extraction algorithms to extract stable and prominent image feature points from the preprocessed images, and record their coordinates in the image coordinate system. Convert the orbit data of Tianwen-1 from the initial coordinate system to the Mars-fixed coordinate system. Based on the imaging principle and geometric properties of the camera, establish the conversion relationships among the image coordinate system, the image space coordinate system, and the Mars-fixed coordinate system. Use the rotation parameter matrix and displacement parameter matrix to convert the coordinates of the image feature points in the image coordinate system to the Mars-fixed coordinate system. According to the coordinates of the projection center (camera optical center) in the Mars-fixed coordinate system and the converted coordinates of the image feature points, construct a straight line connecting the two. Intersect this straight line with the shape model of Mars or Phobos to obtain the intersection point set. By calculating the average elevation plane of the intersection point set, use the interpolation algorithm to obtain the elevation of the intersection point of the straight line and the average elevation plane, and through iterative calculation until the set elevation difference threshold is met, so as to accurately determine the surface feature points.

[0157] 3. Construct Image Observation Model and Calculate Partial Derivatives: Based on the collinear relationship among the projection center, image feature points, and surface feature points, construct an image observation model. Considering the actual situations in Mars exploration, such as the influence of Mars' gravitational field and the attitude changes of the detector, etc., optimize the model to make it more in line with the orbit determination requirements of Tianwen-1. Conduct Taylor expansion linearization processing on the image observation model, ignore the high-order terms, and obtain a linearized formula that is convenient for calculation. According to the linearized formula, calculate the partial derivative matrix and the state transition matrix, providing key data support for subsequent orbit determination.

[0158] 4. Orbit Determination and Optimization: Integrate the obtained image feature point, surface feature point data, and the calculated image observation model and partial derivative information with other measurement data (such as Doppler data). Adopt advanced orbit determination algorithms, such as the Iterative Weighted Batch Least Squares (WBLS), to process the integrated data. Through continuous iterative calculation, adjust the orbit parameters of the detector to minimize the difference between the measurement data and the model calculation results, so as to accurately determine the orbit of Tianwen-1 during the Mars exploration process. Evaluate the orbit determination results, calculate the errors of the orbit position and velocity in the radial, tangential, and normal directions, and compare them with the known accurate orbit data. According to the evaluation results, further optimize the orbit determination algorithm and parameters, such as adjusting the weight coefficients of the algorithm and improving the data fusion strategy, etc., to improve the accuracy and reliability of orbit determination.

[0159] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention 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 or all of the technical features. These modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for improving the precise orbit determination of a Mars probe using image data, characterized in that: include: Construct a Mars image dataset, including image preprocessing and image feature point extraction; Convert image feature points from the image coordinate system to the Mars fixed coordinate system and interpolate the Martian surface feature points; Construct an image observation model, linearize the constructed image observation module and calculate the partial derivative matrix and state transfer matrix; Based on the image feature points, surface feature points, calculated model and partial derivative information, combined with Doppler data, the orbit is determined by iterative calculation using the iterative weighted batch least squares method.

2. The method for improving the precise orbit determination of a Mars probe using image data according to claim 1, characterized in that: The method further comprises: The errors of orbital position and velocity in radial, tangential and normal directions are calculated, and the initial spacecraft state calculated using only Doppler data and the initial spacecraft state calculated using combined Doppler and image data are compared with the initial spacecraft state to evaluate the orbit determination performance; The root mean square of the orbit position and velocity differences under different data combinations is calculated to analyze the orbit determination performance under different parameters; According to the evaluation results, the weight coefficients in the iterative weighted batch least squares method are adjusted to optimize the orbit determination algorithm and parameters.

3. The method for improving precise orbit determination of a Mars probe using image data according to claim 1, characterized in that: Build a Mars image dataset, including: Use the image acquisition equipment on the Mars rover to photograph Mars during the Mars exploration mission and obtain image data at different angles and under different lighting conditions; Collect the orbital data of the Mars rover corresponding to the moment of image data acquisition, including the position and velocity information of the Mars rover in the Mars J2000 coordinate system, and the geometric attribute data of the image acquisition device; Collect high-precision Mars shape model data.

4. The method for improving the precise orbit determination of a Mars probe using image data according to claim 3, characterized in that: After preprocessing the constructed Mars image dataset, it also includes: An algorithm based on corner detection is used to extract stable and significant image feature points from the preprocessed image, and the coordinates of each image feature point in the image coordinate system are recorded.

5. The method for improving precise orbit determination of a Mars probe using image data according to claim 1, characterized in that: Interpolation of Mars surface feature points, including: According to the coordinates of the projection center and the image feature points in the Mars fixed coordinate system, a straight line connecting the image feature points and the corresponding surface feature points is constructed; Intersect the straight line with the approximate spherical model of Mars to obtain a local area point set containing feature points; Calculate the average elevation surface of the local area point set, and calculate the elevation of the intersection of the straight line and the average elevation surface through interpolation of the Mars shape model; The calculated intersection elevation is set as the new elevation, and the difference between the new elevation surface and the previous elevation surface is calculated. If the difference is less than the preset value, the currently calculated point is a surface feature point and the calculation is stopped; otherwise, the calculation process is repeated with the new elevation until the conditions are met.

6. The method for improving precise orbit determination of a Mars probe using image data according to claim 1, characterized in that: Construct an image observation model, including: The image observation model is constructed based on the collinear relationship among the projection center, image feature points and surface feature points.

7. The method for improving precise orbit determination of a Mars probe using image data according to claim 6, characterized in that: The constructed image observation module is linearized and the partial derivative matrix and state transfer matrix are calculated, including: The state vector of the linearized image observation model is Taylor expanded at time t to obtain the partial derivative matrix and state transfer matrix.

8. The method for improving precise orbit determination of a Mars probe using image data according to claim 1, characterized in that: Based on the image feature points, surface feature points, calculated model and partial derivative information, combined with Doppler data, the iterative weighted batch least squares method is used to iteratively calculate and determine the orbit, including: The image feature points, surface feature points, calculated model and partial derivative information are combined with Doppler data to obtain the total measurement vector formula, the total model calculation value vector formula, and the total measurement error vector formula; The iterative weighted batch least squares method is used to find the spacecraft initial state solution that minimizes the residual variance, and the final state vector is output as the determined orbit.

9. A system for improving the precise orbit determination of Mars probes using image data, characterized in that: include: The first main module is used to construct the Mars image dataset, including image preprocessing and image feature point extraction; The second main module is used to convert the image feature points from the image coordinate system to the Mars fixed coordinate system and to interpolate the Martian surface feature points; The third main module is used to construct an image observation model, linearize the constructed image observation module and calculate the partial derivative matrix and state transfer matrix; The fourth main module is used to determine the orbit by iterative calculation using iterative weighted batch least squares method based on image feature points, surface feature points, calculated model and partial derivative information, combined with Doppler data.

10. A non-transitory computer-readable storage medium, characterized in that: The non-transitory computer-readable storage medium stores computer instructions, which enable the computer to execute the steps of the method for improving the precise orbit determination of a Mars probe using image data as described in any one of claims 1 to 8.

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