Method and system for analyzing accuracy of orbit determination of space objects based on optical observations

Abstract

The application provides a space target orbit determination precision analysis method and system based on optical observation, comprising the following steps: step S1: setting optical observation equipment parameters and observation platform parameters; step S2: calculating the position of the platform in the epoch geocentric celestial coordinate system; step S3: calculating the position of the target in the epoch geocentric celestial coordinate system; step S4: calculating the observed time period; step S5: calculating the angle measurement direction of the target relative to the platform in the epoch geocentric celestial coordinate system within the observable time; step S6: generating simulation data under multiple sets of different random noises; step S7: obtaining the target position estimation value, and comparing the target position estimation value with the actual target position to generate the average position deviation; step S8: changing the two-line data of the target orbit, repeating steps S3-S7, and statistically analyzing the results under different targets and different random noises. The application can avoid the inaccuracy of precision analysis caused by randomness, and intuitively reflects the performance that can be achieved by the orbit determination algorithm or scheme.

Description

Technical Field

[0001] This invention relates to the field of precision analysis technology, and more specifically, to a method and system for precision analysis of space target trajectory determination based on optical observation. Background Technology

[0002] Space target trajectory determination based on optical observation refers to the use of optical observation equipment to observe space targets, obtain angular information about the target relative to the observation equipment, and then calculate the target's trajectory parameters. The observation capability of optical observation equipment is generally inversely proportional to the square of the distance, while the observation capability of active equipment (such as microwave radar and lidar) is inversely proportional to the fourth power of the distance. Therefore, optical observation has wide applications in the field of space target trajectory determination.

[0003] Since optical observation equipment can only acquire relative angle measurement information of the target, orbit determination accuracy analysis is indispensable when calculating orbit parameters of space targets and evaluating the effectiveness and robustness of orbit determination algorithms or schemes, especially when cataloging and determining the orbits of space targets and space debris.

[0004] Existing methods for determining the orbit of space targets only perform one or more sets of noise simulations for a specific single target to analyze accuracy. Reference 1 (Huang Pu, "Calculation Method of Initial Orbit for Low-Earth Orbit Satellite Based on Angle Measurement Only", Flight Mechanics, 38(1), 2020) simulated a specific target under different angle measurement accuracies, and simulated a set of data for each angle measurement accuracies. Reference 2 (Li Xinran, "Ultra-Short Arc Orbit Determination Based on Particle Swarm Algorithm", Journal of Spacecraft Measurement and Control, 34(6), 2015) performed 10 sets of simulations for a single target. Reference 3 (Wu Xiaohua, "Determination of Space Target Orbit Based on Space-Based Optical Measurement and Its Accuracy Analysis", Master's Thesis of Harbin Institute of Technology, 2011) performed 100 sets of Monte Carlo simulations for a single target. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method and system for analyzing the accuracy of space target trajectory determination based on optical observation.

[0006] According to the present invention, a method and system for determining the orbit of a space target based on optical observation is provided, the scheme of which is as follows:

[0007] Firstly, a method for analyzing the accuracy of space target orbit determination based on optical observation is provided, the method comprising:

[0008] Step S1: Set the parameters of the optical observation equipment and the observation platform;

[0009] Step S2: Calculate the position of the platform in the epoch geocentric celestial coordinate system;

[0010] Step S3: Input two lines of data for the target orbit and calculate the target's position in the geocentric celestial coordinate system at the epoch;

[0011] Step S4: Observe the target using optical observation equipment and calculate the observation time period;

[0012] Step S5: Calculate the angular orientation of the target relative to the platform in the geocentric celestial coordinate system within the observable time.

[0013] Step S6: By controlling the pseudo-random number seed value, generate multiple sets of simulation data under different random noise conditions;

[0014] Step S7: Obtain the target position estimate by solving the target orbit parameters, and compare it with the actual target position to generate the average position deviation;

[0015] Step S8: Change the two rows of data of the target orbit, repeat steps S3 to S7, and perform statistical analysis on the results under different targets and different random noise.

[0016] Preferably, the method for calculating the position of the target in the epoch-centered celestial coordinate system in step S3 is as follows:

[0017] Step S3.1: Calculate the position of the target in the orbital coordinate system at time t according to SGP4. The orbital coordinate system at time t is defined as follows: the origin is the Earth's center, the XY coordinate plane is the instantaneous equatorial plane at time t, and the X-axis points to the vernal equinox at time t.

[0018] Step S3.2: Based on the transformation relationship between the orbital coordinate system at time t and the epoch-based geocentric celestial coordinate system, calculate the target's position in the epoch-based geocentric celestial coordinate system. If the target's position in the orbital coordinate system at time t is... Its position in the epoch geocentric celestial coordinate system for:

[0019]

[0020] Where T is the transformation matrix;

[0021] T = R z (-z A )R y (θ A )R z (-ζ A )R x (-ε A -Δε)R z (-Δψ)R x (ε A )R z (-Δμ)

[0022] Where, ζA θ A z A The three equatorial precession parameters in the IAU 2006 precession model are ε. A The angle between the ecliptic and the obliquity of the ecliptic is given by R, where Δε is the nutation of the angle, Δψ is the nutation of ecliptic longitude, and Δμ is the nutation of right ascension. x R y R z These are the transformation matrices for rotation around the corresponding coordinate axes. The transformation matrix for the rotation angle θ is as follows:

[0023]

[0024]

[0025]

[0026] Preferably, if the position of the platform in the epoch geocentric celestial coordinate system obtained in step S2 is... (j = 0, 1, 2, ..., N-1), where N is the number of sampling points. The position of the target in the epoch-centered celestial coordinate system obtained in step S3 is... Then, in step S5, the angular orientation of the target relative to the platform within the epoch geocentric celestial coordinate system during the observable time is... The calculation method is as follows:

[0027]

[0028] Here, represents taking the modulus of the vector.

[0029] Preferably, if the position of the platform in the epoch geocentric celestial coordinate system obtained in step S2 is... (j=0,1,2,……,N-1), where N is the number of sampling points; then the platform position construction method in step S6 includes the following steps:

[0030] Step S6.1: Set the pseudo-random number seed value to i = 0;

[0031] Step S6.2: Generate 3×N dimensional normally distributed random numbers with a mean of 0 and a standard deviation of σ. The noise is denoted as

[0032] Step S6.3: Simulated platform position with measurement noise satisfy:

[0033]

[0034] in, This indicates the j-th sampling point of the platform location; The corresponding noise (three-dimensional vector);

[0035] Step S6.4: Change the value of the pseudo-random number seed i, repeat steps S6.2 to S6.3, and obtain platform position simulation data under different measurement noise. The number of simulation data sets shall not be less than 100.

[0036] Preferably, if the position of the target in the epoch geocentric celestial coordinate system obtained in step S3 is... (j=0,1,2,……,N-1), then the method for constructing the simulated angle measurement data in step S6 includes the following steps:

[0037] Step S6.5: Set the pseudo-random number seed value to i+M, where M is an integer and M is greater than 1000;

[0038] Step S6.6: Generate a 3×N dimensional vector with a mean of 0 and a standard deviation of σ. a Normally distributed random numbers, corresponding to The noise is denoted as Standard deviation σ a The following calculations were performed based on the achievable average angular deviation *a* and the average distance *L* between the target and the platform:

[0039]

[0040] Step S6.7: Simulated angle measurement data containing measurement noise

[0041]

[0042] in, This represents the j-th sampling point at the target location; The corresponding noise (three-dimensional vector);

[0043] Step S6.8: Update the value of the pseudo-random number seed i+M as the value i changes in step S6.4, and repeat steps S6.7 to S6.8 to obtain angle measurement simulation data under different measurement noise.

[0044] Preferably, in step S7, the target orbit parameter solution generally obtains the orbit state variables at a certain moment, and the estimated target position at each sampling point needs to be calculated using the solved state variables. and the actual location Compare the generated average positional deviation d:

[0045]

[0046] Preferably, in step S8, when performing statistical analysis on the results under different targets and different random noise, the mean, maximum and standard deviation of the orbital position deviation are statistically analyzed, and the relationship between the results and the changes in observation time, observation arc length and orbital relative inclination angle is analyzed.

[0047] Secondly, a space target orbit determination accuracy analysis system based on optical observation is provided, the system comprising:

[0048] Module M1: Sets the parameters of the optical observation equipment and the observation platform;

[0049] Module M2: The position of the computing platform in the epoch geocentric celestial coordinate system;

[0050] Module M3: Input two lines of target orbit data and calculate the target's position in the geocentric celestial coordinate system at each epoch;

[0051] Module M4: Observes the target using optical observation equipment and calculates the observed time period;

[0052] Module M5: Calculates the angular orientation of the target relative to the platform in the geocentric celestial coordinate system within the observable time.

[0053] Module M6: Generates multiple sets of simulation data under different random noise conditions by controlling the pseudo-random number seed value;

[0054] Module M7: Calculates the target orbit parameters, obtains the target position estimate, and compares it with the actual target position to generate the average position deviation;

[0055] Module M8: Change the two rows of data on the target trajectory, repeat modules M3 to M7, and perform statistical analysis on the results under different targets and different random noise.

[0056] Preferably, the method for calculating the position of the target in the epoch geocentric celestial coordinate system in module M3 is as follows:

[0057] Module M3.1: Calculates the position of the target in the orbital coordinate system at time t based on SGP4. The orbital coordinate system at time t is defined as follows: the origin is the Earth's center, the XY coordinate plane is the instantaneous equatorial plane at time t, and the X-axis points to the vernal equinox at time t.

[0058] Module M3.2: Based on the transformation relationship between the orbital coordinate system at time t and the epoch geocentric celestial coordinate system, calculate the target's position in the epoch geocentric celestial coordinate system. If the target's position in the orbital coordinate system at time t is... Its position in the epoch geocentric celestial coordinate system for:

[0059]

[0060] Where T is the transformation matrix;

[0061] T = R z (-z A )R y (θ A )R z (-ζ A )R x (-ε A -Δε)R z (-Δψ)R x (ε A )R z (-Δμ)

[0062] Where, ζ A θ A z A The three equatorial precession parameters in the IAU 2006 precession model are ε. A The angle between the ecliptic and the obliquity of the ecliptic is given by R, where Δε is the nutation of the angle, Δψ is the nutation of ecliptic longitude, and Δμ is the nutation of right ascension. x R y R z These are the transformation matrices for rotation around the corresponding coordinate axes. The transformation matrix for the rotation angle θ is as follows:

[0063]

[0064]

[0065]

[0066] Preferably, if the position of the platform in the epoch geocentric celestial coordinate system obtained in step S2 is... (j = 0, 1, 2, ..., N-1), where N is the number of sampling points. The position of the target in the epoch-centered celestial coordinate system obtained in step S3 is... Then, in step S5, the angular orientation of the target relative to the platform within the epoch geocentric celestial coordinate system during the observable time is... The calculation method is as follows:

[0067]

[0068] Here, represents taking the modulus of the vector.

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] 1. Based on publicly available two-line satellite orbit data (TLE) datasets, this invention provides a method for obtaining orbit determination errors under different targets and different random noise conditions. By using multiple samples, it avoids inaccurate accuracy analysis caused by randomness.

[0071] 2. The method of the present invention is reasonable, simple to calculate, and easy to implement. It can intuitively reflect the performance that the trajectory determination algorithm or scheme can achieve, and avoid the problem of inaccurate accuracy evaluation caused by randomness. Attached Figure Description

[0072] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0073] Figure 1 This is a flowchart of the present invention;

[0074] Figure 2 The average position deviation was determined for 100 target trajectories under different noise conditions;

[0075] Figure 3 Statistical results were used to determine the positional deviation of 100 tracks under different noise levels;

[0076] Figure 4 Statistical results for determining the positional deviation of tracks under different targets and different noise levels. Detailed Implementation

[0077] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0078] This invention provides a method for analyzing the accuracy of space target trajectory determination based on optical observations, referring to... Figure 1 As shown, the method is as follows:

[0079] Step S1: Set the parameters of the optical observation equipment and the observation platform.

[0080] Step S2: Calculate the position of the platform in the epoch geocentric celestial coordinate system.

[0081] Step S3: Input two lines of data for the target orbit and calculate the target's position in the geocentric celestial coordinate system of the epoch.

[0082] Step S4: Observe the target using optical observation equipment and calculate the observed time period.

[0083] Step S5: Calculate the angular orientation of the target relative to the platform in the geocentric celestial coordinate system within the observable time.

[0084] Step S6: By controlling the pseudo-random number seed value, generate multiple sets of simulation data under different random noise conditions.

[0085] Step S7: Obtain the target position estimate by solving the target orbit parameters, and compare it with the actual target position to generate the average position deviation.

[0086] Step S8: Change the two rows of data of the target orbit, repeat steps S3 to S7, and perform statistical analysis on the results under different targets and different random noise.

[0087] The method for calculating the target's position in the epoch-centered celestial coordinate system in step S3 is as follows:

[0088] Step S3.1: Calculate the position of the target in the orbital coordinate system at time t according to SGP4 (Simplified Conventional Perturbation Model). The orbital coordinate system at time t is defined as follows: the origin is the Earth's center, the XY coordinate plane is the instantaneous equatorial plane at time t, and the X-axis points to the vernal equinox at time t.

[0089] Step S3.2: Based on the transformation relationship between the orbital coordinate system at time t and the epoch-based geocentric celestial coordinate system, calculate the target's position in the epoch-based geocentric celestial coordinate system. If the target's position in the orbital coordinate system at time t is... Its position in the epoch geocentric celestial coordinate system for:

[0090]

[0091] Where T is the transformation matrix;

[0092] T = R z (-z A )R y (θ A )R z (-ζ A )R x (-ε A -Δε)R z (-Δψ)R x (ε A )R z (-Δμ)

[0093] Where, ζ A θ A z A The three equatorial precession parameters in the IAU 2006 precession model are ε. A The angle between the ecliptic and the obliquity of the ecliptic is given by R, where Δε is the nutation of the angle, Δψ is the nutation of ecliptic longitude, and Δμ is the nutation of right ascension. x R y R zThe transformation matrices for rotation around the corresponding coordinate axes are as follows: The transformation matrices for rotation angle θ (in radians) are as follows:

[0094]

[0095]

[0096]

[0097] If the position of the platform in the epochal geocentric celestial coordinate system obtained in step S2 is... N represents the number of sampling points, and the position of the target in the epoch-based geocentric celestial coordinate system obtained in step S3 is... (j=0,1,2,……,N-1), then the angular orientation of the target relative to the platform in the epoch geocentric celestial coordinate system within the observable time in step S5. The calculation method is as follows:

[0098]

[0099] Here, represents taking the modulus of the vector.

[0100] If the position of the platform in the epochal geocentric celestial coordinate system obtained in step S2 is... N is the number of sampling points; therefore, the platform location construction method in step S6 includes the following steps:

[0101] Step S6.1: Set the pseudo-random number seed value to i = 0.

[0102] Step S6.2: Generate 3×N dimensional normally distributed random numbers with a mean of 0 and a standard deviation of σ. The noise is denoted as

[0103] Step S6.3: Simulated platform position with measurement noise satisfy:

[0104]

[0105] in, This indicates the j-th sampling point of the platform location; The corresponding noise (three-dimensional vector).

[0106] Step S6.4: Change the value of the pseudo-random number seed i, repeat steps S6.2 to S6.3, and obtain platform position simulation data under different measurement noise. The number of simulation data sets shall not be less than 100.

[0107] If the position of the target obtained in step S3 in the epochal geocentric celestial coordinate system is The method for constructing the simulated angle measurement data in step S6 includes the following steps:

[0108] Step S6.5: Set the pseudo-random number seed value to i+M, where M is an integer and M is greater than 1000.

[0109] Step S6.6: Generate a 3×N dimensional vector with a mean of 0 and a standard deviation of σ. a Normally distributed random numbers, corresponding to The noise is denoted as Standard deviation σ a The following calculations were performed based on the achievable average angular deviation *a* and the average distance *L* between the target and the platform:

[0110]

[0111] Step S6.7: Simulated angle measurement data containing measurement noise

[0112]

[0113] in, This represents the j-th sampling point at the target location; The corresponding noise (three-dimensional vector).

[0114] Step S6.8: Update the value of the pseudo-random number seed i+M as the value i changes in step S6.4, and repeat steps S6.7 to S6.8 to obtain angle measurement simulation data under different measurement noise.

[0115] In step S7, the target orbit parameter solution typically obtains the orbital state variables at a certain moment (which can be position, velocity, instantaneous Keplerian elements of the orbit, or singularity-free elements of the first kind, etc.). The estimated target position at each sampling point needs to be calculated using the obtained state variables. and the actual location Compare the generated average positional deviation d:

[0116]

[0117] In step S8, when performing statistical analysis on the results under different targets and different random noise, the mean, maximum and standard deviation of the orbital position deviation can be statistically analyzed, and the relationship between the results and the changes in observation time, observation arc length and orbital relative inclination angle can be analyzed.

[0118] This invention also provides a space target trajectory determination accuracy analysis system based on optical observation, characterized in that it includes:

[0119] Module M1: Sets the parameters of the optical observation equipment and the observation platform;

[0120] Module M2: The position of the computing platform in the epoch geocentric celestial coordinate system;

[0121] Module M3: Input two lines of target orbit data and calculate the target's position in the geocentric celestial coordinate system at each epoch;

[0122] Module M4: Observes the target using optical observation equipment and calculates the observed time period;

[0123] Module M5: Calculates the angular orientation of the target relative to the platform in the geocentric celestial coordinate system within the observable time.

[0124] Module M6: Generates multiple sets of simulation data under different random noise conditions by controlling the pseudo-random number seed value;

[0125] Module M7: Calculates the target orbit parameters, obtains the target position estimate, and compares it with the actual target position to generate the average position deviation;

[0126] Module M8: Change the two rows of data on the target trajectory, repeat modules M3 to M7, and perform statistical analysis on the results under different targets and different random noise.

[0127] The method for calculating the target's position in the epoch-centered celestial coordinate system in module M3 is as follows:

[0128] Module M3.1: Calculates the position of the target in the orbital coordinate system at time t based on SGP4. The orbital coordinate system at time t is defined as follows: the origin is the Earth's center, the XY coordinate plane is the instantaneous equatorial plane at time t, and the X-axis points to the vernal equinox at time t.

[0129] Module M3.2: Based on the transformation relationship between the orbital coordinate system at time t and the epoch geocentric celestial coordinate system, calculate the target's position in the epoch geocentric celestial coordinate system. If the target's position in the orbital coordinate system at time t is... Its position in the epoch geocentric celestial coordinate system for:

[0130]

[0131] Where T is the transformation matrix;

[0132] T = R z (-z A )R y (θ A )R z (-ζ A )R x (-ε A -Δε)R z (-Δψ)R x (ε A )Rz (-Δμ)

[0133] Where, ζ A θ A z A The three equatorial precession parameters in the IAU 2006 precession model are ε. A The angle between the ecliptic and the obliquity of the ecliptic is given by R, where Δε is the nutation of the angle, Δψ is the nutation of ecliptic longitude, and Δμ is the nutation of right ascension. x R y R z These are the transformation matrices for rotation around the corresponding coordinate axes. The transformation matrix for the rotation angle θ is as follows:

[0134]

[0135]

[0136]

[0137] If the position of the platform in the epochal geocentric celestial coordinate system obtained in step S2 is... N represents the number of sampling points, and the position of the target in the epoch-based geocentric celestial coordinate system obtained in step S3 is... (j=0,1,2,……,N-1), then the angular orientation of the target relative to the platform in the epoch geocentric celestial coordinate system within the observable time in step S5. The calculation method is as follows: Here, represents taking the modulus of the vector.

[0138] The present invention will now be described in more detail.

[0139] In the accuracy analysis of space target orbit determination, numerous factors influence the final orbit determination, and the results of a single simulation exhibit a degree of randomness, failing to reflect the true accuracy level. Therefore, it is necessary to cover more samples and more operating conditions to evaluate orbit determination accuracy. The Two-Line Satellite Orbit (TLE) dataset, released by the North American Space Defense Command based on its artificial object tracking observation data, covers meteorological satellites, ocean satellites, Earth resource satellites, educational satellites, rocket debris, etc., and can be used as the simulation target input for space target orbit determination accuracy analysis.

[0140] Reference Figure 1 As shown, first, the parameters of the optical observation equipment and the observation platform are set. Then, the position of the observation platform in the epoch geocentric celestial coordinate system is calculated.

[0141] Input two lines of data for the target orbit and calculate the target's position in the geocentric celestial coordinate system at each epoch.

[0142] Since the TLE orbital elements are defined in the orbital coordinate system at time t, which is defined as follows: the origin is the geocenter, the XY coordinate plane is the instantaneous equatorial plane at time t, and the X-axis points to the mean vernal equinox at time t, the calculation of the target's position in the epoch geocentric celestial coordinate system requires transformation. First, the target's position in the orbital coordinate system at time t is calculated using SGP4 (Simplified Conventional Perturbation Model).

[0143] Based on the transformation relationship between the orbital coordinate system at time t and the epoch-based geocentric celestial coordinate system, calculate the target's position in the epoch-based geocentric celestial coordinate system. If the target's position in the orbital coordinate system at time t is... Its position in the epoch geocentric celestial coordinate system for

[0144]

[0145] Where T is the transformation matrix.

[0146] T = R z (-z A )R y (θ A )R z (-ζ A )R x (-ε A -Δε)R z (-Δψ)R x (ε A )R z (-Δμ) (Formula 2)

[0147] Where, ζ A θ A z A The three equatorial precession parameters in the IAU 2006 precession model are ε. A Let Δε be the angle between the ecliptic and the obliquity of the ecliptic, Δψ be the nutation of the angle, and Δμ be the nutation of the right ascension. R x R y R z The transformation matrices for rotation around the corresponding coordinate axes are as follows: The transformation matrices for rotation angle θ (in radians) are as follows:

[0148]

[0149]

[0150]

[0151] Based on the positions of the simulated target and the observation platform, the time period during which the target can be observed by optical observation equipment can be calculated.

[0152] If the position of the observation platform in the epoch geocentric celestial coordinate system is (N is the number of sampling points), if the position of the target in the epoch geocentric celestial coordinate system obtained in step S3 is Then, the angular orientation of the target relative to the platform in the epoch geocentric celestial coordinate system within the observable time. The calculation method is as follows

[0153]

[0154] Here, represents taking the modulus of the vector.

[0155] Since the actual platform position and target angle measurement information both contain measurement errors, noise needs to be artificially introduced into the simulation. To avoid the influence of the randomness of the noise, multiple sets of simulation data under different random noise conditions are generated by controlling the pseudo-random number seed value.

[0156] If the platform's position in the epochal geocentric celestial coordinate system is (N is the number of sampling points), first set the pseudo-random number seed value to i = 0.

[0157] Generate 3×N dimensional normally distributed random numbers with a mean of 0 and a standard deviation of σ. The noise is denoted as

[0158] Simulated platform position with measurement noise satisfy

[0159]

[0160] By changing the value of the pseudo-random number seed i, simulation data of the platform position under different measurement noise levels can be obtained. The number of simulation data sets is generally no less than 100.

[0161] If the obtained target's position in the epochal geocentric celestial coordinate system is Set the pseudo-random number seed value to i+M. (M is an integer, and M can be greater than 1000.) As the value i changes, the pseudo-random number seed i+M is also updated.

[0162] Generate a 3×N dimensional array with a mean of 0 and a standard deviation of σ. a Normally distributed random numbers, corresponding to The noise is denoted as Standard deviation σ a It is calculated based on the achievable average angle measurement deviation 'a' and the average distance L from the target to the platform.

[0163]

[0164] Simulated angle measurement data containing measurement noise

[0165]

[0166] The target position is estimated by solving the target orbit parameters, and then compared with the actual target position to generate the average position deviation.

[0167] The target orbit parameter solution typically obtains orbital state variables at a certain moment (which can be position, velocity, instantaneous Keplerian elements, or singularity-free elements of the first kind, etc.). The estimated target position at each sampling point needs to be calculated using the obtained state variables. and the actual location Compare the generated average positional deviation d.

[0168]

[0169] By replacing the simulation target with the TLE dataset and repeating the above steps, statistical analysis can be performed on the results under different targets and different random noise levels. This allows for the statistical analysis of the mean, maximum, and standard deviation of orbital position deviations, and the relationship between the results and variations in observation duration, observation arc length, and orbital relative inclination.

[0170] The effectiveness of the method of this invention is verified by simulation below. Under the same observation platform, observation target (target Kepler elements are 42140.46km, 0.0005, 2.91°, 39.65°, 75.70°, 126.35°), and observation duration (10min), 100 sets of random noise with the same statistical regularity (standard deviation of observation platform position noise σ = 6.7m, mean angle measurement deviation a = 2000 milliarcseconds, average target distance from platform L = 35715km) are analyzed. The distribution of the target trajectory position deviation is as follows. Figure 2 As shown, the statistical results are as follows: Figure 3 As shown, the mean is 51.55 km, the standard deviation is 36.17 km, and the maximum is 179.82 km. Similarly, the accuracy statistics under different targets and different random noise levels can be obtained by replacing the simulation target in the TLE dataset. Figure 4 The results shown are statistical results for different targets (all on high-orbit tracks) and under different random noise levels. The mean is 53.43 km, the standard deviation is 42.08 km, and the maximum is 287.79 km.

[0171] This invention provides a method and system for analyzing the accuracy of space target orbit determination based on optical observation. Simulations are performed using publicly available two-line orbital (TLE) datasets, covering different targets and varying levels of random noise. The use of multiple samples avoids inaccuracies in accuracy analysis caused by randomness, and directly reflects the performance achievable by the orbit determination algorithm or scheme. This invention is reasonable, computationally simple, and easy to implement, directly reflecting the performance achievable by the orbit determination algorithm or scheme and avoiding inaccurate accuracy assessments due to randomness.

[0172] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0173] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for analyzing the accuracy of space target trajectory determination based on optical observation, characterized in that, include: Step S1: Set the parameters of the optical observation equipment and the observation platform; Step S2: Calculate the position of the platform in the epoch geocentric celestial coordinate system; Step S3: Input two lines of data for the target orbit and calculate the target's position in the geocentric celestial coordinate system at the epoch; Step S4: Observe the target using optical observation equipment and calculate the observation time period; Step S5: Calculate the angular orientation of the target relative to the platform in the geocentric celestial coordinate system within the observable time. Step S6: By controlling the pseudo-random number seed value, generate multiple sets of simulation data under different random noise conditions; Step S7: Obtain the target position estimate by solving the target orbit parameters, and compare it with the actual target position to generate the average position deviation; Step S8: Change the two rows of data of the target orbit, repeat steps S3 to S7, and perform statistical analysis on the results under different targets and different random noise. The method for calculating the target's position in the epoch-based geocentric celestial coordinate system in step S3 is as follows: Step S3.1: Calculate the position of the target in the orbital coordinate system at time t according to SGP4. The orbital coordinate system at time t is defined as follows: the origin is the Earth's center, the XY coordinate plane is the instantaneous equatorial plane at time t, and the X-axis points to the vernal equinox at time t. Step S3.2: Based on the transformation relationship between the orbital coordinate system at time t and the epoch-based geocentric celestial coordinate system, calculate the target's position in the epoch-based geocentric celestial coordinate system. If the target's position in the orbital coordinate system at time t is... Its position in the geocentric celestial coordinate system of the epoch. for: in, This is the transformation matrix; in, , , These are the three equatorial precession parameters in the IAU 2006 precession model. It is the angle between the ecliptic and the obliquity. For intersecting octaves, Moved by Huang Jingzhang, For the movement of the Red Ascension Chapter; , , These are the transformation matrices for rotation about the corresponding coordinate axes, and the rotation angle is... The corresponding transformation matrix is ​​as follows: ； If the position of the platform in the epochal geocentric celestial coordinate system obtained in step S2 is... j=0,1,2,……,N-1, where N is the number of sampling points. The position of the target in the epoch geocentric celestial coordinate system obtained in step S3 is: If j=0,1,2,……,N-1, then the angular orientation of the target relative to the platform in the epoch geocentric celestial coordinate system within the observable time in step S5 is... The calculation method is as follows: in, This indicates taking the modulus of the vector.

2. The method for analyzing the accuracy of space target trajectory determination based on optical observation according to claim 1, characterized in that, If the position of the platform in the epochal geocentric celestial coordinate system obtained in step S2 is... If j = 0, 1, 2, ..., N-1, where N is the number of sampling points; then the platform position construction method in step S6 includes the following steps: Step S6.1: Set the pseudo-random number seed value to i=0; Step S6.2: Generate a 3×N dimensional vector with a mean of 0 and a standard deviation of [missing value]. Normally distributed random numbers, corresponding to The noise is denoted as ; Step S6.3: Simulated platform position with measurement noise For j=0,1,2,……,N-1, the following conditions are met: in, This indicates the j-th sampling point of the platform location. The corresponding noise; Step S6.4: Change the value of the pseudo-random number seed i, repeat steps S6.2 to S6.3, and obtain platform position simulation data under different measurement noise. The number of simulation data sets shall not be less than 100.

3. The method for analyzing the accuracy of space target trajectory determination based on optical observation according to claim 1, characterized in that, If the position of the target obtained in step S3 in the epoch geocentric celestial coordinate system is If j=0,1,2,……,N-1, then the method for constructing the simulated angle measurement data in step S6 includes the following steps: Step S6.5: Set the pseudo-random number seed value to i+M, where M is an integer and M is greater than 1000; Step S6.6: Generate a 3×N dimensional vector with a mean of 0 and a standard deviation of [missing value]. Normally distributed random numbers, corresponding to The noise is denoted as Standard deviation Based on the achievable average angle measurement deviation Average distance from the target platform The calculation yielded: ； Step S6.7: Simulated angle measurement data containing measurement noise , in, This represents the j-th sampling point at the target location. The corresponding noise; Step S6.8: Update the value of the pseudo-random number seed i+M as the value i changes in step S6.4, and repeat steps S6.7 to S6.8 to obtain angle measurement simulation data under different measurement noise.

4. The method for analyzing the accuracy of space target trajectory determination based on optical observation according to claim 1, characterized in that, In step S7, the target orbit parameters are obtained by solving for the orbit state at a certain moment. The estimated target position at each sampling point needs to be calculated using the obtained state. and the actual location Compare the generated average position deviation : 。 5. The method for analyzing the accuracy of space target trajectory determination based on optical observation according to claim 1, characterized in that, In step S8, when performing statistical analysis on the results under different targets and different random noise, the mean, maximum and standard deviation of the orbital position deviation are statistically analyzed, and the relationship between the results and the changes in observation time, observation arc length and orbital relative inclination angle is analyzed.

6. A space target trajectory determination accuracy analysis system based on optical observation, characterized in that, include: Module M1: Sets the parameters of the optical observation equipment and the observation platform; Module M2: The position of the computing platform in the epoch geocentric celestial coordinate system; Module M3: Input two lines of target orbit data and calculate the target's position in the geocentric celestial coordinate system at each epoch; Module M4: Observes the target using optical observation equipment and calculates the observed time period; Module M5: Calculates the angular orientation of the target relative to the platform in the geocentric celestial coordinate system within the observable time. Module M6: Generates multiple sets of simulation data under different random noise conditions by controlling the pseudo-random number seed value; Module M7: Calculates the target trajectory parameters, obtains the estimated target position, and compares it with the actual target position to generate the average position deviation; Module M8: Change the two rows of data on the target trajectory, repeat modules M3 to M7, and perform statistical analysis on the results under different targets and different random noise. The method for calculating the target's position in the epoch-based geocentric celestial coordinate system in module M3 is as follows: Module M3.1: Calculates the position of the target in the orbital coordinate system at time t based on SGP4. The orbital coordinate system at time t is defined as follows: the origin is the Earth's center, the XY coordinate plane is the instantaneous equatorial plane at time t, and the X-axis points to the vernal equinox at time t. Module M3.2: Based on the transformation relationship between the orbital coordinate system at time t and the epoch geocentric celestial coordinate system, calculate the target's position in the epoch geocentric celestial coordinate system. If the target's position in the orbital coordinate system at time t is... Its position in the geocentric celestial coordinate system of the epoch. for: in, This is the transformation matrix; in, , , These are the three equatorial precession parameters in the IAU 2006 precession model. It is the angle between the ecliptic and the obliquity. For intersecting octaves, Moved by Huang Jingzhang, For the movement of the Red Ascension Chapter; , , These are the transformation matrices for rotation about the corresponding coordinate axes, and the rotation angle is... The corresponding transformation matrix is ​​as follows: ； If the position of the platform in the epochal geocentric celestial coordinate system obtained in step S2 is... j=0,1,2,……,N-1, where N is the number of sampling points. The position of the target in the epoch geocentric celestial coordinate system obtained in step S3 is: If j=0,1,2,……,N-1, then the angular orientation of the target relative to the platform in the epoch geocentric celestial coordinate system within the observable time in step S5 is... The calculation method is as follows: in, This indicates taking the modulus of the vector.

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