An asteroid close approach information fusion orbit determination method based on support vector machine

Abstract

The application discloses a near-approaching information fusion orbit determination method for asteroids based on a support vector machine and belongs to the technical field of space. The application realizes the method as follows: a motion model of an asteroid and a probe is established, an observation model of the asteroid near the probe is established, a sampling number and upper and lower bounds of a standard deviation of angle measurement and distance measurement observation noise are set, samples are generated, an SVM model is trained based on the samples, an asteroid near-approaching orbit determination classification model for identifying whether a root mean square information filtering algorithm needs to be used is obtained, for a given asteroid near-approaching orbit determination scene, the trained asteroid near-approaching orbit determination classification model is used to identify whether the root mean square information filtering algorithm needs to be used, if the root mean square information filtering algorithm needs to be used, the root mean square information filtering algorithm is used for near-approaching orbit determination, and a state estimation value of the near-approaching probe is obtained, and if not, an extended Kalman filtering algorithm is used for near-approaching orbit determination, and a state estimation value of the near-approaching probe is obtained. The application has the advantages of high orbit determination precision and small estimation error.

Description

Technical Field

[0001] This invention relates to a method for orbit determination by fusing information on asteroid approach, belonging to the field of space technology. Background Technology

[0002] Asteroid exploration is an important form of deep space exploration. Because asteroids are unaffected by human activity and retain many physical properties from the early solar system, they are often referred to as "ancient fossils of the solar system." By exploring asteroids, we can investigate the origin of the universe, the composition of the solar system, and even search for the origin of life. Asteroid exploration first requires a close approach to the asteroid, with orbit determination being one of the core technologies in this process. By determining the approach orbit, the probe can ascertain its position in the inertial frame, allowing for guidance and control based on the asteroid's relative position. During the asteroid approach, orbit determination is typically performed using two methods: optical angle measurement and radar ranging. Because these two methods have different measurement mechanisms, their error magnitudes differ. This can lead to numerical singularities when fusing the two methods for orbit determination due to the different error magnitudes. Therefore, the root mean square (RMS) information filtering method can be used for orbit determination. Compared to the general extended Kalman filter method, the RMS information filtering method, by using the RMS matrix for orbit determination calculations, can to some extent avoid the numerical singularity problem caused by different error magnitudes. However, when the magnitudes of errors in angle and distance measurements are relatively small, the root mean square information filtering method (RMS information filtering) is less accurate than the extended Kalman filtering method in orbit determination. To improve the accuracy of asteroid approach orbit determination and avoid numerical singularities when the magnitudes of errors in angle and distance measurements are large, it is necessary to train a support vector machine (SVM) model to identify when the extended Kalman filtering algorithm should be used and when the RMS information filtering algorithm should be used. Summary of the Invention

[0003] The purpose of this invention is to provide a method for orbit determination based on asteroid approach information fusion using support vector machines. By training a support vector machine model, this method identifies the algorithm that needs to be switched during the approach of an asteroid for orbit determination. This invention has the advantages of high orbit determination accuracy and small estimation error, which helps to reduce the singularity problem in asteroid approach orbit determination calculations and improves the detection capability of the probe during the asteroid approach process.

[0004] The objective of this invention is achieved through the following technical solutions.

[0005] This invention discloses an asteroid approach information fusion orbit determination method based on support vector machines (SVM). The method sets the initial approach time of the asteroid probe, the asteroid's state at the initial time, the probe's actual state at the initial time, the probe's estimated state at the initial time, the probe's estimated covariance matrix at the initial time, the observation interval, and the number of observations. It establishes a motion model between the asteroid and the probe, and an observation model of the asteroid approach by the probe. It sets the number of samples, and the upper and lower bounds of the standard deviation of the angle and distance measurement observation noise. Based on the set initial approach time, asteroid state at the initial time, probe's actual state at the initial time, probe's estimated state at the initial time, the probe's estimated covariance matrix at the initial time, the observation interval, the number of observations, and the established motion model between the asteroid and the probe, and the observation model of the asteroid approach by the probe, samples are generated. An SVM model is trained based on the obtained samples to obtain an asteroid approach orbit determination classification model used to identify whether the root mean square information filtering algorithm is needed. For a given asteroid approach orbit determination scenario, the trained asteroid approach orbit determination classification model is used to identify whether the root mean square information filtering algorithm is needed. If the root mean square information filtering algorithm is required, it is used for approach orbit determination to obtain the estimated state of the approaching probe; otherwise, the extended Kalman filter algorithm is used. Based on the obtained approach probe state estimates, the approach trajectory of the asteroid probe is planned, and the probe executes guidance and control commands to achieve an approach to the target asteroid, thereby performing flyby, landing, and rover exploration.

[0006] This invention discloses an asteroid approach information fusion orbit determination method based on support vector machines, comprising the following steps:

[0007] Step 1: Set the initial approach time of the asteroid probe, the initial state of the asteroid, the initial actual state of the probe, the initial estimated state of the probe, the initial estimated covariance matrix of the probe, the observation interval, and the number of observations.

[0008] Set the initial approach time t0 for the asteroid probe, and set the initial state of the asteroid. for:

[0009]

[0010] in This represents the x-component of the asteroid's position in an inertial frame. This represents the position component of the asteroid in the y-direction in an inertial frame. This represents the z-axis position component of the asteroid in an inertial frame of reference. This represents the asteroid's velocity component in the x-direction within an inertial frame. This represents the y-axis velocity component of the asteroid in an inertial frame of reference. This represents the z-axis velocity component of the asteroid in an inertial frame.

[0011] Set the detector's true state at the initial moment for:

[0012]

[0013] in This represents the true position component of the detector in the x-direction in the inertial frame. This represents the true position component of the detector in the y-direction in the inertial frame. This represents the true position component of the detector in the z-direction in the inertial frame. This represents the actual velocity component of the detector in the x-direction in the inertial frame. This represents the actual velocity component of the detector in the y-direction in the inertial frame. This represents the actual velocity component of the detector in the z-direction in the inertial frame.

[0014] Set the detector estimated state at the initial time. for:

[0015]

[0016] in This indicates the estimated position component of the detector in the x-direction in the inertial frame. This indicates that the detector estimates its position component in the y-direction in an inertial frame. This indicates the estimated position component of the detector in the z-direction in the inertial frame. This indicates that the detector estimates the velocity component in the x-direction in the inertial frame. This indicates that the detector estimates the velocity component in the y-direction in the inertial frame. This indicates the estimated velocity component of the detector in the z-direction in the inertial frame.

[0017] The detector covariance matrix is ​​estimated at the initial time. Observation interval dt, number of observations N.

[0018] Step 2: Based on the initial state of the asteroid and the probe in Step 1, establish a motion model of the asteroid and the probe, and at the same time establish a model of the asteroid approaching the probe and observing the asteroid.

[0019] The asteroid motion model is established as follows:

[0020]

[0021] Where μ represents the solar gravitational constant, and (t) represents the state at time t.

[0022] The asteroid motion model is established as follows:

[0023]

[0024] The following is a model for the probe's observation of asteroids:

[0025]

[0026] Among them l x The x-direction component of the line-of-sight vector obtained from angle measurement observation, l y Let l be the y-direction component of the line-of-sight vector obtained from angular observation. z d represents the z-direction component of the line-of-sight vector obtained from angle measurement observation, and d represents the radar ranging. and v d This is for measurement error.

[0027] Step 3: Set the number of samples, the upper and lower bounds of the standard deviation of the angle and distance measurement observation noise, and generate samples based on the initial time of the asteroid approach, the asteroid state at the initial time, the actual state of the probe at the initial time, the estimated state of the probe at the initial time, the estimated covariance matrix of the probe at the initial time, the observation interval, and the number of observations set in Step 1, as well as the asteroid and probe motion model and the asteroid approach probe observation model established in Step 2. The input to the samples is the standard deviation of the angle measurement observation noise, σ. l and the standard deviation of ranging observation noise σ d The output of the sample is defined as 1 or -1, where 1 indicates that the root mean square information filtering algorithm is used and -1 indicates that the extended Kalman filtering algorithm is used.

[0028] Set the number of samples M and the upper bound of the standard deviation of the angle measurement observation noise. Lower bound of standard deviation of angle measurement observation noise Upper bound of the standard deviation of distance measurement observation noise Lower bound of standard deviation of distance measurement observation noise For each sampling point, the upper bound of the standard deviation of the angle measurement observation noise is set. Lower bound of standard deviation of angle measurement observation noise Upper bound of the standard deviation of distance measurement observation noise Lower bound of standard deviation of distance measurement observation noise Randomly generated angle measurement observation noise standard deviation σ l and the standard deviation of ranging observation noise σ d The observation noise matrix R is established as follows:

[0029]

[0030] Based on the observation noise matrix R, and using the initial time of the asteroid approach, the asteroid state at the initial time, the actual state of the probe at the initial time, the estimated state of the probe at the initial time, the estimated covariance matrix of the probe at the initial time, the observation interval, and the number of observations set in step one, as well as the asteroid and probe motion model and the asteroid approach probe observation model established in step two, the extended Kalman filter algorithm and the root mean square information filter algorithm are used to solve the estimated state of the probe, respectively. The average estimation error e is calculated according to formula (8) as follows:

[0031]

[0032] The input for this sample is the standard deviation of the angle measurement observation noise, σ. l and the standard deviation of ranging observation noise σ d When the average estimation error obtained by the root mean square information filtering algorithm is less than the average estimation error obtained by the extended Kalman filter algorithm, the output of the sample is defined as 1; otherwise, it is -1.

[0033] Step 4: Train an SVM model based on the samples obtained in Step 3 to obtain an asteroid approach and orbit determination classification model for identifying whether the root mean square information filtering algorithm is needed.

[0034] Step 5: For a given asteroid approach and orbit determination scenario, use the asteroid approach and orbit determination classification model trained in Step 4 to determine whether the root mean square information filtering algorithm is needed. If the root mean square information filtering algorithm is needed, then use it for approach and orbit determination to obtain the estimated state of the approaching probe; if not, use the extended Kalman filter algorithm for approach and orbit determination to obtain the estimated state of the approaching probe, i.e., asteroid approach information fusion and orbit determination based on support vector machines.

[0035] It also includes step six, which involves planning the asteroid probe's approach trajectory based on the approach probe state estimate obtained in step five, generating guidance and control commands for the probe to approach the target asteroid, and then conducting fly-around, landing, and rover exploration of the probe.

[0036] Beneficial effects:

[0037] 1. This invention discloses an asteroid approach information fusion orbit determination method based on support vector machines (SVM). The method sets the initial approach time of the asteroid probe, the asteroid's state at the initial time, the probe's actual state at the initial time, the probe's estimated state at the initial time, the probe's estimated covariance matrix at the initial time, the observation interval, and the number of observations. It establishes a motion model between the asteroid and the probe, and an observation model of the asteroid approaching the probe. It sets the number of samples, and the upper and lower bounds of the standard deviation of the angle and distance measurement observation noise. Based on the set initial approach time, asteroid state at the initial time, probe's actual state at the initial time, probe's estimated state at the initial time, the probe's estimated covariance matrix at the initial time, the observation interval, the number of observations, and the established motion model between the asteroid and the probe, and the observation model of the asteroid approaching the probe, samples are generated. An SVM model is trained based on the obtained samples to obtain an asteroid approach orbit determination classification model used to identify whether a root mean square information filtering algorithm is needed. For a given asteroid approach orbit determination scenario, the trained asteroid approach orbit determination classification model is used to identify whether a root mean square information filtering algorithm is needed. If the root mean square information filtering algorithm is required, it is used for approach orbit determination to obtain the estimated state of the approaching probe. If not, the extended Kalman filter algorithm is used for approach orbit determination to obtain the estimated state of the approaching probe. Based on the obtained estimated state of the approaching probe, the approach trajectory of the asteroid probe is planned, and the probe executes guidance and control commands to complete the approach to the target asteroid, and then performs flyby, landing, and rover exploration.

[0038] 2. The present invention discloses an asteroid approach information fusion orbit determination method based on support vector machine, which trains an asteroid approach orbit determination classification model, reduces numerical singularities in computation, and helps to improve orbit determination accuracy.

[0039] 3. The present invention discloses an asteroid approach information fusion orbit determination method based on support vector machine, which improves the accuracy of the trained asteroid approach orbit determination classification model by randomly generating samples.

[0040] 4. The present invention discloses an asteroid approach information fusion orbit determination method based on support vector machine. On the basis of achieving the above three beneficial effects, the present invention has the advantages of high orbit determination accuracy and small estimation error, which helps to reduce the singularity problem in asteroid approach orbit determination calculation and improve the detection capability of the detector during the asteroid approach process.

[0041] 5. The present invention discloses an asteroid approach information fusion orbit determination method based on support vector machine, which expands its application to near-Earth spacecraft motion estimation and Earth-Moon system spacecraft motion estimation by replacing asteroid approach with near-Earth spacecraft motion model and Earth-Moon spacecraft motion model, and solves related technical problems in the field of spacecraft. Attached Figure Description

[0042] Figure 1 This is a flowchart of an asteroid approach information fusion orbit determination method based on support vector machine disclosed in this invention.

[0043] Figure 2 Visualization results of the trained asteroid approach and orbit determination classification model.

[0044] Figure 3 The training and iteration process of the asteroid approach orbit determination classification model.

[0045] Figure 4 This refers to the positional error of the asteroid's approach orbit.

[0046] Figure 5 This refers to the error in the orbit determination velocity when the asteroid approaches. Detailed Implementation

[0047] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0048] This example uses the probe's close approach to the asteroid Bennu as an example to demonstrate how the method proposed in this invention is used to estimate the motion of a maneuvering target on the water surface.

[0049] like Figure 1 As shown in the figure, this example discloses an asteroid approach information fusion orbit determination method based on support vector machine. The specific implementation steps are as follows:

[0050] Step 1: Set the initial approach time of the asteroid probe, the initial state of the asteroid, the initial actual state of the probe, the initial estimated state of the probe, the initial estimated covariance matrix of the probe, the observation interval, and the number of observations.

[0051] The initial time of the asteroid approach is set to t0 = 0. The asteroid's state at the initial time, the actual state of the probe at the initial time, and the estimated state of the probe at the initial time are shown in Table 1.

[0052] Table 1 Initial state

[0053]

[0054] The detector's estimated covariance matrix is ​​set to the following at the initial time:

[0055]

[0056] The observation interval is set to dt = 600s and the number of observations is N = 2880.

[0057] Step 2: Establish a motion model of the asteroid and the probe, and establish an observation model of the asteroid approaching the probe.

[0058] Step 3: Set the number of samples, the upper and lower bounds of the standard deviation of the angle and distance measurement observation noise, and generate samples based on the initial time of the asteroid approach, the asteroid state at the initial time, the actual state of the probe at the initial time, the estimated state of the probe at the initial time, the estimated covariance matrix of the probe at the initial time, the observation interval, the number of observations set in Step 1, as well as the asteroid and probe motion model and the asteroid approach probe observation model established in Step 2.

[0059] Set the number of samples M and the upper bound of the standard deviation of the angle measurement observation noise. Lower bound of standard deviation of angle measurement observation noise Upper bound of the standard deviation of distance measurement observation noise Lower bound of standard deviation of distance measurement observation noise For each sampling point, the upper bound of the standard deviation of the angle measurement observation noise is set. Lower bound of standard deviation of angle measurement observation noise Upper bound of the standard deviation of distance measurement observation noise Lower bound of standard deviation of distance measurement observation noise Randomly generated angle measurement observation noise standard deviation σ l and the standard deviation of ranging observation noise σ d Establish the observation noise matrix R.

[0060] Based on the observation noise matrix R, and using the initial time of the asteroid approach, the asteroid state at the initial time, the actual state of the probe at the initial time, the estimated state of the probe at the initial time, the estimated covariance matrix of the probe at the initial time, the observation interval, and the number of observations set in step one, as well as the asteroid and probe motion model and the asteroid approach probe observation model established in step two, the estimated state of the probe is solved using the extended Kalman filter algorithm and the root mean square information filter algorithm, respectively. For each method, the average estimation error e is calculated.

[0061] The input for this sample is the standard deviation of the angle measurement observation noise, σ. l and the standard deviation of ranging observation noise σ d When the average estimation error obtained by the root mean square information filtering algorithm is less than the average estimation error obtained by the extended Kalman filter algorithm, the output of the sample is defined as 1; otherwise, it is -1.

[0062] Step 4: Train an SVM model based on the samples obtained in Step 3 to obtain an asteroid approach and orbit determination classification model used to identify whether the root mean square information filtering algorithm is needed. The training model is as follows: Figure 2 As shown, the training process is as follows: Figure 3 As shown.

[0063] Step 5: Set the standard deviation σ of the angle measurement observation noise in the simulation scenario. l=10 -5 and the standard deviation of ranging observation noise σ d =10000km, using the asteroid approach orbit determination classification model trained in step four, the identification result indicates that the root mean square information filtering algorithm is needed. The root mean square information filtering algorithm is used for approach orbit determination to obtain the estimated state value of the approaching probe.

[0064] Track positioning error such as Figure 4 As shown, the orbital speed error is as follows: Figure 5 As shown, the final position error is less than 1km and the velocity error is less than 2mm / s.

[0065] Step six: Based on the estimated state of the approaching probe obtained in step five, the approaching trajectory of the asteroid probe is planned. According to the planning results, relevant guidance and control commands for the probe are generated to achieve the approach to the target asteroid, and then the probe will perform fly-around, landing and rover exploration.

[0066] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for orbit determination based on asteroid approach information fusion using support vector machines, characterized in that: Includes the following steps, Step 1: Set the initial approach time of the asteroid probe, the initial state of the asteroid, the initial actual state of the probe, the initial estimated state of the probe, the initial estimated covariance matrix of the probe, the observation interval, and the number of observations; Step 2: Based on the initial state of the asteroid and the probe in Step 1, establish a motion model of the asteroid and the probe, and at the same time establish a model of the asteroid approaching the probe and observing the asteroid. Step 3: Set the number of samples, the upper and lower bounds of the standard deviation of the angle and distance measurement observation noise, and generate samples based on the initial time of the asteroid approach, the asteroid state at the initial time, the actual state of the probe at the initial time, the estimated state of the probe at the initial time, the estimated covariance matrix of the probe at the initial time, the observation interval, and the number of observations set in Step 1, as well as the asteroid and probe motion model and the asteroid approach probe observation model established in Step 2; the input of the samples is the standard deviation of the angle measurement observation noise. and the standard deviation of distance measurement observation noise The output of the sample is defined as 1 or -1, where 1 indicates that the root mean square information filtering algorithm is used and -1 indicates that the extended Kalman filtering algorithm is used. The method for implementing step three is as follows: Set the number of samples Upper bound of the standard deviation of angle measurement observation noise Lower bound of standard deviation of angle measurement observation noise Upper bound of the standard deviation of distance measurement observation noise Lower bound of the standard deviation of distance measurement observation noise ; For each sampling point, the upper bound of the standard deviation of the angle measurement observation noise is set. Lower bound of standard deviation of angle measurement observation noise Upper bound of the standard deviation of distance measurement observation noise Lower bound of the standard deviation of distance measurement observation noise Randomly generated standard deviation of angle measurement observation noise and the standard deviation of distance measurement observation noise Establish the observation noise matrix as follows: Based on the observation noise matrix Based on the initial time of the asteroid approach, the asteroid state at the initial time, the actual state of the probe at the initial time, the estimated state of the probe at the initial time, the estimated covariance matrix of the probe at the initial time, the observation interval, and the number of observations set in step one, as well as the asteroid and probe motion model and the asteroid approach probe observation model established in step two, the extended Kalman filter algorithm and the root mean square information filter algorithm are used to solve the estimated state of the probe, respectively. The average estimation error is calculated according to formula (8). as follows: For the initial moments of asteroid exploration approach, The number of observations; the input for this sample is the standard deviation of the angle measurement observation noise. and the standard deviation of distance measurement observation noise When the average estimation error obtained by the root mean square information filtering algorithm is less than the average estimation error obtained by the extended Kalman filtering algorithm, the output of the sample is defined as 1; otherwise, it is -1. Step 4: Train an SVM model based on the samples obtained in Step 3 to obtain an asteroid approach and orbit determination classification model for identifying whether the root mean square information filtering algorithm is needed. Step 5: For a given asteroid approach and orbit determination scenario, use the asteroid approach and orbit determination classification model trained in Step 4 to determine whether the root mean square information filtering algorithm is needed; if the root mean square information filtering algorithm is needed, then use the root mean square information filtering algorithm to perform approach and orbit determination and obtain the estimated state value of the approaching probe. If not required, the extended Kalman filter algorithm is used for approach orbit determination to obtain the state estimate of the approaching probe, that is, the asteroid approach information fusion orbit determination is realized based on support vector machine.

2. The asteroid approach information fusion orbit determination method based on support vector machine as described in claim 1, characterized in that: It also includes step six, which involves planning the asteroid probe's approach trajectory based on the approach probe state estimate obtained in step five, generating guidance and control commands for the probe to approach the target asteroid, and then conducting fly-around, landing, and rover exploration of the probe.

3. The asteroid approach information fusion orbit determination method based on support vector machine as described in claim 1 or 2, characterized in that: The implementation method for step one is as follows: Setting the initial moment of asteroid probe approach Set the initial state of the asteroid. for: in This represents the x-component of the asteroid's position in an inertial frame of reference. This represents the position component of the asteroid in the y-direction in an inertial frame. This represents the z-axis position component of the asteroid in an inertial frame of reference. This represents the asteroid's velocity component in the x-direction within an inertial frame. This represents the y-axis velocity component of the asteroid in an inertial frame of reference. This represents the z-axis velocity component of the asteroid in an inertial frame of reference. Set the detector's true state at the initial moment for: in This represents the true position component of the detector in the x-direction in the inertial frame. This represents the true position component of the detector in the y-direction in the inertial frame. This represents the true position component of the detector in the z-direction in the inertial frame. This represents the actual velocity component of the detector in the x-direction in the inertial frame. This represents the actual velocity component of the detector in the y-direction in the inertial frame. This represents the actual velocity component of the detector in the z-direction in the inertial frame. Set the detector estimated state at the initial time. for: in This indicates the estimated position component of the detector in the x-direction in the inertial frame. This indicates that the detector estimates its position component in the y-direction in an inertial frame. This indicates the estimated position component of the detector in the z-direction in the inertial frame. This indicates that the detector estimates the velocity component in the x-direction in the inertial frame. This indicates that the detector estimates the velocity component in the y-direction in the inertial frame. This indicates the estimated velocity component of the detector in the z-direction in the inertial frame. The detector covariance matrix is ​​estimated at the initial time. Observation interval Number of observations .

4. The asteroid approach information fusion orbit determination method based on support vector machine as described in claim 3, characterized in that: The second step is implemented as follows: The motion model of the detector is established as follows: in Represents the solar gravitational constant. Indicates time ; The asteroid motion model is established as follows: The following is a model for the probe's observation of asteroids: in The x-direction component of the line-of-sight vector obtained from angle measurement observation. The y-direction component of the line-of-sight vector obtained from angle measurement observation. The z-direction component of the line-of-sight vector obtained from angle measurement observation. For radar ranging, , , as well as This represents measurement error.

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