Ring fire track passive angle measurement initial orbit determination method for Mars sampling return

Abstract

The invention discloses an initial orbit determination method for passive angle measurement of a ring fire orbit for Mars sampling return, and the method comprises the steps: building an absolute dynamic model, obtaining an absolute motion state of a spacecraft, and deducing a relative motion state X; constructing a data set by using the measurement quantities H and X of the sensor; a network architecture is designed, input data I are position and speed coordinates of the tracker in a Mars equator inertial coordinate system and angle information converted from H, and output data are X; and finally, adjusting an observation interval dt and times k according to a ring fire observation condition, training a physical information neural network by using limited observation data, defining a total loss function F comprising a loss function FY and a physical law penalty term FD, and optimizing a weight coefficient and bias by minimizing the loss function through an F gradient descent method. According to the method, the neural network is trained offline, a network mapping model from a target line-of-sight angle measurement sequence to a target orbit is constructed, and the network mapping model is solidified on a returner for online use, so that sampler short-arc passive measurement rapid orbit determination is realized.

Description

Technical Field

[0001] The present invention relates to the field of spacecraft relative navigation, and in particular to a method for initial orbit determination of a Mars orbit with passive angle measurement for Mars sampling return. Background Art

[0002] In recent years, human space launch missions have gradually increased, and deep space exploration activities have been further developed. my country has formulated the "orbit-land-return" Mars exploration trilogy, and has now entered the stage of tackling the sampling and return mission. In order to realize the Mars sampling and return mission, it is necessary to complete the rendezvous and docking of the returner and the sampler in the Mars orbit. Since there is no navigation satellite system deployed in the Mars orbit, the relative satellite navigation scheme commonly used for Earth orbit rendezvous cannot be adopted. At the same time, due to the long distance between the Earth and Mars, the ground measurement and control delay is very large, so the rendezvous navigation method of ground measurement and control cannot be sampled. However, the launch and use costs of active relative measurement sensors with large mass and high power consumption, such as microwave radar, are too high, and they are not suitable for Mars sampling return rendezvous and docking in the Mars orbit. Therefore, the Mars orbit rendezvous relative measurement scheme based on passive angle measurement of optical cameras is an inevitable choice.

[0003] However, passive angle measurement can only measure the line of sight angle information of the target, lacking distance information, and the relative orbit state of the target is weakly observable or even unobservable. At present, there are no reports on the passive angle measurement relative navigation orbit determination method for circum-Mars orbit rendezvous at home and abroad.

[0004] The traditional Earth orbit relative navigation orbit determination method has problems such as long measurement arc, large amount of calculation, and the need for initial value guessing with a certain accuracy. It is difficult to use it for the autonomous rendezvous and docking mission of Mars sample return. Summary of the invention

[0005] In view of the fact that the existing technology cannot solve the relative navigation problem in the Mars sampling return mission, the present invention provides a method for initial orbit determination of the Mars orbit passive angle measurement for Mars sampling return. The method uses the designed physical information neural network for offline training, constructs a network mapping model from the target's line of sight angle measurement sequence to the target orbit, and solidifies it on the returner for online use, so as to realize the rapid orbit determination of the sampler by short arc passive measurement.

[0006] Step 1: Establish an absolute dynamics model considering the non-spherical perturbation of Mars and the gravitational perturbation of the Sun, obtain the absolute motion state of the spacecraft through orbital integration, and derive the relative motion state X;

[0007] Step 2, constructing a data set of a physical information neural network using the measurement quantity H measured by the sensor in the track system and the relative motion state X;

[0008] Step 3: Design the physical information neural network architecture and construct the physical law penalty term , where the input data The position and velocity coordinates of the tracker in the Martian equatorial inertial coordinate system and the angle information converted from the measured quantity are output as the relative motion state X;

[0009] Step 4: Adjust the observation interval dt and the number of times k according to the ring fire observation conditions, train the physical information neural network with limited observation data, and use the gradient descent method to minimize the loss function to optimize the weight coefficient and bias, so as to obtain the optimal parameter configuration.

[0010] As a preference, in step 1, the relative motion state , where R and V represent the relative position and relative velocity vector between the target spacecraft and the tracker in the orbital system, , ,in, , , and , , They respectively represent the three-axis relative position coordinates and three-axis relative velocity coordinates of the target and the tracker in the local horizontal and local vertical orbit coordinate system with the tracker's center of mass as the origin.

[0011] Preferably, in step 2, the target orbit parameters in the time period m are determined by orbit integration according to the dynamic model and the measurement quantity H; in order to increase the diversity of training data, the initial orbit parameters of the targets within the scatter range L are uniformly selected according to the scatter range L of the initial target orbit entry; in addition, the input of the neural network is and output The minmax transformation is used to map the data to the interval [-1, 1] to improve the efficiency of the neural network during training and prediction.

[0012] Preferably, in step 2, the measured quantity is expressed as ,in , , is the relative position of the target and the observing spacecraft, and are the measurement noise of the elevation angle and azimuth angle, respectively.

[0013] As a preference, the physical law penalty term in step 3 is the acceleration residual in two-body mechanics, which is defined as in, is the known acceleration of the target spacecraft, and is the target acceleration estimated by the network. and It is the non-spherical perturbation and the solar gravitational perturbation. is the Martian gravitational term, is the Martian gravitational constant.

[0014] Preferably, the data set includes output data X and input data , ,in, , , and , , They are the three-axis position coordinates and three-axis velocity coordinates of the tracker in the Martian equatorial inertial system.

[0015] Preferably, for the nth training sample, the minmax transformation normalization process of the kth dimension feature of the ith sample data is as follows: In the formula, and are the maximum and minimum values ​​in the k-th dimension feature respectively.

[0016] Preferably, in step 4, training the physical information neural network includes: transforming a set of measured quantities at time i according to the number of observations k , , … and the motion state of the tracker at the corresponding moment, that is, the position velocity vector, as the input of the neural network, and the relative motion state at the initial moment of observation as the output of the network; in the forward propagation process, the weight coefficient w and bias b in the neural network structure are randomly initialized in advance and are adjusted by the loss function and The optimal parameters are determined by the gradient descent method; the physical information neural network is trained separately to obtain the optimal angle measurement-only orbit determination model under simulation conditions.

[0017] As a preferred option, the input layer of the physical information neural network only plays the role of transmitting data, and the hidden layer is activated by the activation function The input data is transformed nonlinearly, and the output layer performs weighted summation on the data of the hidden layer and then outputs it. The number of neurons in the input layer is determined by the number of input parameters N. Under the condition of n angle measurement sequences, .

[0018] Preferably, the activation function is the Gaussian kernel function, defined as: In the formula, let The samples are , the center of the i-th hidden layer node is , is the width of the hidden layer kernel function; the hidden layer contains p neurons.

[0019] As a preference, the total loss function , is the weight parameter;

[0020] Loss Function The mean square error between the network prediction value and the true value of the target relative motion state is: In the formula, is the relative motion state between the tracker and the target estimated by the neural network, is the true value of the relative motion state between the tracker and the target;

[0021] Physical Law Penalty for: In the formula, is the known acceleration of the target spacecraft, and It is the non-spherical perturbation and the solar gravitational perturbation. is the Martian gravitational term, is the Martian gravitational constant.

[0022] Beneficial Effects

[0023] (1) The present invention can use the physical information neural network to initially determine the orbit of Mars under sparse angle measurement conditions, with short orbit determination time and good position estimation accuracy;

[0024] (2) The algorithm of the present invention can make a relatively accurate estimate of the target position in the initial orbit determination of the Mars orbit, providing a basis for the subsequent Mars rendezvous and docking mission;

[0025] (3) The present invention is mainly aimed at the coplanar orbit of Mars. The algorithm has better generalization performance under general observation conditions and better relative orbit configuration, and has a wide range of applications;

[0026] (4) The present invention constructs an offline database, establishes a Mars orbit dynamics model, trains the physical information neural network, and then uses it for real-time initial orbit determination. It is easy to use and has a short calculation time. At the same time, offline training reduces the demand for onboard computing resources and reduces the dependence on computing resources in real time, thus achieving highly reliable Mars rendezvous orbit determination.

[0027] (5) The present invention balances the observed data and physical laws to construct a total loss function. The physical law penalty term evaluates the performance of the neural network by comparing the difference between the target acceleration predicted by the neural network and the target acceleration calculated by the known physical laws. This ensures that the prediction of the neural network is accurate while ensuring that it complies with the principles of physics, thereby improving the reliability and practicality of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1A schematic diagram of a quantity measurement and estimation trajectory according to an embodiment of the present invention;

[0029] Figure 2 The measurement interval is 60s for one implementation test set of the present invention, and the average absolute percentage error of the orbit position determined by three angle measurements;

[0030] Figure 3 The average absolute percentage error of orbital position determination of 6 angle measurements with a measurement interval of 60s for an implementation test set of the present invention;

[0031] Figure 4 The average absolute percentage error of the orbital position of three angle measurements with a measurement interval of 90s for an implementation test set of the present invention;

[0032] Figure 5 The average absolute percentage error of orbital position determination of 6 angle measurements with a measurement interval of 90s for an implementation test set of the present invention;

[0033] Figure 6 The figure is a histogram of the mean absolute percentage error of the track determination distance under four measurement conditions of a test set for an implementation of the present invention. DETAILED DESCRIPTION

[0034] The following will be combined with the accompanying drawings in the examples of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0035] The present invention discloses a method for initial orbit determination in a Mars orbit using passive angle measurement for sample return from Mars. Aiming at the challenges of poor observation conditions and long telemetry and remote control delay during rendezvous and docking in a Mars orbit, a physical information neural network orbit determination module suitable for long-distance rendezvous and docking is constructed and trained based on existing historical measurements and orbit data. The method can quickly and relatively accurately estimate the position of a target relative to a tracker in a coplanar orbit under sparse measurements, while satisfying the initial orbit determination requirements under the dispersion range of the target when entering orbit.

[0036] like Figure 1 As shown, a passive initial orbit determination method for a non-cooperative target around fire based on a physical information neural network includes the following steps:

[0037] Step 1: Consider the non-spherical perturbation of Mars under the two-body problem and solar gravitational perturbations , construct an absolute dynamics model, and obtain the absolute motion state of the spacecraft by the orbital integration of the absolute dynamics model, and further obtain the relative motion state X in the orbital system.

[0038] Specifically, the Mars non-spherical perturbation considered in this application is include , , Perturbation coefficient. and solar gravitational perturbations Specifically, they are: , where is the Martian gravitational constant; X, Y, Z are the three-axis coordinates of the spacecraft in the Martian equatorial inertial system; r is the distance from the Martian center to the spacecraft; and is the perturbation coefficient considered is the auxiliary angle; is the mean equatorial radius of Mars.

[0039] , In the formula, is the solar gravitational constant; is the position vector of the sun relative to Mars; is the position vector of the detector relative to the sun, .

[0040] The relative motion state is , R, V represent the relative position and relative velocity vector between the target spacecraft and the tracker in the orbital system, specifically: , , where x, y, and z represent the three-axis relative position coordinates of the target and the tracker in the local horizontal and local vertical orbit coordinate system with the center of mass of the tracker as the origin. , , It represents the three-axis relative velocity coordinates of the target and the tracker in the local horizontal and local vertical orbit coordinate system with the center of mass of the tracker as the origin.

[0041] Step 2: Obtain the measurement quantity H measured by the sensor in the orbit system, and combine it with the relative motion state X in step 1 to construct the data set required for physical information neural network training and testing. The data set includes: input data and output data; the position, velocity, measured azimuth and pitch angle of the tracker during the orbit integration period; the position and velocity of the target. The initial position and velocity of the tracker and the target are converted from the orbit parameters of the tracker and the target, and then integrated to obtain all the training data in the time period.

[0042] Specifically,

[0043] Step 2.1, obtain the measurement quantity H measured by the sensor in the orbit system, , where and They are the pitch angle and azimuth angle measured in the orbital system, and their specific forms are as follows: , , where x, y, z are the relative positions of the target and the observation spacecraft, and are the measurement noise of the elevation angle and azimuth angle, respectively.

[0044] According to the dynamic model and the measurement H described in step 1, the target orbit parameters in time period m are determined by orbit integration (the training data period is m seconds). In this embodiment, the training period length is 10 times the tracker orbit period, which is 68226 seconds, that is, m is 68226.

[0045] Step 2.2, according to the initial orbital dispersion range L of the target, the initial orbital parameters of the target are changed (i.e., the initial orbital parameters of the target within the dispersion range L are uniformly selected) to diversify the training data. The target orbital dispersion range L is specifically: the semi-major axis changes , orbital inclination changes , true anomaly change , the right ascension of the ascending node changes , eccentricity change The output data of the neural network is the relative motion state X, and the input data It is composed of the known tracker motion state and the measured pitch angle and azimuth angle sequence, and its specific form is as follows: Among them, X, Y, Z are the three-axis position coordinates of the tracker in the Martian equatorial inertial system. , , are the three-axis velocity coordinates of the tracker in the Martian equatorial inertial system. and They are the pitch angle and azimuth angle measured in the orbital system, respectively. get.

[0046] Step 2.3: Input the neural network and output The minmax transformation is used to map the data to the interval [-1, 1] to improve the efficiency of the neural network during training and prediction.

[0047] For the nth training sample, the minmax transformation normalization process of the kth dimension feature of the i-th sample data is as follows: In the formula, and are the maximum and minimum values ​​in the k-th dimension feature respectively.

[0048] It should be noted that: input data For example, its dimension is 8. In all training data, the position, speed, and observation angle of the target have maximum and minimum values.

[0049] Step 3: Construct a physical neural network. The physical information neural network is divided into three layers: input layer, hidden layer, and output layer. The input layer only plays the role of transmitting data, and the hidden layer is activated by the activation function. The input data is transformed nonlinearly, and the output layer performs weighted summation on the data in the hidden layer and then outputs it. The number of neurons is determined by the number of input parameters N. Activation function Choose a Gaussian kernel function, defined as: In the formula, let The samples are , the center of the i-th hidden layer node is , is the width of the hidden layer kernel function. The hidden layer contains n neurons, and the connection weights are expressed as , and k is the number of neurons in the output layer. The number of input parameters of the neural network is determined by the number of angle measurements. Under the condition of n angle measurement sequences, .

[0050] Step 4, training the physical information neural network: in view of the limited conditions of the ring fire observation, the observation interval dt and the number of observations k are changed accordingly, that is, when the transmission bandwidth is limited, the sampling frequency is reduced, the number of sparse measurements is k, and the observation interval dt is dynamically adjusted to reserve redundancy.

[0051] A set of measurements ( , , … ) and the motion state of the tracker at the corresponding moment are used as the input of the neural network, and the relative motion state X corresponding to the initial moment of observation is used as the output of the network. In the equation, the subscript i is the i-th measurement time, and the subscript k is the number of measurements k. In the forward propagation process, the weight coefficients w and bias b in the neural network structure are randomly initialized in advance, and the optimal parameters are determined by including the loss function and The total loss function F is realized by the gradient descent method. The physical information neural network is trained separately to obtain the optimal orbit determination model of only angle measurement under simulation conditions. In this embodiment, the observation interval dt is taken as 60 seconds and 90 seconds respectively, and the number of observations k is taken as 3 times and 6 times respectively.

[0052] The weight coefficient w and bias b in the neural network are initially given by the following formula: in, and are the i-th weight coefficient and i-th bias in the neural network, and Generates uniformly distributed random numbers.

[0053] The overall loss function used to determine the optimal hyperparameters is defined as , is the weight parameter. Among them, the loss function is the mean square error between the target relative motion state network prediction value and the true value, which is used to measure the difference between the predicted value and the true value, expressed as: In the formula, is the relative motion state between the tracker and the target estimated by the neural network, is the true value of the relative motion state between the tracker and the target.

[0054] Physical Law Penalty It is a physical law penalty term, which is used to ensure that the prediction results conform to the known physical laws. The performance is evaluated by comparing the difference between the target acceleration predicted by the neural network and the target acceleration calculated by the known physical laws, which is expressed as: In the formula, is the known acceleration of the target spacecraft, and It is the non-spherical perturbation and the solar gravitational perturbation. is the Martian gravitational term, is the Martian gravitational constant, is the target acceleration estimated by the neural network.

[0055] The total loss function combines the observed data and physical laws. By minimizing this total loss function, the neural network can not only learn how to accurately predict the motion state of the target, but also ensure that its prediction results conform to the known physical laws, thereby improving the reliability and practicality of the model.

[0056] Step 5: Initial passive orbit determination of a non-cooperative target around a fire. The same operation as step 2 is used to obtain the test data set, define the error index Q, and give the physical information neural network orbit determination error analysis. The error performance index is defined as the mean absolute percentage error , Root Mean Square Error , specifically: In the formula is the ith one of the estimated n target relative motion states, is the true value of the corresponding estimate.

[0057] The feasibility of the present invention is illustrated with reference to the following examples.

[0058] Set the following calculation conditions and technical parameters:

[0059] 1) The initial orbital elements of the target spacecraft are: semi-major axis 3996.190 km, eccentricity 0, orbit inclination 29°, ascending node right ascension 164°, perigee argument 0°, true anomaly 73°.

[0060] 2) The initial orbital elements of the tracking spacecraft are: semi-major axis 3996.230 km, eccentricity 0, orbital inclination 30°, ascending node right ascension 165°, perigee argument 0°, true anomaly 60°

[0061] 3) The pitch angle and azimuth angle measurement noise in the measurement H is taken as 10 -5 rad Gaussian white noise.

[0062] 4) The training orbit period is 68000s, which is 10 times the orbit period of the tracker; the test orbit period is 13000s, which is 2 times the orbit period of the tracker.

[0063] 5) The number of measurements is 3 and 6 respectively; the observation interval is 60 seconds and 90 seconds respectively, and the corresponding number of measurement groups is 4.

[0064] 6) Tracker track error is 5 km ( ), 0.5 m / s( ), the optical camera measurement distance is less than or equal to 1000km.

[0065] Based on the present invention, relevant simulation verification is performed using the measured angle data and the absolute motion state of the tracker and the calculation conditions and technical parameters set above, and the simulation time is 13645s. Figure 2 and Figure 3 The mean absolute percentage errors of orbit determination at 60s, 3 angle measurements and 60s, 6 angle measurements are given respectively; Figure 4 and Figure 5 The average absolute percentage errors of 90s, 3 angle measurements and 90s, 6 angle measurements are given. As can be seen from the figure, large single-axis percentage errors appear in the target simulation tracks 1, 3, and 9. However, the relative motion on the y-axis and z-axis is small compared to the x-axis, within the kilometer level. When rendezvousing and docking at a long distance of nearly 1,000 kilometers, the tracker only needs to aim in one direction to approach the target, and its impact can be ignored. Track 0 in the test set is the initial target track, and the orbit position error is within 4%. Within the target orbital scatter range, the average absolute percentage error of the three-axis x, y, and z estimates of the neural network position is basically within 8%.

[0066] Figure 6 This is the overall orbit determination distance error histogram. It can be seen intuitively that as the number of measurements increases, the overall orbit determination accuracy of PINN improves. As the measurement interval increases, the overall orbit determination accuracy improves, and the accuracy is within 6%.

[0067] Therefore, by adopting the method of the present invention, passive initial orbit determination of non-cooperative targets in the Mars coplanar orbit can be achieved using only offline orbit data training, and the orbit determination accuracy is within 4%. In addition, the target position prediction accuracy can be within 8% during the initial orbit entry with uncertain targets, and the generalization performance is good.

[0068] In view of the weak observability of the co-planar orbit of Mars and the scattered range of the target's initial orbit entry during rendezvous and docking, the present invention uses a physical information neural network to construct a physical law penalty term under the conditions of low angle measurement frequency and sparse angle measurement times, and integrates the random error of the tracker's absolute orbit into the physical information neural network training process, thereby realizing space-based passive rapid and high-precision initial orbit determination for non-cooperative targets around Mars in the presence of angle measurement noise.

[0069] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for initial orbit determination of a Mars orbit with passive angle measurement for Mars sample return, characterized in that: include: Step 1: Establish an absolute dynamics model considering the non-spherical perturbation of Mars and the gravitational perturbation of the Sun, obtain the absolute motion state of the spacecraft through orbital integration, and derive the relative motion state X; Step 2, constructing a data set of a physical information neural network using the measurement quantity H measured by the sensor in the track system and the relative motion state X; Step 3: Design the physical information neural network architecture, where the input data The position and velocity coordinates of the tracker in the Martian equatorial inertial coordinate system and the angle information converted from the measured quantity, and the output data is the relative motion state X; Step 4: adjust the observation interval dt and the number of observations k according to the ring fire observation conditions, train the physical information neural network with limited observation data, and define the loss function including and the physical law penalty The total loss function F is minimized by the gradient descent method of the total loss function F to optimize the weight coefficients and biases, thereby obtaining the optimal parameter configuration.

2. The initial orbit determination method according to claim 1, characterized in that: In step 1, the relative motion state , where R and V represent the relative position and relative velocity vector between the target spacecraft and the tracker in the orbital system, , ,in, , , and , , They respectively represent the three-axis relative position coordinates and three-axis relative velocity coordinates of the target and the tracker in the local horizontal and local vertical orbit coordinate system with the tracker's center of mass as the origin.

3. The initial orbit determination method according to claim 2, characterized in that: In step 2, the target orbit parameters in the time period m are determined by orbit integration according to the dynamic model and the measurement quantity H; in order to increase the diversity of training data, the initial orbit parameters of the targets within the scatter range L are uniformly selected according to the scatter range L of the initial target orbit entry; In addition, the input of the neural network and output It is mapped to the interval [-1, 1] through minmax transformation to improve the efficiency of the neural network in the training and prediction process.

4. The initial orbit determination method according to claim 3, characterized in that: In step 2, the measured quantity is expressed as ,in , , is the relative position of the target and the observing spacecraft, and are the measurement noise of the elevation angle and azimuth angle, respectively.

5. The initial orbit determination method according to claim 3, characterized in that: The data set includes output data X and input data , ,in, , , and , , They are the three-axis position coordinates and three-axis velocity coordinates of the tracker in the Martian equatorial inertial system.

6. The initial orbit determination method according to claim 3, characterized in that: For the nth training sample, The minmax transformation normalization process of the k-th dimension feature of the sample data is as follows: In the formula, and are the maximum and minimum values ​​in the k-th dimension feature respectively.

7. The initial orbit determination method according to any one of claims 1 to 6, characterized in that: In step 4, training the physical information neural network includes: transforming a set of measured quantities at time i into , , … and the corresponding tracker motion state, i.e., the position velocity vector, as the neural network input, and the relative motion state X corresponding to the initial observation time as the network output; in the forward propagation process, the weight coefficient in the neural network structure and bias Initialize randomly in advance and pass and The optimal parameters are determined by the gradient descent method; the physical information neural network is trained separately to obtain the optimal angle measurement-only orbit determination model under simulation conditions.

8. The initial orbit determination method according to claim 7, characterized in that: The input layer of the physical information neural network only plays the role of transmitting data, and the hidden layer is composed of the activation function The input data is transformed nonlinearly, and the output layer performs weighted summation on the data of the hidden layer and then outputs it. The number of neurons in the input layer is determined by the number of input parameters N. Under the condition of n angle measurement sequences, .

9. The initial orbit determination method according to claim 7, characterized in that: The activation function is the Gaussian kernel function, defined as: In the formula, let The samples are , No. The center of the hidden layer nodes is , is the width of the hidden layer kernel function; the hidden layer contains p neurons.

10. The initial orbit determination method according to claim 7, characterized in that: In step 4, the total loss function , is the weight parameter; Loss Function The mean square error between the network prediction value and the true value of the target relative motion state is: In the formula, is the relative motion state between the tracker and the target estimated by the neural network, is the true value of the relative motion state between the tracker and the target; Physical Law Penalty for: In the formula, is the known acceleration of the target spacecraft, and It is the non-spherical perturbation and the solar gravitational perturbation. is the Martian gravitational term, is the Martian gravitational constant.

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