CN112797988A - Unknown maneuvering spacecraft orbit determination method based on neural network - Google Patents
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Abstract
The invention discloses a neural network-based unknown maneuvering spacecraft orbit determination method, and belongs to the technical field of navigation and orbit determination. The implementation method of the invention comprises the following steps: establishing a non-cooperative spacecraft dynamics equation, generating sample points required by neural network training according to different maneuvering modes and a preset observation mode, and calculating the orbit position and maneuvering of the non-cooperative spacecraft corresponding to the sample points; based on the obtained sample points, calculating the weight of the neural network in an iterative updating mode by taking the root mean square error as a loss function to obtain the off-line trained neural network; and inputting the continuous line-of-sight angle information observed in the orbit determination task of the non-cooperative spacecraft into a neural network obtained by training, wherein the output of the neural network is the orbit state and maneuvering acceleration information of the non-cooperative spacecraft at the current moment. The invention has less calculation amount when applying the trained BP neural network, and is suitable for online application. The method can provide technical support and reference for autonomous navigation of the non-cooperative spacecraft.
Description
Technical Field
The invention relates to a method for determining an orbit of a non-cooperative spacecraft with an unknown maneuvering mode, belonging to the technical field of navigation and orbit determination.
Background
The autonomous relative navigation of the non-cooperative spacecraft is used as a key technology in the process of realizing space rendezvous and docking with the non-cooperative spacecraft, is one of the key development directions of the space on-orbit service technology, and has important theoretical value and engineering significance in research. In order to ensure the accuracy and reliability of relative autonomous navigation, the non-cooperative spacecraft orbit determination is carried out by using Kalman filtering and an expansion method thereof under the normal condition. However, the use of the kalman filter algorithm is premised on a relatively accurate dynamic model, and when the non-cooperative spacecraft has an unknown maneuvering mode, the unknown maneuvering mode is difficult to model, so that the kalman filter algorithm cannot be used. Therefore, the orbit determination algorithm is required to have high-precision orbit determination capability for the spacecraft with the unknown maneuvering mode.
Disclosure of Invention
The invention discloses a neural network-based unknown maneuvering spacecraft orbit determination method, which mainly solves the technical problems that: under the condition that the maneuvering mode of the non-cooperative spacecraft is unknown, the orbit state and the maneuvering acceleration of the non-cooperative spacecraft, the position of which is unknown, can be accurately estimated through the off-line sampling training of the neural network and the application of the training result to the on-line orbit determination task of the non-cooperative spacecraft after a period of observation. The invention has the advantages of high precision and high efficiency. The method can provide technical support and reference for autonomous navigation of the non-cooperative spacecraft and solve the related engineering problems.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a method for determining an unknown maneuvering spacecraft orbit based on a neural network. And calculating the weight of the neural network by taking the root mean square error as a loss function and adopting an iterative updating mode based on the obtained sample points so as to obtain the off-line trained neural network. And inputting the continuous line-of-sight angle information observed in the orbit determination task of the non-cooperative spacecraft into a neural network obtained by training, wherein the output of the neural network is the orbit state and maneuvering acceleration information of the non-cooperative spacecraft at the current moment. In addition, the invention has simple and convenient calculation process and small calculation amount when the trained BP neural network is applied, and is suitable for online application.
The invention discloses an unknown maneuvering spacecraft orbit determination method based on a neural network, which comprises the following steps:
step 1: establishing a non-cooperative spacecraft dynamics equation, generating sample points required by neural network training according to different maneuvering modes and a preset observation mode, and calculating the orbit position and maneuvering of the non-cooperative spacecraft corresponding to the sample points.
The dynamics of the near-earth non-cooperative spacecraft meet the following dynamic equation
Wherein r | | | represents the distance from the earth center, and a is unknown controlled quantity. Respectively determining initial orbits of an observation spacecraft and a target spacecraft, and setting a spacecraft maneuvering mode, wherein the spacecraft maneuvering mode comprises constant acceleration and trigonometric function acceleration. Aiming at different forms of acceleration, the orbit determination of the non-cooperative spacecraft is carried out by adopting a mode of determining the orbit by measuring the view angle for preset continuous times, namely t is ti-n,ti-n+1,…,ti,…ti+n-1,ti+nAngle measurement data of time, wherein 2n +1 is continuous observation times, and t is determinediThe track position and maneuver at the moment, so there are sample point correspondences input and output as follows:
wherein the angle measurement, i.e. the line of sight angle, is a three-dimensional unit vector; the track position and the maneuvering are three-dimensional variables.
The method comprises the steps of generating sample points according to different preset maneuvering modes and observation modes based on an established non-cooperative spacecraft dynamics equation (1), and calculating the orbit position and maneuvering of the non-cooperative spacecraft corresponding to the sample points based on an equation (2).
Step 2: and (3) calculating the weight of the neural network in an iterative updating mode by taking the root mean square error as a loss function based on the sample points obtained in the step (1) so as to obtain the off-line trained neural network.
The neural network training belongs to a regression problem, so that the mean square error between a network output value and an expected value is selected as an index for evaluating the predictive performance of the deep neural network model in the training process, and the index is a loss function. The closer the mean square error is to 0, the better the performance of the neural network. Meanwhile, in order to avoid the phenomenon of overfitting, an L2 regularization term is introduced into the loss function, and certain constraint is applied to the weight of the neural network, so that the weight cannot be taken randomly. The loss function is as follows:
substituting the offline sample points obtained by calculation in the step 1 into the formula (3) to calculate the current loss function value, randomly generating the value of the neural network weight w, continuously updating the weight w according to the current loss function value and recalculating the loss function value, wherein the neural network weight w updating formula is as shown in the formula (4):
and stopping updating when the loss function value is smaller than a preset value, namely finishing the training of the neural network.
And step 3: and (3) inputting the continuous line-of-sight angle information obtained by observation in the orbit determination task of the non-cooperative spacecraft into the neural network obtained in the step (2), wherein the output of the neural network is the orbit state and maneuvering acceleration information of the non-cooperative spacecraft at the current moment.
Inputting the continuous line-of-sight angle information observed in the orbit determination task of the non-cooperative spacecraft into the neural network obtained in the step 2, wherein the output of the neural network is the orbit state and maneuvering acceleration information of the non-cooperative spacecraft at the current moment:
wherein theta isj＝[θjx θjy θjz]TIs the viewing angle information at time j.
Because the BP neural network has the advantages of small calculation amount and high calculation speed, the neural network is preferably the BP neural network.
Advantageous effects
1. The unknown maneuvering spacecraft orbit determination method based on the neural network is based on the existing sample point offline training neural network model, the obtained neural network model can calculate the corresponding non-cooperative spacecraft orbit state and maneuvering acceleration information on line according to the input measurement information, and the maneuvering acceleration information can be obtained without acquiring the maneuvering mode of the non-cooperative spacecraft in advance or modeling the maneuvering mode, so that the unknown maneuvering spacecraft orbit determination method based on the neural network is suitable for the spacecraft orbit determination problem of any maneuvering mode.
2. The unknown maneuvering spacecraft orbit determination method based on the neural network calculates the neural network weight in an iterative updating mode by taking the root mean square error as a loss function based on sample data to obtain the neural network trained offline, can predict the orbit position and state of the non-cooperative spacecraft online, is simple and convenient in calculation process and small in calculation amount, and is suitable for online application.
Drawings
FIG. 1 is a flow chart of a method for determining an unknown aerospace vehicle orbit based on a neural network;
FIG. 2 is a schematic diagram of non-cooperative spacecraft angle measurement and orbit determination;
FIG. 3 is the results of the inorganic behaviour test, in which: FIG. 3(a) is the orbit position estimation result, and FIG. 3(b) is the non-cooperative spacecraft maneuver estimation result;
FIG. 4 is a steady maneuver test result, wherein: FIG. 4(a) is the orbit position estimation result, and FIG. 4(b) is the non-cooperative spacecraft maneuver estimation result;
FIG. 5 is a triangle format maneuver testing result, wherein: FIG. 5(a) is the orbit position estimation result, and FIG. 5(b) is the non-cooperative spacecraft maneuver estimation result;
Detailed Description
For a better understanding of the objects and advantages of the present invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples.
Example 1:
the embodiment aims at the non-cooperative spacecraft with the unknown maneuvering mode, trains the BP neural network off line, and applies the neural network obtained by training to the orbit determination of the flying cooperative spacecraft.
As shown in fig. 1, the method for determining an unknown aerospace vehicle orbit based on a neural network disclosed in this example is specifically implemented as follows:
step 1: generating sample points required by neural network training according to different maneuvering modes and preset observation modes, and calculating the position and maneuvering of the non-cooperative spacecraft orbit corresponding to the sample points.
The problem of angle determination is investigated in the form of determining the track by 21 consecutive measurements, i.e. n is 10 and t is usedi-10,ti-9,…,ti,…ti+9,ti+1Angle data of time, determining tiTrack position at the moment and maneuver.
The sample point acquisition method is as follows: the spacecraft S1 runs on a circular orbit with the height of 7400km, and the initial time position r is [ 74000 ]]T0km, initial velocity v ═ 07.3390]Tkm/S, the initial state of spacecraft S2 is Gaussian with respect to the initial state of spacecraft S1, with a mean of zero and a covariance of the components at relative positions of 1km2The covariance of the relative velocity is 10(m/s)2The mechanical mode is inorganicAnd randomly selecting one of three modes of dynamic, constant maneuvering and trigonometric function form maneuvering. The initial state of 150 space vehicles S2 was sampled randomly, the integration was iterated for 1800 seconds, and the line of sight angle and the orbit position and maneuvering vector of space vehicle S2 were calculated every 60 seconds, and since the orbit was determined by 21 consecutive measurements, 11 sets of sample points were obtained at one time, totaling 1650 sample points.
Step 2: and (3) calculating the weight of the neural network in an iterative updating mode by taking the root mean square error as a loss function based on the sample points obtained in the step (1) so as to obtain the off-line trained neural network.
In the step 1, 1650 sample points are generated in total, 1350 sample points are used for training, the number of BP layers is 2, 100 neurons are provided, wherein the neural network adopts MATLAB function newff, and the convergence condition is set to be that the root mean square error is less than 0.0001.
And step 3: testing the precision of the neural network:
the remaining 300 of the samples were used for the accuracy check, with an average error of 2.334km for tracking and an estimated error of 0.0052m/s for motored acceleration2。
And 4, step 4: and (3) respectively considering the non-cooperative spacecraft in a non-maneuvering mode, a constant acceleration maneuvering mode and a trigonometric function maneuvering mode, inputting continuous line-of-sight angle information obtained by observation in the orbit determination task of the non-cooperative spacecraft into the neural network obtained in the step (2), wherein the output of the neural network is the orbit state and maneuvering acceleration information of the non-cooperative spacecraft at the current moment, such as the figure 3, the figure 4 and the figure 5.
Fig. 3, fig. 4, and fig. 5 show the test results of the no-maneuver, constant acceleration maneuver, and trigonometric function maneuver modes in the test case, respectively, and it can be seen from the figure that the neural network prediction result is almost consistent with the real situation, which illustrates the effectiveness of the method.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (5)
1. An unknown maneuvering spacecraft orbit determination method based on a neural network is characterized in that: comprises the following steps of (a) carrying out,
step 1: establishing a non-cooperative spacecraft dynamics equation, generating sample points required by neural network training according to different maneuvering modes and a preset observation mode, and calculating the orbit position and maneuvering of the non-cooperative spacecraft corresponding to the sample points;
step 2: calculating the weight of the neural network in an iterative updating mode by taking the root mean square error as a loss function based on the sample points obtained in the step 1 so as to obtain the off-line trained neural network;
and step 3: and (3) inputting the continuous line-of-sight angle information obtained by observation in the orbit determination task of the non-cooperative spacecraft into the neural network obtained in the step (2), wherein the output of the neural network is the orbit state and maneuvering acceleration information of the non-cooperative spacecraft at the current moment.
2. The neural network-based unknown aerospace vehicle orbit determination method of claim 1, wherein: the step 1 is realized by the method that,
the dynamics of the near-earth non-cooperative spacecraft meet the following dynamic equation
Wherein r | | | represents the distance from the earth center, a is unknown controlled variable; respectively determining initial orbits of an observation spacecraft and a target spacecraft, and setting a spacecraft maneuvering mode, wherein the spacecraft maneuvering mode comprises a constant acceleration and a trigonometric function acceleration; aiming at different forms of acceleration, the orbit determination of the non-cooperative spacecraft is carried out by adopting a mode of determining the orbit by measuring the view angle for preset continuous times, namely t is ti-n,ti-n+1,…,ti,…ti+n-1,ti+nAngular measurement of timeAccording to which 2n +1 is the number of consecutive observations, t is determinediThe track position and maneuver at the moment, so there are sample point correspondences input and output as follows:
wherein the angle measurement, i.e. the line of sight angle, is a three-dimensional unit vector; the track position and the maneuvering are three-dimensional variables;
the method comprises the steps of generating sample points according to different preset maneuvering modes and observation modes based on an established non-cooperative spacecraft dynamics equation (1), and calculating the orbit position and maneuvering of the non-cooperative spacecraft corresponding to the sample points based on an equation (2).
3. The neural network-based unknown aerospace vehicle orbit determination method of claim 2, wherein: the step 2 is realized by the method that,
the neural network training belongs to a regression problem, so that the mean square error between a network output value and an expected value is selected as an index for evaluating the predictive performance of the deep neural network model in the training process, and the index is a loss function; the closer the mean square error is to 0, the better the performance of the neural network is; meanwhile, in order to avoid the phenomenon of overfitting, an L2 regularization term is introduced into the loss function, and certain constraint is applied to the weight of the neural network, so that the weight cannot be taken randomly; the loss function is as follows:
substituting the offline sample points obtained by calculation in the step 1 into the formula (3) to calculate the current loss function value, randomly generating the value of the neural network weight w, continuously updating the weight w according to the current loss function value and recalculating the loss function value, wherein the neural network weight w updating formula is as shown in the formula (4):
and stopping updating when the loss function value is smaller than a preset value, namely finishing the training of the neural network.
4. The neural network-based unknown aerospace vehicle orbit determination method of claim 3, wherein: the step 3 is realized by the method that,
inputting the continuous line-of-sight angle information observed in the orbit determination task of the non-cooperative spacecraft into the neural network obtained in the step 2, wherein the output of the neural network is the orbit state and maneuvering acceleration information of the non-cooperative spacecraft at the current moment:
wherein theta isj＝[θjx θjy θjz]TIs the viewing angle information at time j.
5. The neural network based unknown aerospace vehicle orbit determination method of claim 1, 2, 3 or 4, wherein: the neural network is a BP neural network.
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