CN115081343B - Space-based passive detection orbit determination method based on neural network combined with genetic algorithm - Google Patents

Space-based passive detection orbit determination method based on neural network combined with genetic algorithm Download PDF

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CN115081343B
CN115081343B CN202210888706.0A CN202210888706A CN115081343B CN 115081343 B CN115081343 B CN 115081343B CN 202210888706 A CN202210888706 A CN 202210888706A CN 115081343 B CN115081343 B CN 115081343B
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龚柏春
马钰权
李爽
廖文和
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a space-based passive detection orbit determination method based on a neural network combined with a genetic algorithm, which defines a spacecraft training data generator and obtains training data; standardizing training data, and training the deep neural network off line through the standardized data; defining an improved multi-population non-dominated sorting genetic algorithm, determining a proper parameter and taking the square sum of the cross product of the unit sight vector and the unit relative position vector and the difference of the product of the unit sight vector and the unit relative position vector and 1 as a fitness function; the improved multi-population non-dominated sorting genetic algorithm is combined with a deep neural network to obtain a non-linear relative motion model only measuring angles and relatively determining orbits, the model is deployed on a perception satellite, relative measurement is input, and online determination of the relative orbit of a target satellite is achieved. According to the invention, the absolute state of the sensing satellite input by the model and the three groups of relative measurement angles are set in a one-to-one mapping mode, so that relative orbit determination of any target on the GEO type orbit is realized.

Description

Space-based passive detection orbit determination method based on neural network combined with genetic algorithm
Technical Field
The invention relates to the technical field of relative orbit determination and navigation of an optical camera, in particular to a space-based passive detection orbit determination method based on a deep neural network and an improved non-dominated genetic algorithm.
Background
With the increasing frequency of space activities, the number of space non-cooperative targets such as failed satellites, space debris and the like is rapidly increased. The near-earth space environment becomes an increasingly worsened trend, and the safety problem of the in-orbit spacecraft is more and more prominent. Therefore, it is of great significance to enhance the spatial situation awareness ability and perform on-orbit autonomous service research such as maintenance and off-orbit cleaning on spatial non-cooperative targets such as failed satellites, and the key premise of performing autonomous on-orbit service and enhancing the spatial situation awareness ability is to achieve autonomous relative orbit determination of the targets.
At present, commonly used satellite-borne measuring sensors in autonomous on-orbit service tasks mainly comprise microwave and laser radars, relative satellite navigation and optical cameras. Wherein, only the optical camera can fully meet the requirements of simple and reliable measuring system, small volume, full autonomy, good concealment and the like when the on-orbit service is carried out on the space non-cooperative target. In addition, the relative orbit determination system based on the passive angle measurement only of the optical camera has natural measurement concealment, so that the system is particularly suitable for completing the relative orbit determination measurement task of a space non-cooperative target.
However, for the linearized observation/relative motion model, the only angular relative orbit determination system has the problem of distance unobservability, i.e. 3 sets of angular observations are not sufficient to determine the relative distance between the perception satellite and the target satellite, and thus the relative motion state quantity cannot be determined.
At present, four main types of starting points exist for solving the problem at home and abroad: 1. starting from complex relative motion dynamics, only the problem of angle measurement relative orbit determination is researched. At present, there is a method for obtaining an approximate relative motion solution by a multidimensional convolution theory and a nonlinear QV series. However, these methods require strong nonlinear terms, and when the nonlinear terms are weak, the generated effects are easily submerged in the measurement error, and these methods are only applicable to the determination of the relative orbit under ideal conditions, and the orbit determination accuracy under the condition of measurement noise interference is still to be improved. 2. And a plurality of groups of angle measurement are generated in a multi-star measurement mode to realize relative orbit determination. According to the method, the auxiliary measurement spacecraft is configured to form the measurement baseline, so that distance information is introduced, and observability is improved. The method is only suitable for a plurality of spacecrafts to cooperatively perform tasks, so that the cost of the satellite is increased. 3. The slave sensor orbits maneuver to solve the observability problem of only goniometric tracking. The method combines the idea of estimating the distance of the track maneuver, but different observability exists in different track maneuvers, and the degree of freedom of relative track guidance is restricted in the actual task. 4. The observability problem of the relative distance is solved by the phenomenon that the measuring camera is arranged to deviate from the mass center of the spacecraft. The method generates observability by superposing independent offset on the basis of linearized motion dynamics, but is only suitable for the short-range rendezvous stage due to the limitation of offset position vector length.
A passive detection orbit determination method based on a deep neural network disclosed in chinese patent publication No. CN113761809B at 12/7/2021, which aims to realize passive detection relative orbit determination by using a method of fitting a nonlinear mapping model from a line-of-sight angle measurement to a relative orbit state based on a deep neural network with stronger orbit curvature capture capability, however, a model/algorithm adopted in the method has relatively accurate estimation of relative distance but relatively low estimation accuracy of relative velocity, and the obtained relative state of a target does not completely conform to a motion law on the orbit thereof, and cannot realize a specific evolution situation of the orbit where the target is located.
Disclosure of Invention
Aiming at the problems of poor estimation precision of orbit determination speed and incomplete conformity with the track rule in the prior art, the invention provides a space-based passive orbit determination method based on a neural network and a genetic algorithm, which can continuously and accurately determine the relative track of a target under the condition of light-weight satellite-borne calculation load.
A space-based passive detection orbit determination method based on neural network combined genetic algorithm comprises the following steps:
step 1, defining a spacecraft training data generator, and obtaining training data of a deep neural network through the data generator; step 2, preprocessing the training data generated in the step 1 to obtain standardized data; step 3, defining a deep neural network, determining appropriate parameters, and training the deep neural network off line through the standardized data; step 4, reducing the spatial range of the solution based on the trained deep neural network, specifically, taking the deep neural network as a boundary dereferencing device of the population individual value, and obtaining the dereferencing range of the population individual; step 5, defining an improved genetic algorithm, including a vector difference variation algorithm, a multi-target genetic algorithm and a multi-population genetic algorithm, obtaining n genetic algorithm populations in the value range of population individuals, and performing iterative optimization based on the improved genetic algorithm; and 6, deploying the nonlinear relative motion model on a perception satellite, and inputting the relative measurement angle into the model to realize the online determination of the relative orbit of the target satellite.
Preferably, step 4 includes step 4.1, inputting the observation angle into the deep neural network, and obtaining a set of initial relative motion states of the space target relative to the observation star; and 4.2, expanding the corresponding value of the initial relative motion state upwards/downwards by a certain proportion to serve as an upper/lower bound of the individual value in the population. And 3, taking the deep neural network as a boundary dereferencer for the individual values in the population in the step 5.
Preferably, step 5 specifically comprises: and 5.1, constructing population individuals and forming n genetic algorithm populations, wherein the population individuals comprise three-dimensional positions and speeds of the target satellite, namely six relative motion states. And 5.2, establishing a non-dominated sorting algorithm based on the multi-target genetic algorithm, wherein the multi-target genetic algorithm comprises two fitness functions which are respectively the sum of squares of cross products of the unit sight vector and the unit relative position vector and the difference between the product of the unit sight vector and the unit relative position vector and 1. And 5.3, establishing a congestion degree sorting algorithm based on the congestion degree comparison operator. And 5.4, performing crossing, variation, sorting and retaining operations on the individuals in each population to realize iterative evolution optimization, wherein the variation is realized based on a vector difference variation algorithm, and the sorting is realized based on a non-dominated sorting algorithm and a congestion degree sorting algorithm. And 5.5, realizing the retention of the optimal individuals based on the multi-population genetic algorithm, specifically, performing mutual information communication on the n populations by using a immigration operator in each iterative evolution optimization process, retaining the optimal individuals in the n populations in each iteration, and taking the change of the optimal individuals in each generation as an iteration termination condition.
Preferably, the intersection and selection operator is selected by simulating binary intersection and elite reservation, the mutation operator is vector difference value mutation, the square sum of the cross product of the unit sight vector and the unit relative position vector and the difference between the product of the unit sight vector and the unit relative position vector and 1 are used as fitness functions to carry out non-dominated sorting, the congestion degree comparison operator is used for carrying out congestion degree sorting, the immigration operator is used as a mode of information exchange between populations, and the manual selection operator and the elite population are used as criteria for judging iterative convergence of the genetic algorithm.
Preferably, the non-dominated sorting algorithm is specifically:
Figure DEST_PATH_IMAGE001
wherein, in the step (A),x 0 is a space target and an observation start 0 The state of the relative motion at the moment of time,u i obtained from images captured by a camerat i The unit line-of-sight vector of the time instant, h(t i ,x 0 )is composed oft i The unit relative position vector of the time-of-day spatial target with respect to the observation star, J 1 is a first fitness function and represents the square sum of the cross product of the unit sight vector and the unit relative position vector at the first k moments,J 2 and the second fitness function represents the difference between the product of the unit sight vector and the unit relative position vector at the first k moments and 1.
Preferably, the congestion degree ranking rule established based on the congestion degree comparison operator in step 5.3 is as follows:
Figure DEST_PATH_IMAGE002
wherein
Figure DEST_PATH_IMAGE003
Is as followsiThe degree of crowding of the individual is, f m is as followsmA fitness function.
Preferably, the simulated binary intersection and the elite reservation are selected as the intersection and selection operators of the population, specifically as follows:
Figure DEST_PATH_IMAGE004
wherein
Figure DEST_PATH_IMAGE005
And
Figure DEST_PATH_IMAGE006
is the firstjTwo different parents in the sub-random selection,
Figure DEST_PATH_IMAGE007
and
Figure DEST_PATH_IMAGE008
is two filial individuals obtained by crossing the two parent individuals,tis the t-th bit vector in the individual,γ j is formed by distribution factorsηAccording to the following steps:
Figure DEST_PATH_IMAGE009
the dynamic random decision is carried out on the basis of the dynamic random decision,u j values are randomly taken and obey a uniform distribution of 0-1. And after the crossing is finished, performing non-dominated sorting and crowding degree sorting on the parent population and the child population, and taking n/2 individuals at the top of each of the parent population and the child population to form a new child population.
Preferably, the vector difference mutation is used as a mutation operator of the population, and the specific steps are as follows:
Figure DEST_PATH_IMAGE010
whereinx 1 (t)、x 2 (t) Andx 3 (t)three different parent individuals randomly selected from the current population,
Figure DEST_PATH_IMAGE011
is an offspring individual generated by the variation of the three parent individuals,tis the first in the individualtA bit vector of the bit-vector,Fis a quantization factor.
Preferably, the immigration operator is used for information exchange among different populations, the optimal individuals in each evolutionary generation of each population are stored through the manual selection operator to form the essence population, and the essence population is used as a basis for judging algorithm convergence, and the method specifically comprises the following steps: find outiIn a populationThe worst individual andjthe best individual in the population, and exchange is carried out untilnAnd transferring the population of the individual population, realizing information interaction between the populations, and sorting the individuals of all the populations through a manual selection operator to select the optimal individual to be placed in the elite population.
Preferably, the elite population is used as a basis for judging the iteration termination of the genetic algorithm, and the method specifically comprises the following steps: the essence population is not subjected to selection, crossing and mutation genetic operations, so that the optimal individuals generated in the evolution process are not damaged or lost, the optimal individuals minimum kept algebra is used as a termination criterion, and iteration is terminated when the same optimal individual continuously keeps a certain algebra.
Has the advantages that:
(1) The invention solves the problem of unobservability of distance only existing in the angle measurement relative orbit determination system, and realizes that relative orbit determination can be realized on line by inputting angle observation quantity through off-line training of a nonlinear relative motion model;
(2) The invention can achieve relative orbit determination with higher precision through an algorithm without additionally introducing equipment;
(3) The invention is suitable for GEO type rails, has wider freedom degree for rail guidance and does not need to increase fuel cost;
(4) The traditional structure of the satellite sensor does not need to be changed, the relative distance of the satellite is not limited, and the degree of freedom for determining the relative orbit is wider;
(5) The deep neural network adopted by the invention has nonlinear model approximation capability, information processing capability and end-to-end one-to-one mapping capability which are not possessed by the traditional method, and the internal relation between the sight measurement angle and the relative motion state can be mastered only by training without accurately knowing the mapping structure parameters of the sight measurement angle and the relative motion state; when data outside the training set is input, a correct mapping relation can be obtained;
(6) According to the method, the absolute motion state of the sensing satellite, the relative motion state between the sensing satellite and the target satellite and the relative measurement angle are used as training data, a deep neural network is trained, and optimization is performed by improving a multi-population non-dominated sorting genetic algorithm, so that the observability of only angle measurement relative orbit determination is greatly improved, and the precision of relative orbit determination is improved;
(7) The invention optimizes the deep neural network algorithm by improving the multi-population non-dominated sorting genetic algorithm, thereby not only improving the stability and the precision of only measuring angles relative to orbit determination, but also solving the problems that the estimation of relative speed is inaccurate and the relative state does not completely accord with the rule of orbital motion in the case of only using the deep neural network algorithm. The load of the spaceborne computer is greatly reduced by adding a mode of improving the multi-population non-dominated sorting genetic algorithm based on online use of neural network offline training, and relative orbit determination under lightweight calculation is realized;
(8) The neural network and the genetic algorithm adopted by the invention are intelligent orbit determination methods, have super-strong nonlinear capturing capability and can realize passive measurement orbit determination based on ultra-short arc sections;
(9) The invention takes the relative orbit determination depth neural network model as a boundary valuator of individual values in the genetic algorithm population, greatly reduces the size of a solution space searched by the genetic algorithm, not only can greatly improve the search efficiency, but also solves the problem that convergence cannot be realized due to overlarge solution space;
(10) The vector difference mutation operator provided by the invention has inherent parallelism, can search cooperatively, accelerates the search speed, realizes the proportion change between parents and offspring, and greatly accelerates the speed of evolution iteration;
(11) In the angle-measuring relative orbit determination only, the unit sight line vector and the relative position vector lack the skew distance relationship, so that infinite suboptimal solutions, namely local optimal solutions, exist near the optimal solution, and the traditional genetic algorithm cannot jump out of the local optimal points in the searching process, so that the accurate solution cannot be obtained. The multi-target genetic algorithm provided by the invention ranks, iterates and evolves populations based on two fitness functions, so that the condition that the optimal solution is submerged in the suboptimal solution due to observation noise of a single fitness function is effectively avoided, the genetic algorithm jumps out of the local optimal solution, and finally converges to the global optimal solution;
(12) The multi-population genetic algorithm provided by the invention changes a single population into a plurality of populations, so that each population evolves towards different directions, and the searching speed is increased; the association and the coevolution among all the populations are controlled by setting immigration operators, so that the optimal evolutionary results of all the populations can be obtained; and (4) setting an essence population to judge whether the convergence is caused, protecting the optimal individual of each generation and solving the problem of early maturity of the genetic algorithm.
Drawings
FIG. 1 is a schematic view of a measurement geometry according to one embodiment of the present invention;
FIG. 2 is a flow diagram of a method of one embodiment of the present invention;
FIG. 3 is a relative position estimate error curve obtained by performing a relative orbit determination, in accordance with one embodiment of the present invention;
FIG. 4 is a graph of relative velocity estimation error obtained by making a relative trajectory determination, in accordance with one embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention discloses a method for realizing angle-only relative orbit determination of a space non-cooperative target based on a deep neural network, which aims at solving the problem that 3 groups of angle observed quantities are insufficient to determine the relative distance between a perception satellite and a target satellite and further cannot determine the relative motion state quantity in the current angle-only relative orbit determination based on a linear relative motion model.
With reference to fig. 1 to 2, a passive detection orbit determination method based on a deep neural network and an improved non-dominated sorting genetic algorithm includes the following steps:
step 1, defining a spacecraft training data generator, and obtaining training data of a deep neural network through the data generator.
Step 1.1, installing an optical camera at the centroid of a perception satellite, and establishing a relative sight measurement model of the optical camera, specifically:
Figure DEST_PATH_IMAGE012
wherein, in the step (A),i Los is a unit line-of-sight vector measurement model,R、‖Rii is the relative position vector and the modulus of the relative position vector respectively,фparameter matrixф=[I 3×3 0 3×3 ] ，X、‖X|, is the target state vector and the modulo of the target state vector, respectively. Simple understanding ofф=[1,0] ，X=[ R,V] T ，фX= R。
Step 1.2, establishing an absolute kinematic model based on the assumption of the two-body problem, the absolute kinematic model only considering the earth non-spherical J 2 The terms perturb and simplify to consider only first-order long-term terms, specifically,
a dynamic model:
Figure DEST_PATH_IMAGE013
；
a kinematic model:
Figure DEST_PATH_IMAGE014
，
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE015
、
Figure DEST_PATH_IMAGE016
is the inertial acceleration of the satellite,rThe position of the satellite under the inertial system,
Figure DEST_PATH_IMAGE017
Is the inertial velocity of the satellite,
Figure DEST_PATH_IMAGE018
、
Figure DEST_PATH_IMAGE019
、
Figure DEST_PATH_IMAGE020
Respectively representing the satellite in the inertial systemx、y、zThe speed of the direction,x、y、zTo respectively represent the satellite under the inertial systemx、y、 zPosition of direction, |rII is the center-to-earth distance of the spacecraft, a J2 Denotes J 2 Acceleration caused by item perturbation, mu is an elliptic gravitational constant, R e Representing the radius of the earth.
And step 1.3, solving the absolute motion dynamics model through Runge Kutta integration to obtain the absolute states of the sensing satellite and the target satellite, and converting coordinates to obtain the final relative motion state of the target satellite.
The invention can obtain the motion models of the perception satellite and the target satellite by establishing a satellite absolute motion dynamic model, the essence of the invention is a set of differential equations related to the position and the speed of the satellite, and a numerical solution, namely the satellite absolute motion state, is obtained by Runge Kutta integration.
And 2, preprocessing the training data generated in the step 1, wherein the training data comprises a relative measurement angle in a relative sight line measurement model of the sensing satellite and an absolute state in an absolute motion dynamics model which are respectively obtained in the step 1.1 and the step 1.2, and the relative motion state obtained in the step 1.3, so as to obtain normalized data.
Firstly, training data is normalized, and normalized data is normalized. Taking a relative measurement angle in a preprocessed relative sight measurement model of the perception satellite and an absolute state in an absolute motion dynamics model as input quantities of a deep neural network; and establishing a mapping relation of a nonlinear relative motion model by taking the preprocessed relative motion state of the target satellite as an output quantity of the deep neural network, namely a label value.
And 3, defining a deep neural network, and training the deep neural network in an off-line manner through the standardized data to obtain a nonlinear relative motion model only with angle measurement and orbit determination.
A deep neural network with 3 hidden layer layers, a ReLU (reconstructed Linear Unit) hidden layer activation function and a purelin output layer activation function is designed, as shown in fig. 3, which is a basic structure diagram of the deep neural network. The deep neural network is totally divided into three parts, each part consists of a plurality of neurons, the first part is an input layer, and input quantity is added in the layer; the second part is a hidden layer, which comprises three layers and is used for processing input quantity; the last part is the output layer, resulting in the final output. In which each neuron in the current layer receives data transmitted from the previous layer, and these data are received by the neuron through weighting processing, and when the total input value exceeds the "threshold value" (also called "bias") of the current neuron, the neuron is activated, and the process is implemented by activation function processing.
The deep neural network adopts an Adam algorithm as a gradient descent optimization algorithm. And taking the Mean Square Error (MSE) of the network output value and the expected value as a loss function in the training process, and expressing the deviation of the mapping relation between the model and the actual data through the loss function so as to evaluate the performance of the deep neural network model. The mean square error is obtained by averaging the square accumulation of the difference between the expected value and the actual value, which means that the smaller the mean square error is, the closer the expected value and the actual value obtained by the model for the whole group of data is, and the closer the fitted model is to the real mapping relationship between the group of data.
And when the loss function is larger than or equal to the preset value, the neural network is continuously trained, and when the loss function is smaller than the preset value, the neural network stops training to successfully obtain the model.
And 4, taking the deep neural network obtained by training as a population individual value boundary dereferencing device in the step 5. Specifically, the observation angle is input into the deep neural network to obtain a group of initial relative motion states of the space target relative to the observation star, and then the corresponding values of the initial relative motion states are expanded upwards/downwards by 30% to serve as upper/lower boundaries of individual values in the population.
Because the individual values in the initial population of the genetic algorithm have no prior information, and the magnitude of the relative distance and the relative speed between satellites in space is huge, the individual value selection range of the population needs to be selected greatly, the genetic algorithm needs to search in a huge solution space, and in addition, countless local optimal solutions exist in the solution space, so that the traditional genetic algorithm cannot converge to an accurate solution even if the search is carried out in a large time range, and relative orbit determination cannot be realized. According to the invention, the relatively accurate relative orbit determination deep neural network model is used as the boundary dereferencing device of the individual values in the genetic algorithm population, so that the size of the solution space searched by the genetic algorithm can be greatly reduced, the search efficiency can be greatly improved, and the problem that convergence cannot be realized due to overlarge solution space is solved.
And 5, defining an improved multi-population non-dominated sorting genetic algorithm, determining a proper parameter, and taking the square sum of the cross product of the unit sight vector and the unit relative position vector and the difference between the product of the unit sight vector and the unit relative position vector and 1 as a fitness function to obtain a plurality of genetic algorithm populations and use the genetic algorithm populations for evolution iteration optimization to obtain a nonlinear relative motion model only with angle measurement and relative orbit determination.
The invention changes a single population into a plurality of populations, each population has controllable parameters including crossing and variation probability and vector difference variation quantization factors, and each population can evolve towards different directions, thereby comprehensively enhancing the searching capability and accelerating the searching speed.
In particular, the method comprises the following steps of,
and 5.1, constructing 5 genetic algorithm populations with six relative motion states of the position, the speed and the like of the target satellite as individuals, wherein the number of the individuals is 200, the cross probability is 0.9, the mutation probability is 1, vector difference value mutation quantization factors are 0.9\0.7\0.5\0.3\0.1 respectively, cross and selection operators are simulated binary cross and elite reservation selection, and mutation operators are vector difference value mutation populations.
Firstly, randomly selecting n/2 individuals twice in n parent individuals, and carrying out analog binary crossing in each random selection.
Specifically, the method comprises the following steps: selecting the simulated binary intersection and the elite reservation as the intersection and selection operators of the population, as follows:
Figure DEST_PATH_IMAGE021
wherein
Figure 857693DEST_PATH_IMAGE005
And
Figure 774833DEST_PATH_IMAGE006
is the firstjTwo different parents in the sub-random selection,
Figure 288991DEST_PATH_IMAGE007
and
Figure 356304DEST_PATH_IMAGE008
is two filial individuals obtained by crossing the two parent individuals,tis the t-th bit vector in the individual,γ j is formed by distribution factorsηAccording to the following steps:
Figure DEST_PATH_IMAGE022
the dynamic random decision is carried out on the basis of the dynamic random decision,u j values were randomly taken and obeyed a uniform distribution of 0-1.
Taking the vector difference variation as a variation operator of the population, specifically as follows:
Figure 701835DEST_PATH_IMAGE010
whereinx 1 (t)、x 2 (t) Andx 3 (t)three different parents randomly selected from the current population,
Figure 258718DEST_PATH_IMAGE011
is an offspring individual generated by the variation of the three parent individuals,tis the first in the individualtA bit vector of the bit-vector,Fis the quantization factor.
After the crossing is finished, performing non-dominated sorting and crowding degree sorting on the parent population and the child population, and taking n/2 individuals from the parent population and the child population to form a new child population; and performing vector difference variation on the crossed offspring.
The vector difference mutation operator disclosed by the invention has inherent parallelism, can search in a collaborative manner and accelerates the search speed; secondly, in the relative orbit determination of only angle measurement, a proportional relation exists between the optimal solution and the suboptimal solution, and the vector difference mutation operator can realize the proportional change between a parent and a child, so that the speed of evolution iteration can be greatly increased.
And 5.2, establishing a fitness function which is the difference between the square sum of the cross product of the unit sight vector and the unit relative position vector and the product of the unit sight vector and the unit relative position vector and 1, wherein the smaller the individual fitness value is, the closer the unit relative position vector generated by the individual is parallel to the unit sight vector, the closer the relative position and the speed corresponding to the individual are to the real situation, the earlier the ranking is, and constructing a non-dominant ranking set on the basis.
The non-dominated sorting algorithm is specifically:
Figure 525752DEST_PATH_IMAGE001
wherein, in the step (A),x 0 is a space target and an observation start 0 The state of the relative motion at the moment of time,u i obtained from images captured by a camerat i The unit line-of-sight vector of the time instant, h(t i ,x 0 )is composed oft i The unit relative position vector of the time-space object with respect to the observation star, J 1 is a first fitness function and represents the square sum of the cross product of the unit sight vector and the unit relative position vector at the first k moments,J 2 and the second fitness function represents the difference between the product of the unit sight vector and the unit relative position vector at the first k moments and 1.
Due to the weak observability caused by angle measurement only, how to design an optimization algorithm to ensure that two fitness functions converge to a global minimum is the key to find an accurate IROD problem solution.
The method constructs two fitness functions to sequence, iterate and evolve the population, can effectively avoid the situation that the optimal solution is submerged in the suboptimal solution due to observation noise of the single fitness function, and realizes that the genetic algorithm jumps out of the local optimal solution and finally converges to the global optimal solution.
And 5.3, establishing a congestion degree sequencing set which is sequenced by a congestion degree comparison operator, for each fitness function, firstly performing non-dominated sequencing on the individuals in the population by using two fitness functions based on the function, then setting the congestion degrees of the two individuals at the boundary to be infinite, and finally calculating the congestion degrees of the individuals.
The congestion degree sorting rule is established based on the congestion degree comparison operator as follows:
Figure 144558DEST_PATH_IMAGE002
wherein
Figure DEST_PATH_IMAGE023
Is as followsiThe degree of crowdedness of the individual, f m is as followsmA fitness function.
Step 5.4, listing the relative states in the individuals in each population obtained in the step 5.1, obtaining a list of individuals closest to the true relative motion state after the non-dominated sorting in the step 5.2 and the crowding degree sorting in the step 5.3, then crossing and mutating the relative states represented by the individuals in the 5 populations to obtain new individuals, then carrying out the non-dominated and crowding degree sorting and the retention operation on the relative states of the new individuals to obtain a new population in which the individuals closer to the true relative motion state are stored, and realizing iterative evolution optimization;
and 5.5, performing information communication of relative motion states represented by different individuals on the 5 populations subjected to iterative evolution optimization in the step 5.4 by using immigration operators in each iteration process, reserving the optimal individuals in the 5 populations in each iteration, and obtaining a nonlinear relative motion model only with angle measurement and relative orbit determination by taking the change of the optimal individuals in each generation as an iteration termination condition.
And controlling the connection and the co-evolution among the populations by using immigration operators to obtain the optimal evolution result of all the populations. Specifically, information exchange is carried out among different populations based on immigration operators, the optimal individuals in each evolutionary generation of each population are stored through an artificial selection operator to form an essence population, and the essence population is used as a basis for judging algorithm convergence,
and finding the worst individual in the ith population and the optimal individual in the jth population, exchanging the worst individual and the optimal individual until the n populations move, realizing information interaction among the populations, sequencing the individuals of all the populations through a manual selection operator, and selecting the optimal individual to be placed into the elite population. In the elite population, each individual does not participate in genetic manipulation, so that the best individual in each generation can be protected, and the number of elite individuals is used as a termination condition.
And (5) improving the genetic algorithm based on the vector difference mutation operator, the multi-target genetic algorithm and the multi-population genetic algorithm provided in the step (5), and solving the problems of precocity and falling into local optimum when the genetic algorithm is applied to orbit determination.
And 6, deploying the nonlinear relative motion model on the perception satellite, and measuring three groups of relative measurement angles at intervals of a certain time to determine the relative motion state of the target satellite so as to realize relative orbit determination of the target satellite.
The following examples are presented to illustrate the applicability of the present invention.
The following calculation conditions and technical parameters are set:
1) The semi-major axis of the orbit of the sensing satellite A is 42164.2 km, the eccentricity is 0.0001, the inclination angle of the orbit is 0 degree, the argument of the perigee is 180 degrees, the ascension angle of the ascension point is 56.4020 degrees, and the true perigee angle is 18.3346 degrees;
2) The semi-major axis of the orbit of the target satellite is 42204.2 km, the eccentricity is 0.005, the inclination angle of the orbit is 0.2 degrees, the argument of the perigee is 0 degree, the ascension of the ascension point is 112.8841 degrees, and the true perigee angle is 143.012 degrees;
3) The mean square error of the angle measurement noise of the camera is 0.0001rad, and the mean square error of the noise of the absolute position of the sensing satellite is 100m;
the simulation verification is carried out based on the angle-only relative orbit determination method and the set calculation conditions and technical parameters. As shown in fig. 3 and 4, which are curves of the tracking position error and the velocity error, respectively, it can be seen that the tracking position accuracy and the velocity accuracy of the non-cooperative target are both high by the method of the present disclosure. Under the method, the maximum value of the estimation error of the relative distance in the X, Y, Z direction can be not more than 4.60 percent, and the average error is about 1.18 percent; 5363 the maximum value of the relative speed estimation error in the direction X, Y, Z is not more than 4.61%, and the average error is about 1.18% of the relative orbit determination error.
Therefore, the method can realize the full-autonomous accurate orbit determination of the non-cooperative target only by the passive angle measurement of the satellite-borne optical camera. Particularly, compared with the traditional orbit determination method, the GEO orbit target orbit determination is taken as an example, the equivalent orbit determination precision can be achieved under the condition that the measurement arc length is shortened by 90 percent, and the breakthrough progress brought by the method is fully seen.
Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that changes may be made in the embodiments and/or equivalents thereof without departing from the spirit and scope of the invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (9)

1. A space-based passive detection orbit determination method based on neural network combined genetic algorithm is characterized by comprising the following steps:
step 1, defining a spacecraft training data generator, and obtaining training data of a deep neural network through the data generator;
step 2, preprocessing the training data generated in the step 1 to obtain standardized data;
step 3, defining a deep neural network, determining appropriate parameters, and training the deep neural network off line through the standardized data;
step 4, reducing the spatial range of the solution based on the trained deep neural network, specifically, taking the deep neural network as a boundary dereferencing device of the population individual value, and obtaining the dereferencing range of the population individual;
step 5, defining an improved genetic algorithm, including a vector difference variation algorithm, a multi-target genetic algorithm and a multi-population genetic algorithm, obtaining n populations in the value range of population individuals, and performing iterative optimization based on the improved genetic algorithm to obtain a nonlinear relative motion model of only angle measurement relative orbit determination, specifically including:
step 5.1, constructing population individuals and forming n genetic algorithm populations, wherein the population individuals comprise three-dimensional positions and speeds of a target satellite, namely six relative motion states;
step 5.2, establishing a non-dominated sorting algorithm based on the multi-target genetic algorithm, wherein the multi-target genetic algorithm comprises two fitness functions which are respectively the square sum of the cross product of the unit sight vector and the unit relative position vector and the difference between the product of the unit sight vector and the unit relative position vector and 1;
step 5.3, establishing a congestion degree sorting algorithm based on a congestion degree comparison operator;
step 5.4, performing crossing, variation, sorting and reserving operations on the individuals in each population to realize iterative evolution optimization, wherein the variation is realized based on a vector difference variation algorithm, and the sorting is realized based on a non-dominated sorting algorithm and a congestion degree sorting algorithm;
step 5.5, realizing the reservation of optimal individuals based on a multi-population genetic algorithm, specifically, carrying out mutual information exchange by using a immigration operator in each iterative evolution optimization process for n populations, reserving the optimal individuals in the n populations in each iteration, and taking the change of the optimal individuals in each generation as an iteration termination condition;
and 6, deploying the nonlinear relative motion model on the perception satellite, and inputting the relative measurement angle measured by the optical camera into the model to realize the online determination of the relative orbit of the target satellite.
2. The space-based passive detection and orbit determination method based on the neural network combined with the genetic algorithm as claimed in claim 1, wherein the step 4 is specifically as follows:
step 4.1, inputting the observation angle into a deep neural network to obtain a group of initial relative motion states of the space target relative to the observation star;
and 4.2, expanding the corresponding value of the initial relative motion state upwards/downwards by a certain proportion to serve as an upper/lower bound of the individual value in the population.
3. The space-based passive detection and orbit determination method based on the neural network combined with the genetic algorithm as claimed in claim 2, wherein the non-dominated sorting algorithm in step 5.2 is specifically:
Figure FDA0003879930620000021
wherein x is 0 Is the space target and the observation star at t 0 Relative movement state of time u i Obtained from an image acquired by a camera at t i Unit line-of-sight vector of time, h (t) i ,x 0 ) Is t i Unit relative position vector of time space target relative to observation star, J 1 Is a first fitness function and represents the square sum of cross products of the unit sight line vector and the unit relative position vector at the first k moments, J 2 And the second fitness function represents the difference between the product of the unit sight vector and the unit relative position vector at the first k moments and 1.
4. The space-based passive detection and orbit determination method based on the neural network combined with the genetic algorithm as claimed in claim 3, wherein the congestion degree ranking rule established based on the congestion degree comparison operator in step 5.3 is as follows:
Figure FDA0003879930620000031
wherein
Figure FDA0003879930620000032
Is the degree of congestion of the ith individual, f m Is the mth fitness function.
5. The space-based passive detection and orbit determination method based on the neural network combined with the genetic algorithm as claimed in claim 4, wherein in step 5.4, the crossing adopts analog binary crossing, the variation adopts vector difference variation, and the selection adopts elite reservation selection; and performing non-dominated sorting and crowding sorting on the offspring population and the parent population obtained by performing individual crossing and mutation in each population, and selecting the first n/2 individuals from the parent population and the offspring population respectively containing n individuals to form a new offspring population.
6. The space-based passive detection and orbit determination method based on the neural network combined with the genetic algorithm as claimed in claim 5, wherein the simulated binary crossing and the elite retention selection in step 5.4 are specifically:
Figure FDA0003879930620000033
wherein x 1j (t) and x 2j (t) are two different parents in the jth random selection,
Figure FDA0003879930620000034
and
Figure FDA0003879930620000035
is two filial generation individuals obtained by crossing the above two different parent individuals, t is the t-th bit vector in the individual, gamma j Is dynamically and randomly determined by the distribution factor eta.
7. The space-based passive detection and orbit determination method based on neural network combined with genetic algorithm as claimed in claim 6,
the vector difference variation algorithm specifically comprises:
Figure FDA0003879930620000041
wherein x 1 (t)、x 2 (t) and x 3 (t) three different parents randomly selected from the current population,
Figure FDA0003879930620000042
is the filial individuals generated by the variation of the three different parent individuals, t is the t-th bit vector in the individual, and F is the quantization factor.
8. The space-based passive detection and orbit determination method based on the neural network combined with the genetic algorithm as claimed in claim 7, wherein information exchange is performed between different populations by using immigration operators, and the optimal individuals in each evolutionary generation of each population are stored by using an artificial selection operator to form an elite population as a basis for judging convergence of the algorithm, which is as follows: finding the worst individual in the ith population and the optimal individual in the jth population, exchanging until the n populations are migrated, realizing information interaction among the populations, sequencing the individuals of all the populations through a manual selection operator, and selecting the optimal individual to be placed in the elite population.
9. The space-based passive detection and orbit determination method based on the neural network combined with the genetic algorithm as claimed in claim 8, wherein the elite population is used as a basis for judging the termination of the iteration of the genetic algorithm, and specifically comprises the following steps: the essence population is not subjected to selection, crossing and mutation genetic operations, so that the optimal individuals generated in the evolution process are not damaged or lost, the optimal individuals minimum kept algebra is used as a termination criterion, and iteration is terminated when the same optimal individual continuously keeps a certain algebra.
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