Prediction method and system for measurement information of spatial non-cooperative target

Abstract

The embodiment of the invention provides a method and a system for predicting measurement information of a space non-cooperative target, and the method comprises the following steps: in optical relative navigation, because the non-cooperative target is influenced by an external complex environment, the measurement information is incomplete or missing, and the like. In order to further obtain measurement information when the target is invisible, constructing an optical relative navigation nonlinear measurement model of the non-cooperative target; constructing a Koopman global linear optical measurement model by adopting a Koopman operator, and taking the Koopman global linear optical measurement model as a nonlinear prediction model; a Koopman operator of the prediction model is approximated through a DMD data driving algorithm, and a dimension-reduced Koopman global linear optical measurement model is obtained; and through the dimension-reduced Koopman global linear optical measurement model, predicting measurement information when the non-cooperative target is invisible. Therefore, the prediction precision of the measurement information is improved by 52.07%, and high-precision prediction of the measurement information is realized.

Description

Technical Field

[0001] The present invention relates to the field of space non-cooperative target positioning, and in particular to a method and system for predicting measurement information of space non-cooperative targets. Background Art

[0002] Non-cooperative targets in space usually refer to targets that have no artificial identification and cannot actively cooperate with service spacecraft to obtain measurement information. Their on-orbit services such as orbit maintenance and space debris removal are crucial to ensure the safe operation of service spacecraft in orbit. Relative navigation is a prerequisite for the on-orbit operation of non-cooperative targets in space. Optical cameras have become important and main measurement sensors in current relative navigation because of their light weight, small size, wide measurement distance range and passive concealment. The sequence images taken by optical cameras can provide time series measurement information for the relative navigation system, and accurate and complete time series measurement information is the prerequisite for achieving high-precision relative navigation.

[0003] In a complex space environment, the target sequence image measurement information is affected by many interference factors. For example, when the observed target is affected by factors such as occultation or sunlight, the optical sensor of the spacecraft can no longer obtain the target's measurement information, resulting in incomplete or missing observation information. Therefore, it is crucial to model the prediction of measurement information.

[0004] The optical relative navigation measurement model based on sequence images is a typical nonlinear model. For this type of nonlinear model prediction problem, the current traditional solutions are divided into two ideas: one is to establish a Wiener model, bilinear model, etc. of the nonlinear system. The Wiener model or bilinear model can be used to more deeply analyze the characteristics and nonlinear features of the system. However, it is difficult to establish an accurate Wiener model or bilinear model, and the accuracy of the model is limited; the other idea is to locally linearize the nonlinear system, but local linearization is only linearized at the equilibrium point, which will lose nonlinear information. Therefore, it is urgent to solve the problem that the target sequence image measurement information is affected by many interference factors (occultation or illumination) in the complex space environment of non-cooperative targets, resulting in the optical sensor of the spacecraft being unable to continue to obtain the measurement information of the target, resulting in incomplete or missing observation information. Summary of the invention

[0005] The embodiments of the present invention provide a method and system for predicting measurement information of a non-cooperative target in space, which can solve the technical problem in the prior art that "in a complex space environment, the measurement information of a target sequence image is affected by many interference factors. For example, when the observed target is affected by factors such as occultation or sunlight, the optical sensor of the spacecraft can no longer obtain the measurement information of the target, resulting in incomplete or missing observation information."

[0006] To achieve the above-mentioned object, in a first aspect, an embodiment of the present invention provides a method for predicting measurement information of a space non-cooperative target, comprising:

[0007] In view of the situation that when a non-cooperative target is affected by external complex factors, the non-cooperative target is invisible to the optical sensor of the service spacecraft, resulting in the optical sensor of the service spacecraft being unable to obtain the measurement information of the non-cooperative target, when the non-cooperative target is not affected by the external complex factors, the measurement information of the non-cooperative target for a period of time is obtained by the service spacecraft to construct an optical relative navigation nonlinear measurement model of the non-cooperative target; and the Koopman operator is used to construct a Koopman global linear optical measurement model for the optical relative navigation nonlinear measurement model of the non-cooperative target, and the Koopman global linear optical measurement model is used as a prediction model for the measurement information when the non-cooperative target is invisible, and the external complex factors include at least one of the following: occultation and sunlight;

[0008] By using the DMD data-driven algorithm, a finite-dimensional subspace is sought to approximate the Koopman operator of the prediction model, so as to simplify and reduce the dimension of the prediction model, and a low-dimensional approximate matrix of the Koopman operator is obtained. The Koopman global linear optical measurement model using the low-dimensional approximate matrix of the Koopman operator is used as the Koopman global linear optical measurement model after dimensionality reduction;

[0009] The measurement information of non-cooperative targets is predicted when they are invisible through the dimensionality-reduced Koopman global linear optical measurement model.

[0010] In a second aspect, an embodiment of the present invention provides a system for predicting measurement information of a space non-cooperative target, including:

[0011] A prediction model building unit is used for obtaining measurement information of the non-cooperative target for a period of time through the service spacecraft when the non-cooperative target is not affected by external complex factors and the non-cooperative target is invisible to the optical sensor of the service spacecraft, resulting in the optical sensor of the service spacecraft being unable to obtain measurement information of the non-cooperative target. The non-cooperative target is not affected by external complex factors, and the measurement information of the non-cooperative target for a period of time is obtained through the service spacecraft, and the optical relative navigation nonlinear measurement model of the non-cooperative target is combined with the Koopman operator to build the Koopman global linear optical measurement model, and the Koopman global linear optical measurement model is used as a prediction model of measurement information when the non-cooperative target is invisible. The external complex factors include at least one of the following: occultation and sunlight.

[0012] A dimension reduction unit is used to seek a finite-dimensional subspace to approximate the Koopman operator of the prediction model through a DMD data-driven algorithm, so as to simplify and reduce the dimension of the prediction model, obtain a low-dimensional approximate matrix of the Koopman operator, and use the Koopman global linear optical measurement model using the low-dimensional approximate matrix of the Koopman operator as the Koopman global linear optical measurement model after dimension reduction.

[0013] The measurement information prediction unit is used to predict the measurement information when the non-cooperative target is invisible through the Koopman global linear optical measurement model after dimensionality reduction.

[0014] In a third aspect, an embodiment of the present invention provides a computer-readable storage medium, which stores one or more programs. When the one or more programs are executed by a computer device, the computer device executes the aforementioned method for predicting measurement information of a spatial non-cooperative target.

[0015] In a fourth aspect, an embodiment of the present invention provides a computer device, including:

[0016] A processor; and a memory arranged to store computer executable instructions, which, when executed, cause the processor to perform the aforementioned method for predicting measurement information of a spatial non-cooperative target.

[0017] The above technical solution has the following beneficial effects: for non-cooperative targets, affected by factors such as occultation or sunlight, the optical sensor of the spacecraft cannot continue to obtain the measurement information of the target, resulting in incomplete or missing observation information. The measurement information of the non-cooperative target is predicted by the method of the embodiment of the present invention, so that the prediction accuracy of the measurement information is improved by 52.07%, which provides an effective solution for the high-precision prediction of the subsequent optical relative navigation target measurement information, and provides a valuable reference for the model prediction of the measurement information of future space non-cooperative targets, thereby realizing the high-precision prediction of the measurement information. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0019] Figure 1 is a flow chart of a method for predicting measurement information of a space non-cooperative target according to an embodiment of the present invention;

[0020] Figure 2It is a structural diagram of a prediction system for measurement information of a space non-cooperative target according to an embodiment of the present invention;

[0021] Figure 3 This is the evolution graph defined by the Koopman operator;

[0022] Figure 4 is a schematic diagram of an invisible trajectory of a target according to an embodiment of the present invention;

[0023] Figure 5 is a schematic diagram of a non-cooperative target in a camera measurement space according to an embodiment of the present invention;

[0024] Figure 6 is a trajectory of space target measurement in an embodiment of the present invention;

[0025] Figure 7 It is a comparison of the measurement trajectory "10-point prediction" method of the embodiment of the present invention;

[0026] Figure 8 is the X-direction measurement information prediction trajectory and prediction error of an embodiment of the present invention;

[0027] Fig. 9 is the Y-direction measurement information prediction trajectory and prediction error of an embodiment of the present invention;

[0028] Fig.10 is the Z-direction measurement information prediction trajectory and prediction error of an embodiment of the present invention;

[0029] Fig.11 is a prediction error curve of the embodiment of the present invention that changes with the number of samples. DETAILED DESCRIPTION

[0030] The following will be combined with the drawings in the embodiments 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.

[0031] like Figure 1 As shown, in combination with an embodiment of the present invention, a method for predicting measurement information of a space non-cooperative target is provided, comprising:

[0032] S101: When a non-cooperative target is affected by external complex factors, the non-cooperative target is invisible to the optical sensor of the service spacecraft, resulting in the optical sensor of the service spacecraft being unable to obtain measurement information of the non-cooperative target. When the non-cooperative target is not affected by the external complex factors, the service spacecraft obtains measurement information of the non-cooperative target for a period of time, and constructs an optical relative navigation nonlinear measurement model of the non-cooperative target; and uses a Koopman operator to construct a Koopman global linear optical measurement model for the optical relative navigation nonlinear measurement model of the non-cooperative target, and uses the Koopman global linear optical measurement model as a prediction model for measurement information when the non-cooperative target is invisible, wherein the external complex factors include at least one of the following: occultation and sunlight;

[0033] S102: Seeking a finite-dimensional subspace to approximate the Koopman operator of the prediction model through a DMD data-driven algorithm, so as to simplify and reduce the dimension of the prediction model, obtain a low-dimensional approximate matrix of the Koopman operator, and use the Koopman global linear optical measurement model using the low-dimensional approximate matrix of the Koopman operator as the Koopman global linear optical measurement model after dimensionality reduction;

[0034] S103: Predict the measurement information when the non-cooperative target is invisible through the Koopman global linear optical measurement model after dimensionality reduction.

[0035] Preferably, the optical relative navigation nonlinear measurement model includes a state model and an optical measurement model, wherein the state model refers to a relative motion state equation between the service spacecraft and the non-cooperative target established in an orbital system when the service spacecraft and the non-cooperative target are in orbit;

[0036] The optical measurement model refers to the equation that the optical camera used in relative navigation can only collect measurement data in the line of sight direction of non-cooperative targets, and uses the pinhole imaging model to describe the imaging process of the optical camera.

[0037] Preferably, in S101, a Koopman operator is used to construct a Koopman global linear optical measurement model for an optical relative navigation nonlinear measurement model of a non-cooperative target, including:

[0038] Koopman operator is a global linearization method, which uses Koopman operator to express the nonlinear measurement model of optical relative navigation of non-cooperative targets as an infinite-dimensional linear operator in the Hibbert space of dimensional ascending function.

[0039] The Koopman global linear optical measurement model is obtained through the infinite dimensional linear operator in the Hibbert space of the dimensionality-raising function.

[0040] Preferably, in S102, a finite-dimensional subspace is sought to approximate the Koopman operator of the prediction model through a DMD data-driven algorithm, so as to simplify and reduce the dimension of the prediction model, and obtain a low-dimensional approximate matrix of the Koopman operator, including:

[0041] In the Koopman global linear optical measurement model, the Koopman operator includes three features: Koopman eigenvalue, the Koopman eigenvalue, the corresponding eigenfunction and the corresponding Koopman mode. The three features included in the Koopman operator provide the dynamic law of the nonlinear system in the future evolution over time;

[0042] For any Koopman eigenvalue, a global linearization of a nonlinear measurement model is achieved by a linear combination of the Koopman eigenvalue, a characteristic function corresponding to the Koopman eigenvalue, and a Koopman mode corresponding to the Koopman eigenvalue;

[0043] The Koopman pattern corresponding to the Koopman eigenvalue reflects the dynamic law of the system evolving over time;

[0044] If the absolute value of any Koopman eigenvalue of the Koopman operator is greater than 1, the influence of the coefficient of the Koopman eigenvalue on the measurement information becomes more and more important over time, indicating that the influence of the Koopman mode corresponding to the Koopman eigenvalue on the measurement information will weaken over time; the coefficient of the Koopman eigenvalue refers to the Koopman mode ν j ;

[0045] If the absolute value of any Koopman eigenvalue of the Koopman operator is less than 1, the influence of the coefficient of the Koopman eigenvalue over time on the measurement information is not important, indicating that the influence of the Koopman pattern corresponding to the Koopman eigenvalue on the measurement information will weaken over time.

[0046] Preferably, in S102, a finite-dimensional subspace is sought to approximate the Koopman operator of the prediction model through a DMD data-driven algorithm, so as to simplify and reduce the dimension of the prediction model and obtain a low-dimensional approximate matrix of the Koopman operator, and further includes:

[0047] In the optical measurement model, the measurement data sequence of the collected non-cooperative target is used to construct two measurement data matrices: a previous measurement data matrix and a subsequent measurement data matrix;

[0048] Assuming that the sampling time used for the measurement data sequence is small enough, the two measurement data matrices satisfy an approximate linear relationship. The low-dimensional matrix A representing the relationship between the two measurement data matrices is the Koopman operator A low-dimensional approximation of .

[0049] Preferably, in S102, a finite-dimensional subspace is sought to approximate the Koopman operator of the prediction model through a DMD data-driven algorithm, so as to simplify and reduce the dimension of the prediction model and obtain a low-dimensional approximate matrix of the Koopman operator, and further includes:

[0050] The specific calculation process of the low-dimensional approximate matrix of the Koopman operator is as follows:

[0051] Calculate the SVD decomposition of the previous measurement data matrix;

[0052] Combine the coefficients in the SVD decomposition of the previous measurement data matrix and the subsequent measurement data matrix to define an approximate matrix of the low-dimensional matrix A

[0053] Compute the approximate matrix The eigenvalue λ and eigenvector ω of , where the eigenvalue of the matrix A is also λ, which is called the DMD eigenvalue;

[0054] Then construct the eigenvector υ of the low-dimensional matrix A, and the eigenvector υ is called the DMD mode; then the DMD mode corresponds to the Koopman mode, and the DMD eigenvalue corresponds to the Koopman eigenvalue, and the low-dimensional approximate matrix of the Koopman operator is obtained.

[0055] Preferably, S103: predicting measurement information when the non-cooperative target is invisible by using the Koopman global linear optical measurement model after dimensionality reduction, includes:

[0056] When the non-cooperative target at the current moment is not affected by external complex factors and the non-cooperative target is affected by external complex factors at the current moment, the measurement information of the non-cooperative target at the current moment and the subsequent moments is predicted by the Koopman global linear optical measurement model after dimensionality reduction.

[0057] like Figure 2 As shown, in combination with an embodiment of the present invention, a prediction system for measurement information of a space non-cooperative target is provided, comprising:

[0058] The prediction model building unit 21 is used for obtaining the measurement information of the non-cooperative target for a period of time through the service spacecraft when the non-cooperative target is not affected by the external complex factors, combining the optical relative navigation nonlinear measurement model of the non-cooperative target and using the Koopman operator to build the Koopman global linear optical measurement model, and using the Koopman global linear optical measurement model as the prediction model of the measurement information when the non-cooperative target is invisible, wherein the external complex factors include at least one of the following: occultation and sunlight;

[0059] The dimension reduction unit 22 is used to seek a finite-dimensional subspace to approximate the Koopman operator of the prediction model through the DMD data-driven algorithm, so as to simplify and reduce the dimension of the prediction model, obtain a low-dimensional approximate matrix of the Koopman operator, and use the Koopman global linear optical measurement model using the low-dimensional approximate matrix of the Koopman operator as the Koopman global linear optical measurement model after dimension reduction.

[0060] The measurement information prediction unit 23 is used to predict the measurement information when the non-cooperative target is invisible by using the Koopman global linear optical measurement model after dimensionality reduction.

[0061] Preferably, the optical relative navigation nonlinear measurement model includes a state model and an optical measurement model, wherein the state model refers to a relative motion state equation between the service spacecraft and the non-cooperative target established in an orbital system when the service spacecraft and the non-cooperative target are in orbit;

[0062] The optical measurement model refers to the equation that the optical camera used in relative navigation can only collect measurement data in the line of sight direction of non-cooperative targets, and uses the pinhole imaging model to describe the imaging process of the optical camera.

[0063] Preferably, the prediction model building unit 21 is specifically used for:

[0064] Koopman operator is a global linearization method, which uses Koopman operator to express the nonlinear measurement model of optical relative navigation of non-cooperative targets as an infinite-dimensional linear operator in the Hibbert space of dimensional ascending function.

[0065] The Koopman global linear optical measurement model is obtained through the infinite dimensional linear operator in the Hibbert space of the dimensionality-raising function.

[0066] Preferably, the dimension reduction unit 22 is specifically used for:

[0067] In the Koopman global linear optical measurement model, the Koopman operator includes three features: Koopman eigenvalue, the Koopman eigenvalue, the corresponding eigenfunction and the corresponding Koopman mode. The three features included in the Koopman operator provide the dynamic law of the nonlinear system in the future evolution over time;

[0068] For any Koopman eigenvalue, a global linearization of a nonlinear measurement model is achieved by a linear combination of the Koopman eigenvalue, a characteristic function corresponding to the Koopman eigenvalue, and a Koopman mode corresponding to the Koopman eigenvalue;

[0069] The Koopman pattern corresponding to the Koopman eigenvalue reflects the dynamic law of the system evolving over time;

[0070] If the absolute value of any Koopman eigenvalue of the Koopman operator is greater than 1, the influence of the coefficient of the Koopman eigenvalue on the measurement information becomes more and more important over time, indicating that the influence of the Koopman mode corresponding to the Koopman eigenvalue on the measurement information will weaken over time; the coefficient of the Koopman eigenvalue refers to the Koopman mode ν j ;

[0071] If the absolute value of any Koopman eigenvalue of the Koopman operator is less than 1, the influence of the coefficient of the Koopman eigenvalue over time on the measurement information is not important, indicating that the influence of the Koopman pattern corresponding to the Koopman eigenvalue on the measurement information will weaken over time.

[0072] The dimension reduction unit 22 is specifically used for:

[0073] In the optical measurement model, the measurement data sequence of the collected non-cooperative target is used to construct two measurement data matrices: a previous measurement data matrix and a subsequent measurement data matrix;

[0074] Assuming that the sampling time used for the measurement data sequence is small enough, the two measurement data matrices satisfy an approximate linear relationship. The low-dimensional matrix A representing the relationship between the two measurement data matrices is the Koopman operator A low-dimensional approximation of .

[0075] The dimension reduction unit 22 is specifically used for:

[0076] The specific calculation process of the low-dimensional approximate matrix of the Koopman operator is as follows:

[0077] Calculate the SVD decomposition of the previous measurement data matrix;

[0078] Combine the coefficients in the SVD decomposition of the previous measurement data matrix and the subsequent measurement data matrix to define an approximate matrix of the low-dimensional matrix A

[0079] Compute the approximate matrix The eigenvalue λ and eigenvector ω of , where the eigenvalue of the matrix A is also λ, which is called the DMD eigenvalue;

[0080] Then construct the eigenvector υ of the low-dimensional matrix A, and the eigenvector υ is called the DMD mode; then the DMD mode corresponds to the Koopman mode, and the DMD eigenvalue corresponds to the Koopman eigenvalue, and the low-dimensional approximate matrix of the Koopman operator is obtained.

[0081] Preferably, the measurement information prediction unit 23 is specifically configured to:

[0082] When the non-cooperative target at the current moment is not affected by external complex factors and the non-cooperative target is affected by external complex factors at the current moment, the measurement information of the non-cooperative target at the current moment and the subsequent moments is predicted by the Koopman global linear optical measurement model after dimensionality reduction.

[0083] In combination with an embodiment of the present invention, a computer-readable storage medium is provided, which stores one or more programs. When the one or more programs are executed by a computer device, the computer device executes any one of the aforementioned methods for predicting measurement information of a non-cooperative target in space.

[0084] In conjunction with an embodiment of the present invention, a computer device is provided, including:

[0085] A processor; and a memory arranged to store computer executable instructions, wherein when the executable instructions are executed, the processor executes any one of the aforementioned methods for predicting measurement information of a non-cooperative space target.

[0086] The beneficial technical effects achieved by the embodiments of the present invention are as follows:

[0087] For non-cooperative targets, due to the influence of factors such as occultation or sunlight, the optical sensor of the spacecraft can no longer obtain the measurement information of the target, resulting in incomplete or missing observation information. The measurement information of non-cooperative targets is predicted by the method of the embodiment of the present invention, so that the prediction accuracy of the measurement information is improved by 52.07%, which provides an effective solution for the high-precision prediction of subsequent optical relative navigation target measurement information, provides a valuable reference for the model prediction of future space non-cooperative target measurement information, and realizes the high-precision prediction of measurement information.

[0088] The above technical solution of the embodiment of the present invention is described in detail below in conjunction with specific application examples. For technical details not introduced during the implementation process, please refer to the relevant description in the previous text.

[0089] The embodiment of the present invention provides a model prediction method for spatial non-cooperative target measurement information based on the Koopman operator. Aiming at the problem of incomplete or missing measurement information in optical relative navigation, the global linear representation theory of the Koopman operator is combined to predict spatial non-cooperative measurement information. Firstly, the nonlinear measurement model is projected into the Hilbert space through the dimension-raising function, and the optical relative navigation measurement model based on the Koopman operator is established; secondly, the global linearization of the measurement model is realized by using the linear combination of the Koopman mode, eigenvalue and eigenfunction, thereby reducing the loss of nonlinear information.

[0090] Again, the model algorithm based on the DMD method is used to approximate the Koopman operator, and the main mode of the operator is used to obtain the phase space topological structure of the measurement model, revealing the long-term evolution law of the target motion trajectory. Finally, the Monte Carlo simulation shows that the method of the embodiment of the present invention improves the prediction accuracy of measurement information by 52.07% compared with the prior art, providing an effective solution for the high-precision prediction of subsequent optical relative navigation target measurement information, and providing a valuable reference for the model prediction of measurement information of future non-cooperative targets in space, thereby achieving high-precision prediction of measurement information.

[0091] 1. Basic knowledge

[0092] 1.1 Koopman operator theory

[0093] The Koopman operator describes the dynamic system by constructing functionals, expanding the originally finite-dimensional nonlinear system space to the infinite-dimensional Hilbert space, thereby achieving a linear representation of the original system.

[0094] First, consider a discrete system with a nonlinear evolution law:

[0095] x t+1 =F(x t ) (1)

[0096] in, represents the system state at time t, represents the nonlinear function of state evolution, and n represents the dimension of the state space. For the discrete system with nonlinear evolution law corresponding to equation (1), the next moment system state x of the discrete system with nonlinear evolution law is t+1 Depends only on the current system state x t and the nonlinear mapping F.

[0097] Define a set of scalar-valued dimension-raising functions in, represents the infinite-dimensional Hilbert space spanned by the scalar-valued up-dimensional function. With the up-dimensional function g defined, the Koopman operator The phase space of the discrete system with nonlinear evolution law in equation (1) can be embedded into the Hilbert space Characterizes the dynamic evolution of the dimensional function g in Hilbert space, such as Figure 3 As shown. The Koopman operator is defined as follows:

[0098]

[0099] According to the definition of the Koopman operator, even if the nonlinear structure of equation (1) is very complex, the Koopman operator Still in Hilbert space The infinite-dimensional linear operator in satisfies the following expression:

[0100]

[0101] Among them, the scalar

[0102] Based on the linear characteristics and infinite-dimensional space structure of the Koopman operator, the Koopman operator has spectral properties, which are shown as follows:

[0103]

[0104] Among them, λ j Represents the Koopman operator The jth eigenvalue of Denotes the eigenvalue λ j The corresponding characteristic function.

[0105] Each component of the dimension-raising function g is located in the Hilbert space spanned by all characteristic functions, then we can use the Koopman operator The spectrum of g is decomposed into the following form:

[0106]

[0107] Among them, x0 represents the initial value represents the Koopman pattern. In addition, since x t is a vector, x t Each component in can be expanded through basis functions in the following form:

[0108]

[0109] Formula (6) shows that the evolution law of the dynamic system (Formula (1)) over time can be reflected by the Koopman model. j |>1, and the eigenvalue λ j The corresponding Koopman model is becoming more and more important; the Koopman model is used to map nonlinear dynamic systems into high-dimensional linear spaces, so that linear system methods can be used to analyze, model, and predict nonlinear systems. On the contrary, when |λ j When |<1, the corresponding Koopman mode gradually decreases.

[0110] 1.2 Dynamic Mode Decomposition (DMD)

[0111] According to equation (6), the expansion of equation (6) has infinite terms because the Koopman operator is infinite-dimensional. However, in practical applications, it is unrealistic to use an infinite-dimensional Koopman operator. Currently, many high-dimensional systems can be approximated using low-dimensional subspaces. Among them, the data-driven algorithm seeks a finite-dimensional subspace to approximate the Koopman operator. With the approximate Koopman operator The two main data-driven algorithms are the Arnoldi algorithm and dynamic mode decomposition (DMD). However, the Arnoldi algorithm will have the numerical ill-conditioned problem of the Vandermonde matrix during the calculation process. In contrast, the DMD algorithm suppresses the ill-conditioned nature of the Vandermonde matrix by unitary transformation and truncating the minimum singular value. Therefore, the DMD algorithm is adopted in the embodiment of the present invention, and the DMD algorithm can be understood as an ideal combination of spatial dimensionality reduction technology and Fourier transform in time.

[0112] Schmid and Sesterhenn proposed the DMD algorithm in the context of fluids. The DMD algorithm is given N data sequences x1, x2, ..., x N and Construct two dimensions as The matrix:

[0113]

[0114] Next, we need to find a best-fitting linear operator A so that the square of the Frobenius norm between the two matrices X1 and X2 in equation (7) is minimized, that is, A must satisfy:

[0115]

[0116] Among them, the minimized is the Koopman operator The finite-dimensional approximation of . Equation (8) has a closed solution, which can be obtained by using the singular value decomposition (SVD) of the matrix X1, as shown below:

[0117]

[0118] in, represents the pseudo-inverse. Since the rank of matrix X1 is R(X1)=r≤min(M,N-1), R represents the dimension of matrix X1, so U and V both represent matrices. If M is very large, it is complicated to directly calculate the eigendecomposition of A. In order to solve this problem, the DMD algorithm is used to approximate equation (8) into an eigendecomposition of a low-order matrix A, that is:

[0119]

[0120] If there is a low-rank structure in the dynamics, we can further obtain a low-dimensional matrix by truncating the number of singular values ​​of X1 to Make

[0121]

[0122] Among them, represents the number of singular values ​​of X1, All represent matrices. It is determined according to the attenuation of the singular values ​​of X1.

[0123] The DMD algorithm was originally designed for the dimension of the ascending function space with M>>N. If M<<N, then the original DMD algorithm cannot adequately capture the nonlinear dynamics.

[0124] To overcome this problem, add h time data series to the data matrices X1 and X2 and reconstruct the matrices:

[0125]

[0126] in, The parameter h is selected as

[0127] 2. Construction of global linear optical measurement model based on Koopman operator

[0128] After the service spacecraft has acquired the measurement information of the non-cooperative target for a period of time, the optical sensor of the spacecraft can no longer acquire the measurement information of the target due to the influence of complex external factors such as occultation and sunlight. Figure 4In order to further obtain measurement information when the target is invisible, the embodiment of the present invention combines the optical relative navigation nonlinear model based on the sequence image and uses the Koopman operator to construct the Koopman global linear optical measurement model to obtain a prediction model of the measurement information when the non-cooperative target is invisible, thereby obtaining complete measurement information.

[0129] When the service spacecraft and the non-cooperative target in space are in orbit, the relative motion state equation between the two can be established in the orbital system. The embodiment of the present invention adopts the state equation based on the rendezvous and docking mission of two spacecraft, namely the CW equation. Let r = [x, y, z] T is the relative position vector of the non-cooperative target in the orbital system. When the distance between the service spacecraft and the non-cooperative target is much smaller than the distance between the centers of the Earth and the orbits of the service spacecraft and the non-cooperative target are both near-circular orbits, the relative motion state (state model) between the service spacecraft and the non-cooperative target can be expressed by the CW equation:

[0130]

[0131] Where, based on r = [x, y, z] T is the relative position vector of the non-cooperative target in the orbital system, It also represents the relative position vector of a non-cooperative target in the orbital system, and cannot be separated into different meanings. is the average angular velocity of the service spacecraft orbit, μ is the earth's gravitational constant, a is the orbit radius of the service spacecraft, w = [w x ,w y ,w z ] T is the process noise, and it is assumed that the process noise obeys a Gaussian distribution with a mean of 0 and a covariance of Q.

[0132] Let the relative state vector be Then the CW equation in equation (13) can be rewritten as:

[0133]

[0134] in,

[0135]

[0136] If the relative state vector at time t0 is known to be When only the process noise is considered, the relative state vector at time t can be expressed as:

[0137] X(t)=Φ(t,t0)X(t0)+w t (15)

[0138] in,

[0139]

[0140] The optical relative navigation model based on sequential images includes a system state model and a measurement model. The measurement model uses a pinhole imaging model to describe the imaging process of the optical camera. For the convenience of calculation, it is considered that the camera coordinate system coincides with the orbital coordinate system of the service spacecraft, such as Figure 5 As shown, the optical camera can only measure the sight direction of non-cooperative targets, so the measurement equation is:

[0141]

[0142] Where z represents the camera measurement value, h represents the measurement function, and x t represents the relative state at time t, u t It is assumed that the measurement noise follows a Gaussian distribution with a mean of 0 and a covariance of R.

[0143] Obviously, the measurement model corresponding to equation (17) is a typical nonlinear model. For this nonlinear model, local linear approximation methods are usually used for linearization. However, local linearization has certain linear errors, which may lose key nonlinear information, and when the non-cooperative target is invisible, the measurement information is incomplete or missing. The Koopman operator, as an effective global linearization method, represents the nonlinear system as a dimensional function. Infinite-dimensional linear operators in space can capture the main nonlinear information of nonlinear systems and predict the future evolution of the system to obtain complete measurement information when non-cooperative targets are invisible.

[0144] Therefore, in view of the above problems, the Koopman operator theory and measurement model are combined to construct a Koopman global linear optical measurement model based on the Koopman operator, which is as follows:

[0145]

[0146] Among them, z t+1 represents the camera measurement value at time t+1, is the Koopman operator, g refers to the dimension-raising function, represents the infinite dimensional Hilbert space spanned by the scalar-valued up-dimensional function, where ξ represents the measurement noise, and it is assumed that the measurement noise obeys a Gaussian distribution with mean 0 and covariance R.

[0147] According to the infinite-dimensional linear structure and spectral decomposition properties of Koopman theory, the equation (18) corresponding to the constructed Koopman global linear optical measurement model is derived and simplified to obtain the following form:

[0148]

[0149] in, The superscript t+2 represents the power of t+2, and x0 represents the initial value of the state prediction of x in equation (13). represents the Koopman pattern, λ j Represents the Koopman operator The jth eigenvalue of Denotes the eigenvalue λ j The corresponding characteristic function.

[0150] Koopman operator theory generally assumes that the observation space z (Eq. (17)) is the observation space g(z) of the dimension-raising function, that is, z t+1 =g(z t+1 ). Therefore, the Koopman global linear optical measurement model corresponding to equation (19) can be further written as follows:

[0151]

[0152] Where x0 represents the initial value of the state prediction (r = [x, y, z] T The initial value of the state prediction within j Represents the Koopman operator The jth eigenvalue of Denotes the eigenvalue λ j The corresponding characteristic function is Indicates the Koopman mode.

[0153] By observing the equation (20) corresponding to the Koopman global linear optical measurement model, we can find that, first, the Koopman eigenvalue and eigenfunction and Koopman mode ν j The linear combination of the three features realizes the global linearization of the nonlinear measurement model of optical relative navigation of non-cooperative targets, thereby reducing the loss of nonlinear information; secondly, the Koopman mode ν j It reflects the law of evolution of the nonlinear measurement model of optical relative navigation of non-cooperative targets over time. Finally, through the analytical Koopman global linear optical measurement model corresponding to equation (20), it is further found that if the |λ of a certain eigenvalue j |>1, then the coefficient before the eigenvalue (Koopman mode ν j ) will become more important over time. On the contrary, if |λ j |<1, the influence of the Koopman pattern associated with this eigenvalue over time

[0154] Will weaken.

[0155] Therefore, the Koopman operator The three characteristics provide the dynamic laws of the future evolution of the nonlinear measurement model of optical relative navigation of non-cooperative targets, thereby achieving high-precision prediction of measurement information.

[0156] 3. Algorithm design based on Koopman global linear optical measurement model

[0157] The measurement model based on the Koopman operator is an infinite-dimensional linear model. In practical applications, it is unrealistic to consider an infinite-dimensional model. Therefore, the data-driven algorithm DMD algorithm is used to simplify and reduce the dimension of the equation (20) corresponding to the Koopman global linear optical measurement model. The purpose is to use the data-driven algorithm DMD algorithm to find a finite-dimensional subspace to approximate the Koopman operator.

[0158] Before being affected by occultation or sunlight, the first t measurement data sequences z1, z2, ..., z are obtained by using an optical camera. t and Represents the real number field of dimension M. Two measurement matrices are constructed through these measurement data; the previous measurement data matrix Z1 and the latter measurement data matrix Z2, as shown below:

[0159]

[0160] Assuming that the total sampling time of t measurement data is small enough, the two matrices Z1 and Z2 satisfy an approximate linear relationship, that is,

[0161] Z2=AZ1(22)

[0162] Here A is the Koopman operator The low-dimensional approximation of . The DMD algorithm is used to solve the eigenvalues ​​and eigenvectors of A. The specific algorithm derivation is as follows:

[0163] Step1. Calculate the SVD decomposition of the matrix Z1 as follows:

[0164] Z1=UΣV T (twenty three)

[0165] in, is an orthogonal matrix, is a diagonal matrix, is an orthogonal matrix.

[0166] Step 2. Define the matrix

[0167]

[0168] Among them, the matrix is an approximation matrix of matrix A.

[0169] Step 3. Calculate the matrix The eigenvalue λ and eigenvector ω of

[0170]

[0171] Among them, the eigenvalue of matrix A is also λ, which is called the DMD eigenvalue.

[0172] Step 4. Then the eigenvector υ of matrix A is:

[0173] υ=Uω(26)

[0174] Among them, the eigenvector υ is called the DMD mode.

[0175] The DMD mode corresponds to the Koopman mode, and the DMD eigenvalue corresponds to the Koopman eigenvalue.

[0176] Step 5. Predict the measurement information after time t+1 according to (20) corresponding to the Koopman global linear optical measurement model.

[0177] 4. Simulation Analysis

[0178] The Koopman global linear optical measurement model and DMD algorithm proposed in Sections 2 and 3 are simulated and verified, and compared with traditional methods. First, the optical relative navigation state model (13) and measurement model (17) described in Section 2 are used to simulate and generate measurement data at time t (t = 3500). Secondly, it is assumed that after time t+1, the measurement information is missing because the target is invisible. In order to further complete the measurement data, the approximate Koopman operator is obtained through the DMD algorithm designed in Section 3. And obtained the operator The eigenvalues, eigenfunctions and Koopman modes are used to predict the measurement information. Finally, based on the Koopman global linear optical measurement model (20) established in Section 2, the measurement information is predicted. Among them, the linear combination of eigenvalues, eigenfunctions and Koopman modes realizes the global linearization of the model, while the Koopman main mode provides the topological structure of the model in the phase space. The model prediction method proposed in the embodiment of the present invention can provide certain measurement information for optical relative navigation when the target is not visible. The simulation conditions are shown in Table 1.

[0179] Table 1 Simulation conditions of the measurement model based on Koopman operator

[0180]

[0181] 4.1 “One-point prediction” and performance comparison based on Koopman global linear optical measurement model

[0182] In order to verify the feasibility of the model prediction method of space non-cooperative target measurement information based on Koopman operator proposed in the embodiment of the present invention in practical application, 50 Monte Carlo simulations were performed. First, the trajectory of space target measurement information was generated using the optical relative navigation state model (Formula (13)) and the measurement model (Formula (17)). The data form is a unit direction vector in three-dimensional space, such as Figure 6 As shown. Secondly, the Koopman global linear optical measurement model constructed by the embodiment of the present invention is used to perform "1-point prediction" on the measurement information, and the prediction results in the three directions of X, Y, and Z are obtained respectively. For each direction, the root mean square error (RMSE) between the predicted vector and the actual vector is calculated as an indicator of accuracy. At the same time, the situation where the measurement information is affected by noise is also considered, in which it is assumed that the noise obeys a Gaussian distribution. Finally, the prediction results of the embodiment of the present invention obtained in 50 Monte Carlo simulation experiments are compared with three existing model prediction methods in the literature, namely the local linearization method, the ARIMA model prediction method, and the LSTM model prediction method. By comparing the experimental results, the accuracy in the three directions of X, Y, and Z is obtained, as shown in Tables 2 and 3.

[0183] Table 2 RMSE of “1-point prediction” under the influence of measurement noise

[0184]

[0185] Table 3 RMSE of “1-point prediction” without measurement noise

[0186]

[0187] According to the experimental results in Table 2, in the presence of measurement noise, both the local linearization method and the ARIMA method show lower accuracy, while the LSTM method has relatively good accuracy. However, the Koopman global linear optical measurement model constructed in the embodiment of the present invention shows the highest accuracy in the three directions of X, Y, and Z, and the accuracy is improved by 35.09% compared with the three existing model prediction methods.

[0188] According to the experimental results in Table 3, in the absence of measurement noise, the accuracy of the three methods, namely the local linearization method, the ARIMA method and the LSTM method, is slightly improved, but the Koopman global linear optical measurement model still shows the highest accuracy, which is 52.07% higher than the existing three model prediction methods.

[0189] Comparing the experimental results in Table 2 and Table 3, there are obvious differences in the accuracy of "1-point prediction" of measurement information by different methods with and without the influence of measurement noise. The accuracy with the influence of measurement noise is lower than that without the influence of noise. This is because noise introduces uncertainty, which causes the model to be unable to accurately capture the true relationship between data, thereby reducing the accuracy. Therefore, regardless of whether the influence of measurement noise is considered, the Koopman global linear optical measurement model is superior to the existing three model prediction methods, and its accuracy meets the measurement information prediction requirements in actual optical relative navigation.

[0190] 4.2 “10-point prediction” and performance comparison based on Koopman global linear optical measurement model

[0191] The simulation results of 4.1 show that the "1-point prediction" accuracy of the Koopman global linear optical measurement model meets the prediction accuracy requirements of actual optical measurement information. However, in actual situations, due to the optical invisibility, the measurement information will be missing for a period of time, so multi-point prediction is needed to complete the missing information. Taking the three-dimensional unit direction vector in space as the measurement information, a "10-point prediction" simulation experiment was carried out, and the prediction error was measured by 50 Monte Carlo average root mean square errors to evaluate the accuracy of the Koopman global linear optical measurement model. During the simulation process, only the impact of measurement error on accuracy was considered, assuming that the noise obeys a Gaussian distribution. In addition, the Koopman global linear optical measurement model was compared with three existing model prediction methods, including the local linearization method, the ARIMA method, and the LSTM method, and the "10-point prediction" effect diagram of the measurement information was obtained, as shown in the figure. Figure 7 shown.

[0192] The corresponding measurement information accuracy is shown in Table 4, where the accuracy is measured by the average root mean square error.

[0193] Table 4 Comparison of RMSE of “10-point prediction” under different methods

[0194]

[0195] according to Figure 7 , with the increase of the number of prediction points, the prediction error gradually increases. However, compared with the other three existing model prediction methods, the Koopman global linear optical measurement model shows lower prediction errors at all prediction point numbers.

[0196] Table 4 shows the average root mean square error comparison results of the "10-point prediction" of measurement information under different methods. Compared with three existing methods, namely the local linearization method, the LSTM method and the ARIMA method, the accuracy of the Koopman global linear optical measurement model is improved by 52.07%, which is far superior to other methods, and the accuracy meets the requirements of optical relative navigation measurement information.

[0197] This significant performance advantage is mainly due to the Koopman operator's ability to effectively capture nonlinear information in nonlinear systems. Through the linear combination of Koopman modes, eigenvalues, and eigenfunctions, the global linearization of the nonlinear observation model is achieved, thereby reducing the loss of nonlinear information. In high-dimensional space, the Koopman mode is used to obtain the phase space topological structure of nonlinear information, so that the Koopman operator model can more comprehensively describe the evolution of the system. Compared with traditional methods, the Koopman operator global measurement model can better predict measurement information, solve the problem of missing measurement information when optically invisible during relative navigation, and provide a reliable solution for space target trajectory prediction.

[0198] 4.3 Effect of sample size on prediction error of Koopman global linear measurement model

[0199] Since the Koopman operator It is approximated by the DMD data-driven algorithm, so the number of training samples is The characteristics of the operator, such as eigenvalues, eigenvectors and modes, have an important influence on the ability to obtain nonlinear information, which in turn affects the prediction performance of the model. Therefore, this section aims to study the influence of the number of training samples on the prediction error of the Koopman global linear optical measurement model, and to infer the number of training samples required for actual optical relative navigation.

[0200] First, the trajectory of the measurement information in the three directions of X, Y, and Z is generated using the optical relative navigation state model (see formula (13)) and the measurement model (see formula (17)). Subsequently, the measurement information is predicted by the Koopman global linear optical measurement model constructed by the embodiment of the present invention, and the predicted trajectory and prediction error of the measurement information in the three directions of X, Y, and Z are obtained, where the prediction error in each direction uses the residual absolute value as a measurement indicator to evaluate the accuracy of the Koopman global linear optical measurement model. Finally, the predicted trajectory and prediction error of the measurement information are given, as shown in detail. Figure 8-Figure 10 shown.

[0201] according to Figure 8-Figure 10, the blue line represents the actual measurement value of the optical camera, the red line represents the prediction result of the global linear measurement model based on the Koopman operator for the actual measurement value, and the magenta line represents the prediction error.

[0202] It is observed that in the X direction, as the number of sampling points increases, the prediction error gradually increases until it reaches a maximum value. Subsequently, the prediction error begins to decrease gradually until it reaches a minimum value. However, as the number of sampling points continues to increase, the prediction error increases again, and then decreases again, and the subsequent increase and decrease are smaller than before. In the Y direction, as the number of sampling points increases, the prediction error continues to increase. In the Z direction, as the number of sampling points increases, the prediction error shows a trend of first increasing, then decreasing, then increasing, then decreasing, and then increasing.

[0203] The reason for this phenomenon in the X and Z directions is that the model exhibits different fitting abilities when dealing with different numbers of sampling points. The model overfits a small amount of training data at the beginning of training, resulting in a gradual increase in the prediction error. Subsequently, the model gradually adapts to and learns the general properties of the data, and the prediction error begins to decrease gradually. However, as the number of sampling points continues to increase, the model overfits the data again, resulting in an increase in the prediction error again. Subsequently, the model adapts to and learns the general properties of the data again, and the prediction error decreases again. The reason for this phenomenon in the Y direction is that the number of predicted samples is too large, resulting in the model being unable to fully capture the changing trends and laws of the data. These two phenomena indicate that there is a trade-off between the complexity of the model and the number of training samples. In practical applications, special attention is paid to the impact of the number of training samples on the prediction accuracy of the model.

[0204] In order to further analyze the influence of the number of training samples on the prediction accuracy of the global linear measurement model based on the Koopman operator. 500 measurement samples were selected as training data. First, the method of gradually increasing the number of training samples was adopted, starting from 5 training samples and then increasing to 500 training samples. Secondly, for each number of training samples, the global linear measurement model based on the Koopman operator was retrained, and the model was used to perform a "10-point prediction". Finally, the prediction error corresponding to different numbers of training samples was analyzed, and a prediction error curve graph that changed with the number of training samples was plotted, where the prediction error used the root mean square error (RMSE) as the evaluation indicator. Fig.11 shown.

[0205] according to Fig.11As a result, it is observed that with the increase in the number of training samples, the prediction error of the global linear measurement model based on the Koopman operator gradually decreases. When the number of training samples reaches 400, the prediction error is 0.038, and this accuracy is sufficient to meet the actual optical relative navigation needs. Further increasing the number of training samples will not significantly reduce the prediction error, but will increase the computational complexity. In practical applications, it is necessary to weigh the prediction accuracy and computational cost. Therefore, this simulation conclusion obtains the number of training samples required to predict the "10-point" measurement information when the target is not visible, which provides certain guidance for the selection of the number of subsequent training measurement samples.

[0206] In summary, the embodiment of the present invention proposes a prediction method for spatial non-cooperative measurement information based on the Koopman operator to solve the problems of incomplete or missing sequence image information in space optical relative navigation. Based on the Koopman theory, a global linear optical measurement model for optical relative navigation is constructed; a model algorithm based on the DMD method is designed to approximate the Koopman operator. The characteristics of the operator, such as eigenvalue, eigenvector and mode, are obtained, and the linear combination of these characteristics is used to achieve high-precision prediction of measurement information. Finally, the model constructed by the embodiment of the present invention is verified by Monte Carlo simulation. The results show that:

[0207] (1) Compared with three existing model prediction methods, namely the local linearization method, the ARIMA method and the LSTM method, the Koopman global linear optical measurement model constructed in the embodiment of the present invention has an accuracy improvement of 52.07% in the "1-point prediction" task;

[0208] (2) Compared with three existing model prediction methods, namely, the local linearization method, the ARIMA method and the LSTM method, the Koopman global linear optical measurement model constructed in the embodiment of the present invention has an accuracy improvement of 52.07% in the task of "10-point prediction";

[0209] (3) The embodiment of the present invention also provides the minimum number of training samples required for optical relative navigation accuracy, which provides an important basis for selecting the number of training samples required for subsequent measurement information prediction.

[0210] It should be understood that the specific order or hierarchy of steps in the disclosed process is an example of an exemplary method. Based on design preferences, it should be understood that the specific order or hierarchy of steps in the process can be rearranged without departing from the scope of protection of the present disclosure. The attached method claims present the elements of the various steps in an exemplary order and are not intended to be limited to the specific order or hierarchy described.

[0211] In the above detailed description, various features are grouped together in a single embodiment to simplify the disclosure. This method of disclosure should not be interpreted as reflecting an intention that the embodiments of the claimed subject matter require more features than are clearly stated in each claim. On the contrary, as reflected in the appended claims, the invention is in a state of having less than all the features of the disclosed individual embodiments. Therefore, the appended claims are hereby expressly incorporated into the detailed description, with each claim standing on its own as a separate preferred embodiment of the invention.

[0212] The disclosed embodiments are described above to enable any person skilled in the art to implement or use the present invention. Various modifications of these embodiments are obvious to those skilled in the art, and the general principles defined herein may also be applied to other embodiments without departing from the spirit and scope of the present disclosure. Therefore, the present disclosure is not limited to the embodiments given herein, but is consistent with the broadest scope of the principles and novel features disclosed in this application.

[0213] The above description includes examples of one or more embodiments. Of course, it is impossible to describe all possible combinations of components or methods for the purpose of describing the above embodiments, but it should be recognized by those skilled in the art that the various embodiments may be further combined and arranged. Therefore, the embodiments described herein are intended to cover all such changes, modifications and variations that fall within the scope of protection of the appended claims. In addition, with respect to the term "comprising" used in the specification or claims, the word is covered in a manner similar to the term "including", just as "including," is explained as a transitional word in the claims. In addition, any term "or" used in the specification of the claims is intended to mean "non-exclusive or".

[0214] Those skilled in the art may also understand that the various illustrative logical blocks, units, and steps listed in the embodiments of the present invention may be implemented by electronic hardware, computer software, or a combination of the two. In order to clearly demonstrate the interchangeability of hardware and software, the various illustrative components, units, and steps described above have generally described their functions. Whether such functions are implemented by hardware or software depends on the specific application and the design requirements of the entire system. Those skilled in the art may use various methods to implement the described functions for each specific application, but such implementation should not be understood as exceeding the scope of protection of the embodiments of the present invention.

[0215] The various illustrative logic blocks or units described in the embodiments of the present invention can be implemented or operated by a general-purpose processor, a digital signal processor, an application-specific integrated circuit (ASIC), a field programmable gate array or other programmable logic device, a discrete gate or transistor logic, a discrete hardware component, or any combination of the above. The general-purpose processor can be a microprocessor, and optionally, the general-purpose processor can also be any conventional processor, controller, microcontroller or state machine. The processor can also be implemented by a combination of computing devices, such as a digital signal processor and a microprocessor, a plurality of microprocessors, one or more microprocessors combined with a digital signal processor core, or any other similar configuration.

[0216] The steps of the method or algorithm described in the embodiments of the present invention can be directly embedded in hardware, a software module executed by a processor, or a combination of the two. The software module can be stored in a RAM memory, a flash memory, a ROM memory, an EPROM memory, an EEPROM memory, a register, a hard disk, a removable disk, a CD-ROM, or other storage media of any form in the art. Exemplarily, the storage medium can be connected to the processor so that the processor can read information from the storage medium and can write information to the storage medium. Optionally, the storage medium can also be integrated into the processor. The processor and the storage medium can be arranged in an ASIC, and the ASIC can be arranged in a user terminal. Optionally, the processor and the storage medium can also be arranged in different components in the user terminal.

[0217] In one or more exemplary designs, the above functions described in the embodiments of the present invention can be implemented in hardware, software, firmware or any combination of the three. If implemented in software, these functions can be stored on a computer-readable medium, or transmitted in the form of one or more instructions or codes on a computer-readable medium. Computer-readable media include computer storage media and communication media that facilitate the transfer of computer programs from one place to another. The storage medium can be any available medium that can be accessed by any general or special computer. For example, such computer-readable media can include but are not limited to RAM, ROM, EEPROM, CD-ROM or other optical disk storage, disk storage or other magnetic storage devices, or any other medium that can be used to carry or store program codes in the form of instructions or data structures and other forms that can be read by general or special computers, or general or special processors. In addition, any connection can be appropriately defined as a computer-readable medium, for example, if the software is transmitted from a website site, server or other remote resource through a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL) or wirelessly, such as infrared, wireless and microwave, it is also included in the defined computer-readable medium. The disk and disc include compact disk, laser disk, optical disk, DVD, floppy disk and blue-ray disk. Disks usually copy data magnetically, while discs usually copy data optically with lasers. The above combination can also be included in computer readable media.

[0218] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting measurement information of a space non-cooperative target, characterized in that: include: In view of the situation that when a non-cooperative target is affected by external complex factors, the non-cooperative target is invisible to the optical sensor of the service spacecraft, resulting in the optical sensor of the service spacecraft being unable to obtain the measurement information of the non-cooperative target, when the non-cooperative target is not affected by the external complex factors, the measurement information of the non-cooperative target for a period of time is obtained by the service spacecraft to construct an optical relative navigation nonlinear measurement model of the non-cooperative target; and the Koopman operator is used to construct a Koopman global linear optical measurement model for the optical relative navigation nonlinear measurement model of the non-cooperative target, and the Koopman global linear optical measurement model is used as a prediction model for the measurement information when the non-cooperative target is invisible, and the external complex factors include at least one of the following: occultation and sunlight; By using the DMD data-driven algorithm, a finite-dimensional subspace is sought to approximate the Koopman operator of the prediction model, so as to simplify and reduce the dimension of the prediction model, and a low-dimensional approximate matrix of the Koopman operator is obtained. The Koopman global linear optical measurement model using the low-dimensional approximate matrix of the Koopman operator is used as the Koopman global linear optical measurement model after dimensionality reduction; The measurement information of non-cooperative targets is predicted when they are invisible through the dimensionality-reduced Koopman global linear optical measurement model.

2. The prediction model of measurement information of a space non-cooperative target according to claim 1, characterized in that: The optical relative navigation nonlinear measurement model includes a state model and an optical measurement model, wherein the state model refers to the relative motion state equation of the service spacecraft and the non-cooperative target established in the orbital system when the service spacecraft and the non-cooperative target are in orbit; The optical measurement model refers to the equation that the optical camera used in relative navigation can only collect measurement data in the line of sight direction of non-cooperative targets, and uses the pinhole imaging model to describe the imaging process of the optical camera.

3. The method for predicting measurement information of a space non-cooperative target according to claim 2, characterized in that: The Koopman operator is used to construct the Koopman global linear optical measurement model for the optical relative navigation nonlinear measurement model of non-cooperative targets, including: Koopman operator is a global linearization method, which uses Koopman operator to express the nonlinear measurement model of optical relative navigation of non-cooperative targets as an infinite-dimensional linear operator in the Hibbert space of dimensional ascending function. The Koopman global linear optical measurement model is obtained through the infinite dimensional linear operator in the Hibbert space of the dimensionality-raising function.

4. The method for predicting measurement information of a space non-cooperative target according to claim 3, characterized in that: Through the DMD data-driven algorithm, a finite-dimensional subspace is sought to approximate the Koopman operator of the prediction model, so as to simplify and reduce the dimension of the prediction model, and obtain a low-dimensional approximate matrix of the Koopman operator, including: In the Koopman global linear optical measurement model, the Koopman operator includes three features: Koopman eigenvalue, the Koopman eigenvalue, the corresponding eigenfunction and the corresponding Koopman mode. The three features included in the Koopman operator provide the dynamic law of the nonlinear system in the future evolution over time; For any Koopman eigenvalue, a global linearization of a nonlinear measurement model is achieved by a linear combination of the Koopman eigenvalue, a characteristic function corresponding to the Koopman eigenvalue, and a Koopman mode corresponding to the Koopman eigenvalue; The Koopman pattern corresponding to the Koopman eigenvalue reflects the dynamic law of the system evolving over time; If the absolute value of any Koopman eigenvalue of the Koopman operator is greater than 1, the influence of the coefficient of the Koopman eigenvalue on the measurement information becomes more and more important over time, indicating that the influence of the Koopman mode corresponding to the Koopman eigenvalue on the measurement information will weaken over time; the coefficient of the Koopman eigenvalue refers to the Koopman mode ν j ; If the absolute value of any Koopman eigenvalue of the Koopman operator is less than 1, the influence of the coefficient of the Koopman eigenvalue over time on the measurement information is not important, indicating that the influence of the Koopman pattern corresponding to the Koopman eigenvalue on the measurement information will weaken over time.

5. The method for predicting measurement information of a space non-cooperative target according to claim 4, characterized in that: Through the DMD data-driven algorithm, a finite-dimensional subspace is sought to approximate the Koopman operator of the prediction model, so as to simplify and reduce the dimension of the prediction model, and obtain a low-dimensional approximate matrix of the Koopman operator, which also includes: In the optical measurement model, the measurement data sequence of the collected non-cooperative target is used to construct two measurement data matrices: a previous measurement data matrix and a subsequent measurement data matrix; Assuming that the sampling time used for the measurement data sequence is small enough, the two measurement data matrices satisfy an approximate linear relationship. The low-dimensional matrix A representing the relationship between the two measurement data matrices is the Koopman operator A low-dimensional approximation of .

6. The method for predicting measurement information of a space non-cooperative target according to claim 5, characterized in that: Through the DMD data-driven algorithm, a finite-dimensional subspace is sought to approximate the Koopman operator of the prediction model, so as to simplify and reduce the dimension of the prediction model, and obtain a low-dimensional approximate matrix of the Koopman operator, which also includes: The specific calculation process of the low-dimensional approximate matrix of the Koopman operator is as follows: Calculate the SVD decomposition of the previous measurement data matrix; Combine the coefficients in the SVD decomposition of the previous measurement data matrix and the subsequent measurement data matrix to define an approximate matrix of the low-dimensional matrix A Compute the approximate matrix The eigenvalue λ and eigenvector ω of , where the eigenvalue of the matrix A is also λ, which is called the DMD eigenvalue; Then construct the eigenvector υ of the low-dimensional matrix A, and the eigenvector υ is called the DMD mode; then the DMD mode corresponds to the Koopman mode, and the DMD eigenvalue corresponds to the Koopman eigenvalue, and the low-dimensional approximate matrix of the Koopman operator is obtained.

7. The method for predicting measurement information of a space non-cooperative target according to claim 1, characterized in that: The Koopman global linear optical measurement model after dimensionality reduction is used to predict the measurement information when the non-cooperative target is invisible, including: When the non-cooperative target at the current moment is not affected by external complex factors and the non-cooperative target is affected by external complex factors at the current moment, the measurement information of the non-cooperative target at the current moment and the subsequent moments is predicted by the Koopman global linear optical measurement model after dimensionality reduction.

8. A method for predicting measurement information of a space non-cooperative target, characterized in that: include: A prediction model building unit is used for obtaining measurement information of the non-cooperative target for a period of time through the service spacecraft when the non-cooperative target is not affected by external complex factors and the non-cooperative target is invisible to the optical sensor of the service spacecraft, resulting in the optical sensor of the service spacecraft being unable to obtain measurement information of the non-cooperative target. The non-cooperative target is not affected by external complex factors, and the measurement information of the non-cooperative target for a period of time is obtained through the service spacecraft, and the optical relative navigation nonlinear measurement model of the non-cooperative target is combined with the Koopman operator to build the Koopman global linear optical measurement model, and the Koopman global linear optical measurement model is used as a prediction model of measurement information when the non-cooperative target is invisible. The external complex factors include at least one of the following: occultation and sunlight. A dimension reduction unit is used to seek a finite-dimensional subspace to approximate the Koopman operator of the prediction model through a DMD data-driven algorithm, so as to simplify and reduce the dimension of the prediction model, obtain a low-dimensional approximate matrix of the Koopman operator, and use the Koopman global linear optical measurement model using the low-dimensional approximate matrix of the Koopman operator as the Koopman global linear optical measurement model after dimension reduction. The measurement information prediction unit is used to predict the measurement information when the non-cooperative target is invisible through the Koopman global linear optical measurement model after dimensionality reduction.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores one or more programs, which, when executed by a computer device, enable the computer device to execute the method for predicting measurement information of a space non-cooperative target as described in any one of claims 1-7.

10. A computer device, characterized in that: include: processor; And, a memory arranged to store computer executable instructions, which, when executed, cause the processor to execute the method for predicting measurement information of a space non-cooperative target as described in any one of claims 1-7.

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