Space target state sensing method based on luminosity micro-change signal

Abstract

The invention relates to a method for perceiving a space target state by using a luminosity micro-change signal, which reconstructs a phase space through a luminosity sequence embedding technology and perceives the space target state. The method comprises the following specific steps: 1) based on a phase space reconstruction theory, embedding a one-dimensional luminosity sequence into a phase space, and constructing a phase space zero-order trajectory matrix; further, describing a satellite state by using a third-order system, and expanding the trajectory matrix into a first-order differential trajectory matrix, a second-order differential trajectory matrix and a third-order differential trajectory matrix; 2) in a phase space, constructing two-dimensional analysis signal representation of a multi-order track moment sequence based on Riesz transformation, and obtaining a local amplitude, a local phase and a local direction component matrix of a multi-order track matrix; and 3) on the basis of the multi-track moment and the two-dimensional permutation entropy of the local amplitude, the local phase and the local direction of the corresponding two-dimensional analysis signal, constructing a 16-dimensional space target state mode for sensing state abnormity. The method has the advantage of high timeliness, and is suitable for online space target state monitoring.

Description

Technical Field

[0001] The present invention relates to the field of space target monitoring, and in particular to a space target state perception method based on photometric micro-variation signals. Background Art

[0002] The perception of the on-orbit state of space targets is one of the important tasks of the space target monitoring system. Telemetry data is a direct observation of the state of space targets, so it is the main basis for cooperative space target state detection and anomaly detection, and is also the source of perception and prediction of key components such as power system operating state parameters. In the satellite image sequence observed by ground-based or space-based optical telescopes, there is a correlation between the luminosity change of space targets and their state. Therefore, luminosity changes can be used to perceive the state of cooperative and non-cooperative space targets.

[0003] A space target that is operating normally in orbit can be regarded as a controlled system. The theory of dynamical systems uses phase space (state space) to describe all possible state evolutions of a controlled system. In the study of space target state perception, it is impossible for monitoring equipment to detect all states of the system. It can only use an optical telescope to obtain the photometric sequence of the target within a photometric time period, and use the photometric sequence embedding technology to model it in the phase space, reconstruct a phase space that is topologically equivalent to the dynamic system, and reveal the dynamic characteristics and structure of the controlled system, such as the stability of the system.

[0004] The basic idea of ​​the present invention is: 1) The problem of space target state perception is regarded as the problem of dynamic system state evolution. Based on the phase space reconstruction theory, the one-dimensional photometric sequence is embedded into the phase space, and the phase space trajectory matrix is ​​constructed to perceive the evolution of space target state. Further, the satellite state is described by a third-order system, and the trajectory matrix is ​​expanded into first-order, second-order and third-order differential trajectory matrices; 2) Permutation entropy is a powerful tool for detecting the randomness and dynamic mutation behavior of time series, and can reflect the evolution of the dynamic state of complex systems by reflecting the micro-change information of time series. It also has the advantages of simple calculation, strong anti-noise ability, and suitability for online analysis. The present invention calculates the two-dimensional permutation entropy of the trajectory matrix as the characteristic parameter of the space target state; 3) Based on the hypercomplex number method and Riesz transformation, the two-dimensional analytical signal of the trajectory moment sequence and the corresponding multi-order differential trajectory matrix is ​​constructed to obtain the local amplitude, local phase and local direction matrix of the trajectory matrix. Based on the two-dimensional permutation entropy of the above matrix, the 16-dimensional pattern vector of the space target state is constructed. Summary of the invention

[0005] 1. Technical issues to be resolved

[0006] In order to solve the problem of on-orbit state perception of space targets, the present invention proposes a state perception method based on the hypercomplex two-dimensional arrangement entropy of photometric micro-variation signals. The method takes the photometric sequence signal of the space target obtained by an offline or online photometric telescope as input to perceive whether the target state is abnormal or not. The method can realize the integration of photometric perception based on a short photometric sequence of 32 photometric data points.

[0007] (II) Technical solution

[0008] The present invention proposes a method for sensing the state of a space target based on a photometric micro-variation signal, comprising the following steps:

[0009] S1: Based on the phase space reconstruction theory, the one-dimensional luminosity sequence obtained by an optical telescope in one circle observation is embedded into the phase space to construct a phase space trajectory matrix, called the zero-order trajectory matrix. Furthermore, the satellite state is described by a third-order system, and the trajectory matrix is ​​expanded into first-order, second-order and third-order differential trajectory matrices to achieve a multi-order trajectory matrix phase space representation of the luminosity sequence;

[0010] S2: In phase space, a two-dimensional analytical signal representation of a multi-order trajectory moment sequence is constructed based on Riesz transform to obtain the local amplitude, local phase and local direction component matrices of the multi-order trajectory matrix;

[0011] S3: Construct a 16-dimensional spatial target state pattern based on the two-dimensional permutation entropy of the local amplitude, local phase and local direction of the multi-trajectory moment and its corresponding two-dimensional analytical signal;

[0012] S4: Construct a 16-dimensional model of the normal working state of the space target on orbit as the standard model. Perform similarity identification between the 16-dimensional state model constructed by the online photometry sequence and the standard model to detect whether the target state is abnormal.

[0013] In the above scheme, the step S1 is to construct a homeomorphic phase space describing the state evolution of the space target using a one-dimensional photometric sequence, which specifically includes the following process:

[0014] S11: The state equation of the satellite in orbit is expressed by a third-order jerk system, where the first-order variation represents the luminosity change caused by the satellite state change, the second-order variation represents the rate of luminosity change, and the third-order variation is used to extract luminosity mutation information;

[0015] S12: Using the time delay embedding method, the photometric sequence is embedded into a d-dimensional phase space through the time delay parameter τ and the embedding dimension d, and a phase point sequence representing the satellite state change in the phase space is constructed;

[0016] S13: Use the difference of adjacent columns of the phase space trajectory matrix to approximate the estimation of different orders of phase space changes and construct the first-order, second-order and third-order trajectory matrices.

[0017] In the above scheme, the step S2 is to construct a trajectory matrix sequence representing the space target in the phase space based on the hypercomplex number method and Riesz transformation, which specifically includes the following process:

[0018] S21: Based on the hypercomplex method and Riesz transform, the two-dimensional analytical signals of the zero-order trajectory matrix, the first-order trajectory matrix, the second-order trajectory matrix and the third-order trajectory matrix are constructed respectively;

[0019] S22: based on the two-dimensional analytical signals of different order trajectory matrices constructed in S21, local amplitude, local phase and local direction matrices of the two-dimensional analytical signals are generated respectively;

[0020] S23: The zero-order trajectory matrix, the first-order trajectory matrix, the second-order trajectory matrix and the third-order trajectory matrix and their corresponding local amplitude, local phase and local direction matrices of the two-dimensional analytical signal constitute 16 matrices representing the state of the spatial target in the phase space.

[0021] In the above scheme, the step S3 is to calculate the two-dimensional permutation entropy of the trajectory matrix sequence constructed in step S2, and construct a 16-dimensional two-dimensional permutation entropy model of the phase space characterizing the state of the spatial target, which specifically includes the following process:

[0022] S31: Based on the idea of ​​time-delay phase space reconstruction, the trajectory matrix is ​​reconstructed into a two-dimensional phase space to construct a fourth-order tensor space;

[0023] S32: In the fourth-order tensor space, each matrix block generated in the two-dimensional phase space reconstruction process is vectorized into a one-dimensional sequence, and then the sequence is sorted in ascending order to obtain the sorted position sequence. According to the number of occurrences of each matrix block position sequence, the probability distribution of the arrangement pattern is estimated, and the probability distribution of the arrangement pattern is substituted into the Shannon entropy formula to obtain the normalized two-dimensional arrangement entropy;

[0024] S33: Based on the 16 state matrices representing the space target in the phase space generated in step S23, a 16-dimensional two-dimensional arrangement entropy pattern of the space target is constructed.

[0025] In the above scheme, the step S4 is to perform similarity recognition between the state mode constructed based on the online photometry sequence and the standard mode, which specifically includes the following process:

[0026] S41: Construct a 16-dimensional model of the normal working state of the space target on orbit as a standard model;

[0027] S42: Based on the online photometry sequence, a 16-dimensional state pattern is constructed to perform similarity recognition with the standard pattern to sense whether the target state is abnormal.

[0028] The above technical solution has the following beneficial effects:

[0029] 1. The phase space reconstruction of multi-order differences approximates the differential trajectory matrix sequence, which can enhance the amplitude ratio between different slightly varying signals coupled to the photometric sequence, and is conducive to using the slightly varying photometric signals coupled in the photometric sequence to perceive the on-orbit state of the target.

[0030] 2. Constructing a 16-dimensional target state pattern vector is suitable for machine learning. On the other hand, this local information expression can enhance the ability to analyze the evolution of the state of the dynamic system in the phase space.

[0031] 3. The 16-dimensional vector of the target state pattern is composed of 16 two-dimensional permutation entropies of four groups of trajectory matrices. When calculating the two-dimensional permutation entropy, a phase space reconstruction is performed again. The process of constructing the one-dimensional photometric sequence to the 16-dimensional two-dimensional permutation entropy pattern is twice nested in the phase space reconstruction, realizing the mapping from the one-dimensional photometric sequence to the two-dimensional phase space and then to the four-dimensional phase space (fourth-order tensor space). In the probability sense, the ascending order in the two-dimensional permutation entropy calculation is recombined and the information generated when the relevant state of the dynamic system changes slightly is quantified in the form of relatively unbalanced permutation entropy.

[0032] 4. Online sensing and calculation integration: Select 32 photometric data sequences to sense satellite status. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The accompanying drawings, which constitute a part of this specification, are included to provide a further understanding of the present invention.

[0034] Figure 1 It is the overall algorithm flow chart of the present invention; DETAILED DESCRIPTION

[0035] The following detailed descriptions are all exemplary and are intended to provide further explanation of the present invention and to clearly and completely describe the technical solutions in the embodiments of the present invention. All technical and scientific terms used herein have the same meanings as those generally understood by ordinary technicians in the technical field to which the present invention belongs.

[0036] In this embodiment, if Figure 1 As shown in FIG. 1 , it is an overall flow chart of an algorithm for calculating and amplifying a slight change in the luminosity of a space target proposed by the present invention, which includes the following steps:

[0037] S1: Based on the phase space reconstruction theory, the one-dimensional luminosity sequence obtained by an optical telescope in one circle observation is embedded into the phase space to construct a phase space trajectory matrix, called the zero-order trajectory matrix. Furthermore, the satellite state is described by a third-order system, and the trajectory matrix is ​​expanded into first-order, second-order and third-order differential trajectory matrices to achieve a multi-order trajectory matrix phase space representation of the luminosity sequence;

[0038] S2: In phase space, a two-dimensional analytical signal representation of a multi-order trajectory moment sequence is constructed based on Riesz transform to obtain the local amplitude, local phase and local direction component matrices of the multi-order trajectory matrix;

[0039] S3: Construct a 16-dimensional spatial target state pattern based on the two-dimensional permutation entropy of the local amplitude, local phase and local direction of the multi-trajectory moment and its corresponding two-dimensional analytical signal;

[0040] S4: Construct a 16-dimensional model of the normal working state of the space target on orbit as the standard model. Perform similarity identification between the 16-dimensional state model constructed by the online photometry sequence and the standard model to detect whether the target state is abnormal.

[0041] In the above scheme, the step S1 uses a one-dimensional photometric sequence to construct a homeomorphic phase space trajectory matrix sequence describing the state evolution of the space target. Suppose the satellite photometric sequence obtained by an optical telescope in one observation cycle is x = {x1, x2, ..., x N The time delay embedding method is used to embed the photometric sequence into a d-dimensional phase space through the time delay parameter τ and the embedding dimension d, and the phase point sequence in the phase space is constructed. The phase point x reconstructed by time delay embedding i It can be regarded as a point in the d-dimensional phase space, also known as the delay vector:

[0042] x i ={x i ,x i+τ ,…,x i+(d-1)τ}(i=1,…,M)

[0043] Where, M = N-(d-1)τ. M phase points constitute a phase space trajectory. If regarded as coordinates of a rectangular coordinate system, the phase space trajectory forms a phase space M×d trajectory matrix. The present invention takes the time delay parameter τ = 1 and the embedding dimension N is the number of photometric points in the photometric sequence, represents rounding down, then the phase space trajectory matrix is:

[0044]

[0045] The trajectory matrix X is called the zero-order trajectory matrix.

[0046] In order to correspond to the third-order system, it is necessary to construct the first-order, second-order and third-order trajectory matrices. The present invention uses the difference of adjacent columns of the phase space trajectory matrix to approximate the estimation of the multi-order trajectory matrix. The embedding dimension of the trajectory matrices of different orders is reduced by one dimension successively.

[0047]

[0048]

[0049] In the above scheme, the step S2 is to construct a trajectory matrix sequence that characterizes the space target in the phase space based on the hypercomplex method and Riesz transform. The two-dimensional analytical signal that constructs the trajectory matrix sequence based on the hypercomplex method and Riesz transform is called a single-shot signal. The Riesz transform frequency domain and spatial domain of the trajectory matrix X are expressed by the following formula:

[0050]

[0051] Where ω = [ω1, ω2] is the frequency domain variable, i, j are imaginary units, x = [x, y], the symbol “·” represents the product operation, and “*” represents the convolution operation. (R1, R2) and X F denote the Riesz transform and Fourier transform of the trajectory matrix X. The original trajectory matrix and its two Riesz transform components together constitute the single-shot signal X M :

[0052] X M (x) = X(x) + iR1(x) + jR2(x)

[0053] As with the one-dimensional analytical signal, we can obtain the local amplitude, local phase and local direction information of the two-dimensional signal through the constructed single-phase signal. The two Riesz transform components and the original signal constitute a three-dimensional signal vector, denoted as X M =[X,R1,R2]. In the spherical coordinate system, the local amplitude A and the local phase and the local direction θ and X M The relationship between the quantities is:

[0054]

[0055] The local amplitude of the single-evolution signal is related to the local energy change, the local phase can reflect the local structural evolution of the trajectory matrix, and the local direction describes the local geometric information of the trajectory matrix and the direction of the maximum variance of the structural evolution. This local information expression is conducive to analyzing the evolution of the state of the dynamic system in the phase space.

[0056] In the above scheme, step S3 is to calculate the two-dimensional permutation entropy of the trajectory matrix sequence constructed in step S2. Based on the photometric luminosity sequence of one observation circle of the satellite, the phase space reconstruction can obtain the zero-order, first-order, second-order and third-order trajectory matrices and their corresponding three single component matrices of local amplitude, local phase and local direction. A total of 16 phase space sub-matrices can be constructed to generate the satellite state mode vector.

[0057] The luminosity sequence of a satellite in normal working state shows relatively regular changes. Changes in satellite state cause the luminosity curve to fluctuate, irregularly change, and increase complexity. Permutation entropy is an indicator that introduces the idea of ​​permutation in phase space and calculates the complexity between reconstructed subsequences. It increases with abnormal fluctuations in time series, so it is suitable for using time series to detect changes in the state of dynamic systems.

[0058] Generalize the one-dimensional permutation entropy algorithm to two dimensions and calculate N x ×N y Trajectory Matrix Permutation entropy. The principle is the same as the one-dimensional permutation entropy algorithm. First, the trajectory matrix is ​​reconstructed into a two-dimensional phase space. Let the embedding dimension be d x ×d y , 1≤d x ≤N x ,1≤d y ≤N y , and 1<d x d y <N x N y The time delay parameters in both x and y directions are set to 1.

[41] , then the number of phase points in the x and y directions in the phase space are K x =N x -d x +1, K y =N y -d y +1. Trajectory matrix phase space reconstruction is based on the idea of ​​time-delay phase space reconstruction, reconstructing the trajectory matrix X into K x K y A sequence matrix block L, at this time the phase point in the phase space corresponds to a matrix block. The specific implementation formula is as follows:

[0059]

[0060] in,

[0061]

[0062] After phase space reconstruction, K x K y Each matrix block is vectorized into a one-dimensional sequence, and then the sequence is sorted in ascending order to obtain a sorted position sequence. Each matrix block is vectorized into d x d y dimensional sequences are mapped to all possible permutations (d x d y )! One of them. The πth permutation pattern is one of all K x K y The probability of appearing in the position sequence is:

[0063]

[0064] Among them, C π It represents the number of times the πth permutation pattern appears in all position sequences. Substituting the formula P(π) into the Shannon entropy formula, we get the normalized two-dimensional permutation entropy:

[0065]

[0066] in, S max =log[(d x d y )! ] means that each position sequence has and they are equally likely, at which time the time series complexity is the highest and the entropy is the largest.

[0067] The abnormal state of the space target causes a slight change in the light curve, or the light intensity change signal generated by the target state is wrapped in the light curve. In order to better use the light intensity change to perceive the change of the target state, the relative imbalance permutation entropy is further calculated based on the permutation entropy:

[0068] R[P]=G[P,P e ]H[P]

[0069] Among them, G[P,P e ] is the empirical probability P = P[π] and the equal probability P e =1 / (d x d y )! The relative entropy measure between them is called imbalance, which is defined by Jensen-Shannon divergence:

[0070]

[0071] in,

[0072]

[0073] R max is G[P,P e ]The maximum possible value.

[0074] The relative imbalance permutation entropy quantifies the information generated when the relevant states of a dynamic system change slightly, and uses time series to perceive slight changes in system states.

[0075] In the above scheme, the step S4 is to construct a state mode based on the online photometry sequence and perform similarity recognition with the standard mode. Based on step S3, a 16-dimensional two-dimensional relatively unbalanced permutation entropy mode of the space target state is constructed. Assuming that the 16-dimensional two-dimensional relatively unbalanced permutation entropy mode of the space target in the normal on-orbit state is PNormal , the online photometry sequence construction state mode is P test .

[0076] The present invention regards the two modes as the probability distribution of the space target state mode and uses the Wassertein distance metric P Normal and P test This distance metric can capture the structural differences between distributions and is therefore suitable for identifying whether the state of a spatial target is abnormal.

[0077] Although the specific implementation methods of the present invention are described above in conjunction with the accompanying drawings, this does not limit the scope of protection of the present invention. All other embodiments obtained by ordinary technicians in this field without making creative work on the basis of the technical solution of the present invention are within the scope of protection of the present invention.

Claims

1. A method for sensing the state of a space target based on a photometric micro-variation signal, characterized in that: The space target in normal orbit is regarded as a controlled dynamic system. The photometric telescope is used to obtain the photometric sequence of the target within a photometric time period. The photometric sequence embedding technology is used to reconstruct a phase space in the phase space that is topologically equivalent to the dynamic system to perceive the state of the space target, including the following steps: S1: Based on the phase space reconstruction theory, the one-dimensional luminosity sequence obtained by an optical telescope in one circle observation is embedded into the phase space to construct a phase space trajectory matrix, called the zero-order trajectory matrix. Furthermore, the satellite state is described by a third-order system, and the trajectory matrix is ​​expanded into first-order, second-order and third-order differential trajectory matrices to achieve a multi-order trajectory matrix phase space representation of the luminosity sequence; S2: In phase space, a two-dimensional analytical signal representation of a multi-order trajectory moment sequence is constructed based on Riesz transform to obtain the local amplitude, local phase and local direction component matrices of the multi-order trajectory matrix; S3: Construct a 16-dimensional spatial target state pattern based on the two-dimensional permutation entropy of the local amplitude, local phase and local direction of the multi-trajectory moment and its corresponding two-dimensional analytical signal; S4: Construct a 16-dimensional model of the normal working state of the space target on orbit as the standard model. Perform similarity identification between the 16-dimensional state model constructed by the online photometry sequence and the standard model to detect whether the target state is abnormal.

2. A method for sensing a space target state based on a photometric micro-variation signal according to claim 1, characterized in that: The step S1 is specifically The process includes: S11: The state equation of the satellite in orbit is expressed by a third-order jerk system, where the first-order variation represents the luminosity change caused by the satellite state change, the second-order variation represents the rate of luminosity change, and the third-order variation is used to extract luminosity mutation information; S12: Using the time delay embedding method, the photometric sequence is embedded into a d-dimensional phase space through the time delay parameter τ and the embedding dimension d, and a phase point sequence representing the satellite state change in the phase space is constructed; S13: Use the difference of adjacent columns of the phase space trajectory matrix to approximate the estimation of different orders of phase space changes and construct the first-order, second-order and third-order trajectory matrices.

3. The method for sensing the state of a space target based on a photometric micro-variation signal according to claim 1, characterized in that: The step S2 specifically includes the following process: S21: Based on the hypercomplex method and Riesz transform, the two-dimensional analytical signals of the zero-order trajectory matrix, the first-order trajectory matrix, the second-order trajectory matrix and the third-order trajectory matrix are constructed respectively; S22: based on the two-dimensional analytical signals of different order trajectory matrices constructed in S21, local amplitude, local phase and local direction matrices of the two-dimensional analytical signals are generated respectively; S23: The zero-order trajectory matrix, the first-order trajectory matrix, the second-order trajectory matrix and the third-order trajectory matrix and their corresponding local amplitude, local phase and local direction matrices of the two-dimensional analytical signal constitute 16 matrices representing the state of the spatial target in the phase space.

4. The method for sensing the state of a space target based on a photometric micro-variation signal according to claim 1, characterized in that: The step S3 is specifically The process includes: S31: Based on the idea of ​​time-delay phase space reconstruction, the trajectory matrix is ​​reconstructed into a two-dimensional phase space to construct a fourth-order tensor space; S32: In the fourth-order tensor space, each matrix block generated in the two-dimensional phase space reconstruction process is vectorized into a one-dimensional sequence, and then the sequence is sorted in ascending order to obtain the sorted position sequence. According to the number of occurrences of each matrix block position sequence, the probability distribution of the arrangement pattern is estimated, and the probability distribution of the arrangement pattern is substituted into the Shannon entropy formula to obtain the normalized two-dimensional arrangement entropy; S33: Based on the 16 state matrices representing the space target in the phase space generated in step S23, a 16-dimensional two-dimensional arrangement entropy pattern of the space target is constructed.

5. A method for sensing space target state based on photometric micro-variation signals as claimed in claim 0, characterized in that: The specific process of step S4 is as follows: S41: Construct a 16-dimensional model of the normal working state of the space target on orbit as a standard model; S42: Based on the online photometry sequence, a 16-dimensional state pattern is constructed to perform similarity recognition with the standard pattern to sense whether the target state is abnormal.

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