A method for space target state perception based on slight photometric variation signals

Abstract

This invention relates to a method for sensing the state of space targets using photometric micro-variation signals. It reconstructs the phase space using photometric sequence embedding technology to sense the state of space targets. The specific steps are as follows: 1) Based on phase space reconstruction theory, a one-dimensional photometric sequence is embedded into the phase space to construct a zero-order trajectory matrix. Further, a third-order system is used to describe the satellite state, expanding the trajectory matrix into first-order, second-order, and third-order difference trajectory matrices; 2) In the phase space, a two-dimensional analytical signal representation of the multi-order trajectory moment sequence is constructed based on the Riesz transform, obtaining the local amplitude, local phase, and local direction component matrices of the multi-order trajectory matrix; 3) Based on the multi-track moments and the corresponding two-dimensional analytical signal's local amplitude, local phase, and local direction two-dimensional arrangement entropy, a 16-dimensional space target state pattern is constructed for sensing state anomalies. This invention has the advantage of high timeliness and is suitable for online space target state monitoring.

Description

Technical Field

[0001] This invention relates to the field of space target surveillance, specifically to a method for sensing the state of space targets based on photometric micro-variation signals. Background Technology

[0002] On-orbit status awareness of space targets is one of the important tasks of space target surveillance systems. Telemetry data is a direct observation of the status of space targets, and therefore serves as the primary basis for detecting the status and anomalies of cooperative space targets. It is also a source for sensing and predicting the operating status parameters of key components such as power systems. In satellite image sequences observed by ground-based or space-based optical telescopes, there is a correlation between changes in the light intensity of space targets and their status. Therefore, changes in light intensity can be used to sense the status of cooperative and non-cooperative space targets.

[0003] A space target operating normally in orbit can be considered a controlled system. Dynamical systems theory uses phase space (state space) to describe all possible state evolutions of a controlled system. In space target state perception research, monitoring equipment cannot detect all states of the system. It can only use optical telescopes to obtain the photometric sequence of the target within a photometric time period. By using photometric sequence embedding technology to model in phase space, a phase space that is topologically equivalent to the dynamical system can be reconstructed, revealing the dynamic characteristics and structure of the controlled system, such as system stability.

[0004] The basic idea of ​​this invention is as follows: 1) Treating the problem of space target state perception as a dynamic system state evolution problem, based on phase space reconstruction theory, a one-dimensional photometric sequence is embedded into the phase space to construct a phase space trajectory matrix to perceive the evolution of the space target state. Furthermore, a third-order system is used to describe the satellite state, extending the trajectory matrix to first-order, second-order, and third-order difference trajectory matrices; 2) Permutation entropy is a powerful tool for detecting the randomness and dynamic mutation behavior of time series, reflecting the subtle changes in time series information, and detecting the dynamic state evolution of complex systems. It also has advantages such as simple calculation, strong noise resistance, and suitability for online analysis. This invention calculates the two-dimensional permutation entropy of the trajectory matrix as a characteristic parameter of the space target state; 3) Based on the hypercomplex number method and Riesz transform, a two-dimensional analytic signal of the trajectory moment sequence and the corresponding multi-order difference 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, a 16-dimensional pattern vector of the space target state is constructed. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] To address the problem of on-orbit status perception of space targets, this invention proposes a status perception method based on the supercomplex two-dimensional arrangement entropy of photometric micro-variation signals. Using the photometric sequence signal of the space target acquired by offline or online photometric telescopes as input, it can perceive whether the target status is abnormal. It can achieve integrated photometric perception based on a short photometric sequence of 32 photometric data points.

[0007] (II) Technical Solution

[0008] This invention proposes a spatial target state sensing method based on photometric micro-variation signals, comprising the following steps:

[0009] S1: Based on phase space reconstruction theory, the one-dimensional photometric sequence obtained from one orbit of an optical telescope is embedded into phase space to construct a phase space trajectory matrix, called the zero-order trajectory matrix. Furthermore, a third-order system is used to describe the satellite state, extending the trajectory matrix into first-order, second-order, and third-order difference trajectory matrices, thus realizing a multi-order trajectory matrix phase space representation of the photometric sequence.

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

[0011] S3: Based on the two-dimensional arrangement entropy of the local amplitude, local phase, and local direction of the multi-trajectory moments and their corresponding two-dimensional analytical signals, a 16-dimensional spatial target state pattern is constructed.

[0012] S4: Construct a 16-dimensional model of the normal on-orbit operation status of the space target as a standard model. The 16-dimensional state model constructed using online photometric sequences is compared with the standard model for similarity identification to detect any anomalies in the target's state.

[0013] In the above scheme, step S1 involves constructing a homeomorphic phase space describing the evolution of the spatial target state using a one-dimensional photometric sequence, specifically including the following process:

[0014] S11: The state equation of the satellite in orbit is represented by a third-order jerk system, in which the first-order change represents the change in luminosity caused by the change in satellite state, the second-order change represents the rate of change in luminosity, and the third-order change is used to extract information on abrupt changes in luminosity.

[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 changes in satellite state in the phase space is constructed.

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

[0017] In the above scheme, step S2 involves constructing a sequence of trajectory matrices representing spatial targets in phase space based on the hypercomplex number method and Riesz transform, specifically including the following process:

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

[0019] S22: Based on the two-dimensional analytic signals of different order trajectory matrices constructed in S21, the local amplitude, local phase, and local direction matrices of the two-dimensional analytic 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, together with the local amplitude, local phase, and local direction matrices of their corresponding two-dimensional analytical signals, form 16 matrices in phase space that characterize the state of the spatial target.

[0021] In the above scheme, step S3 involves calculating the two-dimensional permutation entropy of the trajectory matrix sequence constructed in step S2, and constructing a 16-dimensional two-dimensional permutation entropy pattern that represents the spatial target state in phase space. Specifically, this includes the following process:

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

[0023] S32: In the fourth-order tensor space, each matrix block generated during the reconstruction of the two-dimensional phase space is vectorized into a one-dimensional sequence. Then, the sequence is sorted in ascending order to obtain the sorted position sequence. Based on the number of times each matrix block position sequence appears, the probability distribution of the arrangement pattern is estimated. 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 spatial targets generated in step S23, construct a 16-dimensional two-dimensional entropy pattern of the spatial targets.

[0025] In the above scheme, step S4 involves constructing a state mode based on an online photometric sequence and performing similarity recognition with a standard mode. Specifically, this includes the following process:

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

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

[0028] The above technical solutions have the following beneficial effects:

[0029] 1. The phase space reconstruction of the multi-order difference approximation differential trajectory matrix sequence can enhance the amplitude ratio between different micro-variable signals coupled to the photometric sequence, which is beneficial for using the micro-variable photometric signals coupled in the photometric sequence to sense the target's on-orbit status.

[0030] 2. Constructing a 16-dimensional target state pattern vector is beneficial for machine learning, and this local information representation enhances the ability of analytical dynamical systems to represent state evolution in phase space.

[0031] 3. The 16-dimensional vector of the target state pattern is composed of 16 two-dimensional permutation entropies of four sets of trajectory matrices. During the calculation of the two-dimensional permutation entropy, a phase space reconstruction is performed. The process of constructing the 16-dimensional two-dimensional permutation entropy pattern from a one-dimensional photometric sequence involves two nested phase space reconstructions, realizing the mapping from a one-dimensional photometric sequence to a two-dimensional phase space and then to a four-dimensional phase space (fourth-order tensor space). In a probabilistic sense, the ascending permutation in the calculation of the two-dimensional permutation entropy is recombined and quantifies the information generated by the subtle changes in the relevant states of the dynamic system through the form of relatively unbalanced permutation entropy.

[0032] 4. The online sensing and computing system can sense the satellite status by selecting 32 photometric data sequences. Attached Figure Description

[0033] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention.

[0034] Figure 1 This is the overall algorithm flowchart of the present invention; Detailed Implementation

[0035] The following detailed descriptions are exemplary and 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 meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0036] In this embodiment, as Figure 1 The diagram shown is an overall flowchart of an algorithm for calculating and amplifying minute changes in the photometric intensity of a spatial target proposed in this invention, which includes the following steps:

[0037] S1: Based on phase space reconstruction theory, the one-dimensional photometric sequence obtained from one orbit of an optical telescope is embedded into phase space to construct a phase space trajectory matrix, called the zero-order trajectory matrix. Furthermore, a third-order system is used to describe the satellite state, extending the trajectory matrix into first-order, second-order, and third-order difference trajectory matrices, thus realizing a multi-order trajectory matrix phase space representation of the photometric sequence.

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

[0039] S3: Based on the two-dimensional arrangement entropy of the local amplitude, local phase, and local direction of the multi-trajectory moments and their corresponding two-dimensional analytical signals, a 16-dimensional spatial target state pattern is constructed.

[0040] S4: Construct a 16-dimensional model of the normal on-orbit operation status of the space target as a standard model. The 16-dimensional state model constructed using online photometric sequences is compared with the standard model for similarity identification to detect any anomalies in the target's state.

[0041] In the above scheme, step S1 utilizes a one-dimensional photometric sequence to construct a homeomorphic spatial trajectory matrix sequence describing the state evolution of a space target. Let the satellite photometric sequence acquired by the optical telescope in one observation orbit be x = {x1, x2, ..., x...}. N The time-delay embedding method is used to embed the photometric sequence into a d-dimensional phase space using a time delay parameter τ and an embedding dimension d, constructing a phase point sequence in the phase space. The phase point x reconstructed by time-delay embedding is shown below. i It can be viewed as a point in d-dimensional phase space, or as a time 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 considered as coordinates in a Cartesian coordinate system, the phase space trajectory forms an M×d trajectory matrix. This invention uses a time delay parameter τ = 1, and the embedding dimension... N is the number of photometric points in the photometric sequence. If we denote rounding down, then the phase space trajectory matrix is:

[0044]

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

[0046] To correspond to a third-order system, first-order, second-order, and third-order trajectory matrices need to be constructed. This invention uses the difference approximation of adjacent columns of the phase space trajectory matrix to estimate the multi-order trajectory matrix. The embedding dimension of the trajectory matrices of different orders decreases by one dimension in successive steps.

[0047]

[0048]

[0049] In the above scheme, step S2 involves constructing a sequence of trajectory matrices representing the spatial target in phase space based on the hypercomplex method and Riesz transform. The two-dimensional analytic signal of the trajectory matrix sequence constructed based on the hypercomplex method and Riesz transform is called the single-transformation signal. The Riesz transform of the trajectory matrix X in the frequency and spatial domains is expressed by the following formula:

[0050]

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

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

[0053] Similar to a one-dimensional analytic signal, we can obtain the local amplitude, local phase, and local direction information of a two-dimensional signal from a constructed univariate signal. Two Riesz transform components and the original signal constitute a three-dimensional signal vector, denoted as X. M = [X, R1, R2]. In spherical coordinates, the local amplitude A and local phase are... and local direction θ and X M The relationship between the components is as follows:

[0054]

[0055] The local amplitude of a single-evolutionary signal is related to local energy changes, 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 maximum variance in structural evolution. This representation of local information is beneficial for analyzing the evolution of the state of a dynamical system in 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 sequence of one satellite observation orbit, phase space reconstruction can obtain zero-order, first-order, second-order, and third-order trajectory matrices and their corresponding three single-evolutionary component matrices, local amplitude, local phase, and local direction, for a total of 16 phase space sub-matrices, which are used to generate satellite state mode vectors.

[0057] Under normal operating conditions, the photometric sequence of a satellite exhibits relatively regular changes. Changes in the satellite's state cause fluctuations in the photometric curve, resulting in irregular changes and increased complexity. Permutation entropy is an index that introduces the concept of permutation into phase space to calculate the complexity between reconstructed subsequences. It increases abnormally with time series fluctuations, thus making it suitable for detecting changes in the state of dynamic systems using time series analysis.

[0058] Extending the one-dimensional permutation entropy algorithm to two dimensions, we calculate N. x ×N y trajectory matrix Permutation entropy. Similar to the one-dimensional permutation entropy algorithm, it first reconstructs the trajectory matrix 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 the x and y directions are set to 1.

[41] Then the number of phase points in the x and y directions in phase space are K and K respectively. x =N x -d x +1, K y =N y -d y +1. Trajectory matrix phase space reconstruction is based on the time-delay phase space reconstruction approach, reconstructing K from the trajectory matrix X. x K y There are L sequence matrix blocks, where each phase point in the phase space corresponds to one matrix block. The specific implementation formula is as follows:

[0059]

[0060] in,

[0061]

[0062] After phase space reconstruction, for 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 the sorted position sequence. Each matrix block is vectorized into d. x d y The dimensional sequences are all mapped to all possible permutation patterns (d x d y One of them! The π-th permutation pattern in all K! x K y The probability of it appearing in the position sequence is:

[0063]

[0064] Among them, C π Let P(π) represent the number of times the π-th permutation pattern appears in all positional sequences. Substituting P(π) into the Shannon entropy formula, we obtain the normalized two-dimensional permutation entropy:

[0065]

[0066] in, S max =log[(d x d y )! ] indicates that each position sequence has an equal probability, and the time series complexity is the highest and the entropy is the largest.

[0067] Anomalies in the spatial target's state cause subtle changes in the photometric curve, or in other words, the minute photometric variation signal generated by the target's state is wrapped around the photometric curve. To better utilize these minute photometric variations to perceive changes in the target's state, the relative unbalanced 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 [ ] represents the empirical probability P = P[π] and the equal probability P e =1 / (d x d y The relative entropy between ! and ! is called the imbalance quantity, which is defined by the Jensen-Shannon divergence:

[0070]

[0071] in,

[0072]

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

[0074] Relative unbalanced permutation entropy quantifies the information generated by minor changes in the state of a dynamic system, and uses time series to perceive minor changes in the system state.

[0075] In the above scheme, step S4 involves constructing a state pattern based on an online photometric sequence and performing similarity recognition with a standard pattern. Based on step S3, a 16-dimensional two-dimensional relatively unbalanced arrangement entropy pattern of the space target state is constructed. It is assumed that the 16-dimensional two-dimensional relatively unbalanced arrangement entropy pattern of the space target in a normal on-orbit state is P.Normal The online photometric sequence constructs a state mode of P. test .

[0076] This invention views the two modes as probability distributions of spatial target state patterns and uses the Wassertein distance metric P. Normal and P test The distance metric captures the structural differences between distributions, making it suitable for identifying whether the state of a spatial target is abnormal.

[0077] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. All other embodiments obtained by those skilled in the art based on the technical solutions of the present invention without creative effort are within the scope of protection of the present invention.

Claims

1. A method for sensing the state of a spatial target based on photometric micro-variation signals, characterized in that, A normally operating space target is considered as a controlled dynamic system. A photometric sequence of the target over a photometric time period is acquired using a photometric telescope. A phase space topologically equivalent to that of the dynamic system is reconstructed in phase space using photometric sequence embedding technology. This allows for the perception of the space target's state, including the following steps: S1: Based on the phase space reconstruction theory, the one-dimensional photometric sequence obtained by one orbit of the optical telescope is embedded into the phase space to construct the phase space trajectory matrix, which is called the zero-order trajectory matrix. Furthermore, the satellite state is described by a third-order system, and the trajectory matrix is ​​extended to the first-order, second-order and third-order difference trajectory matrices to realize the phase space representation of the photometric sequence using a multi-order trajectory matrix. S2: In phase space, construct a two-dimensional analytical signal representation of the multi-order trajectory moment sequence based on the Riesz transform, and obtain the local amplitude, local phase and local direction component matrices of the multi-order trajectory matrix; S3: Based on the two-dimensional arrangement entropy of the local amplitude, local phase, and local direction of the multi-trajectory moments and their corresponding two-dimensional analytical signals, a 16-dimensional spatial target state pattern is constructed. S4: Construct a 16-dimensional model of the normal working state of the space target in orbit as a standard model. The 16-dimensional state model constructed by the online photometric sequence is similar to the standard model to detect whether the target state is abnormal. The specific steps of S1 are as follows: The process includes the following steps: S11: The state equation of the satellite in orbit is represented by a third-order jerk system, in which the first-order change represents the change in luminosity caused by the change in satellite state, the second-order change represents the rate of change in luminosity, and the third-order change is used to extract information on abrupt changes in luminosity. 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 changes in satellite state in the phase space is constructed. S13: Use the difference approximation of adjacent columns of the phase space trajectory matrix to estimate the phase space changes of different orders, and construct first-order, second-order and third-order trajectory matrices.

2. The spatial target state perception method based on photometric micro-variation signals as described in claim 1, characterized in that, Step S2 specifically includes the following process: S21: Based on the hypercomplex method and Riesz transform, construct two-dimensional analytic signals of zero-order trajectory matrix, first-order trajectory matrix, second-order trajectory matrix and third-order trajectory matrix respectively; S22: Based on the two-dimensional analytic signals of different order trajectory matrices constructed in S21, the local amplitude, local phase, and local direction matrices of the two-dimensional analytic 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, together with the local amplitude, local phase, and local direction matrices of their corresponding two-dimensional analytical signals, form 16 matrices in phase space that characterize the state of the spatial target.

3. The spatial target state perception method based on photometric micro-variation signals as described in claim 1, characterized in that, Step S3, specifically The process includes the following steps: S31: Based on the idea of ​​reconstructing the phase space by time delay, the trajectory matrix is ​​reconstructed in two-dimensional phase space to build a fourth-order tensor space; S32: In the fourth-order tensor space, each matrix block generated during the reconstruction of the two-dimensional phase space is vectorized into a one-dimensional sequence. Then, the sequence is sorted in ascending order to obtain the sorted position sequence. Based on the number of times each matrix block position sequence appears, the probability distribution of the arrangement pattern is estimated. 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 spatial targets generated in step S23, construct a 16-dimensional two-dimensional entropy pattern of the spatial targets.

4. The spatial target state perception method based on photometric micro-variation signals as described in claim 1, characterized in that, The specific process of step S4 is as follows: S41: Construct a 16-dimensional model of the normal on-orbit operation status of a space target as a standard model; S42: Based on the online photometric sequence, a 16-dimensional state pattern is constructed and similarity recognition is performed with the standard pattern to detect whether the target state is abnormal.

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