Spacecraft observable matrix lightweight characterization method based on common subspace

Abstract

The invention relates to a spacecraft observable matrix lightweight characterization method based on a common subspace. The method comprises the following steps: S1, giving a state equation and an observation equation of a spacecraft; s2, giving a Lie derivative calculation rule suitable for the state equation and the observation equation in the S1; s3, giving a high-order iterative algorithm of observability distribution according to the Lie derivative calculation rule in the S2; s4, initial distribution of observability is given; and S5, obtaining complete observability distribution of the spacecraft through the observability distribution high-order iterative algorithm in the S3 and the observability initial distribution in the S4, performing polar coordinate transformation on a system state to obtain a common subspace of the observability distribution, and realizing dimensionality reduction representation of a system observability matrix. According to the dimensionality reduction characterization method for the observation capability of the nonlinear autonomous control system, a system control item is included in an observation capability characterization range, dimensionality expansion is not carried out on the state quantity of the system, and dimensionality reduction characterization of the observation capability of the system is achieved.

Description

Technical Field

[0001] The invention relates to a lightweight characterization method of a spacecraft energy observable matrix based on a shared subspace, and belongs to the technical field of space autonomous operation. Background Art

[0002] As the number of spacecraft launched in my country increases year by year, the traditional operation and management method that relies on ground stations can no longer meet the needs of large-scale constellation operation and control, and it is urgent to break through the technology of autonomous operation of spacecraft. Autonomous navigation is the process by which a spacecraft obtains navigation information such as position and speed through its own sensors, and is the key to achieving autonomous operation of spacecraft.

[0003] In order to ensure the safety and reliability of the autonomous navigation process, a multi-sensor navigation configuration scheme is usually adopted. However, the computing resources of the spacecraft are limited, and it is difficult to process the multi-source heterogeneous data generated by multiple sensors. At this time, it is necessary to realize the autonomous evaluation of the observation capability of the navigation system on the spacecraft, and then guide the optimization of navigation data, and realize navigation solution under strict computing resource conditions. For the spacecraft autonomous navigation system, when the controller is state feedback control, it belongs to a type of nonlinear autonomous control system. Therefore, it is necessary to study a dimensionality reduction characterization method for the observation capability of the nonlinear autonomous control system, realize the observation capability characterization on the spacecraft, and lay the foundation for the autonomous operation of the navigation system.

[0004] Traditional methods for characterizing the observability of nonlinear systems include differential geometry and observability distribution. The differential geometry method is applicable only when the system is uncontrolled or the control amount is zero, which makes it difficult to apply to nonlinear autonomous control systems. The observability distribution method uses Lie derivatives to construct the observability distribution of the system, and analyzes the number of independent basis vectors of the distribution to determine the observability of the system. The applicable conditions of this method are that the control input of the system is a constant or is only associated with the time variable, so it is also not applicable to nonlinear autonomous control systems. In addition, both the differential geometry method and the observability distribution method involve high-dimensional matrix operations, which are difficult to implement on spacecraft with strictly limited computing resources. Summary of the invention

[0005] The technical problem solved by the present invention is: to overcome the deficiencies of the prior art, to provide a lightweight characterization method for a spacecraft observability matrix based on a shared subspace, and to achieve a dimensionality reduction characterization of the system observability matrix.

[0006] The technical solution of the present invention is:

[0007] A lightweight characterization method for a spacecraft observable matrix based on a common subspace comprises the following steps:

[0008] S1. Determine the state equation and observation equation of the spacecraft;

[0009] S2. Determine a Lie derivative calculation rule applicable to the state equation and the observation equation;

[0010] S3, determining a high-order iterative algorithm for observability distribution according to the Lie derivative calculation rule;

[0011] S4, determine the initial distribution of observability;

[0012] S5. Obtain the complete observability distribution of the spacecraft through the high-order iterative algorithm of observability distribution and the initial observability distribution, perform polar coordinate transformation on the system state, obtain the common subspace of observability distribution, and realize the dimensionality reduction representation of the system observability matrix.

[0013] Furthermore, the state equation of the spacecraft is:

[0014]

[0015] Where X is the system state; t is the time variable; f0(X,t) is the nonlinear function vector related to the system state X and the time variable t; f i (X, t), i = 1, ..., n is the function vector associated with the system control input; n is the dimension of the system control input; T i (X), i = 1, ..., n is the system control input, which is related to the system state; is the first-order derivative of the system state quantity.

[0016] Furthermore, the observation equation of the spacecraft is:

[0017] z=[h1(X,t),…,h p (X,t)] T

[0018] Among them, z is the observed quantity; h1(X,t),…,h p (X, t) is the observation function, which is related to the system state quantity X and the time variable t.

[0019] Furthermore, the Lie derivative calculation rule is:

[0020]

[0021] Among them, L f χ k-1 Represents the function χ k-1 Lie derivative with respect to the function vector f; is a partial differential operator; Represents the function χ k-1 Differentiation with respect to time of the Lie derivative of the function vector f.

[0022] Furthermore, the high-order iterative algorithm for determining the observability distribution is specifically:

[0023]

[0024] in, x k is the observability distribution of the k-th order system, k is an integer greater than or equal to 1 and less than the system state dimension; x k-1 is the observability distribution of the k-1th order system; Follow the Lie derivative calculation rules described above; f0, f1, f2, f3, ..., f n is f0(X,t) in the system state equation, f i (X, t), i = 1, ..., n, T1, T2, T3, ..., T n is the system state equation T i (X), the abbreviation of i=1,...,n.

[0025] Furthermore, the initial distribution of observability x 0 is:

[0026] χ0=span{dh1,…,dh p}

[0027] The operator d(·) is the partial differential of the function with respect to the system state quantity X, and span{} is the subspace spanning operator.

[0028] Furthermore, the observability distribution of the spacecraft is:

[0029] x =span{ x 0, x 1…, x m}

[0030] in, x represents the observability distribution of the spacecraft; x 0 is the initial distribution of the observability; x 1…, x m is the observability distribution of 1st-order to m-order systems, m is the system state dimension; span{·} is the subspace spanning operator.

[0031] Furthermore, the polar coordinate transformation of the system state is specifically as follows:

[0032]

[0033] Among them, α, β are azimuth and elevation angles respectively, ρ is the relative distance information, is the new state quantity after polar coordinate transformation.

[0034] Furthermore, the common subspace of the observability distribution is specifically:

[0035]

[0036] in, is the common subspace obtained, is the remaining term after decomposing the common subspace of the observability distribution.

[0037] In a second aspect, the present invention further proposes a computer program product, which, when executed by a processor, implements the lightweight characterization method of the spacecraft energy observable matrix based on the common subspace.

[0038] The beneficial effects of the present invention compared with the prior art are:

[0039] (1) Compared with the traditional nonlinear system observation capability characterization method, the present invention incorporates the system control item into the observation capability characterization scope, thus realizing the observation capability characterization of the nonlinear autonomous control system;

[0040] (2) In the process of incorporating control items into the scope of observation capability representation, the method of the present invention does not expand the dimension of the system state quantity, thereby realizing the dimension reduction representation of the observation capability of the nonlinear autonomous control system, with lower computational complexity, and is suitable for implementation on spacecraft;

[0041] (3) In the characterization process of the method of the present invention, the system state equation and observation equation are not linearized, and there is no need to restrict the control input. Therefore, the versatility of this method is better than that of the traditional method. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0043] The specific embodiments of the present invention are further described in detail below with reference to the accompanying drawings.

[0044] like Figure 1 As shown, the present invention is a lightweight characterization method of a spacecraft observable matrix based on a shared subspace, comprising the following steps:

[0045] S1. Give the state equation and observation equation of the spacecraft;

[0046] S2, give the Lie derivative calculation rules applicable to the state equation and observation equation in S1;

[0047] S3. According to the Lie derivative calculation rules in S2, a high-order iterative algorithm for observability distribution is given;

[0048] S4, give the initial distribution of observability;

[0049] S5. Through the high-order iterative algorithm of observability distribution in S3 and the initial observability distribution in S4, the observability distribution of the complete spacecraft is obtained, the system state is transformed into polar coordinates, the common subspace of the observability distribution is obtained, and the dimensionality reduction representation of the system observability matrix is ​​realized.

[0050] The dimension reduction characterization method for observation capability of a nonlinear autonomous control system obtained by the present invention includes system control items in the scope of observation capability characterization, does not expand the dimension of system state quantities, and realizes the dimension reduction characterization of system observation capability.

[0051] The following is a detailed introduction to steps S1 to S5. The steps are as follows:

[0052] S1. Give the state equation and observation equation of the spacecraft:

[0053] Equation of state:

[0054]

[0055] in, is the first-order derivative of the system state quantity, X is the system state quantity; t is the time variable; f0(X,t) is the nonlinear function vector related to the system state quantity X and the time variable t; f i (X, t), i = 1, ..., n is the function vector associated with the system control input; n is the dimension of the system control input; T i (X), i = 1, ..., n is the system control input, which is related to the system state.

[0056] Observation equation:

[0057] z=[h1(X,t),…,h p (X,t)] T

[0058] Among them, z is the observed quantity; h1(X,t),…,h p (X, t) is the observation function, which is related to the system state quantity X and time variable t.

[0059] S2. Give the Lie derivative calculation rules applicable to the state equation and observation equation in S1:

[0060]

[0061] Among them, L f χ k-1 Represents the function χ k-1 Lie derivative with respect to the function vector f; is a partial differential operator.

[0062] Represents the function χ k-1 Differentiation with respect to time of the Lie derivative of the function vector f.

[0063] S3. According to the Lie derivative calculation rules in S2, a high-order iterative algorithm for observability distribution is given:

[0064]

[0065] in, x k is the observability distribution of the k-th order system, k is an integer greater than or equal to 1 and less than the system state dimension; x k-1 is the observability distribution of the k-1th order system; Follow the Lie derivative calculation rules described in S2. f0,f1,f2,f3,…,f n is f0(X,t) in the system state equation in S1, f i (X, t), i = 1, ..., n, T1, T2, T3, ..., T n is T in the system state equation in S1 i (X), the abbreviation of i=1,…,n.

[0066] S4. Give the initial distribution of observability:

[0067] x 0=span{dh1,…,dh p}

[0068] The operator d(·) is the partial differential of the function with respect to the system state quantity X.

[0069] S5. Through the high-order iterative algorithm of observability distribution in S3 and the initial observability distribution in S4, the observability distribution of the complete spacecraft is obtained, the polar coordinate transformation of the system state is performed, the common subspace of the observability distribution is obtained, and the dimension reduction representation of the system observability matrix is ​​realized. The observability distribution of the spacecraft is:

[0070] x =span{ x 0, x 1…, x m}

[0071] in, x Represents the observability distribution of nonlinear autonomous control systems; x 0 is the initial distribution of observability described in S4; x 1…, xm is the observability distribution of 1st-order to m-order systems, m is the system state dimension; span{·} is the subspace spanning operator.

[0072] The polar coordinate transformation of the system state is:

[0073]

[0074] Among them, α, β are azimuth and elevation angles respectively, ρ is the relative distance information, is the new state quantity after polar coordinate transformation.

[0075] The total subspace is:

[0076]

[0077] in, is the common subspace obtained, is the remaining term after decomposing the common subspace of the observability distribution.

[0078] The system observation capability dimensionality reduction characterization method of the present invention includes system control items in the observation capability characterization range, and realizes the observation capability characterization of the nonlinear autonomous control system; in the process of including the control items in the observation capability characterization range, the method does not expand the dimension of the system state quantity, and realizes the observation capability dimensionality reduction characterization of the nonlinear autonomous control system, with lower calculation complexity, and is suitable for implementation on spacecraft; in the characterization process of the method, the system state equation and the observation equation are not linearized, and there is no need to restrict the control input, so the versatility of the method is better than that of the traditional method.

[0079] Parts of the present invention that are not described in detail belong to common knowledge among those skilled in the art.

Claims

1. A lightweight representation method for spacecraft observable matrix based on common subspace, characterized by include: Determine the spacecraft's equations of state and observations; Determining a Lie derivative calculation rule applicable to the state equation and the observation equation; Determine a high-order iterative algorithm for observability distribution according to the Lie derivative calculation rule; Determine the initial distribution of observability; Through the high-order iterative algorithm of observability distribution and the initial observability distribution, the observability distribution of the complete spacecraft is obtained, the system state is transformed into polar coordinates, the common subspace of the observability distribution is obtained, and the dimensionality reduction representation of the system observability matrix is ​​realized.

2. The method for lightweight characterization of spacecraft observable matrix based on common subspace according to claim 1 is characterized in that: The state equation of the spacecraft is: Where X is the system state; t is the time variable; f0(X,t) is the nonlinear function vector related to the system state X and the time variable t; f i (X, t), i = 1, ..., n is the function vector associated with the system control input; n is the dimension of the system control input; T i (X), i = 1, ..., n is the system control input, which is related to the system state; is the first-order derivative of the system state quantity.

3. The method for lightweight characterization of spacecraft observable matrix based on common subspace according to claim 2 is characterized in that: The observation equation of the spacecraft is: z=[h1(X,t),…,h p (X,t)] T Among them, z is the observed quantity; h1(X,t),…,h p (X, t) is the observation function, which is related to the system state quantity X and the time variable t.

4. The method for lightweight characterization of spacecraft observable matrix based on common subspace according to claim 3 is characterized by: The Lie derivative calculation rule is: Among them, L f χ k-1 Represents the function χ k-1 Lie derivative with respect to the function vector f; is a partial differential operator; Represents the function χ k-1 Differentiation with respect to time of the Lie derivative of the function vector f.

5. The method for lightweight characterization of spacecraft observable matrix based on common subspace according to claim 4 is characterized in that: The high-order iterative algorithm for determining the observability distribution is specifically: Among them, χ k is the observability distribution of the k-th order system, k is an integer greater than or equal to 1 and less than the system state dimension; χ k-1 is the observability distribution of the k-1th order system; Follow the Lie derivative calculation rules described above; f0, f1, f2, f3, ..., f n is f0(X,t) in the system state equation, f i (X, t), i = 1, ..., n, T1, T2, T3, ..., T n is the system state equation T i (X), the abbreviation of i=1,...,n.

6. The method for lightweight characterization of spacecraft observable matrix based on common subspace according to claim 5 is characterized in that: Initial distribution of observability χ 0 is: χ 0=span{dh1,…,dh p } The operator d(·) is the partial differential of the function with respect to the system state quantity X, and span{} is the subspace spanning operator.

7. The method for lightweight characterization of spacecraft observable matrix based on common subspace according to claim 6 is characterized by: The observability distribution of the spacecraft is: χ =span{ χ 0, χ 1…, χ m } in, χ represents the observability distribution of the spacecraft; χ 0 is the initial distribution of the observability; χ 1…,χ m is the observability distribution of 1st-order to m-order systems, m is the system state dimension; span{·} is the subspace spanning operator.

8. The method for lightweight characterization of spacecraft observable matrix based on common subspace according to claim 7 is characterized in that: The polar coordinate transformation of the system state is specifically as follows: Among them, α, β are azimuth and elevation angles respectively, ρ is the relative distance information, is the new state quantity after polar coordinate transformation.

9. The method for lightweight characterization of spacecraft observable matrix based on common subspace according to claim 8 is characterized in that: The common subspace of the observability distribution is specifically: in, is the common subspace obtained, is the remaining term after decomposing the common subspace of the observability distribution.

10. A computer program product, characterized in that When the computer program product is executed by a processor, the steps of the method according to any one of claims 1 to 9 are implemented.

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