Space tether formation flying intelligent perception method for precise observation

Abstract

The application discloses a space tether formation state intelligent sensing method for accurate observation, which comprises the following steps: step 1, establishing a dynamics model of the space tether formation; step 2, selecting a sensor and establishing an observation model; and step 3, using a learning-based particle filtering algorithm to intelligently sense the state of the space tether formation. The application takes a space three-body tether formation system as a research object and studies the state sensing problem of the formation system out of the orbital plane.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of multi-spacecraft formation system sensing technology, and particularly relates to a space tether formation state intelligent sensing method for accurate observation. BACKGROUND

[0002] High-resolution target imaging is of great significance in the field of observation. Spatial resolution is an important indicator to measure the performance of an observation system. According to the Rayleigh criterion, the resolution of an optical system is limited by the aperture and wavelength of the system. If you want to improve the resolution of the optical system, you can only increase the aperture of the optical system. However, in actual engineering, the single mirror processing capacity of the reflector, the size of the fairing of the launch vehicle and the weight of the launch vehicle and many other factors limit the further increase of the optical system space. To solve the above problems, the concept of micro-satellite formation composed of multiple small spacecraft is proposed. Distributed sensors are installed on each micro-satellite, and the formation configuration is maintained in orbit, which can realize a larger observation aperture, and the size and mass of the entire system before launch will not be too high. However, due to the need for formation keeping, the fuel consumption of multi-spacecraft formation flight is too large, and the orbit control accuracy is too high. Large size and long time space formation flight will be limited by fuel. In order to solve this problem, the concept of space three-body tether formation is proposed, which has become a research hotspot for scholars around the world. Space three-body tether formation is a triangular configuration space system composed of three satellites connected by three flexible tethers. The entire formation revolves around the earth while rotating around its center of mass. This unique configuration allows the system to rely on the spin of the formation and the force of the tether to reduce the control difficulty of the system during operation and better maintain the formation configuration required for space missions. Compared with a single satellite system, space three-body tether formation has significant advantages in reliability, observation range and reusability. However, the space three-body tether formation system is used as the research object, and there is little research on the state sensing problem of the out-of-plane formation system. SUMMARY

[0003] The purpose of the present application is to provide a space tether formation state intelligent sensing method for accurate observation, which uses a space three-body tether formation system as the research object and studies the state sensing problem of the out-of-plane formation system.

[0004] The present application adopts the following technical scheme: a space tether formation state intelligent sensing method for accurate observation, comprising the following steps:

[0005] Step 1, establishing a dynamics model of the space tether formation;

[0006] Step 2, selecting sensors and establishing an observation model;

[0007] Step 3, using a learning-based particle filter algorithm to intelligently perceive the space tether formation state.

[0008] Further, the specific content of step 1 is:

[0009] Step 1.1, establish the total kinetic energy T of the formation system as:

[0010]

[0011] Where μi represents the mass coefficient of each satellite in the system, which can be specifically represented as μi = mi / m, (i = 1, 2, 3), where m = m1 + m2 + m3 represents the total mass of the system, the position vector r i of each satellite in the orbital coordinate system is represented as r i ; the absolute velocity vector v i of each satellite is represented as v i , Ω represents the cross multiplication operator of Ω, Ω is the rotation angular velocity of the formation system around the earth, R0 represents the position vector of the center of mass of the formation system in the earth-centered inertial coordinate system, the mass of the satellite is represented as mi, i = 1, 2, 3; ω0 represents the constant angular velocity of the system running in a circular orbit around the earth;

[0012] Orbital coordinate system o-xyz: the origin o is located at the center of mass of the system, the x-axis always points to the center of mass of the system along the direction of the earth's center, the y-axis is perpendicular to the x-axis in the orbital plane and points to the direction of the system's forward movement, and the z-axis is determined by the right-hand coordinate system;

[0013] Establish the system potential energy V of the formation system, where the system potential energy V includes the gravitational potential energy V1 and the elastic potential energy V2,

[0014] The gravitational potential energy V1 is represented as:

[0015]

[0016] In the formula: μ e is the gravitational constant, which can be represented as μ e = ω0 2 R0 3 ; R i is the position vector of each satellite; x i , y i , z i represent the position vector of the satellite in the orbital coordinate system;

[0017] The elastic potential energy V2 is represented as:

[0018]

[0019] In the formula: EA represents the elastic stiffness of the tether, which is determined by the physical properties of the tether, where E is the elastic modulus of the tether and A is the cross-sectional area of the tether; l0i ε is the length of the rope when it is not deformed; i Indicates the strain of the tether; l i i = 1, 2, 3: These represent the lengths of the tethers connecting the i-th satellite and the (i+1)-th satellite, where l1 represents the length of the tether connecting satellite S1 and S2, l2 represents the length of the tether connecting satellite S2 and S3, and l3 represents the length of the tether connecting m3 and m1. 0i i = 1, 2, 3 represents the length of the rope when it is not deformed; e i The coefficients i = 1, 2, 3 describe the property that the rope can only be stretched and not compressed.

[0020] Step 1.2: Combine the system's kinetic energy T, system's potential energy V, and generalized external force. Substituting into the Lagrange equations, the dynamic model of the space rope formation is obtained as follows:

[0021]

[0022] In the formula: q=[l1 l2 θ1 θ2 α β] T ∈R 6 Generalized coordinates; The first derivative of the generalized coordinate q; The matrix M(q) represents the second derivative of the generalized coordinate q; the matrix M(q) is a symmetric matrix, and the generalized external force Q... q ∈R 6 The specific expression is:

[0023] Furthermore, the specific content of step 2 is as follows:

[0024] Step 2.1: A gyroscope and tether release mechanism are installed on each node satellite to obtain the angular velocity of each satellite and the distance between satellites; the gyroscope measurement model of the space tether formation system is established as follows:

[0025] U=ω bi +b g +b θ +v θ ,

[0026] In the formula: U=[ω 1m ω 2m ω 3m ] T ∈R 9 Represents the gyroscope measurement value; ω bi ∈R 9 b represents the attitude angular velocity of a satellite outside the orbital plane relative to the geocentric inertial frame; g ∈R 9 —This represents the constant drift of the gyroscope; represents the gyro measurement time-dependent drift; v θ represents the zero-mean white noise during the gyro measurement process;

[0027] Step 2.2, the state equation of the space tether formation system is established as follows:

[0028]

[0029] In the formula, f(X k-1 ) is a state equation function, and its specific expression is as follows:

[0030]

[0031] In the formula, W k-1 ∈R 21 is a noise vector;

[0032] Step 2.3, the observation equation of the space tether formation system is established based on the satellite angular velocity information obtained by the gyro measurement and the tether length information obtained by the tether release mechanism, and is as follows:

[0033] Z k =h(X k )+V k ;

[0034] In the formula, Z k =[l im ω im ] T ∈R 12 represents a sensor observation vector, wherein the inter-satellite distance vector measured by the tether release mechanism is l im =[l 1m l 2m l 3m ] T , and the angular velocity vector measured by the gyro is ω mi =[ω mxi ω myi ω mzi ] T ; V k represents a noise vector in the measurement process, and can be expressed as V k =[v l v θ ] T ∈R 6 ; wherein the first three dimensions vl=[v1 v2 v3] T represent the tether release mechanism measurement noise, and the last nine items v θ represent the gyro measurement noise; h(X k ) represents an output equation function.

[0035] Further, the specific content of step 3 is:

[0036] Step 3.1, particle initialization: at k = 0, the particle swarm is generated from the spatial tethered formation system prior distribution Calculate the variance σ0of the particle swarm at this time, prepare for the next iteration operation at k = 1;

[0037] Step 3.2, particle update: when k > 0, let the process noise ω k-1 = ε + Υ k-1 determined, where Υ k-1 ~ N(0, σ k-1 ), ε is the state equation error, N(·) is the normal distribution probability density function; based on the state space model, the particle at k-1 is updated to obtain the new particle swarm Calculate the mean and variance σ k of the updated particle swarm, and obtain the probability distribution function

[0038] Step 3.3, particle weight calculation: the probability density function of the particle swarm at k is used to determine the importance density function Then the weight of each particle can be calculated by the following formula:

[0039] is a first-order Markov process;

[0040] Step 3.4, smoothing the particles using a radial basis function (RBF) neural network: the particle value and its corresponding weight are taken as the training input and training output of the neural network respectively, and a RBF neural network is trained based on the gradient descent method, denoted as N RBF The network output is the smoothed particle weight Finally, the smoothed particle and weight are obtained

[0041] Step 3.5, particle resampling: the particle swarm obtained in step 3.4 is resampled, that is, the particles with larger weights are copied and the particles with smaller weights are discarded, thereby generating a new particle swarm Each particle has the same weight 1 / N;

[0042] Step 3.6, state estimation: using the updated particle and weight, the estimated value of the current state x k is obtained Then return to step two to enter the next loop; that is, the intelligent perception of the state of the spatial tethered formation for accurate observation is completed.

[0043] The beneficial effects of the present application are: the present application adopts a minimum sensor layout strategy, only uses three gyroscopes and three tether release mechanisms, uses fewer sensors, and has low cost; the system communication burden can be effectively reduced, and the reliability of the system can be improved. The present application designs an intelligent filtering algorithm to realize accurate perception of the full state of the system including the in-plane and out-of-plane angles. The intelligent filtering algorithm optimizes the particle weight distribution based on the RBF neural network learning algorithm, improves the diversity of the particle filtering particles, overcomes particle depletion, and improves the estimation accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 A space triangular tether formation system structure diagram of the present application;

[0045] Figure 2 A satellite m1 rotation angular velocity perception error result comparison diagram in the formation system of the present application;

[0046] Figure 3 A formation system out-of-plane angle perception result diagram.

[0047] Wherein: 1. Gyroscope; 2. Tether release mechanism; 3. Orbit; 4. Earth. DETAILED DESCRIPTION

[0048] The present application will be described in detail below in combination with the drawings and specific embodiments.

[0049] The present application provides a space tether formation state intelligent perception method for accurate observation, considers the connection constraint and elastic constraint of the tether, considers the tether as a massless elastic rod model, applies the Lagrange method to establish a dynamics model of the space three-body tether satellite formation, and develops a state estimation scheme based on an intelligent particle filtering algorithm by using a minimum sensor configuration strategy.

[0050] In order to achieve the above purpose, the technical scheme adopted by the present application includes the following steps:

[0051] Step 1, establishing a dynamics model of the space tether formation;

[0052] Step 2, selecting a sensor and establishing an observation model;

[0053] Step 3, using a learning-based particle filtering algorithm to intelligently perceive the state of the space tether formation.

[0054] As described above in step 1, the following reasonable assumptions are made:

[0055] (1) Only the satellite mass is considered, and the satellite size is ignored;

[0056] (2) The tether is considered as an elastic rod model, that is, only the elastic potential energy of the tether is considered;

[0057] (3) The system runs on a circular orbit around the earth with constant angular velocity ω0, and the running orbit radius is R0; and only the earth's universal gravitation is considered and the Newton's law of motion is met.

[0058] Some parameters are defined as follows in this paper:

[0059] S i i = 1, 2, 3: represents the ith node satellite, and the corresponding satellite mass is represented as m i i = 1, 2, 3;

[0060] l i i = 1, 2, 3: represents the length of each tether connecting the ith satellite and the ith + 1 satellite, where l1 represents the tether length connecting satellites S1 and S2, and the others are similar. It is worth noting that when the tether is tight, this length is the distance between the two satellites connected by the tether;

[0061] θ i i = 1, 2, 3: used to describe the rotation of each satellite in the spin plane, collectively referred to as the in-plane spin angle;

[0062] α, β: are the attitude angles between the system spin plane and the orbit plane;

[0063] R0: represents the position vector of the center of mass of the formation system in the earth-centered inertial system, with a size of R0;

[0064] R i i = 1, 2, 3: represents the position vector of each satellite in the earth-centered inertial system;

[0065] r i = (x i , y i , z i ): represents the position vector of each satellite in the orbit coordinate system;

[0066] r a = (a i , b i , c i ): represents the position vector of each satellite in the system coordinate system, where c i ≡ 0;

[0067] As shown in the following, in order to establish the dynamics model of the formation system, the following three coordinate systems are defined: Figure 1

[0068] (1) Earth-centered inertial coordinate system E-XYZ: defined as the traditional earth-centered inertial coordinate system, where the coordinate system origin E is located at the earth's center of mass, the X axis points to the ascending node, the Z axis is perpendicular to the orbit plane, and the Y axis is determined by the right-hand rule. ​

[0069] (2)Orbital coordinate system o-xyz: The origin o is located at the system center of mass, the x-axis always points to the system center of mass along the direction of the earth center, the y-axis is perpendicular to the x-axis in the orbital plane and points to the direction of the system forward, and the z-axis is determined by the right-hand rule.

[0070] (3)System coordinate system o-abc: The coordinate system established on the system body, the aob plane of which coincides with the system spin plane, which can be obtained by rotating the o-xyz by α angle around the-z axis and then by β angle around the-y axis.

[0071] The specific content of step 1 is to construct a dynamic model of a space three-body tethered satellite formation by using Lagrange equation based on energy model. The tether lengths l1, l2 and the corresponding in-plane spin angles θ1, θ2, and the attitude angles α, β describing the relationship between the orbital plane and the system spin plane are selected as a group of independent generalized coordinates to describe the system.

[0072] Step 1.1, since the mass of the tether is not taken into account, the kinetic energy of the system mainly includes the kinetic energy of the three satellites. The key to obtaining the kinetic energy is to obtain the position vector and velocity vector functions of each satellite particle described by generalized coordinates, generalized velocities and time. The origin of the system coordinate system is always located at the center of mass of the space triangular tethered satellite formation system, so the system center of mass constraint can be expressed as:

[0073]

[0074] Expand to:

[0075]

[0076] In the formula, c i ≡0, which is because according to the definition of the coordinate system, the system spin plane coincides with the aob plane in the system coordinate system.

[0077] According to the geometric relationship of the triangle, the coordinates of each coordinate in the system spin plane have the following relationship:

[0078]

[0079] By combining the above two formulas, the coordinate expression of the position vector r a of each satellite in the system coordinate system is obtained as:

[0080]

[0081] In the formula, μ i represents the mass coefficient of each satellite in the system, which can be specifically expressed as μ i =m iwhere m = m1+m2+m3 represents the total mass of the system, and μ1+μ2+μ3=1 by definition.

[0082] The system coordinate frame o-abc is first rotated by β around the y-axis and then rotated by α around the z-axis to obtain the orbit coordinate frame o-xyz, and thus the coordinate transformation relationship between the system coordinate frame and the orbit coordinate frame is obtained as follows:

[0083]

[0084] The position vectors r i of the satellite mass points in the orbit coordinate frame are obtained by combining the above equations. i The absolute velocity vectors v c of the satellites can be expressed by the relative velocity and the tethered velocity as follows:

[0085]

[0086] where v c is the tethered velocity of the formation system, which can be obtained according to the Coriolis theorem as follows: where the derivative of the position vector of the center of mass of the formation system in the inertial frame is denoted as Ω is the rotation angular velocity of the formation system around the Earth, and Ω = [0 0 ω0] T ∈ R 3 ; Ω is the rotation angular velocity of the formation system around the Earth, and Ω = [0 0 ω0] T ∈ R 3 ;

[0087]

[0088] The total kinetic energy T of the formation system is:

[0089] where μ i represents the mass coefficient of each satellite in the system, and can be expressed as μ i = m i / m,(i = 1, 2, 3), where m = m1+m2+m3 represents the total mass of the system, and the position vectors r i of the satellite mass points in the orbit coordinate frame are i Ω is the rotation angular velocity of the formation system around the Earth, and Ω = [0 0 ω0] T ∈ R 3 ; i i = 1, 2, 3; ω0 represents the constant angular velocity of the system running in a circular orbit around the Earth.

[0090] The potential energy of the spatial three-body tethered satellite formation system includes two parts: the gravitational potential energy V1 of the three satellites and the elastic potential energy V2 of the three tethers.

[0091] The gravitational potential energy V1 of the system is generated by the gravitational field of the position where the system satellite is located, and is related to the weight of the satellite itself and the position where it is located, which can be expressed as:

[0092]

[0093] In the formula: μ e is the gravitational constant, which can be expressed as μ e = ω0 2 R0 3 ; R i is the position vector of each satellite, x i , y i , and z i represent the position vector of the satellite in the orbital coordinate system.

[0094] The elastic potential energy of the system refers to the total elastic potential energy of the three tethers in the system. Considering that the tether is a model of an elastic rod that can only be pulled and cannot be compressed, the mass and vibration and other characteristics of the tether are ignored, so the elastic potential energy of the tether is related to the elastic coefficient of the tether itself and the deformation of the tether. According to Hooke's law, the elastic potential energy V2 of the tether can be expressed as:

[0095]

[0096] In the formula: EA represents the elastic stiffness of the tether, which is determined by the physical properties of the tether, where E is the elastic modulus of the tether and A is the cross-sectional area of the tether; l 0i is the length of the tether when it is not deformed; ε i represents the strain of the tether, which can be obtained by ε i =(l i -l 0i ) / l0;

[0097] l i , i = 1, 2, 3: represents the corresponding length of each tether connecting the i th satellite and the i + 1 th satellite, where l1 represents the length of the tether connecting satellite S1 and satellite S2, l2 represents the length of the tether connecting satellite S2 and satellite S3, and l3 represents the length of the tether connecting m3 and m1, and the others are similar. It is worth noting that when the tether is pulled tight, this length is the distance between the two satellites connected by the tether;

[0098] According to the cosine law of a triangle, it can be obtained that:

[0099] l 0i , i = 1, 2, 3 is the length of the tether when it is not deformed;

[0100] e i , i = 1, 2, 3 describes the coefficient of the tether that can only be stretched and cannot be compressed, and the specific expression is:

[0101]

[0102] The total potential energy V of the formation system is obtained by summing the gravitational potential energy and the elastic potential energy:

[0103] V = V1 + V2.

[0104] Step 1.2, according to the Lagrange equation, there is:

[0105]

[0106] In the formula: q i represents the selected generalized coordinates for describing the space triangular tethered satellite formation system; Q qi corresponds to the generalized external force of the generalized coordinates q i .

[0107] The system kinetic energy T, the system potential energy V and the generalized external force Q qi are substituted into the Lagrange equation to derive the formation system dynamics model. For ease of display, the dynamics equation is arranged as:

[0108]

[0109] In the formula: q = [l1 l2 θ1 θ2 α β] T ∈R 6 is the generalized coordinate; represents the first derivative of the generalized coordinate q; represents the second derivative of the generalized coordinate q; the matrix M(q) is a symmetric matrix. The specific expression of the generalized external force Q q ∈R 6 is:

[0110]

[0111] As described above in step 2, as shown in the attached Figure 1 structure diagram of the space three-body tethered satellite formation system is given, and a gyroscope 1 and a tether release mechanism 2 are installed on each node satellite for obtaining the angular velocity of each satellite and the distance information between satellites. Before filtering estimation, the system model needs to be established first. According to the running condition of the formation system in three-dimensional space, the measurement information of the gyroscope and the tether release mechanism is taken as the system observation, and the system dynamics model is combined to complete the establishment of the system state equation and the observation equation.

[0112] The specific content of step 2 is:

[0113] Step 2.1, the gyroscope is used to measure the rotational angular velocity information of the three satellites out of the plane, and a gyroscope measurement model applied to the three-body tethered satellite formation system out of the orbital plane is established:

[0114] U = ω bi + b g + b θ + v θ ,

[0115] where U = [ω 1m ω 2m ω 3m ] T ∈ R 9 represents the gyro measurement; ω bi ∈ R 9 represents the satellite's attitude angular velocity relative to the earth-centered inertial frame; b g ∈ R 9 is the gyro constant bias; represents the gyro measurement time-correlated bias, which can be represented by a first-order Markov process:

[0116]

[0117] where Ξ is a 9-order diagonal matrix with diagonal elements being 1 / τ, τ is the time-correlation constant, is a zero-mean white noise vector; v θ ∈ R 9 is the zero-mean white noise in the gyro measurement process.

[0118] The satellite's rotational angular velocity ω bi relative to the earth-centered inertial frame can be obtained from the satellite's angular velocity ω bo relative to the orbit frame and the orbit frame's angular velocity ω oi relative to the earth-centered inertial frame, and is expressed in vector form as:

[0119]

[0120] where the subscript b represents the body frame, o represents the orbit frame, and i represents the inertial frame.

[0121] Step 2.2, define the state vector X as:

[0122]

[0123] where: represents the gyro measurement process bias.

[0124] The state equation of the space tether formation system can be expressed as:

[0125]

[0126] where f(X k-1 ) is the state equation function, and its specific expression is:

[0127]

[0128] where W k-1 ∈R 21 is the noise vector.

[0129] Step 2.3, based on the satellite angular velocity information obtained by gyro measurement and the tether length information obtained by tether release mechanism measurement, the observation equation of the out-of-plane three-body tethered satellite formation system is established as follows:

[0130] Z k = h(X k ) + v k ,

[0131] In the formula, Z k = [l im ω im ] T ∈R 12 represents the sensor observation vector, wherein the inter-satellite distance vector measured by the tether release mechanism is l im = [l 1m l 2m l 3m ] T , the angular velocity vector measured by the gyro is ω mi = [ω mxi ω myi ω mzi ] T ; v H represents the noise vector in the measurement process, which can be expressed as V k = [v l v θ ] T ∈R 12 , wherein the first three dimensions v l = [v1 v2 v3] T represent the tether release mechanism measurement noise, and the last nine items v θ represent the gyro measurement noise; h(X k ) represents the output equation function, and its specific expression is as follows:

[0132]

[0133] wherein,

[0134]

[0135] As described above in step 3, the state space model of the system can be obtained after discretization as follows:

[0136]

[0137] Wherein, Delta T is a discrete time interval. Given the state space model of the system, the application will design a learning-based intelligent particle filtering algorithm.

[0138] The specific content of step 3 is:

[0139] Step 3.1, particle initialization: at k=0, the particle group is generated by the spatial tethered formation system prior distribution Calculate the variance of the particle group at this time sigma0, prepare for the iteration operation at the next time;

[0140] Step 3.2, particle update: when k>0, let the process noise omega k-1 = epsilon + Y k-1 Determine, wherein Y k-1 ~ N(0, sigma k-1 ), epsilon is the state equation error, N(·) is the normal distribution probability density function; based on the state space model, the particle at k-1 is updated to obtain a new particle group Calculate the mean And the variance sigma k Of the updated particle group, and obtain the probability distribution function

[0141] Step 3.3, particle weight calculation: the probability density function of the particle group at k is used to determine the importance density function Then the weight of each particle can be calculated by the following formula:

[0142]

[0143] Step 3.4, using radial basis function (RBF) neural network to smooth the particles: taking the particle value xi k And its corresponding weight As the training input and training output of the neural network respectively, an RBF neural network is trained based on the gradient descent method, denoted as N RBF The network output is the smoothed particle weight Finally, the smoothed particle and weight are obtained

[0144] Step 3.5, particle resampling: the particle group obtained in step 3.4 is resampled, that is, the particles with larger weights are copied, and the particles with smaller weights are discarded, thereby generating a new particle group Each particle has the same weight 1 / N;

[0145] Step 3.6, state estimation: using the updated particle and weight, the estimated value of the current state x k Is obtained Then return to step two to enter the next cycle, that is, complete the intelligent perception of the space tether formation state for accurate observation.

[0146] Observability analysis is an important factor to judge the goodness of the estimation result, considering that the system is a strong coupling nonlinear system, the widely used observability rank condition criterion based on Lie derivative is used for observability analysis of the system. First, the system is separated according to the input, and in the case of not considering the system noise term, the system state equation and the observation equation can be rewritten as:

[0147]

[0148] In the formula: the function f0(X) is the input Q q The state equation function of the system when the function f0(X) is zero, its expression is:

[0149]

[0150] In the formula, the function f1(X) is the input Q q The corresponding system state equation function, which can be expressed as f1(X) = [0 6×6 M -1 (q) 0 9×6 ] T ∈R 21×6 , the generalized external force Q q is the system input.

[0151] According to the definition of Lie derivative and its gradient, the zero-order Lie derivative and its gradient, the first-order Lie derivative and its gradient, or higher-order Lie derivative and its gradient of the output function h(X) are calculated, and the Lie derivative gradients of each order are arranged in rows to form an observability matrix :

[0152]

[0153] From the zero-order Lie derivative gradient and the first-order Lie derivative gradient of the function h(X), twenty-one rows of Lie derivative gradients are selected to form a sub-matrix , which is full rank, these rows are: The 1st to 3rd rows of , the 4th to 6th rows of , the 1st to 3rd rows of , the 7th to 9th rows of , the 4th to 6th rows of , the 7th to 9th rows of , the 10th to 12th rows of. The specific expression of the matrix is:

[0154]

[0155] where each block matrix is expressed as

[0156]

[0157]

[0158] where matrix are all 3x3 matrices, and their specific expressions are as follows:

[0159]

[0160]

[0161]

[0162] The specific expressions of matrices X1,...,X5do not affect the observability proof, and are not given here.

[0163] Since the observability matrix has a high dimension, and the expressions of many element items in the matrix are relatively complex, it is difficult to directly prove the full rank of the matrix. Here, the rank of matrix is calculated by using MATLAB symbolic operation and matrix block dimension reduction method, and it is proved that matrix is a full rank matrix. First, it is proved that matrix c 6×6 is full rank. The determinant of matrix is calculated directly as: Therefore, matrix is full rank; moreover, it can be seen directly that the determinant of matrix is zero, and the expression of matrix is too complex to be given here, but the determinant of matrix is not zero and full rank, which can be obtained by MATLAB symbolic operation. Therefore, matrix c 6×6 can be converted into a lower triangular matrix by Gaussian elimination and elementary transformation of matrix, so that it can be known that matrix c 6×6 is full rank. Similarly, the determinant of matrix G 6×6 is calculated as: det|G 6×6 |=|-sinβl1l2sin(θ1-θ2) / l3|≠0, which is not equal to zero, i.e., matrix G 6×6 is full rank; it can also be seen directly that matrix K 9×9 is a diagonal matrix with all diagonal elements not being zero, therefore, matrix K 9×9 is also a full rank matrix.

[0164] Similarly, matrix D 6×6sum matrix F 6×6 The determinant det|D 6×6 |=det|F 6×6 |=0. Based on the preceding analysis, Gaussian elimination can be used to eliminate the matrix c. 6×6 Elimination matrix F 6×6 and H 9×6 Through D 6×6 Elimination matrix J 9×6 Thus, the matrix Convertable to

[0165]

[0166] Therefore, the matrix can be obtained. Full rank, i.e., matrix Full rank means that a full-rank observability matrix has been found. According to the observability rank criterion based on the Lie derivative, it can be seen that the filter designed in this invention is observable, which also verifies that the state estimation scheme designed in this invention is feasible.

[0167] Figure 2 The image shows a comparison of the sensing errors for the rotational angular velocity of satellite m1 in the formation system. It can be seen that the LPF estimation error is smaller. Here, LPF is the algorithm proposed in this invention, EKF is the extended Kalman filter algorithm, and Sensor represents the sensor measurement error. All the physical quantities shown in the image are state quantities with observational information. The error comparison image shows that both estimation errors are relatively small. Overall, compared to the EKF algorithm, the LPF estimation result has a smaller absolute estimation error and higher accuracy.

[0168] Figure 3 The exterior angle perception result of the formation system can still be estimated even without direct measurement of the exterior angle by a sensor, indicating that the sensor design of this invention is effective, i.e., the system is observable. Furthermore, the LPF estimation of this invention is closer to the ideal result (Real) than the EKF, thus demonstrating high LPF perception accuracy.

[0169] This invention considers the tethering constraints and establishes a dynamic model of a space-rotating three-body tethered satellite formation. Based on a minimum sensor layout strategy, it proposes a fusion estimation method using only gyroscope and tether release mechanism observations, completing the observability analysis of the nonlinear system. Based on an intelligent particle filter algorithm, it estimates the system's inter-satellite distances, attitude angles, and satellite rotation angular velocities, particularly estimating the in-plane spin angle and out-of-plane attitude angle information that cannot be directly measured. Without the need for direct measurement of the system's in-plane and out-of-plane angles, and using a minimum sensor layout strategy based on an intelligent filtering algorithm, it can achieve accurate perception of the entire system state, including in-plane and out-of-plane angles.

[0170] The present application relates to a kind of space triangulation tether satellite formation state intelligent perception method for high-precision observation, using minimum sensor layout strategy, only using three gyroscopes and three tether release mechanisms, based on intelligent filtering algorithm, system full state accurate perception including in-plane and out-of-plane angle can be realized.The method has the following advantages:(1) the sensor used in the present application is less, and the cost is low.The communication burden of system can be effectively reduced, and the reliability of system is improved;(2) the present application designs intelligent filtering algorithm, optimizes the particle weight distribution based on RBF neural network learning algorithm, improves the diversity of particle filtering particle, overcomes particle depletion, and improves the estimation accuracy.

Claims

1. A method for intelligent sensing of the state of space tethered formations for precise observation, characterized in that, Includes the following steps: Step 1: Establish a dynamic model of the spatial rope formation; Step 2: Select sensors and establish observation models; Step 3: Use a learning-based particle filter algorithm to intelligently perceive the spatial rope formation state; The specific content of step 3 is as follows: Step 3.1, Particle Initialization: At time k=0, the particle swarm is generated by the prior distribution of the space tether formation system. Calculate the variance σ0 of the particle swarm at this time to prepare for the iterative calculation at the next time step; Step 3.2, Particle Update: When k > 0, let the process noise ω k-1 =ε+Υ k-1 Confirmed, among which Υ k-1 ~N(0,σ k-1 ), where ε is the error of the state equation, and N(·) is the normal probability density function; based on the state-space model, the particles at time k-1 are updated to obtain a new particle swarm. Calculate the mean of the updated particle swarm. and variance σ k And obtain the probability distribution function. Step 3.3, Particle Weight Calculation: Determine the importance density function using the probability density function of the particle swarm at time k. The weight of each particle can then be calculated using the following formula: It is a first-order Markov process; Step 3.4: Smooth the particles using a radial basis function (RBF) neural network: smooth the particle values. and its corresponding weights Using these as the training input and output of the neural network respectively, an RBF neural network is obtained by training based on the gradient descent method, denoted as N. RBF The network output is the smoothed particle weights. Finally, the smoothed particles and weights are obtained. Step 3.5, Particle Resampling: The particle swarm obtained in Step 3.4 is resampled, that is, particles with larger weights are copied and particles with smaller weights are discarded, thereby generating a new particle swarm. Each particle has the same weight 1 / N; Step 3.6, State Estimation: Using the updated particles and weights, obtain the current state x. k The estimated value Then return to step two to enter the next loop; that is, to complete the intelligent perception of the state of a space tether formation for precise observation.

2. The intelligent sensing method for the state of space rope formations for precise observation as described in claim 1, characterized in that, The specific content of step 1 is as follows: Step 1.1: Establish the total kinetic energy T of the formation system as follows: Where, μ i This represents the mass coefficient of each satellite in the system, specifically expressed as μ. i =m i / m, (i = 1, 2, 3), where m = m1 + m2 + m3 represents the total mass of the system, and r is the position vector of each satellite mass point in the orbital coordinate system. i The absolute velocity vector v of each satellite i , R0 represents the cross product operator of Ω, where Ω is the angular velocity of the formation system around the Earth, R0 represents the position vector of the center of mass of the formation system in the geocentric inertial frame, and the satellite mass is represented by m. i ,i=1,2,3;ω0 represents the constant angular velocity of the system as it orbits the Earth in a circular orbit; Orbital coordinate system o-xyz: The origin o is located at the system's center of mass. The x-axis always points from the Earth's center to the system's center of mass. The y-axis is perpendicular to the x-axis in the orbital plane and points in the direction of the system's movement. The z-axis is determined by the right-hand coordinate criterion. Establish the system potential energy V of the formation system, where the system potential energy V includes gravitational potential energy V1 and elastic potential energy V2. The gravitational potential energy V1 is expressed as: Where: μ e The gravitational constant can be expressed as μ. e =ω0 2 R0 3 ;R i The position vectors of each satellite; x i ,y i ,z i This represents the satellite's position vector in the orbital coordinate system. The elastic potential energy V2 is expressed as: In the formula: EA represents the elastic stiffness of the tether, which is determined by the physical properties of the tether, where E is the elastic modulus of the tether, and A is the cross-sectional area of ​​the tether; 0i ε is the length of the rope when it is not deformed; i Indicates the strain of the tether; l i i = 1, 2, 3: These represent the lengths of the tethers connecting the i-th satellite and the (i+1)-th satellite, where l1 represents the length of the tether connecting satellite S1 and S2, l2 represents the length of the tether connecting satellite S2 and S3, and l3 represents the length of the tether connecting m3 and m1. 0i i = 1, 2, 3 represents the length of the rope before deformation; e i The coefficients i = 1, 2, 3 describe the property that the rope can only be stretched and not compressed. Step 1.2: Combine the system's kinetic energy T, system's potential energy V, and generalized external force. Substituting into the Lagrange equations, the dynamic model of the space rope formation is obtained as follows: In the formula: q=[l1 l2 θ1 θ2 α β] T ∈R 6 Generalized coordinates; The first derivative of the generalized coordinate q; The matrix M(q) represents the second derivative of the generalized coordinate q; the matrix M(q) is a symmetric matrix, and the generalized external force Q... q ∈R 6 The specific expression is:

3. The intelligent sensing method for the state of space tethered formations for precise observation as described in claim 1, characterized in that, The specific content of step 2 is as follows: Step 2.1: A gyroscope and tether release mechanism are installed on each node satellite to obtain the angular velocity of each satellite and the distance between satellites; the gyroscope measurement model of the space tether formation system is established as follows: U=ω bi +b g +b θ +v θ , In the formula: U=[ω 1m ω 2m ω 3m ] T ∈R 9 Represents the gyroscope measurement value; ω bi ∈R 9 b represents the attitude angular velocity of a satellite outside the orbital plane relative to the geocentric inertial frame; g ∈R 9 —This represents the constant drift of the gyroscope; Indicates the time-dependent drift of the gyroscope measurement; v θ This is represented as zero-mean white noise during the gyroscope measurement process; Step 2.2, establish the state equation of the spatial rope formation system as follows: In the formula: f(X) k-1 ) is the state equation function, and its specific expression is: Among them, W k-1 ∈R 21 This is the noise vector; Step 2.3: Based on the satellite angular velocity information obtained from gyroscope measurements and the tether length information obtained from the tether release mechanism, the observation equations for the space tether formation system are established as follows: Z k =h(X k )+V k ; In the formula: Z k =[l im ω im ] T ∈R 12 Let l represent the sensor observation vector, where the inter-satellite distance vector measured by the tether release mechanism is l. im =[l 1m l 2m l 3m ] T The angular velocity vector obtained by the gyroscope measurement is ω mi =[ω mxi ω myi ω mzi ] T V k The noise vector representing the measurement process can be represented as V. k =[v l v θ ] T ∈R 6 ; where the first three dimensions v l =[v 1 v 2 v 3 ] T This indicates the noise level measured by the tether release mechanism; the last nine items are v. θ The gyroscope measurement noise is represented by h(X). k ) represents the output equation function.

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