A GEO spacecraft multi-view fusion near-field perception formation design method

Abstract

The application relates to a GEO spacecraft multi-line-of-sight fusion near-field perception formation design method. The method comprises the following steps: according to a space triangle formed by a main star, a satellite and a space target, a relative position vector and a line-of-sight vector are established to form a relationship formula of the angle between the relative position vector and the line-of-sight vector; the line-of-sight angle is simultaneously derived on both sides of the relationship formula to obtain a formation optimization criterion; according to spacecraft illumination constraints and bounded relative constraints, constraint conditions of a near-field perception formation optimization problem are set; and a target function of the near-field perception formation optimization problem is set based on the formation optimization criterion; a solving model is established according to the constraint conditions and the target function, a nonlinear optimization algorithm is used to solve the solving model, and an optimized near-field perception formation is obtained. The method can improve the near-field perception observability under the condition of only measuring angle information.

Description

Technical Field

[0001] This application relates to the field of spacecraft mission analysis and design technology, and in particular to a multi-line-of-sight fusion near-field perception formation design method for GEO spacecraft. Background Technology

[0002] As the number of non-cooperative targets such as space debris increases, the safety risks faced by GEO spacecraft in orbit are also growing, necessitating the development of near-field sensing technology for GEO spacecraft to warn of dangerous behaviors such as space debris collisions. Driven by the development of microsatellite technology, one approach is to use multiple microsatellites carrying optical sensors to fly in formation near the GEO spacecraft, measuring and estimating the relative state of space targets through multi-satellite cooperation.

[0003] However, this approach also has some shortcomings, mainly in the following aspects: First, most existing technologies develop different multi-line-of-sight fusion algorithms in order to improve the accuracy of relative state estimation of space targets, but in reality, the perception formation of multi-star cooperation also has a significant impact on the accuracy of relative state estimation, and there is currently little research on this; Second, optical sensors are quite sensitive to illumination conditions, and existing technologies do not consider the impact of illumination constraints on line-of-sight angle measurement, which can easily reduce the performance of near-field perception in real-world situations. Summary of the Invention

[0004] Therefore, it is necessary to provide a GEO spacecraft multi-line-of-sight fusion near-field perception formation design method that can improve the near-field perception observability under only angle measurement information, in order to address the above-mentioned technical problems.

[0005] A method for designing near-field perception formations for GEO spacecraft using multi-line-of-sight fusion, the method comprising:

[0006] The relative motion equations of the spacecraft are established in the orbital coordinate system. The relative motion equations of the spacecraft are discretized and linearized according to the specified discrete time to obtain the state equations of near-field sensing.

[0007] The angle information of the space target is obtained by measuring multiple spacecraft. The observation equation is constructed based on the relative position vector of the space target and the observation spacecraft and the angle information of the space target. The observation equations of multiple spacecraft are combined and linearized to obtain the linear form of the observation equation.

[0008] Based on the state equation, the linear form of the observation equation, and the measured angle information of the space target, the relative state of the space target and the host star is estimated using the extended Kalman filter algorithm, and the relative position vector and velocity of the space target relative to the host star are obtained.

[0009] Using the spatial triangle formed by the primary star, secondary stars, and space targets, establish the relationship between the angle between the relative position vector and the line-of-sight vector based on the relative position vector;

[0010] By taking the partial derivative of both sides of the relationship between the relative position vector and the line-of-sight vector with respect to the line-of-sight angle, the formation optimization criterion is obtained.

[0011] Based on spacecraft illumination constraints and bounded relative constraints, the constraints of the near-field perception formation optimization problem are set; and the objective function of the near-field perception formation optimization problem is set based on the formation optimization criterion.

[0012] Based on the constraints and objective function, a solution model for the near-field perception formation optimization problem is established, and the solution model for the near-field perception formation optimization problem is transformed into a solution model for a nonlinear programming problem.

[0013] The nonlinear optimization algorithm is used to solve the nonlinear programming problem model to obtain the optimized near-field sensing formation.

[0014] In one embodiment, the spacecraft's relative motion equations are discretized and linearized according to a specified discrete time to obtain the near-field sensing state equations, including:

[0015] Discretize and linearize the spacecraft's relative motion equations according to a specified discrete time, and obtain the near-field sensing state equation as X. k+1 =Φ k X k , where X k+1 and X k The state column vectors at time k+1 and time k are Φ respectively. k Let be the state transition matrix.

[0016] In one embodiment, the observation equations of multiple spacecraft are combined and then linearized to obtain linear observation equations, including:

[0017] After simulating the observation equations of multiple spacecraft and linearizing them, we obtain the linear form of the observation equation Z. k =H k X c,k +V k ,in, Let h(X) represent the Jacobian matrix. all ) represents the theoretical value of the line-of-sight angle, X all =(X c ;X d1 ;…;X dN ), This represents the relative position and velocity state of the space target within the orbital coordinates of the primary star. X represents the relative position and velocity state of a space target in the orbital coordinates of the i-th satellite. c,k V represents the relative state of a space target in the coordinate system of the primary star's orbit. kZ represents the measurement noise. k This represents the actual measured value.

[0018] In one embodiment, the relative position vector of the space target relative to the primary star is the position vector of the space target in the primary star's orbital coordinate system; using the spatial triangle formed by the primary star, secondary stars, and the space target, a relationship between the relative position vector and the line-of-sight vector is established based on the relative position vector, including:

[0019] Using the law of cosines, we calculate the unit vectors of the space target's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system. This yields the line-of-sight angle between the space target's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system, as well as the supplementary angle of the line-of-sight angle between the secondary star's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system.

[0020] Based on the sine theorem, the angle between the line of sight between the position vector of the space target in the primary star's orbital coordinate system and the position vector of the space target in the secondary star's orbital coordinate system, and the supplementary angle between the line of sight between the position vector of the secondary star in the primary star's orbital coordinate system and the position vector of the space target in the secondary star's orbital coordinate system, are calculated to obtain the relationship between the angle between the relative position vector and the line of sight vector.

[0021] In one embodiment, the cosine theorem is used to calculate the unit vectors of the space target's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system. This yields the line-of-sight angle between the space target's position vectors in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system, and the supplementary angle of the line-of-sight angle between the secondary star's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system. This includes:

[0022] Using the law of cosines, we calculate the unit vectors of the space target's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system. The supplementary angles of these angles are:

[0023]

[0024] Where, θ t and θ cd1Let ρ be the angle between the line of sight between the position vector of the space target in the primary star's orbital coordinate system and the position vector of the space target in the secondary star's orbital coordinate system, and the supplementary angle between the line of sight between the position vector of the secondary star in the primary star's orbital coordinate system and the position vector of the space target in the secondary star's orbital coordinate system. t and ρ t1 The position vectors of the space target in the primary star's orbital coordinate system and the space target in the secondary star's orbital coordinate system, dt and dt1, are respectively ρ t and ρ t1 The unit vector, ρ d1 This represents the position vector of star 1 in the coordinate system of the main star's orbit.

[0025] In one embodiment, the line-of-sight angle between the position vector of the space target in the primary star's orbital coordinate system and the position vector of the space target in the secondary star's orbital coordinate system, and the supplementary angle of the line-of-sight angle between the position vector of the secondary star in the primary star's orbital coordinate system and the position vector of the space target in the secondary star's orbital coordinate system, are calculated according to the sine theorem to obtain the relationship between the relative position vector and the line-of-sight vector, including:

[0026] Based on the sine theorem, the angle between the relative position vectors and the line-of-sight vectors of the space target in the primary star's orbital coordinate system and the space target in the secondary star's orbital coordinate system, and the supplementary angle between the position vectors of the secondary star in the primary star's orbital coordinate system and the space target in the secondary star's orbital coordinate system, are calculated. The relationship between the angles between the relative position vectors and the line-of-sight vectors is then obtained as follows:

[0027] In one embodiment, the objective function of the near-field perception formation optimization problem is set based on the formation optimization criterion, including:

[0028] Based on the formation optimization criterion, the objective function of the near-field perception formation optimization problem is set.

[0029]

[0030] Where N represents the number of satellites and M is the number of discrete time points. This represents the angle between star i at the k-th discrete time point and the line-of-sight vector from the main star to the target in space.

[0031] In one embodiment, the spacecraft illumination constraint is... Where, r i2sun r i2t These represent the direction of sunlight illumination and the position vector of the space target in the orbital coordinate system of star i, respectively. Indicates r i2sun r i2t The supplementary angle of the angle between the vector lines of sight, θ min This represents the critical solar constraint angle of an optical camera.

[0032] In one embodiment, the bounded relative constraint is

[0033]

[0034] Among them, a c a j The semi-major axes of the primary and secondary stars are respectively, and b is the semi-major axis of the primary star and the secondary star. j For the natural motion of the ellipse from star j in x c o c y c The length of the minor semi-axis of the plane projection, C j For the natural motion of the ellipse from star j in z c The amplitude of the axis, y c,j For the natural motion of the ellipse from star j in x c o c y c The distance from the center of the planar projection to the origin O.

[0035] In one embodiment, the solution model for the near-field perception formation optimization problem is transformed into a solution model for a nonlinear programming problem, including:

[0036] The solution model for the near-field perception formation optimization problem is transformed into a nonlinear programming problem solution model.

[0037] find:X design

[0038]

[0039] s·t:

[0040]

[0041] in, Xdesign =[ a1 ,e1,I1,Ω1,ω1,M1… aN ,e N ,I N ,Ω N ,ω N M N ] represents the initial orbital root numbers of each satellite, a i e i I i Ω i ω i M i These are the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of perigee, and mean perigee angle, respectively.

[0042] The above-mentioned GEO spacecraft multi-line-of-sight fusion near-field perception formation design method integrates the line-of-sight angle information measured by multiple spacecraft into a single measurement equation, effectively improving the observability of relative state estimation based solely on angle measurements. Under the framework of relative motion, spacecraft illumination constraints and bounded relative constraints are constructed, and a near-field perception formation optimization strategy is established, effectively solving the problems of limited communication distance for small spacecraft and the high sensitivity of optical sensors to sunlight. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating a multi-line-of-sight fusion near-field perception formation design method for a GEO spacecraft in one embodiment;

[0044] Figure 2 This is a schematic diagram of a multi-star near-field sensing coordinate system in one embodiment;

[0045] Figure 3 Here is a flowchart of an extended Kalman filter implementation in one embodiment;

[0046] Figure 4 This is a schematic diagram of spacecraft illumination constraints in another embodiment;

[0047] Figure 5 This is a curve showing the relative distance estimation error over time before near-field perception formation optimization in one embodiment;

[0048] Figure 6 The curve showing the relative velocity estimation error over time before near-field perception formation optimization in one embodiment;

[0049] Figure 7 The curve showing the change of the angle of sunlight before near-field perception formation optimization in one embodiment is shown.

[0050] Figure 8 The curve showing the relative distance estimation error over time after near-field perception formation optimization in one embodiment;

[0051] Figure 9 The curve showing the change of the magnitude error of the relative velocity estimation after near-field perception formation optimization in one embodiment over time;

[0052] Figure 10 This is a curve showing the change of the sunlight angle over time after near-field sensing formation optimization in one embodiment. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0054] In one embodiment, such as Figure 2 As shown, a multi-line-of-sight fusion near-field perception formation design method for GEO spacecraft is provided, including the following steps:

[0055] Step 102: Establish the spacecraft's relative motion equations in the orbital coordinate system, and discretize and linearize the spacecraft's relative motion equations according to the specified discrete time to obtain the state equations for near-field sensing.

[0056] like Figure 2 As shown, this is a near-field sensing formation consisting of a primary star and two secondary stars, O, O c O d1 O d2 O t These represent the centers of mass of Earth, the primary star, secondary star 1, secondary star 2, and the space target, respectively. O-XYZ represents the geocentric inertial coordinate system, with O as the origin. The positive X-axis points from the Earth's center to the vernal equinox, the positive Z-axis is perpendicular to the equatorial plane and points from the Earth's center to the North Pole, and the Y-axis is determined by the right-hand rule. c -x c y c z c O represents the primary star's orbital coordinate system. c Origin of the main star's orbital coordinate system, x c From O to O c y c Within the orbital plane of the primary star and x c The axis is perpendicular, and the direction of motion is positive; z c The axis is perpendicular to the orbital plane and is perpendicular to the x-axis. c y c This forms a right-handed coordinate system. From the orbital coordinate system O of stars 1 and 2... d1 -x d1 y d1 z d1 With O d2 -x d2 y d2 z d2 Definition and O c -x c y c z c Similarly, I won't go into details. ρ t ρ t1 ρ t2 ρ represents the position vector of the space target in the orbital coordinate systems of the primary star, slave star 1, and slave star 2, respectively. d1 ρ d2 Let ρ represent the position vectors of slave star 1 and slave star 2 in the coordinate system of the master star's orbit. The master star and slave stars can exchange information; that is, ρ can be considered... d1 ρ d2 α is a known quantity. c ρ represents the azimuth angle. t In xc O c y c Plane projection and x c Positive angle of the axis, β c Let ρ represent the pitch angle. t In x c O c y c Plane projection and ρ t Included angles. α1, β1 and α2, β2 represent the azimuth and elevation angles of the target in their respective orbital coordinate systems, measured from satellite 1 and satellite 2, respectively. θ t Represents ρ t With ρ t1 included angle, θ cd1 Represents ρ d1 With ρ t1 The supplementary angle of an included angle.

[0057] set up Let u be the position and velocity vector of the secondary star relative to the primary star, u = (u x ,u y ,u z ) T To determine the acceleration applied to the slave star, assuming the distance between the slave star and the master star is much smaller than the orbital radius of the master star, and the master star has a near-circular orbit, we can ignore the third-order and higher-order terms and obtain the second-order relative motion equations.

[0058]

[0059] Further transforming the above equation into a state equation form, we can obtain... In equation (2),

[0060]

[0061] To facilitate subsequent filtering, equation (3) is discretized and linearized. Let the discrete time step be T, then at the k-th discrete point, the discrete form of equation (3) is X. k+1 =X k +f(X k )T(4)

[0062] Assuming neither the master nor the slave star exerts active control, let

[0063]

[0064] Then in X = X k The linearized form of equation (5) is

[0065]

[0066] In summary, the discretized and linearized state equation can be obtained as X k+1 =Φk X k (7), in equation (7),

[0067]

[0068] Step 104: Obtain the angle information of the space target by measuring multiple spacecraft. Construct observation equations based on the relative position vectors of the space target and the observation spacecraft and the angle information of the space target. Linearize the observation equations of multiple spacecraft to obtain the linear form of the observation equations.

[0069] The spatial target angle information in this application consists of the target azimuth angle α and elevation angle β measured by multiple satellites in their own orbital coordinate system. Let... Let be the position, velocity, and state variables of the space target in the orbital coordinates of the primary star. This can be known from geometric relationships.

[0070]

[0071] The line-of-sight angle observations obtained by the primary star and N secondary stars at the same time are as follows:

[0072] Z = [α] c ,β c ,α1,β2,…,α N ,β N ] T (10)

[0073] set up Let X represent the relative position and velocity state of a space target in the orbital coordinates of the i-th satellite. all =(X c ;X d1 ;…;X dN ).

[0074] The calculated line-of-sight angles of the primary star and N secondary stars at the same moment are:

[0075]

[0076] Considering the error in angle measurement, the observation equation can be obtained as follows:

[0077] Z = h(X) all )+V (12)

[0078] In equation (12), V represents the measurement error matrix.

[0079] The primary and secondary stars can exchange information, meaning the position and velocity of the secondary star relative to the primary star can be precisely determined. Therefore, only X needs to be obtained. c Then, X can be obtained by vector addition and coordinate transformation. di To reduce the dimensionality of subsequent filtering solutions, both sides of equation (11) are simultaneously applied to X.c Taking the partial derivative, we obtain the corresponding Jacobian matrix as follows:

[0080]

[0081]

[0082]

[0083]

[0084] In equations (14) and (15), R i2c Let represent the state transition matrix from the orbital coordinate system of star i to the orbital coordinate system of the main star, which can be obtained from the corresponding orbital elements of the main star and the slave star i. Then, at the k-th discrete time point, the linearized and discretized form of equation (12) is:

[0085] Z k =H k X c,k +V k

[0086] Step 106: Based on the state equation, the linear form of the observation equation, and the measured angle information of the space target, the extended Kalman filter algorithm is used to estimate the relative state of the space target and the host star, and the relative position vector and velocity of the space target relative to the host star are obtained.

[0087] Based on the state equation, the linear observation equation, and the measured angle information of the space target, the relative state of the space target and the primary star is estimated using the extended Kalman filter algorithm. This process is existing technology and will not be described in detail in this application. Figure 3 As shown, Let P be the estimated position, velocity, and state variables of the target in the main star's orbital coordinate system at time k. P is the state transition covariance matrix, which converges to an accurate value as the number of iterations increases. Q is the model noise covariance matrix caused by external interference during the state transition prediction process. R is the measurement noise covariance matrix caused by the inaccuracy of sensor measurements. The angle information is converted into position information using the Kalman filter algorithm, and the relative position and velocity of the non-cooperative space target are estimated using multi-line-of-sight angle information obtained from multiple satellites.

[0088] Step 108: Using the spatial triangle formed by the primary star, secondary stars, and space targets, establish the relationship between the angle between the relative position vector and the line-of-sight vector based on the relative position vector.

[0089] Substituting the estimated position and velocity state variables of the space target in the main star's orbital coordinate system into formula (17), the azimuth and pitch angles can be obtained, and then d can be derived. t d t1d t d t1 ρ t ρ t1 The unit vector is as follows:

[0090]

[0091] According to the law of cosines, the included angle θ can be obtained. t θ cd1 They are respectively

[0092]

[0093] Further, using the law of sines, the distance between the target and the primary star can be obtained as follows:

[0094]

[0095] Step 110: Take partial derivatives of both sides of the relationship between the relative position vector and the line-of-sight vector with respect to the line-of-sight angle to obtain the formation optimization criterion; set the constraint conditions for the near-field perception formation optimization problem based on the spacecraft illumination constraint and the bounded relative constraint; and set the objective function for the near-field perception formation optimization problem based on the formation optimization criterion.

[0096] Analysis of equation (19) shows that for ||ρ t ||2 The most influential factor is θ t Applying both sides of equation (19) to θ t Taking the partial derivative yields

[0097]

[0098] If θ t The deviation of ||ρ t The influence of ||2 is minimal. Setting equation (20) to 0, we can obtain θ. t = 90°, that is, theoretically speaking, θ t The closer the angle is to 90°, the more accurate the relative position of the target with respect to the host star. Based on this criterion, this application sets the objective function for the near-field perception formation optimization problem, such that the average angle θ between the relative position vectors of the host star and the target is θ throughout the entire mission. t Approaching 90°, the specific expression is:

[0099]

[0100] Where N represents the number of satellites and M is the number of discrete time points. This represents the angle between star i at the k-th discrete time point and the line of sight from the main star to the target in space.

[0101] For optical cameras, illumination is the main factor affecting their performance. When the optical camera carried by the satellite observes space targets against the sunlight, the background light is too strong, the observation results are blurry, and the position of the space target cannot be determined. Therefore, this application solves the problem of blurry observation results by constructing spacecraft illumination constraints. At the same time, in order to ensure that the slave star and the host star maintain normal information exchange distance and avoid collisions, it is assumed that the slave star is in bounded relative motion around the host star. The difference in orbital elements between the slave star and the host star satisfies certain conditions to construct bounded relative constraints.

[0102] Step 112: Based on the constraints and objective function, establish a solution model for the near-field perception formation optimization problem, and transform the solution model for the near-field perception formation optimization problem into a solution model for a nonlinear programming problem; use a nonlinear optimization algorithm to solve the solution model for the nonlinear programming problem to obtain the optimized near-field perception formation.

[0103] This application utilizes the penalty function method to transform a constrained programming problem into an unconstrained programming problem, that is, to transform the solution model of the near-field perception formation optimization problem into a nonlinear programming problem solution model. The nonlinear optimization algorithm in MATLAB software is used to solve the nonlinear programming problem solution model to obtain the optimized near-field perception formation.

[0104] In the aforementioned GEO spacecraft multi-line-of-sight fusion near-field perception formation design method, this application integrates the line-of-sight angle information measured by multiple spacecraft into a single measurement equation, effectively improving the observability of relative state estimation based solely on angle measurements. Under the framework of relative motion, spacecraft illumination constraints and bounded relative constraints are constructed, and a near-field perception formation optimization strategy is established, effectively solving the problems of limited communication distance for small spacecraft and the high sensitivity of optical sensors to sunlight.

[0105] In one embodiment, the spacecraft's relative motion equations are discretized and linearized according to a specified discrete time to obtain the near-field sensing state equations, including:

[0106] Discretize and linearize the spacecraft's relative motion equations according to a specified discrete time, and obtain the near-field sensing state equation as X. k+1 =Φ k X k , where X k+1 and X k The state column vectors at time k+1 and time k are Φ respectively. k Let be the state transition matrix.

[0107] In one embodiment, the observation equations of multiple spacecraft are combined and then linearized to obtain linear observation equations, including:

[0108] After simulating the observation equations of multiple spacecraft and linearizing them, we obtain the linear form of the observation equation Z. k =H k X c,k +V k ,in, Let h(X) represent the Jacobian matrix. all ) represents the theoretical value of the line-of-sight angle, X all =(X c ;X d1 ;…;X dN ), This represents the relative position and velocity state of the space target within the orbital coordinates of the primary star. X represents the relative position and velocity state of a space target in the orbital coordinates of the i-th satellite. c,k V represents the relative state of a space target in the coordinate system of the primary star's orbit. k Z represents the measurement noise. k This represents the actual measured value.

[0109] In one embodiment, the relative position vector of the space target relative to the primary star is the position vector of the space target in the primary star's orbital coordinate system; using the spatial triangle formed by the primary star, secondary stars, and the space target, a relationship between the relative position vector and the line-of-sight vector is established based on the relative position vector, including:

[0110] Using the law of cosines, we calculate the unit vectors of the space target's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system. This yields the line-of-sight angle between the space target's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system, as well as the supplementary angle of the line-of-sight angle between the secondary star's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system.

[0111] Based on the sine theorem, the angle between the line of sight between the position vector of the space target in the primary star's orbital coordinate system and the position vector of the space target in the secondary star's orbital coordinate system, and the supplementary angle between the line of sight between the position vector of the secondary star in the primary star's orbital coordinate system and the position vector of the space target in the secondary star's orbital coordinate system, are calculated to obtain the relationship between the angle between the relative position vector and the line of sight vector.

[0112] In one embodiment, the cosine theorem is used to calculate the unit vectors of the space target's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system. This yields the line-of-sight angle between the space target's position vectors in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system, and the supplementary angle of the line-of-sight angle between the secondary star's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system. This includes:

[0113] Using the law of cosines, we calculate the unit vectors of the space target's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system. The supplementary angles of these angles are:

[0114]

[0115] Where, θ t and θ cd1 Let ρ be the angle between the line of sight between the position vector of the space target in the primary star's orbital coordinate system and the position vector of the space target in the secondary star's orbital coordinate system, and the supplementary angle between the line of sight between the position vector of the secondary star in the primary star's orbital coordinate system and the position vector of the space target in the secondary star's orbital coordinate system. t and ρ t1 The position vectors of the space target in the primary star's orbital coordinate system and the space target in the secondary star's orbital coordinate system, dt and dt1, are respectively ρ t and ρ t1 The unit vector, ρ d1 This represents the position vector of star 1 in the coordinate system of the main star's orbit.

[0116] In one embodiment, the line-of-sight angle between the position vector of the space target in the primary star's orbital coordinate system and the position vector of the space target in the secondary star's orbital coordinate system, and the supplementary angle of the line-of-sight angle between the position vector of the secondary star in the primary star's orbital coordinate system and the position vector of the space target in the secondary star's orbital coordinate system, are calculated according to the sine theorem to obtain the relationship between the relative position vector and the line-of-sight vector, including:

[0117] Based on the sine theorem, the angle between the relative position vectors and the line-of-sight vectors of the space target in the primary star's orbital coordinate system and the space target in the secondary star's orbital coordinate system, and the supplementary angle between the position vectors of the secondary star in the primary star's orbital coordinate system and the space target in the secondary star's orbital coordinate system, are calculated. The relationship between the angles between the relative position vectors and the line-of-sight vectors is then obtained as follows:

[0118] In one embodiment, the objective function of the near-field perception formation optimization problem is set based on the formation optimization criterion, including:

[0119] Based on the formation optimization criterion, the objective function of the near-field perception formation optimization problem is set.

[0120]

[0121] Where N represents the number of satellites and M is the number of discrete time points. This represents the angle between star i at the k-th discrete time point and the line-of-sight vector from the main star to the target in space.

[0122] In one embodiment, the spacecraft illumination constraint is... Where, r i2sun r i2t These represent the direction of sunlight illumination and the position vector of the space target in the orbital coordinate system of star i, respectively. Indicates r i2sun r i2t The supplementary angle of the angle between the vector lines of sight, θ min This represents the critical solar constraint angle of an optical camera.

[0123] In a specific embodiment, such as Figure 4 The image shown is a schematic diagram of the spacecraft's illumination constraint.

[0124] In one embodiment, the bounded relative constraint is

[0125]

[0126] Among them, a c a j The semi-major axes of the primary and secondary stars are respectively, and b is the semi-major axis of the primary star and the secondary star. j For the natural motion of the ellipse from star j in x c o c y c The length of the minor semi-axis of the plane projection, C j For the natural motion of the ellipse from star j in z c The amplitude of the axis, y c,j For the natural motion of the ellipse from star j in x c o c y c The distance from the center of the planar projection to the origin O.

[0127] In one embodiment, the solution model for the near-field perception formation optimization problem is transformed into a solution model for a nonlinear programming problem, including:

[0128] The solution model for the near-field perception formation optimization problem is transformed into the solution model for a nonlinear programming problem, as found:X design

[0129]

[0130] s·t:

[0131]

[0132] Among them, X design =[a1,e1,I1,Ω1,ω1,M1…a N ,eN ,I N ,Ω N ,ω N M N ] represents the initial orbital root numbers of each satellite, a i e i I i Ω i ω i M i These are the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of perigee, and mean perigee angle, respectively.

[0133] In one embodiment, the performance of the method of this application is verified by numerical simulation. Table 1 shows the orbital parameters before formation optimization, and Table 2 shows the orbital parameters after formation optimization. The simulation time is 2000s. The angular measurement accuracy of the optical camera is 0.001rad and the angular measurement error follows a Gaussian distribution. The target line-of-sight angle information is acquired every 0.5s. The initial relative state estimation error is [10000m, 10000m, 10000m, 10m / s, 10m / s, 10m / s]. The number of slave stars N = 2, the critical solar illumination angle is 80°, and it is bounded.

[0134] Table 1

[0135]

[0136] Before formation optimization, by Figure 5 It can be seen that the spatial target distance error converges to 10m within 692s. Figure 6 The graph shows the changes in the magnitude of the spatial target velocity and the corresponding triaxial component estimation error over time. The gray curve in the small block diagram is a magnified view of the last 100 seconds. Figure 6 It can be seen that the error in the velocity of the space target converges to 0.15 m / s within 569 s. Figure 7 The curves show the change in the angle of sunlight irradiation of two stars over time. Figure 7 It can be seen that the solar illumination angle of spacecraft 1 is greater than 80 degrees, while that of spacecraft 2 is less than 80 degrees. Table 2 shows the orbital parameters after formation optimization.

[0137] Table 2

[0138]

[0139] After formation optimization, by Figure 8 It can be seen that the spatial target distance error converges to 5m within 500s. Figure 9 The graph shows the changes in the magnitude of the spatial target velocity and the corresponding triaxial component estimation error over time. The gray curve in the small block diagram is a magnified view of the last 100 seconds. Figure 9It can be seen that the error in the velocity of the space target converges to 0.05 m / s within 450 s. Figure 10 The curves show the change in the angle of sunlight irradiation of two stars over time. Figure 9 However, the angle of sunlight exposure is greater than the critical constraint angle of 80 degrees. In summary, the method of this application improves both the filtering convergence speed and the filtering convergence accuracy.

[0140] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated in this application, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Furthermore, Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0141] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0142] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for designing near-field perception formations for GEO spacecraft using multi-line-of-sight fusion, characterized in that, The method includes: The relative motion equations of the spacecraft are established in the orbital coordinate system. The relative motion equations of the spacecraft are discretized and linearized according to the specified discrete time to obtain the state equations for near-field sensing. The angle information of the space target is obtained by measuring multiple spacecraft. The observation equation is constructed based on the relative position vector of the space target and the observation spacecraft and the angle information of the space target. The observation equations of multiple spacecraft are combined and linearized to obtain the linear form of the observation equation. Based on the state equation, the linear observation equation, and the measured angle information of the space target, the relative state of the space target and the host star is estimated using the extended Kalman filter algorithm to obtain the relative position vector and velocity of the space target relative to the host star. Using the spatial triangle formed by the primary star, secondary stars, and space targets, establish the relationship between the angle between the relative position vector and the line-of-sight vector based on the relative position vector; By taking the partial derivative of both sides of the relationship between the relative position vector and the line-of-sight vector with respect to the line-of-sight angle, the formation optimization criterion is obtained. Based on spacecraft illumination constraints and bounded relative constraints, the constraints of the near-field perception formation optimization problem are set; and the objective function of the near-field perception formation optimization problem is set based on the formation optimization criteria. Based on the constraints and the objective function, a solution model for the near-field perception formation optimization problem is established, and the solution model for the near-field perception formation optimization problem is transformed into a solution model for a nonlinear programming problem. The solution model of the nonlinear programming problem is solved using a nonlinear optimization algorithm to obtain the optimized near-field sensing formation; Based on the aforementioned formation optimization criteria, the objective function for the near-field perception formation optimization problem is set, including: Based on the aforementioned formation optimization criterion, the objective function for the near-field perception formation optimization problem is set. in, N Indicates the number of stars. M The number of discrete time points. Indicates from the star i In the k The angle between a discrete time point and the line-of-sight vector from the primary star to the target in space; The spacecraft's illumination constraint is ,in, , These represent the direction of sunlight illumination and the space target's position from the star. i Position vector in the orbital coordinate system express , Supplementary angle of the angle between vector lines of sight θ min This indicates the critical solar constraint angle of an optical camera; The bounded relative constraint is in, a c , a j They are the primary star and the secondary star, respectively. j Semi-long shaft, b j For the stars j The natural motion of an ellipse x c o c y c The length of the minor semi-axis of the plane projection. C j For the stars j The natural motion of an ellipse z c Amplitude of the shaft, y c,j For the stars j The natural motion of an ellipse x c o c y c The distance from the center of the plane projection to the origin O The distance; The solution model for the near-field perception formation optimization problem is transformed into a solution model for a nonlinear programming problem, including: The solution model for the near-field perception formation optimization problem is transformed into a nonlinear programming problem solution model. in, This represents the initial six-element orbital numbers of each satellite. a i , e i , I i , Ω i , ω i , M i From the stars i Semi-major axis, eccentricity, orbital inclination, right ascension of ascending node, argument of perigee, and angle of approach to perigee. , These represent the direction of sunlight illumination and the space target's position from the star. j The position vector in the orbital coordinate system.

2. The method according to claim 1, characterized in that, Discretize and linearize the spacecraft's relative motion equations according to a specified discrete time to obtain the near-field sensing state equations, including: Discretize and linearize the spacecraft's relative motion equations according to a specified discrete time, and obtain the state equation for near-field sensing as follows: ,in, and respectively k +1 time and k The state column vector at time t, Let be the state transition matrix.

3. The method according to claim 1, characterized in that, After simulating the observation equations from multiple spacecraft, a linear form of the observation equations is obtained, including: After simulating the observation equations from multiple spacecraft and linearizing them, we obtain the linear form of the observation equations as follows: ,in, Represents the Jacobian matrix, This represents the theoretical value of the line-of-sight angle. , This represents the relative position and velocity state of the space target within the orbital coordinates of the primary star. Indicates that the space target is in the first place. i The relative position and velocity state of a star in its orbital coordinates. This represents the relative state of a space target in the coordinate system of the primary star's orbit. Indicates measurement noise. This represents the actual measured value.

4. The method according to claim 1, characterized in that, The relative position vector of the space target with respect to the primary star is the position vector of the space target in the primary star's orbital coordinate system; using the spatial triangle formed by the primary star, secondary stars, and the space target, an angle relationship between the relative position vector and the line-of-sight vector is established based on the relative position vector, including: Using the law of cosines, we calculate the unit vectors of the space target's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system. This yields the line-of-sight angle between the space target's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system, as well as the supplementary angle of the line-of-sight angle between the secondary star's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system. Based on the sine theorem, the angle between the line of sight between the position vector of the space target in the main star's orbital coordinate system and the position vector of the space target in the slave star 1's orbital coordinate system, and the supplementary angle between the line of sight between the position vector of slave star 1 in the main star's orbital coordinate system and the position vector of the space target in the slave star 1's orbital coordinate system, are calculated to obtain the relationship between the angle between the relative position vector and the line of sight vector.

5. The method according to claim 4, characterized in that, Using the law of cosines, the unit vectors of the space target's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system are calculated to obtain the line-of-sight angle between the space target's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system, and the supplementary angle of the line-of-sight angle between the secondary star's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system. These angles include: Using the law of cosines, the unit vectors of the space target's position vector in the primary star's orbital coordinate system and the space target's position vector in the secondary star's orbital coordinate system are calculated. The supplementary angles of the line-of-sight angle between these two vectors are then obtained. in, θ t and θ cd1 These are the supplementary angles of the line of sight between the position vector of the space target in the primary star's orbital coordinate system and the position vector of the space target in the secondary star's orbital coordinate system, respectively, and the line of sight between the position vector of the secondary star in the primary star's orbital coordinate system and the position vector of the space target in the secondary star's orbital coordinate system. ρ t and ρ t1 Let dt and dt1 represent the position vectors of the space target in the primary star's orbital coordinate system and the space target in the secondary star's orbital coordinate system, respectively. ρ t and ρ t1 unit vector, ρ d1 This represents the position vector of star 1 in the coordinate system of the main star's orbit.

6. The method according to claim 5, characterized in that, Based on the sine theorem, the angle between the relative position vectors and the line-of-sight vectors of the space target in the primary star's orbital coordinate system and the space target in the secondary star's orbital coordinate system, and the supplementary angle between the position vectors of secondary star 1 in the primary star's orbital coordinate system and the space target in the secondary star's orbital coordinate system, are calculated to obtain the relationship between the relative position vectors and the line-of-sight vectors, including: Based on the sine theorem, the angle between the relative position vectors and the line-of-sight vectors of the space target in the primary star's orbital coordinate system and the space target in the secondary star's orbital coordinate system, and the supplementary angle between the position vectors of secondary star 1 in the primary star's orbital coordinate system and the space target in the secondary star's orbital coordinate system, are calculated to obtain the relationship between the angles of the relative position vectors and the line-of-sight vectors. .

Images