Optimal star selection for spacecraft high-precision pointing measurement navigation

Abstract

The spacecraft high-precision pointing measurement navigation observability optimal star selection method disclosed by the application belongs to the field of spacecraft autonomous navigation. The implementation method of the application is: in view of the requirement of selecting a small number of suitable star angular distances as observation quantities for spacecraft autonomous navigation, a star selection criterion is constructed based on system observability analysis, and a plurality of optimal star angular distances are selected as observation objects in the photographed star map. A star angular distance rapid selection method is constructed, the image plane is divided into a plurality of regions by selecting star pairs in steps, a pair of stars is selected in different ranges of the image plane each time to form an angular distance, the calculation amount of global traversal selection is reduced, and the positions of the projection points of the angle bisectors of different angular distances on the image plane are constrained by setting a position constraint epsilon between the projection points, the collinearity of the angle bisectors is avoided to cause the system observability to decrease, the system observability of the spacecraft observation system can be improved, the calculation amount can be reduced, and the navigation precision of the spacecraft can be improved.

Description

TECHNICAL FIELD

[0001] The present application relates to a spacecraft high-precision pointing measurement navigation optimal star selection method, and belongs to the technical field of spacecraft autonomous navigation. BACKGROUND

[0002] When performing space tasks, spacecraft often use autonomous navigation technology to navigate using their own equipment without any information exchange with the outside world, and autonomously obtain relevant information to estimate the state of the spacecraft. Autonomous navigation methods include inertial navigation, optical navigation, pulsar navigation, etc. Relativity navigation, as a new type of navigation method, is a potential means to achieve high-precision autonomous navigation of spacecraft. It mainly measures two types of information, i.e., the star aberration caused by the motion of the spacecraft and the light deflection caused by the gravitational field of celestial bodies, establishes a spacecraft state observation equation, and further combines a spacecraft orbit dynamics model to estimate the motion state of the carrier in real time using a navigation filter.

[0003] Due to the existence of relativistic effects such as star aberration and light deflection, it is difficult for a moving spacecraft to measure the true line-of-sight direction of a star, which leads to the inability to establish a high-precision inertial reference. In the case where the measured star line-of-sight direction is offset due to relativistic effects and cannot be corrected, the conversion relationship between the sensor coordinate system and the inertial coordinate system is uncertain, making it difficult to directly convert the star line-of-sight direction measured in the sensor coordinate system to the inertial coordinate system for direct estimation of the spacecraft state. To address this situation, the angle between the two star line-of-sight directions, i.e., the star angular distance, is used as the navigation observation information instead of a single star line-of-sight direction. Since the star angular distance is the same in different coordinate systems, it can solve the problem of converting the star line-of-sight direction vector from the sensor coordinate system to the inertial coordinate system, i.e., the inertial attitude information of the spacecraft is not needed in the positioning calculation process, and the estimation of the spacecraft position and velocity can be completed even in the case of uncertain spacecraft attitude.

[0004] Considering that there are a large number of stars in the star map obtained by the spacecraft in orbit and the limited computing power on the spacecraft, it is necessary to select a small number of suitable stars to form a star angular distance. Existing methods are mostly based on heuristic algorithms and use experience to design the star selection method. However, due to the lack of detailed mathematical demonstration, the algorithm itself has certain defects, and the obtained star selection result is often a suboptimal solution. Therefore, it is necessary to analyze the influence of different star selection results on navigation accuracy, study the size and distribution of star angular distances, and design an optimal star selection method to improve the autonomous navigation accuracy of the spacecraft. SUMMARY

[0005] The main purpose of the present application is to provide a spacecraft extremely high precision pointing measurement navigation optimal star selection method, aiming at the need of selecting a small number of suitable star angular distances as observation quantities for spacecraft autonomous navigation, based on system observability analysis and design star selection criteria, selecting several groups of optimal star angular distances as observation objects in the photographed star map. A fast star angular distance selection method is constructed, and the image plane is divided into multiple regions by selecting star pairs step by step. A pair of stars is selected in different ranges of the image plane each time to form an angular distance, which reduces the calculation amount caused by global traversal selection. The position constraint epsilon between the projection points of the angle bisector of different angular distances is set to constrain the position of the projection point of the angle bisector of each angular distance on the image plane, avoiding the collinearity of the angle bisector to cause the decrease of system observability, thereby improving the observability of the spacecraft observation system while reducing the calculation amount and improving the navigation accuracy of the spacecraft.

[0006] The purpose of the present application is realized by the following technical solutions.

[0007] The spacecraft extremely high precision pointing measurement navigation optimal star selection method disclosed by the present application comprises the following steps:

[0008] Step one, aiming at the influence of star aberration and light deflection on the observation of star line of sight direction, a high-precision pointing measurement navigation observation model is constructed, the Fisher information matrix is used as the system observability matrix, the influence of different number and size of star angular distances on system observability is analyzed, and a star angular distance selection criterion is established.

[0009] The state quantity is constructed as the combination of the position vector r of the spacecraft in the inertial coordinate system k =[r xk r yk r zk ] T , the velocity vector v k =[v xk v yk v zk ] T and the sensor reference bias κ k , the first-order Gauss-Markov process time parameter τ k , that is

[0010]

[0011] Wherein: represents the position of the spacecraft at time k, represents the velocity of the spacecraft at time k, κ k represents the reference bias of the spacecraft at time k, τ k represents the Markov process parameter of the spacecraft at time k, and x k represents the state quantity of the spacecraft at time k.

[0012] Based on the spacecraft orbit dynamics model, the state equation is established

[0013] x k = f(x k-1 ) + w k (2)

[0014] Wherein: f(·) represents the spacecraft state equation, w k represents the process noise at k time.

[0015] Considering the influence of stellar aberration and light deflection effect, the high-precision pointing measurement navigation observation model is established

[0016] y k = h(x k ) + v k (3)

[0017] Wherein: y k represents the observation at k time, h(·) represents the spacecraft observation equation, v k represents the observation noise at k time.

[0018] Neglecting the second order and above small amount to get the linear observation equation about spacecraft velocity

[0019] y k = H V v k + κ k (4)

[0020] In the formula, H V represents the observation matrix about spacecraft velocity

[0021]

[0022] In the formula, u Iik represents the unit line of sight of the i th star in the inertial coordinate system at k time. The overall observation matrix H corresponding to formula (3) is

[0023]

[0024] The degree of observability is used to represent the ability of the system to determine its state through observation information. Fisher information matrix is used as an evaluation means to measure the degree of observability of nonlinear system. The degree of observability of navigation system is analytically derived, and the minimum observation information required for spacecraft state estimation and on-orbit calibration of sensor reference deviation is analyzed. The degree of observability of navigation system is calculated based on the Cramer-Rao lower bound. The sensor reference deviation is introduced into the linear observation equation of spacecraft velocity to calibrate the system error of spacecraft, and the navigation precision of spacecraft is improved.

[0025] Fisher information matrix F i defined as the mean of the second order partial derivative of the loss function with respect to the state

[0026]

[0027] where J(x) is the index function, σ i is the standard deviation of the observation noise.

[0028]

[0029] The Fisher information matrix corresponding to a set of star angular distance observations is obtained from equation (6), equation (7), and equation (8)

[0030]

[0031] where is a 1x3 matrix.

[0032] Cramér-Rao inequality The relationship between the state estimation error and the Fisher information matrix is described, and the state estimation error covariance P k and the trace of the Fisher information matrix F ij satisfies

[0033]

[0034] where λ1,..., λ n are the eigenvalues of the Fisher information matrix. The eigenvalues of the Fisher information matrix are used to evaluate the size of the navigation estimation error, and also reflect the system observability: the larger the eigenvalues of the Fisher information matrix, the smaller the estimation error, i.e. the stronger the observability, and vice versa. By calculating the trace or determinant of the Fisher information matrix, the influence of the size of the star angular distance on the navigation performance is quantitatively analyzed, and the upper bound of the theoretical estimation accuracy of the navigation system is calculated in combination with the Cramér-Rao lower bound.

[0035] According to equation (9) and equation (10), when only one set of star angular distance observations is used, the corresponding Fisher information matrix is obtained by extracting the non-zero part of the 4x4 matrix

[0036]

[0037] where σ v is the standard deviation of the spacecraft velocity observation noise. In equation (11), the rank of the matrix is 1, and the non-zero eigenvalue is

[0038] λ = 1 + a 2 (x 2 +y 2 +z2 ) (12)

[0039] The corresponding eigenvector is [ax1 ay1 az1 1] T , the system is only observable on the bisector of the angle. The trace of the Fisher information matrix (the sum of the non-zero eigenvalues of the matrix) is 1+a 2 (x 2 +y 2 +z 2 ).

[0040] Two star angles are observed. The 4x4 matrix obtained by cutting the effective information part of the Fisher information matrix is

[0041]

[0042] In the formula, The rank of the matrix in formula (13) is 2, and there are 2 non-zero eigenvalues. The trace of the corresponding Fisher information matrix is

[0043]

[0044] The eigenvector corresponding to the zero eigenvalue in the velocity space is

[0045] [y1z2-z1y2 z1x2-x1z2 x1y2-y1x2 0] T (15) In the formula, the size of the eigenvector is the cross product of the vector sum of the respective unit line-of-sight directions of the two angles, and the spacecraft velocity is not observable in the direction perpendicular to the bisector of the two angles.

[0046] The spacecraft velocity is not observable in the direction perpendicular to the bisector of the two angles in the case where the bisectors of the two angles do not coincide. If the bisectors of the two sets of angles coincide, there are

[0047]

[0048] Matrix (13) degenerates into matrix (11).

[0049] Three star angles are used as observation information, and the corresponding Fisher information matrix is

[0050] In the formula, The rank of the matrix in formula (17) is 3, and there are 3 non-zero eigenvalues. The bisectors of the three sets of angles should not coincide with each other, otherwise matrix (17) will degenerate into matrix (11) and (13). The trace of the corresponding Fisher information matrix is

[0051]

[0052] When n≥4 angular distances are observed and the bisector directions of each angular distance are not coincident, the non-zero part of the Fisher information matrix is obtained by intercepting a 4×4 matrix

[0053]

[0054] wherein, The rank of the matrix in formula (19) is 4, and the matrix is full rank. The trace of the corresponding Fisher information matrix is

[0055]

[0056] In the case where the bisector directions of each star angular distance are not coincident, the more the number of observed star angular distances, the higher the observability of the spacecraft observation system.

[0057] According to formula (20), the influence of the size of the star angular distance on the system observability is further obtained. The trace of the Fisher information matrix is expressed as a form containing the star angular distance

[0058]

[0059] The derivation of formula (21) shows that each star angular distance θ1=θ2=...=θ n When θ=109.5°, the trace of the Fisher information matrix reaches the maximum value, that is, when multiple star angular distances are used as observation quantities and the size of the star angular distance is 109.5°, the trace of the Fisher information matrix formed by the spacecraft observation system is the largest, and the observability is the best. The field of view of the star sensor is limited, so when selecting the star angular distance, it is determined that the larger the star angular distance is, the better.

[0060] When selecting subsequent star pairs, by making the non-diagonal elements of the measurement noise covariance matrix R to be 0, the measurement noise covariance matrix R is simplified, the navigation filtering calculation efficiency is improved, and each star is only selected once, that is, all star angular distance measurement errors are independent of each other, and the covariance is 0.

[0061] Establish a star angular distance selection criterion:

[0062] ① Select the angular distance with the largest angle in the field of view as much as possible;

[0063] ② The bisector directions of the selected star angular distances are not coincident;

[0064] ③ Each star is only selected once.

[0065] Step two, construct the fast selection method of star angular distance, through the step selection of star pair, divide the image plane into several regions, select a pair of stars in different ranges of image plane to form the angular distance each time, reduce the calculation amount caused by global traversal selection, and through setting the position constraint ε between the projection points of the angle bisector of different angular distances, constrain the position of the projection points of the angle bisector of each angular distance on the image plane, avoid the collinearity of the angle bisector to cause the decrease of system observability. Repeat the above star pair selection process until the nth selection of star pair, expand the selection range to the entire star map, complete the selection of all star angular distances, that is, obtain n groups of optimal star angular distances as observations.

[0066] According to the star angular distance selection criteria established in step one, when selecting stars, the star pair with the largest angular distance should be selected as the observation target as much as possible, and the angle bisectors of the selected star angular distances cannot be collinear. Design an index ε on the image plane to constrain the position of the projection points of the angle bisectors of each angular distance on the image plane, avoid the approximate coincidence of the angle bisectors of two angular distances caused by the relativistic effect and measurement error, and make the system observability matrix degenerate, the observability of the spacecraft observation system decreases, and the navigation accuracy decreases.

[0067] When selecting observation targets, when there are s stars in the image plane, select n groups of star angular distances from the s stars, number the stars in order according to the imaging position to form the candidate sequence {u1, u2,..., un}, and select the first group of star angular distances from the candidate sequence. s}。

[0068] Construct the s×s pairing matrix M p . Update the element value of the pairing matrix M p , record the selection process of the star pair and the remaining selectable star pair. The element M p (i,j) = 1 represents that the star i is paired with the star j, and vice versa. The element M p (i,j) = 0 represents that the star i cannot be paired with the star j. Initialize M p .

[0069]

[0070] In order to avoid traversing all star angular distances, design an s×s angular distance matrix M p corresponding to the pairing matrix M a , and initialize M a = 0.

[0071] Select the first group of star angular distances. Divide the image plane into four regions with a / n and b / n as the length and width of the field of view, respectively. Record that the four regions contain the following stars, respectively:

[0072]

[0073] For any two stars in the same region, such as Figure 2 Lower right corner area The two stars in the pair are considered as a star combination that cannot be paired because the angular distance between them is too small. p The corresponding elements are set to 0.

[0074] for For any two stars in the four regions that do not belong to the same region, update M according to formula (24) a :

[0075] if M p (i,j)=1, then M a (i,j)=θ ij (twenty four)

[0076] M a All elements greater than 0 are put into the column matrix V a

[0077]

[0078] By traversing V a And select the two stars with the largest angular separation As the first set of sidereal angular distances.

[0079] Since a star can only be selected once, the first set of star angular distances and their corresponding star pairs are obtained. Then, the pairing matrix M p Updated to

[0080]

[0081] That is M p Middle Row and All column elements are set to 0.

[0082] Considering that the angular bisectors of the selected star angular distances cannot be collinear, and the star line of sight direction has deviations due to the relativistic effect and measurement noise, the angular bisectors of the star angular distances are projected on the image plane. No other angular bisector projection points should exist near the selected angular bisector projection point. After obtaining the first set of star angular distances, a detection range with a radius of ε is set with the corresponding angular bisector projection point as the center of the circle. The current and subsequent star pairs for angular distance calculation are detected. If other angular bisector projection points fall within this range, they are removed from the angular bisector projection point map, and the corresponding star pairs are added to the pairing matrix M. p The corresponding elements are set to 0, and the angular distance matrix M a The corresponding elements are set to -1.

[0083] After the first group of star angular distances is selected, the corresponding star pairs are removed from the image plane, the angular distance matrix M a is updated, and the corresponding elements are set to -1.

[0084] The second group of star angular distances is selected. The four divided areas in the star map are expanded to 2a / n and 2b / n. Similarly, for any two stars in the same area, the corresponding elements in the pairing matrix M p are set to 0. For any two stars in different areas in the four areas, there are the following cases when updating M a :

[0085] a) M p (i,j) = 1 and M a (i,j) = 0, indicating that the star pair can be paired and is first selected, the corresponding angular distance is calculated, and M a (i,j) = θ ij is updated;

[0086] b) M p (i,j) = 1 and M a (i,j) = θ ij , indicating that the star pair can be paired and the angular distance has been calculated, the corresponding element in M a remains unchanged;

[0087] c) M p (i,j) = 0 and M a (i,j) = -1 and, indicating that the star pair has been selected before and will not be selected again in the subsequent steps; or the star pair can be paired, but the projection point of the corresponding angular bisector falls within the detection range and is excluded. The corresponding element in M a remains unchanged.

[0088] All elements greater than 0 in M a are placed in the column matrix V a , and the two stars with the largest angular distance in V a are selected as the second group of star angular distances.

[0089] The elements in the first row and the first column of M p are all set to 0, and a detection range with a radius of ε is set with the projection point of the angular bisector corresponding to the second group of star angular distances as the center. The star pairs currently and subsequently calculated for angular distance are detected, and if other projection points of the angular bisector fall within the range, they are removed from the projection point diagram of the angular bisector, and the corresponding star pairs in the pairing matrix M p ​​The corresponding element is 0, and the angular distance matrix M a The corresponding element is -1.

[0090] The above star pair selection process is repeated, until the nth time of selecting a star pair, the selection range is expanded to the entire star map, the entire star angular distance selection is completed, and n sets of optimal star angular distances are obtained as observations.

[0091] Step three: the n sets of optimal star angular distances obtained in step two are used as observations to form an observation equation, and the spacecraft state is estimated in real time, so that autonomous navigation of the spacecraft is realized.

[0092] The n sets of optimal star angular distances obtained in step two are used as observations to form an observation equation, and the spacecraft state is estimated in real time, so that autonomous navigation of the spacecraft is realized. The observation equation is substituted into formula (4), wherein

[0093]

[0094]

[0095] The system observation matrix of the spacecraft observation system as a whole is

[0096]

[0097] The state equation shown in formula (2) is combined, the spacecraft state is estimated in real time, and autonomous navigation of the spacecraft is realized.

[0098] Beneficial effects:

[0099] 1. The spacecraft high-precision pointing measurement navigation optimal star selection method disclosed in the application starts from system observability, analyzes the influence of the number, size and distribution factors of the star angular distance on the system observability according to the rank of the Fisher information matrix, establishes a star angular distance selection criterion, searches for a star pair from a star map based on the star angular distance selection criterion to form a star angular distance, and improves the autonomous navigation precision of the spacecraft.

[0100] 2. The spacecraft high-precision pointing measurement navigation optimal star selection method disclosed in the application divides an image plane into multiple regions in a step-by-step selection manner, selects a pair of stars in different ranges of the image plane each time to form an angular distance, reduces the calculation amount caused by global traversal selection, and avoids the system observability from being reduced due to the collinearity of the angular bisector by setting the position constraint between the projection points of different angular distances. DETAILED DESCRIPTION

[0101] Figure 1 The spacecraft high-precision pointing measurement navigation optimal star selection method disclosed in the application;

[0102] Figure 2 The image plane division schematic diagram;

[0103] Figure 3 is a schematic diagram of star distribution;

[0104] Figure 4 is a simulation diagram of star angular distance angle bisector projection point;

[0105] Figure 5 is a simulation diagram of selecting a first group of angular distances;

[0106] Figure 6 is a simulation diagram of selecting a second group of angular distances;

[0107] Figure 7 is a simulation diagram of selecting a third group of angular distances;

[0108] Figure 8 is a position state estimation error diagram of two star selection methods;

[0109] Figure 9 is a velocity state estimation error diagram of two star selection methods. DETAILED DESCRIPTION

[0110] In order to better illustrate the purposes and advantages of the present application, the following further illustrates the content of the application in combination with the drawings and examples.

[0111] Example 1:

[0112] The scene of the spacecraft in the earth-moon space based on the spacecraft extremely high precision pointing measurement navigation observability optimal star selection method for celestial navigation. The node dynamics equation is established in the spacecraft body system, formula (2) is:

[0113] f(x k )=x k +Φ(x k )Δt (30)

[0114]

[0115] In the formula, Δt is the state prediction time step, p(r k ) is the environmental disturbance, w k is the system unmodeled error, the variance of which is Q k , and Φ k is the change rate of the reference bias.

[0116] As shown in Figure 1 , the spacecraft extremely high precision pointing measurement navigation observability optimal star selection method disclosed in the embodiment has the following specific implementation steps:

[0117] Step one, in view of the influence of star aberration and light deflection on the observation of star visual direction, a high-precision pointing measurement navigation observation model is constructed, the Fisher information matrix is taken as the system observability matrix, the influence of different number and size of star angular distance on the system observability is analyzed, and a star angular distance selection criterion is established.

[0118] Since the system observation performance reaches the optimal value when the angular distance is 109.5°, and the larger the angular distance is, the higher the system observability is when it does not reach the optimal value. In combination with the actual situation, the maximum field of view of the star sensor is generally much smaller than 109.5°, and for this situation, as long as the star angular distance with the largest included angle is selected.

[0119] Step two, a star angular distance rapid selection method is constructed, the image plane is divided into multiple regions by selecting star pairs in steps, an angular distance is formed by selecting a pair of stars in different ranges of the image plane each time, the calculation amount caused by global traversal selection is reduced, and the position of the angular bisector projection point of each angular distance on the image plane is constrained by setting a position constraint ε between the angular bisector projection points of different angular distances, so as to avoid the co-linearity of the angular bisector and cause the system observability to decrease. The above star pair selection process is repeated until the selection range is expanded to the entire star map when the star pair is selected for the nth time, the entire star angular distance selection is completed, and n groups of optimal star angular distances are obtained as the observation quantities.

[0120] As shown in Figure 2 , the star map is constructed according to formula (23), and the star selection range is continuously expanded in sequence, so that the two stars of each star pair exist in different regions, and the size of the star angular distance is increased. Figure 3 and Figure 4 are schematic diagrams of star distribution and angular bisector projection point of star angular distance. Since other angular bisector projection points should not exist near the selected angular bisector projection point. Therefore, after obtaining the first group of star angular distances, a detection range (blue dashed circle) with a radius of ε is set with the corresponding angular bisector projection point (red solid circle) as the center, and if other angular bisector projection points fall within the range, they are removed from the angular bisector projection point diagram.

[0121] The focal length of the spacecraft star sensor is f=0.02m, the star map is a square with a length and width of , a plane coordinate system is constructed with the center of the star map as the origin, and the constraint index is set as ε=a / 2. The initial star map is provided with 10 stars, and 3 pairs of star angular distances are selected as observation targets.

[0122] As shown in Figure 5 , in the first angular distance selection process, all stars in the first step region are found, and all star combinations (two stars are not in the same region) that meet the conditions are listed, the two stars with the largest included angle are selected to form the star angular distance, that is, the 6th star and the 10th star, and the M aM p matrix, draw all the feasible angle distance angle bisector projection points in the image plane, draw the selected angle distance projection points and their ε neighborhood range, and mark the angle distance projection points in the constraint range (orange projection points), and update M a matrix, and remove the 6th star and the 10th star from the figure to prevent secondary use.

[0123] As Figure 6 shown, in the second star angle distance selection process, repeat the first step operation, select the 3rd star and the 9th star to form an angle distance, and update M a M p matrix, draw all the feasible angle distance angle bisector projection points in the image plane, draw the selected angle distance projection points and their ε neighborhood range, and mark the angle distance projection points in the constraint range, and update M a matrix and remove the 3rd star and the 9th star in the image plane.

[0124] As Figure 7 shown, in the second star angle distance selection process, repeat the first step operation, select the 2nd star and the 1st star to form an angle distance, and update M a M p matrix, draw all the feasible angle distance angle bisector projection points in the image plane, draw the selected angle distance projection points and their ε neighborhood range, and mark the angle distance projection points in the constraint range, and update M a matrix, remove the 2nd star and the 1st star in the image plane.

[0125] The entire star selection process is completed.

[0126] Step three, use the n groups of optimal star angle distances obtained in step two as observations to form observation equations, and estimate the spacecraft state in real time to realize autonomous navigation of the spacecraft.

[0127] The spacecraft operates in the Earth-Moon space and operates in a GEO orbit around the Earth. Its initial position is r0=10 3 ×-17408,-38405.1,-2.5651e-12m, the initial velocity of the spacecraft is v0=10 3 ×2.80034,-1.26932,-8.47784e-17m / s, the initial value of the reference bias is 1 mas, the initial value of the Markov process parameter is τ=1000, the camera focal length is f=0.02m, the star sensor accuracy is 1 mas, the simulation time is 24h, and the step size is 10s. The initial error of the spacecraft three-axis velocity is 10m / s, the initial error of the star sensor is 200 angular seconds, and the initial error of the Markov process parameter is 10.

[0128] Figure 8 ,Figure 9 The spacecraft high-precision pointing measurement navigation observability optimal star selection method and the random star selection method designed by the application are compared, and the spacecraft position and velocity error distribution are finally obtained. The three angular distances of the optimal method are 68.90°, 48.27° and 46.85° respectively. The three angular distances of the random star selection are 9.92°, 20.25° and 32.07° respectively. Among them, the root mean square errors of the velocity estimates obtained by the two methods are 1.2518 m / s and 3.0048 m / s respectively. In summary, the spacecraft high-precision pointing measurement navigation observability optimal star selection method designed by the application has faster convergence speed in spacecraft state estimation and higher navigation accuracy, which is consistent with the results obtained by the previous observability analysis.

[0129] The above specific description further details the purpose, technical solutions and beneficial effects of the application. It should be understood that the above description is only a specific embodiment of the application and is not used to limit the protection scope of the application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the application shall be included in the protection scope of the application.

Claims

1. The optimal star selection method for extremely high-precision pointing measurement and navigation observability of spacecraft is characterized by: The following steps are included: Step 1: Considering the effects of stellar aberration and gravitational deflection of light on the line-of-sight observation of stars, we construct an extremely high-precision pointing measurement navigation observation model. Using the Fisher information matrix as the system observability matrix, we analyze the effects of different numbers and sizes of stellar angular distances on the system observability and establish a stellar angular distance selection criterion. Step 2: Construct a fast star angular distance selection method. By selecting star pairs in steps, the image plane is divided into multiple regions. Each time, a pair of stars is selected from a different range of the image plane to form an angular distance, reducing the amount of calculation caused by the global traversal selection. The position constraint ε between the angular bisector projection points of different angular distances is set to constrain the position of each angular distance angular bisector projection point on the image plane to avoid the angular bisectors being collinear, which leads to a decrease in the observability of the system. Repeat the above star pair selection process until the nth star pair is selected, the selection range is expanded to the entire star map, and all star angular distances are selected, that is, n sets of optimal star angular distances are obtained as observation quantities. Step 3: Use the n groups of optimal star angular distances obtained in step 2 as observation quantities to form observation equations, make real-time estimates of the spacecraft state, and realize autonomous navigation of the spacecraft.

2. The method for optimizing the observability of spacecraft pointing measurement and navigation according to claim 1, characterized in that: The implementation method of step one is: The state quantity is constructed as the position vector r of the spacecraft in the inertial coordinate system k =[r xk r yk r zk ] T , velocity vector v k =[v xk v yk v zk ] T and the sensor reference deviation κ k , time parameter τ of the first-order Gauss-Markov process k The combination of in: represents the position of the spacecraft at time k, represents the velocity of the spacecraft at time k, κ k represents the reference deviation of the spacecraft at time k, τ k represents the Markov process parameters of the spacecraft at time k, x k represents the state of the spacecraft at time k; Based on the spacecraft orbital dynamics model, the state equation is established x k =f(x k-1 )+w k (2) Where: f(·) represents the spacecraft state equation, w k represents the process noise at time k; Considering the influence of stellar aberration and the gravitational deflection effect of light, an extremely high-precision pointing measurement navigation observation model is established y k =h(x k )+v k (3) Where: y k represents the observed quantity at the kth moment, h(·) represents the spacecraft observation equation, v k represents the observation noise at time k; Ignoring the second-order and higher components, we can obtain the linear observation equation for the spacecraft velocity: y k =H V v k +κ k (4) Where H V Represents the observation matrix about the spacecraft velocity Where u Iik represents the unit line of sight direction of the i-th star in the inertial coordinate system at time k; the overall observation matrix H of the system corresponding to formula (3) is Observability is used to characterize a system's ability to determine its state through observational information. The Fisher information matrix is ​​used as an evaluation method to measure the observability of nonlinear systems. The observability of navigation systems is analytically derived. The minimum observational information required to achieve spacecraft state estimation and on-orbit calibration of sensor reference biases is analyzed. The observability of navigation systems is calculated based on the Cramer-Laur lower bound. The sensor reference bias is introduced into the linear observation equation of spacecraft velocity to calibrate the spacecraft's systematic errors and improve the spacecraft's navigation accuracy. Fisher information matrix F i Defined as the mean of the second-order partial derivatives of the loss function with respect to the state Where J(x) is the indicator function, σ i is the standard deviation of the observation noise; From equations (6), (7), and (8), the Fisher information matrix corresponding to a set of stellar angular distance observations is: Where, is a 1×3 matrix; Cramér-Rao inequality Describes the relationship between the state estimation error and the Fisher information matrix, the state estimation error covariance P k and the trace of the Fisher information matrix F ij satisfy Among them, λ1,…,λ n is the eigenvalue of the Fisher information matrix; the eigenvalue of the Fisher information matrix is ​​used to evaluate the magnitude of the navigation estimation error and reflect the observability of the system: the larger the eigenvalue of the Fisher information matrix, the smaller the estimation error, that is, the stronger the observability, and vice versa; by calculating the trace or determinant of the Fisher information matrix, the influence of the angular distance of the stars on the navigation performance is quantitatively analyzed, and the upper bound of the theoretical estimation accuracy of the navigation system is calculated in combination with the Cramer-Laur lower bound; According to equations (9) and (10), when only one set of star angular distances is used for observation, the corresponding Fisher information matrix is ​​intercepted by the non-zero part of the 4×4 matrix to obtain Where, σ v is the standard deviation of the spacecraft velocity observation noise; in formula (11), the matrix rank is 1 and the non-zero eigenvalue is λ=1+a 2 (x 2 +y 2 +z 2 ) (12) The corresponding eigenvector is [ax1 ay1 az1 1] T , the system is only observable on the angular distance bisector; the trace of the corresponding Fisher information matrix is ​​1+a 2 (x 2 +y 2 +z 2 ); Observe the angular distances of two stars; the corresponding Fisher information matrix intercepts the effective information part of the 4×4 matrix to obtain Where, The matrix rank in formula (13) is 2, and it has two non-zero eigenvalues; the trace of the corresponding Fisher information matrix is The eigenvalue 0 in velocity space corresponds to the eigenvector [y1z2-z1y2 z1x2-x1z2 x1y2-y1x2 0] T (15) Where, the magnitude of the eigenvector is the cross product of the sum of the vectors in the unit line of sight of the two angular distances. The spacecraft velocity is not observable in the direction perpendicular to the bisector of the two angular distances. The spacecraft velocity is not observable in the direction perpendicular to the two angular distance bisectors. This is obtained when the two angular distance bisectors do not coincide. If the two sets of angular distance bisectors coincide, we have Matrix (13) degenerates into matrix (11); Using the angular distances of three stars as observation information, the corresponding Fisher information matrix Where, The matrix rank in formula (17) is 3, with three non-zero eigenvalues; the angle bisectors of the three sets of angular distances should not overlap with each other, otherwise the matrix (17) will degenerate into matrices (11) and (13); the trace of the corresponding Fisher information matrix is When observing n ≥ 4 angular distances and the directions of the angular bisectors of the angular distances do not coincide, the corresponding Fisher information matrix intercepts the non-zero part of the 4×4 matrix to obtain Where, The matrix rank in formula (19) is 4, and the matrix is ​​full rank; the trace of the corresponding Fisher information matrix is In the case that the directions of the bisectors of the angular distances of various stars do not coincide, the more angular distances of stars observed, the higher the observability of the spacecraft observation system; According to formula (20), we can further obtain the influence of the size of the star angular distance on the observability of the system; the trace of the Fisher information matrix is ​​expressed as a form containing the star angular distance By derivation of equation (21), we can get the angular distance of each star θ1=θ2=...=θ n =109.5°, the trace of the Fisher information matrix reaches its maximum value. That is, when multiple stellar angular distances are used as observation quantities and the stellar angular distances are all 109.5°, the trace of the Fisher information matrix formed by the spacecraft observation system is the largest, and the observability is the best. The field of view of the star sensor is limited, so when choosing the stellar angular distance, the larger the stellar angular distance, the better. When selecting subsequent star pairs, the measurement noise covariance matrix R is simplified by setting the off-diagonal elements of the measurement noise covariance matrix R to zero, thereby improving the efficiency of navigation filter calculation. Each star is required to be selected only once, that is, the angular distance measurement errors of all stars are independent of each other and the covariance is zero. Establish the stellar distance selection criteria: ① Select an angular distance with the largest possible angle within the field of view; ② The directions of the selected star angular distance bisectors do not coincide; ③Each star is selected only once.

3. The method for optimizing the observability of spacecraft pointing measurement and navigation according to claim 2, characterized in that: The implementation method of step 2 is: According to the stellar angular distance selection criteria established in step 1, when selecting stars, star pairs with the largest angular distance possible should be selected as observation targets, and the angular bisectors of the selected star angular distances cannot be collinear; the index ε is designed on the image plane to constrain the position of the projection points of each angular distance bisector on the image plane to avoid the relativistic effect and measurement error causing the two angular distance bisectors to approximately coincide, thereby degrading the system observability matrix, reducing the observability of the spacecraft observation system, and reducing the navigation accuracy; When selecting an observation target, if there are s stars in the image plane, select n groups of star angular distances from the s stars, and number the stars in sequence according to the imaging position to form a candidate sequence {u1, u2, ..., u s }; Construct s×s pairing matrix M p ; By updating the pairing matrix M p The element value of M records the selection process of star pairs and the remaining selectable star pairs; p (i,j)=1 means star i is paired with star j, otherwise element M p (i,j)=0 means that star i and star j cannot be paired; initialize M p for In order to avoid traversing and calculating all the star angular distances, the pairing matrix M is designed. p The corresponding s×s angular distance matrix M a , initialize M a =0; Select the first set of sidereal angular distances; Divide the area based on the four vertices of the image plane The length and width are 1 / n of half the length and width of the field of view, i.e. a / n and b / n respectively; the four regions contain the following stars: For any two stars in the same region, since the angular distance between them is too small, they are considered as a star combination that cannot be paired. p The corresponding element is set to 0; for For any two stars in the four regions that do not belong to the same region, update M according to formula (24) a : if M p (i,j)=1,then M a (i,j)=θ ij (24) M a All elements greater than 0 are put into the column matrix V a By traversing V a And select the two stars with the largest angular separation As the angular distance of the first group of stars; Since a star can only be selected once, the first set of star angular distances and their corresponding star pairs are obtained. Then, the pairing matrix M p Updated to That is M p Middle Row and All column elements are set to 0; After obtaining the first set of star angular distances, a detection range with a radius of ε is set with the corresponding angle bisector projection point as the center of the circle. The current and subsequent star pairs for angular distance calculation are detected. If other angle bisector projection points fall within this range, they are removed from the angle bisector projection point map and the corresponding star pairs are added to the pairing matrix M. p The corresponding elements are set to 0, and the angular distance matrix M a The corresponding elements are set to -1; After selecting the first set of star angular distances, the corresponding star pairs Removed from the image plane, the angular distance matrix M a The corresponding elements are set to -1; Continue to select the second group of star angular distances; expand the length and width of the four divided areas in the star map to 2a / n and 2b / n; similarly, for any two stars in the same area, put them in the pairing matrix M p The corresponding element is set to 0; Any two stars in the four regions that do not belong to the same region are different from formula (26). a There are the following situations: a)M p (i, j)=1 and M a (i, j) = 0, indicating that the star pair can be paired and appears for the first time, calculate the corresponding angular distance and update M a (i,j)=θ ij ; b)M p (i, j)=1 and M a (i,j)=θ ij , indicating that the star pair can be paired and the angular distance has been calculated, M a The corresponding elements remain unchanged; c)M p (i, j)=0 and M a (i, j) = -1 and, it indicates that the star pair has been selected and will not be selected again in the next step; or the star pair can be paired, but the corresponding angular distance bisector projection point falls within the detection range and is eliminated; M a The corresponding elements remain unchanged; M a All elements greater than 0 are put into the column matrix V a , by traversing V a And select the two stars with the largest angular separation As the angular distance of the second group of stars; M p Middle Row and All column elements are set to 0, and a detection range with a radius of ε is set with the angular bisector projection point corresponding to the second group of star angular distances as the center of the circle. The star pairs for the current and subsequent angular distance calculations are detected. If other angular bisector projection points fall within this range, they are removed from the angular bisector projection point map, and the corresponding star pairs are added to the pairing matrix M. p The corresponding elements are set to 0, and the angular distance matrix M a The corresponding elements are set to -1; The above star pair selection process is repeated until the nth star pair is selected, at which point the selection range is expanded to the entire star map, and the selection of all star angular distances is completed, thus obtaining n sets of optimal star angular distances as observation quantities.

4. The method for optimizing the observability of spacecraft pointing measurement and navigation according to claim 3, characterized in that: The implementation method of step three is: Using the n sets of optimal star angular distances obtained in step 2 Substitute into the observation equation (4), where The system observation matrix of the spacecraft observation system as a whole is: Combined with the state equation shown in formula (2), the spacecraft state is estimated in real time to achieve autonomous navigation of the spacecraft.

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