A method for constructing a navigation star library with approximate uniform distribution under a small field of view condition

Abstract

The application discloses a kind of navigation star library construction methods of approximate uniform distribution under small field of view condition, comprising: (1) using VMT algorithm, set threshold to SAO star table is segmented, only keep following navigation star, store in star library StarLib;(2) in star library StarLib, eliminate the navigation star of brightness and position not fixed, star distance value is too small, that is, eliminate variable star and binary star, obtain basic star library (StarLib1);(3) using approximate uniform distribution of spherical spiral reference point, according to the angle distance between reference point and star, star, the combination characteristics of three star density to rough navigation star, obtain preliminary navigation star library (StarLib2) and alternative star library (StarLib3);(4) on the basis of StarLib2, using KernelSVM-SMO from nonlinear distribution StarLib3 star library, select navigation star, calculate the average value of angle distance between selected star and existing navigation star in current field of view, judge whether less than set threshold, to effectively avoid redundant star, obtain final navigation star library (StarLib4).

Description

Technical Field

[0001] This invention relates to the field of astronomical starlight attitude measurement technology, specifically to a method for constructing a navigation star library with an approximately uniform distribution under small field-of-view conditions. Background Technology

[0002] Star sensors are crucial instruments in astronomical attitude measurement, primarily involving key steps such as star image preprocessing, star centroid extraction, navigation star library construction, star image matching, and attitude calculation. The navigation star library, constructed in advance on the ground and stored within the star sensor based on its field of view, angular distance, and the accuracy requirements of the actual engineering mission, is a critical step ensuring the proper functioning of the star sensor. The selection of navigation stars directly impacts the accuracy and efficiency of subsequent star image matching and attitude calculation. Too many stars in the field of view lead to prolonged matching times and redundant matching, while too few stars prevent star image matching altogether; both reduce matching accuracy. Therefore, a small-field-of-view star sensor navigation star library with good uniformity, high average brightness, and low storage requirements is of great significance for astronomical attitude measurement.

[0003] The spiral reference point-based star selection method helps to screen out navigation stars with good uniformity, and is therefore a commonly used method in star library construction. However, due to the limitations of the algorithm itself, the selected navigation star library will have a large number of gaps in the sky in practical engineering applications. Since the magnitude information of the navigation stars is not effectively utilized, the condition of selecting bright stars in the construction of the navigation star library is not met. According to Chen Cong et al.'s "Navigation Star Selection Method Based on Spiral Reference Point" (see "Journal of Projectiles, Rockets and Guidance", 2012(4) 29-32), magnitude information is added to the spiral reference point that only considers angular distance information. Although the brightness of the navigation stars can be guaranteed, the problem of gaps in local sky areas is still not solved.

[0004] According to Cui Xiangxiang et al.'s "Method for Constructing Navigation Star Catalog Applicable to Small Field-of-View Star Sensors" (see Infrared and Laser Engineering, Vol. 44 (4), pp. 1249-1253, 2015), after the navigation stars are coarsely selected based on the spiral reference point, the navigation stars in the empty area are manually added. The process is cumbersome, labor-intensive, and lacks autonomy. Summary of the Invention

[0005] This invention addresses the problems of uneven distribution and redundancy of faint stars in navigation satellite libraries under small field-of-view conditions. It provides a method for constructing a nearly uniformly distributed navigation satellite library under such conditions, based on a solution using a nearly uniformly distributed spherical spiral reference point and Kernel SVM-SMO. This method employs the VMT algorithm to classify star magnitudes as Mag. thThe above navigation stars were removed from the basic SAO star catalog, and binary and variable stars were also removed to obtain the basic star library. Using approximately uniformly distributed spherical spiral reference points, a preliminary selection was made based on the angular distances and magnitude combinations between navigation stars, resulting in the preliminary navigation star library StarLib2 and the candidate star library StarLib3. StarLib2 was then labeled y. i =1, remaining stars are labeled y i =0. Subsequently, KernelSVM-SMO was used, leveraging StarLib2 and class y. i Stars with a value of 0 were used as the training set to train a classifier, which was then used to classify and predict StarLib3, selecting the appropriate class y. i The system selects a navigation star with a value of 1. Finally, it calculates the average angular distance between the newly added navigation star and existing navigation stars within the field of view, compares it to a set threshold, and stores the newly added star in StarLib4 if the distance is greater than the threshold; otherwise, it is not added. This reduces the occurrence of gaps in the number of navigation stars while avoiding the addition of redundant stars. The entire process is performed by the algorithm, demonstrating high autonomy.

[0006] The technical solution adopted in this invention is as follows: A method for constructing an approximately uniformly distributed navigation satellite library under small field-of-view conditions, comprising the following steps:

[0007] Step (1): Using the SAO star catalog as the original star library, the magnitude threshold is set to Mag according to the VMT algorithm. th The above navigation stars were removed from the basic SAO star catalog. Each navigation star has unique right ascension and declination information, denoted as (β). i ,δ i ), and based on this, binary stars and variable stars are removed to obtain the basic star library (StarLib1);

[0008] The specific process of step (1) is as follows:

[0009] Step (11): Using the VMT algorithm, set the star magnitude threshold to Mag. th The segmentation formula is expressed as:

[0010]

[0011] Among them, StarLib(β) i ,δ i Let be the i-th navigation star in the star database, Mag i Let be the magnitude of the i-th navigation star;

[0012] Step (12): Based on step (11), calculate the direction vector v of the i-th navigation star in the celestial coordinate system according to the right ascension and declination information. i , is represented as:

[0013]

[0014] Step (13): Angular distance is usually used to determine the distance between two stars. Using the StarLib star database obtained in step (11), the binary star angular distance threshold is calculated using the following formula:

[0015]

[0016] Where n and N TagSize f and f represent the pixel diffusion size, target size, and focal length, respectively.

[0017] Step (2): Using the approximately uniformly distributed spiral reference points as the line of sight, calculate the angular distance between the reference points and the stars and the interstellar density to ensure the uniformity requirement when selecting navigation stars, and take into account the characteristics of navigation stars to ensure the requirement of selecting bright stars when constructing the navigation star library.

[0018] The specific process of step (2) is as follows:

[0019] Step (21): First, the spiral eye axis direction is generated using an algorithm. The generation formula can be expressed as:

[0020]

[0021] Where, x k y k , z k Let t be the coordinate of each spiral line of sight in the celestial coordinate system. k =[x k y k z k ], Let be the coordinates in the spherical coordinate system, denoted as . The subscript k indicates the sequence number of the spiral reference point.

[0022] Step (22): Determine the number of spiral reference points M based on the star sensor's field of view (FOV) and the expected number of stars N within the field of view. This can be expressed as:

[0023]

[0024] Based on steps (23), (12), and (22), select the N brightest points within the field of view. e N stars e <5, and using the i-th navigation star as the primary star, calculate the average density within a unit area:

[0025]

[0026] Where m is the number of navigation stars in the field of view, v jLet be the direction vector of the j-th navigation star within the unit area of ​​the i-th navigation star in the celestial coordinate system;

[0027] Next, calculate the angular distance between the i-th primary star and the current spiral reference point k:

[0028]

[0029] Among them, t k This is the direction vector of the current spiral reference point k in the celestial coordinate system;

[0030] Calculate d a d i and navigation stars, etc. i Combined feature r i The expression is as follows:

[0031] r i =ρ i (M i +d i )-(1-ρ i )d a

[0032] Where, ρ i d represents the feature combination weight value. a The interstellar average density, combined feature r i While ensuring uniformity during the navigation satellite selection process, the average brightness of the navigation satellite library should be improved; for example, r i The navigation stars selected for each screening have the following characteristics: their magnitude M i As low as possible, interstellar average density -d a The smaller the value, the closer the navigation star is to the current spiral reference point, i.e., d i As small as possible;

[0033] Sort the stars in ascending order according to the magnitude of their combined features, and label the star with the first-ranked feature as y. i =1, store in the navigation star library StarLib2, and label the last two stars as y. i =0, and store the remaining stars in the alternative star library StarLib3;

[0034] Step (3) shows that the irregular and uneven distribution of navigation stars across the entire celestial sphere indicates that the classification method used to separate navigation stars from non-navigation stars must be linearly inseparable. The Kernel SVM-SMO algorithm can effectively solve nonlinear classification problems in low-dimensional space using a nonlinear kernel function. Mapping to a high-dimensional space transforms it into a linearly separable problem in that space. Using the navigation star and label y from StarLib2 in step (2)... iStars with a value of 0 are used as the training set to classify and filter stars in the candidate star library StarLib3, and some navigation stars are added to effectively reduce the occurrence of gaps in the number of navigation stars in some areas of the sky.

[0035] The specific process of step (3) is as follows:

[0036] Step (31): To increase the learning rate of the classification hyperplane, the right ascension (β) of the navigation star ranges from 0 to 360°. i ), and the declination (δ) ranging from -90° to 90°. i The feature is transformed into a unit direction cosine feature ν according to step (12). i Combining the category labels from step (23), the training set features can be obtained as follows:

[0037] x i =(v i r i y i )

[0038] Step (32): Use the Sigmoid kernel function:

[0039]

[0040] Here, γ and b are kernel parameters, with γ having a default value of 1 / l, l being the number of classes, and b having a default value of 0.

[0041] By mapping the nonlinear navigation star classification problem to a high-dimensional space through kernel functions, the nonlinearity of the navigation star classification surface is solved. The heuristic SMO algorithm is used to solve the convex quadratic programming problem in SVM, giving the model a strong generalization ability.

[0042] The quadratic optimization model in the dual space of Kernel SVM-SMO is:

[0043]

[0044]

[0045] Where, α i ,α j It is a Lagrange multiplier, K is y i =1 and y i The total number of samples where y = 0 i ,y j C represents the category corresponding to each navigation satellite, and C is the penalty for classification errors.

[0046] Step (33): The heuristic SMO algorithm is used to solve the above optimization problem. In each iteration, two variables α1 and α2 are fixed:

[0047]

[0048] In the outer loop, the first variable α1 is selected, and the above training sample set x is first judged. i To determine if the KKT conditions are met, the sample point that most severely violates the KKT conditions is selected as the value of α1. The inner loop selects a second variable α2 and chooses the sample point that causes the maximum change in the value of α2. The iteration continues until all sample points meet the KKT conditions, at which point the above iteration stops, the sample set training is completed, and a linear classification hyperplane is obtained. The above classification hyperplane is used to classify the stars in the candidate star library StarLib3. Stars with a category of "+1" are classified as navigation stars, and stars with a category of "0" are classified as non-navigation stars. All stars with a category of "+1" in the candidate star library StarLib3 are combined with the star library StarLib2 to obtain the final navigation star library StarLib4 under the small field of view conditions.

[0049] The advantages of this invention compared to the prior art are:

[0050] (1) This invention fills the gap in navigation satellite library construction algorithms under small field of view;

[0051] (2) This invention solves the problems of uneven distribution of navigation stars, large storage capacity and low average brightness in the construction of traditional navigation star libraries;

[0052] (3) The principle of this invention is simple, the amount of calculation is small, and the optimal star library can be quickly obtained according to the actual engineering task. Attached Figure Description

[0053] Figure 1 This is a flowchart illustrating the specific process of constructing a navigation satellite library with an approximately uniform distribution under small field-of-view conditions according to the present invention.

[0054] Figure 2 A two-dimensional distribution map of navigation stars selected by magnitude threshold segmentation.

[0055] Figure 3 The color scale image of the navigation stars selected by the star magnitude threshold segmentation.

[0056] Figure 4 A three-dimensional distribution diagram of approximately uniformly distributed spherical spiral reference points.

[0057] Figure 5 This is a two-dimensional distribution map of navigation stars selected by this invention.

[0058] Figure 6 This is a color scale image of navigation stars selected by the present invention.

[0059] Figure 7 This represents the proportion of different numbers of stars within the field of view in the navigation satellite database selected by this invention. Detailed Implementation

[0060] The present invention will be further described in detail below with reference to specific embodiments.

[0061] The detailed flowchart of the method for constructing an approximately uniformly distributed navigation satellite library under small field-of-view conditions according to the present invention is as follows: Figure 1 As shown, the magnitude threshold is set to 8.5 Mv. The distribution map of the navigation satellite library below 8.5 Mv selected by VMT is shown below. Figure 2 The probability distribution of star magnitudes is as follows Figure 3 As shown in Table 1, a full-sky Monte Carlo test was conducted using a star sensor with a field of view (FOV) of 4°×4°. The specific parameters are shown in Table 1. The test results indicate that the VMT star screening redundancy is too high, which will inevitably lead to a high mismatch rate in subsequent star map matching.

[0062] Table 1. Parameter test indicators for FOV=4° after VMT filtration

[0063]

[0064] The specific steps of this invention are as follows:

[0065] Step (1): Using the SAO star catalog as the original star library, set the magnitude threshold Mag according to the VMT algorithm. th Mag th The above navigation stars were removed from the basic SAO star catalog. Each navigation star has unique right ascension and declination information, denoted as (β). i ,δ i ), and based on this, binary stars and variable stars are removed to obtain the basic star library (StarLib1);

[0066] The specific process of step (1) is as follows:

[0067] Step (11): Using the VMT algorithm, set the star magnitude threshold to Mag. th The segmentation formula is expressed as:

[0068]

[0069] Step (12): Based on step (11), calculate the direction vector of the i-th navigation star in the celestial coordinate system according to the right ascension and declination information, which is expressed as:

[0070]

[0071] Step (13): Angular distance is usually used to determine the distance between two stars. Using the StarLib star database obtained in step (11), the binary star angular distance threshold is calculated using the following formula:

[0072]

[0073] Diffuse pixels n×n, target size N TagSize ×N TagSize Calculation values ​​of focal length f and angular distance threshold D th As shown in Table 2:

[0074] Table 2. Relevant parameters of small field-of-view star sensors

[0075] parameter n / pixel <![CDATA[N pixel / pixel]]> f / (mm) <![CDATA[D th / (°)]]> numerical values 3*3 2048*2048 161.4 0.33

[0076] Step (2): Using the approximately uniformly distributed spiral reference points as the line of sight, calculate the angular distance between the reference points and the stars and the interstellar density to ensure the uniformity requirement when selecting navigation stars, and take into account the characteristics of navigation stars to ensure the requirement of selecting bright stars when constructing the navigation star library.

[0077] The specific process of step (2) is as follows:

[0078] Step (21): First, an algorithm is used to generate the spiral eye axis direction, such as... Figure 4 As shown, the generating formula can be expressed as:

[0079]

[0080] Step (22): Determine the number of spiral reference points M based on the star sensor's field of view (FOV) and the expected number of stars N within the field of view. This can be expressed as:

[0081]

[0082] Based on steps (23), (12), and (22), select the N brightest points within the field of view. e N stars e <5, and using the i-th navigation star as the primary star, calculate the average density within a unit area:

[0083]

[0084] Next, calculate the angular distance between the i-th primary star and the current spiral reference point k:

[0085]

[0086] Calculate d a d i and navigation stars, etc. i Combined feature r i The expression is as follows:

[0087] r i =ρ i (M i +d i)-(1-ρ i )d a

[0088] Sort the stars in ascending order according to the magnitude of their combined features, and label the star with the first-ranked feature as y. i =1, store in the navigation star library StarLib2, and label the last two stars as y. i =0, and store the remaining stars in the alternative star library StarLib3;

[0089] Step (3) shows that the irregular and uneven distribution of navigation stars across the entire celestial sphere indicates that the classification method used to separate navigation stars from non-navigation stars must be linearly inseparable. The Kernel SVM-SMO algorithm can effectively solve nonlinear classification problems in low-dimensional space using a nonlinear kernel function. Mapping to a high-dimensional space transforms it into a linearly separable problem in that space. Using the navigation star and label y from StarLib2 in step (2)... i Stars with a value of 0 are used as the training set to classify and filter stars in the candidate star library StarLib3, and some navigation stars are added to effectively reduce the occurrence of gaps in the number of navigation stars in some areas of the sky.

[0090] The specific process of step (3) is as follows:

[0091] Step (31): To increase the learning rate of the classification hyperplane, the right ascension (β) of the navigation star ranges from 0 to 360°. i ), and the declination (δ) ranging from -90° to 90°. i The feature is transformed into a unit direction cosine feature v according to step (12). i Combining the category labels from step (23), the training set features can be obtained as follows:

[0092] x i =(v i r i g i )

[0093] Step (32): Use the Sigmoid kernel function:

[0094]

[0095] By mapping the nonlinear navigation star classification problem to a high-dimensional space through kernel functions, the nonlinearity of the navigation star classification surface is solved. The heuristic SMO algorithm is used to solve the convex quadratic programming problem in SVM, giving the model a strong generalization ability.

[0096] The quadratic optimization model in the dual space of Kernel SVM-SMO is:

[0097]

[0098]

[0099] Step (33): The heuristic SMO algorithm is used to solve the above optimization problem. In each iteration, two variables α1 and α2 are fixed:

[0100]

[0101] In the outer loop, the first variable α1 is selected, and the above training sample set x is first judged. i To determine if the KKT conditions are met, the sample point with the most severe violation of the KKT conditions is selected as the value of α1. The inner loop selects a second variable α2 and chooses the sample point that causes the maximum change in the value of α2. The above iteration stops when all sample points meet the KKT conditions, completing the sample set training and obtaining the classification hyperplane. The above classification hyperplane is used to classify the stars in the candidate star library StarLib3. Stars with a category of "+1" are classified as navigation stars, and stars with a category of "0" are classified as non-navigation stars. All stars with a category of "+1" in the candidate star library StarLib3 are combined with the star library StarLib2 to obtain the final navigation star library StarLib4 under the small field of view conditions.

[0102] The final distribution map of the navigation satellite array points is as follows: Figure 5 As shown, the probability distribution diagram of star magnitudes is as follows: Figure 6 As shown, the full-sphere Monte Carlo test results for StarLib4 are as follows: Figure 7 As shown in Table 4, the specific parameters are as follows. It can be seen that the star library selected by the present invention has a more uniform distribution, lower storage capacity, and higher average brightness.

[0103] Table 4. Parameter test indicators for FOV=4° under this invention.

[0104]

[0105]

[0106] The parts of this invention not described in detail belong to the well-known technology in this field. The above description is only a specific example of this invention and is not intended to limit this invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the protection scope of this invention.

Claims

1. A method for constructing a navigation star library with approximately uniform distribution under small field of view conditions, characterized in that, The method comprises the following steps: Step (1), using SAO star catalog as the original star library, using VMT algorithm to set the star threshold according to the detection ability of the star sensor , the The above navigation stars are removed from the basic SAO star catalog, each navigation star has unique right ascension and declination information, denoted as , and on this basis, double stars and variable stars are removed to obtain the basic star library StarLib1; The specific process of the step (1) is as follows: Step (11), set the magnitude threshold value as The segmentation formula is represented as: wherein, is the number of stars in the star library, is the number of navigation stars, is the magnitude of the navigation star; Step (12), based on the information of right ascension and declination, calculate the 4th The direction vector of the guide star in the celestial coordinate system is represented as: Step (13), the distance between two stars is usually determined by the angle distance, the StarLib star library obtained in the step (11) is used, and the following formula is used to calculate the double-star angle distance threshold value: wherein respectively the pixel dispersion size, the target surface size, the focal length; Step (2), the approximately uniformly distributed spiral reference points are used as the visual axis direction, the angle distance between the reference points and the stars and the star density are calculated, the uniformity requirement in the navigation star screening is ensured, the star brightness characteristics are considered, and the requirement of selecting the bright stars in the navigation star library construction is ensured; The specific process of the step (2) is as follows: Step (21), the spiral visual axis direction is firstly generated by using the algorithm, and the generation formula can be represented as: wherein is the coordinate of each helix visual axis pointing in the celestial coordinate system, denoted as , is the coordinate in the spherical coordinate system, denoted as , the subscript represents the helix reference point number; Step (22), the number M of the spiral reference points is determined according to the star sensor field of view size FOV and the number N of the stars expected to appear in the field of view, and can be represented as: Step (23), based on step (12) and (22), take the brightest N e constellations, N e <5, and take the first navigation star as the main star, calculate the average density in the unit field: wherein, is the number of navigation stars within the field of view, is the number of navigation stars within the field of view, is the direction vector of the i-th navigation star in the celestial coordinate system, is the direction vector of the i-th navigation star in the celestial coordinate system, Second, the first angle value of the current spiral reference point and the main star is calculated the angle value of the current spiral reference point and the main star ​ wherein, current helix reference point direction vector in the celestial coordinate system; Computing and navigation star magnitudes combination features The expression is as follows: wherein, ρ i is a characteristic combination weight value, d a is an interstellar average density, the combination characteristic r i In the process of ensuring the uniformity requirement of the navigation star screening, the average brightness of the navigation star library is improved. According to the size of the combination feature, ascending arrangement is performed, the first ranked star is labeled with a category label , stored in the navigation star library StarLib2, the last two ranked stars are labeled with a category label , and the remaining stars are stored in the candidate star library StarLib3; Step (3), the irregular and uneven distribution of navigation stars in the whole sky, indicates that the classification method for screening navigation stars and non-navigation stars is linearly inseparable. The Kernel SVM-SMO algorithm can effectively map the non-linear classification problem in low-dimensional space to high-dimensional space through a non-linear kernel function , and convert it into a linearly separable problem in high-dimensional space. In step (2), the navigation stars and the stars labeled in StarLib2 are used as the training set to classify and screen the star points in the candidate star library StarLib3, add some navigation stars, and effectively reduce the occurrence of navigation star number holes in some sky areas. The specific process of the step (3) is as follows: Step (31), to increase the learning rate of the classification hyperplane, the right ascension of the navigation star is in the range of 0~360° , and the declination is in the range of -90°~90° The features are converted into unit direction cosine features according to step (12) , and the training set features are obtained in combination with the category labels in step (23): Step (32), the Sigmoid kernel function is used: wherein, and b is a nuclear parameter, The default value of b is , is the number of classes, and the default value of b is 0; The non-linear navigation star classification problem is mapped to the high-dimensional space through the kernel function, that is, the non-linear problem of the navigation star classification surface is solved, and the heuristic SMO algorithm is used to solve the convex quadratic programming problem in the SVM, so that the model has strong generalization ability; The quadratic optimization model in the dual space of the Kernel SVM-SMO is as follows: wherein, is a Lagrange multiplier, is and the total number of samples, , is the category corresponding to each navigation star, C is a classification error penalty term; Step (33), the above optimization problem is solved by using a heuristic SMO algorithm, and two variables are fixed in each iteration : Select the first variable in the outer loop First, determine the above training sample set. To determine whether the KKT conditions are met, select the sample point that most severely violates the KKT conditions as... The value; the inner loop selects the second variable. , choose to The sample point where the value changes the most; until all sample points satisfy the KKT condition, the above iteration stops, the sample set training is completed, and the classification hyperplane is obtained; the above classification hyperplane is used to classify the stars in the candidate star library StarLib3, the category "+1" is determined to be the navigation star, and the category "0" is determined to be the non-navigation star; all "+1" categories in the candidate star library StarLib3 are combined with the star library StarLib2 to obtain the final navigation star library StarLib4 under the small field of view condition.

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