CN115689915A

CN115689915A - Method for realizing geometric distortion correction of on-orbit star map based on two-dimensional Legendre neural network and star sensor

Info

Publication number: CN115689915A
Application number: CN202211235723.0A
Authority: CN
Inventors: 师晨光; 张锐; 刘芳; 兰青; 林晓冬
Original assignee: Shanghai Engineering Center for Microsatellites; Innovation Academy for Microsatellites of CAS
Current assignee: Shanghai Engineering Center for Microsatellites; Innovation Academy for Microsatellites of CAS
Priority date: 2022-10-10
Filing date: 2022-10-10
Publication date: 2023-02-03

Abstract

The invention relates to an on-orbit star map geometric distortion correction method and a star sensor based on a two-dimensional Legendre neural network, wherein the method comprises the following steps of: s1, shooting an image of a sky area through an optical lens, and obtaining a measurement star map through star point extraction; s2, performing star identification on the sky area image, and giving a reference star coordinate to the identified star to obtain a reference star map; s3, expressing a position mapping relation between a distorted star point of the measurement star map and a reference star point of the reference star map by using a two-dimensional Legendre polynomial, and constructing a two-dimensional Legendre neural network to solve an optimal solution of the coefficients of the two-dimensional Legendre polynomial; and S4, fitting the measured star coordinates of the measured star map and the reference star coordinates of the reference star map by using the pre-correction pixel flow, solving the corrected star coordinates of unidentified stars, and finally obtaining the corrected star map after distortion correction. The method has the advantages that the star point position in the on-orbit star map is automatically corrected, and the method is insensitive to the image distortion type.

Description

Method for realizing geometric distortion correction of on-orbit star map based on two-dimensional Legendre neural network and star sensor

[ technical field ] A method for producing a semiconductor device

The invention relates to the technical field of spaceflight, in particular to an on-orbit star map geometric distortion correction method and a star sensor based on a two-dimensional Legendre neural network.

[ background of the invention ]

The star sensor is an attitude measuring instrument with the highest precision on a spacecraft, and is widely applied to various space missions. Autonomous navigation, global communication, environment monitoring and deep space exploration tasks all rely on a star sensor to output accurate attitude information. In recent years, with the release and execution of the constellation satellite plan of each country, the star sensor is developing towards miniaturization and low cost, and the requirement for the accuracy of the star sensor is not reduced or increased, which brings greater challenges to the star sensor.

Although the manufacturing process of the star sensor is fine, all optical lenses generate geometric distortion due to various factors. The optical lens with a large field of view can introduce a large amount of nonlinear distortion, and the edge distortion of an image plane can reach more than two pixels. Different sources of distortion produce different distortions on the star map. The source of distortion may be static, due to errors in the shape and position of the optical system or imperfections in the manufacture of the detector; such errors are often calibrated and tested on the ground before launch of the spacecraft, and contribute little to the star map distortion. The distortion source may also be dynamic, for example, after violent vibration in the emission process and a period of on-orbit operation, the performance of electronic components of the sensor is reduced, and the sensor is influenced by radiation, vibration, gravity, stress, temperature and the like, and the parameters of the optical system are changed to cause uneven distribution of imaging energy of the star spot and asymmetric shape, so that the centroid extraction precision is directly influenced. Therefore, in order to ensure the attitude accuracy of the spacecraft and the safety of the spacecraft, establishing a distortion model of the in-orbit star sensor and optimizing a geometric correction algorithm are important.

The on-orbit calibration of the star sensor is proposed for the first time by Samaan [ Malak a. Samaan, todd s. Griith, punet Singla, and John l. Junkins. ] et al, and in the Autonomous on-orbit calibration of star routers.2001.1 ], the author proposes for the first time to estimate the parameters of the star sensor by using the rotational invariance of the angular distance between the stars. Because the focal distance is needed for calculating the angular distance, the on-line calibration of the star sensor is carried out by two steps: the principal point (x 0, y 0) and the focal length f are estimated, and then the distortion parameter estimation of the star map is carried out on the basis of the estimation. From the thought, various on-orbit calibration algorithms are developed. For example, based on the method relying on the attitude, a device such as a gyroscope is often required to determine initial attitude information. For another example, based on the attitude independent method, the optimal camera parameters are solved by directly utilizing the star point coordinates of the image and the rotation invariance of the inter-satellite angular distance of the corresponding navigation star vector of the inertial navigation star library, and then the parameters of the camera are updated. The most used of these methods are the least squares method and the kalman filter algorithm. These methods only take into account the types of distortions that are common in star sensors, such as distortions caused by changes in optical system parameters. And the errors of the focal length and the principal point can reduce the accuracy of star map identification, and the estimation of the star sensor optical system parameters by the method is based on the assumption that the principal point and the focal length have large changes.

To correct other complex types of distorted star maps, methods based on polynomial fitting are proposed. [ Quan Wei, fang Jianche, and Zhang Weina. A method of optimization for the deformed model of star map based on improved genetic algorithm, aerospace Science and Technology,15 (2): 103-107,2011.1,2.3,4 ] and [ Liu Yuan, xie Ruida, zhao Lin, and Yong Hao.machine learning base on-arbitrary transformation Technology for large field-of-view star tracker, 45 (12): 282-290,2016.1,2.3] all use a mapping relationship between common polynomial and reference points, and an optimized learning algorithm using an improved genetic algorithm. However, it has been demonstrated in the paper of "Ardeshir Goshtasby. Image registration by local approximation methods. Image and Vision Computing,6 (4): 255-261,1988.1] that the solution of the general polynomial is a linear system of equations called normal equations. However, as the order or number of polynomials increases, solving large scale linear systems of equations becomes unstable and inaccurate. The biggest challenge in on-orbit correction compared to ground correction is that the type of distortion of the star sensor in space is often unknown. Some distortions are stable, such as radial and tangential distortions caused by the transformation of optical system parameters; there are also some image distortions caused by other factors, such as perspective projection distortion, etc.

The geometric distortion correction method is technically improved aiming at the technical problems of instability and inaccuracy of the star sensor on-orbit calibration method based on polynomial fitting when a common polynomial is used.

[ summary of the invention ]

The invention aims to provide a geometric distortion correction method which can automatically correct the star position in an on-orbit star map and is insensitive to the image distortion type.

In order to achieve the purpose, the invention adopts the technical scheme that the method for realizing geometric distortion correction of the on-orbit star map based on the two-dimensional Legendre neural network comprises the following steps:

s1, shooting a sky area image through an optical lens, and obtaining a measurement star map through star point extraction;

s2, performing star identification on the sky area image, and giving a reference star coordinate to the identified star to obtain a reference star map;

s3, expressing a position mapping relation between the actual measurement star coordinate of the measurement star map and the reference star coordinate of the reference star map by using a common polynomial, obtaining a pre-correction pixel stream, and optimizing to obtain an optimal solution of the common polynomial coefficient;

s4, fitting the measured star coordinate of the measured star atlas and the reference star coordinate of the reference star atlas by using a pre-correction pixel flow, solving the corrected star coordinate of the unidentified star, and finally obtaining a corrected star atlas after distortion correction;

the step S3: expressing a position mapping relation between a distorted star point of a measurement star map and a reference star point of a reference star map by using a two-dimensional Legendre polynomial, and constructing a two-dimensional Legendre neural network to solve an optimal solution of a two-dimensional Legendre polynomial coefficient;

the two-dimensional legendre polynomial is obtained by:

s31, measuring the position mapping relation between the star map distorted star points and the reference star map reference star points:

wherein,

is to measure the measured star coordinate of the ith observation star point in the star map,

is that the reference star coordinate of the reference star map corresponding to the ith observation star point is expressed as

Function D _j，X And D _j，Y Respectively representing the distortion of the X direction and the Y direction of the measured star map of the jth frame;

s32, an n-order Legendre polynomial P _n (x) Expressed as:

the two-dimensional distortion base is expressed as:

wherein, N _modes Is the number of distortion modes, determines a two-dimensional distortion basis vector b _Nmodes Dimension (c):

s33, n is the order of Legendre polynomial, L _n Is the nth order normalized legendre polynomial expressed as:

the distortion mode is represented by its index m as:

s34, the mode of the two-dimensional Legendre polynomial is expressed as: b _m (x，y)＝L _n-k (x)×L _k (y), distortion D of i star points of j-th frame star map _j，X And D _j，Y Expressed as:

wherein, ω is _i，m，X And omega _i，m，Y Coefficients of Legendre polynomials respectively representing two directional distortion modes;

s35, measuring the distortion D of i star points of the star map of the jth frame if the star map comprises observation errors _j，X And D _j，Y Expressed as:

wherein n is _i，X ，n _i，Y Indicating an observation error.

Preferably, the method for realizing geometric distortion correction on an orbit star map based on the two-dimensional legendre neural network includes the following steps: according to the equation

Constructing a single-layer two-dimensional Legendre neural network structure; the input of the two-dimensional Legendre neural network is the mass center coordinate of a star point of a measuring star map, namely the measured star coordinate X _mea ，Y _mea The output is the estimated value of the coordinate deviation of the actual measurement star

Preferably, the method for realizing the geometric distortion correction of the orbit star map based on the two-dimensional legendre neural network includes the following steps of constructing the two-dimensional legendre neural network in step S3:

s301, equation

The abbreviation is:

the two-dimensional legendre network constructed is represented as:

in the formula,

the estimated value of the coordinate deviation of the actually measured star is shown,

representing a two-dimensional Legendre polynomial coefficient estimation value;

s302, normalizing Legendre polynomial

Reproduces the neuron b of the two-dimensional Legendre network in the recursion formula _m (x, y), the nth neuron being an nth expanded term of the normalized legendre polynomial;

s303, weight omega of two-dimensional Legendre network middle layer and output layer _mx ，ω _my Weights representing the need to update, and equation

Weight ω in _m Correspondingly, two sets of adjustable weights ω _mx ，ω _my Respectively representing polynomial coefficients of two directions, and obtaining ideal omega by updating a training algorithm _mx ，ω _my Weights, such that the trained weights ω _mx ，ω _my And two dimensionsLegendre polynomial coefficient estimation

The error is minimal.

Preferably, the method for implementing geometric distortion correction on an orbit star map based on a two-dimensional legendre neural network, in step S303, specifically includes the following steps:

s3031, realizing initial correction of the two-dimensional Legendre neural network based on a batch star point ground off-line training method;

s3032, the lifelong autonomous distortion correction of the two-dimensional Legendre neural network is realized based on the on-orbit online learning method of the frame-by-frame star map.

Preferably, the method for realizing geometric distortion correction on an orbit star map based on the two-dimensional legendre neural network includes the steps of S3031: capturing a star map from a random sky area, distributing the positions of star points in the star map over the whole optical lens field of view, training a two-dimensional Legendre neural network by a point-to-point training method, and learning the mapping relation between distorted star point coordinates and reference coordinate offset from the whole star map data set;

the method specifically comprises the following steps:

s30311, the estimation error E is expressed as:

s30312, defining loss function J _p Comprises the following steps:

s30313, updating the weight by using a gradient descent algorithm, and obtaining the weight according to a chain type derivation rule J _p By calculating J _p The first partial differential of (d) yields:

s30314, updating the weight value by comprehensively considering the first moment and the second moment of the gradient by using an Adam algorithm, and calculating the step length of the gradient updating and the weight of the two-dimensional Legendre neural networkThe re-update is represented as:

wherein,

m represents the exponential moving average of the gradient, β ₁ Controlling the movement of first order gradients, exponential moving means, beta, representing the square of the gradient ₂ The influence of the square of the gradient is controlled,

and

the results show that the influence of the variation on the initial training stage is reduced by correcting the gradient.

Preferably, the method for implementing geometric distortion correction on an orbit star map based on a two-dimensional legendre neural network includes the steps of S3032: the star points are considered to be drawn in the optical lens field of view at a certain angular speed; when the star point moves to a position with small distortion, the probability that the star point is correctly identified is higher, and the correctly identified star is tracked in real time; when the star point moves to a position with larger distortion, the tracked star point is continuously used for distortion correction; star points enter the field of view of the optical lens from multiple directions, and the two-dimensional Legendre neural network learns the star map distortion at different positions to complete the global distortion correction of the star map;

the method specifically comprises the following steps:

s30321, the loss function is determined by the root mean square error of all available star points of each frame star map, and the loss function during training of a single frame star map is represented as follows:

in the formula, N represents the number of correct identified star points in a single-frame star map, i represents the ith measurement star point coordinate in the single-frame star map, and the i value of each frame of star map in the online distortion correction is different;

s30322, the gradient of the loss function in the on-track on-line training is derived by a chainThe rule gives:

s30323, calculating the minimum gradient of the loss function to obtain the optimal solution of the two-dimensional Legendre polynomial coefficient:

s30324, updating the weight value comprehensively considers the first moment and the second moment of the gradient by using an Adam algorithm, and calculates the step length of updating the gradient, wherein the updating of the weight value of the two-dimensional Legendre neural network is represented as:

wherein,

m represents the exponential moving average of the gradient, β ₁ Controlling the movement of first order gradients, exponential moving averages, beta, representing the squares of the gradients ₂ The influence of the square of the gradient is controlled,

and

Preferably, the method for realizing geometric distortion correction of the on-orbit star map based on the two-dimensional Legendre neural network is implemented by the on-orbit online learning method, wherein the on-orbit online learning method is carried out frame by frame and sample by sample, all star points in a period of time need to cover most positions of the star map, and the two-dimensional Legendre neural network is guaranteed to learn the distortion model of the whole focal plane of the optical lens.

Preferably, the method for correcting geometric distortion of the orbit star map is implemented based on a two-dimensional Legendre neural network, and the order of the two-dimensional Legendre polynomial is 4-6.

Preferably, the method for correcting geometric distortion of the orbit star atlas is implemented based on a two-dimensional Legendre neural network, and the observation error is represented by Gaussian noise which is independently distributed.

The invention further aims to provide a geometric distortion correction star sensor which can automatically correct the star point position in the on-orbit star map and is insensitive to the image distortion type.

In order to achieve the above-mentioned another object, the present invention adopts a technical solution that a star sensor for realizing geometric distortion correction on an orbit star map based on a two-dimensional legendre neural network includes an optical lens and a two-dimensional legendre neural network, and is used for executing the above-mentioned method for realizing geometric distortion correction on an orbit star map based on a two-dimensional legendre neural network.

The invention discloses an implementation method for correcting geometric distortion of an orbit star map based on a two-dimensional Legendre neural network and a star sensor, which have the following beneficial effects: in order to avoid the problems of instability and inaccuracy which can occur when using ordinary polynomials to correct complex distorted star maps, 2D Legendre polynomials (orthogonal polynomials) are used instead of ordinary polynomials; constructing a 2D Legendre neural network (2 DLNN) to solve the optimal solution of the polynomial coefficient of the 2D Legendre polynomial; the 2D Legendre neural network has strong adaptability and high convergence speed, and can correct star maps of any distortion types; further, the initial correction of the geometric distortion correction equipment is realized based on a ground offline training method of batch star points; further, the lifelong autonomous distortion correction of the geometric distortion correction equipment is realized based on the on-orbit online learning method of the frame-by-frame star map.

[ description of the drawings ]

FIG. 1 is a schematic diagram of an ideal measurement model of a star sensor represented by an aperture imaging model.

Fig. 2 is an original star map and six kinds of distorted star maps, in which fig. 2 (a) is the original star map, fig. 2 (b) is a shear-transformed star map, fig. 2 (c) is a perspective-transformed star map, fig. 2 (d) is a barrel-shaped distorted star map, fig. 2 (e) is a pincushion-shaped distorted star map, fig. 2 (f) is a tangential distorted star map, and fig. 2 (g) is a thin prism-distorted star map.

FIG. 3 is a flow chart of a method for correcting geometric distortion of an orbit star map based on a two-dimensional Legendre neural network.

Fig. 4 is a diagram of a single-layer two-dimensional legendre neural network structure.

Fig. 5 is a graph of the results of geometric distortion correction for a single star point.

[ detailed description ] embodiments

The invention is further described with reference to the following examples and figures.

Example 1

The embodiment realizes a method for realizing geometric distortion correction of the on-orbit star map based on a two-dimensional Legendre neural network.

The star sensor is an important single machine for realizing high-precision attitude control of the spacecraft. However, due to the influences of lens processing errors, light path assembly errors, rail temperature alternation and the like, an optical system generates distortion, and the precision of the star sensor is reduced. And the calibration of the star sensor is required to be realized on orbit. The embodiment provides a method for realizing geometric distortion correction of an on-orbit star map based on a two-dimensional Legendre neural network, and provides a single-layer two-dimensional Legendre neural network (2 DLNN) capable of automatically realizing geometric distortion correction of an optical system; an off-line training method based on batch star maps and a sequential on-line star map training algorithm based on single star maps are respectively designed, so that off-line and on-line correction of optical geometric distortion is realized. According to the method for realizing geometric distortion correction of the on-orbit star atlas based on the two-dimensional Legendre neural network, the single-layer two-dimensional Legendre neural network can be used for autonomous learning and lifelong learning, has strong adaptability, can adapt to various distortions and can correct star atlases of any distortion types; the single-layer network has simple structure, can quickly converge and is suitable for on-orbit implementation; aiming at different possible distortions of the service life cycle of the on-orbit operation of the star sensor, a distortion model can be learned in a self-adaptive manner by adjusting the number of neurons. Simulation experiments show that after off-line training, the average distortion can be reduced to be below 0.04 pixel; in the low orbit satellite ground orientation mode, the algorithm can be converged in 2500 frames of star maps under the condition of 1 frame/second through the online sequential training algorithm. Compared with the traditional method, the method for realizing geometric distortion correction on the orbit star map based on the two-dimensional Legendre neural network can realize sub-pixel distortion correction, effectively improves attitude determination precision of the star sensor, and has the potential of becoming a general geometric distortion correction framework for the star sensor.

In the method for realizing geometric distortion correction of the on-orbit star map based on the two-dimensional Legendre neural network, errors caused by changes of principal points and focal lengths are taken into consideration as system errors, and random errors are not considered.

The method for realizing geometric distortion correction on the orbit star map based on the two-dimensional Legendre neural network can automatically correct the star positions in the orbit star map and is insensitive to the image distortion type.

In this embodiment, a method for correcting geometric distortion of an orbit star atlas is implemented based on a two-dimensional legendre neural network, in order to avoid the problems of instability and inaccuracy that may occur when using a general polynomial, a 2D legendre polynomial (orthogonal polynomial) is used instead of the general polynomial; meanwhile, the optimal solution of solving polynomial coefficients of a 2D Legendre neural network (2 DLNN) is constructed.

The method for realizing geometric distortion correction of the orbit star map based on the two-dimensional Legendre neural network has no strong dependence on the type of distortion, and mainly comprises the following implementation steps: 1. a two-dimensional Legendre neural network learns the distortion coefficient of the star map; 2. the method comprises the steps of realizing initial correction of a star sensor based on a ground offline training method of batch star points; 3. and realizing the lifelong autonomous distortion correction of the star sensor based on an on-orbit online learning method of a frame-by-frame star map.

The following specifically explains an implementation concept of the method for implementing geometric distortion correction on an orbit star map based on a two-dimensional Legendre neural network.

1. Star sensor measurement model

1.1 ideal model

FIG. 1 is a schematic diagram of an ideal measurement model of a star sensor represented by an aperture imaging model. As shown in the attached figure 1, the star sensor is a precision instrument for determining the attitude of the spacecraft by measuring a star direction vector, and an ideal measurement model of the star sensor is represented by a pinhole imaging model.

The starlight vector of the ith observation star point is represented by equation (1):

in the formula (x) ₀ ，y ₀ ) Is the principal point of the focal plane, (x) _i ，y _i ) Is the centroid of the i observation star points, and f is the focal length of the optical system.

1.2 typical Star map distortion model

Errors and noises in the optical imaging system are inevitable, and the actual imaging model of the star sensor does not completely conform to the pinhole imaging model. Due to the influence of various factors in space, the system parameters of the star sensor can be changed, and various distortions of an imaging star map can be avoided. Distorted star coordinates (x) _i ’，y _i ') and true star point coordinates (x) _i ，y _i ) The relationship between them is expressed as equation (2):

x′ _i ＝x _i +Δx _i

y′ _i ＝y _i +Δy _i (2)

in the formula,. DELTA.x _i ，y _i Is the amount of change in the position of the star point due to the distortion of the star map. Fig. 2 is an original star map and six distorted star maps, as shown in fig. 2, the method for implementing geometric distortion correction on an orbit star map based on a two-dimensional legendre neural network in the embodiment describes 6 different distortion models; fig. 2 (b) to fig. 2 (g) show 6 different distorted star maps, the corresponding distorted star map pixel flow and the star point position relative error, respectively. Several common distortion models of star sensors are as follows:

radial distortion

The vertical magnification of the optical system under different fields of view is different, the light rays are more curved at a position far away from the center of the lens than at a position close to the center, and the radial distortion is also the most main distortion in the optical lens distortion. The radial distortion can be expressed as equation (3):

wherein n is the order of Taylor expansion,

representing the distance of the distorted star from the center of the image sensor, q _i Representing the ith radial distortion coefficient.

Tangential distortion

The on-axis error of an optical element in an optical system results in tangential distortion, which can be expressed as equation (4):

in the formula, p ₁ And p ₂ Representing the coefficients of the tangential distortion.

Distortion of thin prism

The thin prism distortion is caused by the tilt of the optical element, which is equivalent to inserting a thin prism into a non-tilted optical element, and can be expressed as equation (5):

in the formula s ₁ And s ₂ The coefficient representing the distortion of the thin prism.

The star sensor distortion is often a superposition of the three distortions. In order to check the generalization ability and the adaptability of the method, the influence of image transformation on the star sensor is also considered in the embodiment. Different types of image transformations can be expressed as:

shear transformation

In the formula, tan phi _x And tan phi _y Is the distortion coefficient of the shear distortion.

Perspective projective transformation

The perspective projective transformation can be expressed as a transformation of the imaging plane to a new viewing plane [8], and the relationship between the two viewing planes is expressed by a transformation matrix.

h ₁₁ ，h ₁₂ ，h ₁₃ ，h ₂₁ ，h ₂₂ ，h ₂₃ ，h ₃₁ ，h ₃₂ Respectively representing elements of a perspective distortion transformation matrix.

1.3 Legendre polynomial model

The coordinates of the ith observation star point in the star map are expressed as

Y _i ^mea The coordinates of the reference star point of the corresponding star library are expressed as

Using function D _j Representing a distortion model, the relationship between the two is shown in equation (9):

in the formula, D _j，X And D _j，Y Respectively representing the distortion of the X direction and the Y direction of the star map of the j frame.

There are many polynomials that can fit the distortion of the star point locations, e.g., high order two-dimensional polynomials are often used as image distortion models. [ Quan Wei, yang Jianging, and Zhang Weina. A method of optimization for the discrete model of stator map based on improved genetic algorithm. Aerospace Science and Technology,15 (2): 103-107,2011.1,2.3,4 ] use 3rd common polynomial fit based on modified genetic algorithm to correct for star map distortion; [ Liu Yuan, xie Ruida, zhao Lin, and Yong Hao.machine learning based on-restriction displacement detection technique for large field-of-view stage tracker. Contaminated and Laser Engineering,45 (12): 282-290,2016.1,2.3, correct for distortion of star point positions using ordinary polynomials and solve for optimal values using machine learning. But ordinary polynomials are unstable and inaccurate when solving high-order polynomial systems. To avoid this problem, an orthogonal polynomial fitting distortion model should be used. Service, j.r.lu, r.campbell, b.n.sitarski, a.m.ghez, and j.an-derson.a new dispersion solution for nicc 2 on the keck ii telescope.pass, 128 (967): 095004, september 2016.2.3] compared the potency of the different models: 2D cartesian polynomials, binary B-splines and 2D legendre polynomials. The paper concludes that: the 2D legendre polynomial can produce faster convergence and less redundancy. Meanwhile, [ Jingfei Ye, zhishan Gao, shuai Wang, jinlong Cheng, wei Wang, and Wen-q Sun. Comparative assessment of orthogonal polymers for wave front orientation. JOSA, 31 (10): 2304-2311,2014.2.3] defines an orthogonal polynomial and can well describe the distortion of a square image. The distortion can be conveniently described using a finite number of orders.

Each n-order Legendre polynomial P _n (x) Can be expressed as equation (10):

in order for each mode to contain distortions in both directions (X and Y) of the image, the polynomial needs to be normalized. The final 2D distortion base b is expressed as equation (11):

N _modes is the number of distortion modes that determines the vector b _Nmodes Dimension N of _modes Can be determined by the following formula:

n is the order of the Legendre polynomial, L _n Is an nth order normalized legendre polynomial expressed as:

the distortion mode can be expressed by its index m as:

thus, the pattern of each 2D legendre polynomial may be expressed as:

b _m (x，y)＝L _n-k (x)×L _k (y) (16)

finally, distortion D of i star points of the j frame star map _j，X And D _j，Y Can be expressed as equation (17):

wherein, ω is _i，m，X And ω _i，m，Y Coefficients of Legendre polynomials respectively representing two directional distortion modes.

n _i，X ，n _i，Y Expressed as observation errors caused by image noise, star point extraction algorithm errors, etc. The observation error may be represented by an independently distributed gaussian noise.

2. Legendre neural network

Conventional neural networks can approximate arbitrary functions, such as the paper [ Liang Wu, qian Xu, chao Han, and Kaixuan zhang.an on-orbit caliibra-formation method of stator sensor based on systematic distance subset. Ieee Photonics Journal,13:1-13, 2021.1,3] correct distortion of optical lenses using a fully connected network. The traditional neural network needs proper hyper-parameters to have a better correction result. The traditional network structure is complex, and the convergence speed is low when a back propagation algorithm is applied. FIG. 3 is a flow chart of a method for correcting geometric distortion of an orbit star map based on a two-dimensional Legendre neural network. As shown in fig. 3, therefore, in this embodiment, a method for implementing geometric distortion correction on an orbit star map based on a two-dimensional legendre neural network is constructed based on a 2D legendre polynomial, and is named as a two-dimensional legendre neural network (2 DLNN). The single-layer network has the advantages of simple structure, short calculation time, no need of activating functions and high convergence speed, and is suitable for on-track implementation. [ shine-backing Yang and Ching-shine Tseng.Ann orthogonal neural networks for function approximation. IEEE Transactions on Systems, man, and Cybernetics, part B (Cybernetics), 26 (5): 779-785,1996.3] and [ B frame. Orthogonal relations in the design of neural networks for function approximation. Mathesics and computers in the simulation,41 (1-2): 95-108,1996.3] have demonstrated that any function can be approximated using orthogonal polynomials (such as Legendre polynomials) and that the coefficients of polynomials are unique and bounded. Furthermore, the recursive nature of the orthogonal polynomials allows for a fast determination of the expansion terms of the polynomials without excessive adjustment of the hyper-parameters of the network.

2.1 network architecture

The distortion model of the coordinates of the star points in the star map is expressed as equation (18). In the formula of omega _i,m,X 、ω _i,m,Y 、m、N _moses Is the distortion model parameter to be found. In this embodiment, a method for implementing geometric distortion correction on an orbit star map based on a two-dimensional legendre neural network is provided, a 2D legendre neural network is built, and an optimal solution of a distortion model is obtained by using the network. The input of the network is the mass center coordinate X of the star point of the star sensitive measurement _mea ，Y _mea The output is the estimated value of the coordinate deviation of the star point

Therefore, the network learns a mapping relationship between the coordinates of the star points of the distorted star map and the positional deviations of the star points, which is expressed by a 2D legendre polynomial. The estimated value of the star point coordinate deviation is a two-dimensional vector, and the deviation vector determines the coordinate movement amount of the distorted star point and the real star point. The advantage of this design is that the amount by which each coordinate should be moved can be determined quickly, without the need for complex transformations.

Fig. 4 is a diagram of a single-layer two-dimensional legendre neural network structure. As shown in fig. 4, in this embodiment, a two-dimensional legendre neural network based on a two-dimensional legendre neural network is implemented in an orbital star map geometric distortion correction method, and a single-layer two-dimensional legendre neural network structure is obtained according to equation (18).

In this embodiment, a method for implementing geometric distortion correction on an orbit star map based on a two-dimensional legendre neural network is implemented, and the difference between the estimation error of the network and the position deviation between a measured star point and a theoretical star point is minimized through training of 2 DLNN. Equation (18) can be abbreviated as:

according to equation (18), the constructed legendre network can be represented as equation (20).

In the formula

The error in the estimation of the position of the star point,

coefficient estimation values representing a 2D legendre polynomial.

As can be seen from FIG. 5, the input of the network is the coordinates (x, y) of the centroid of the measured star point in the star map, and the output is the estimated star point position error

And

network neurons b _m (x, y) is replicated from the recursion formula of the normalized Legendre polynomial (equation (11)). And the nth neuron is exactly the nth expansion term of the normalized legendre polynomial.

Weight ω of intermediate layer and output layer _m，X/Y Represents the weight to be updated, and the weight ω in equation (19) _m And (7) correspondingly. With two sets of adjustable weights omega _mx ，ω _my The polynomial coefficients representing the two directions respectively, and the weights are updated by a training algorithm to obtain the ideal weights. Since each input isThe outputs have independent weights, and the corresponding two groups of weights can be trained respectively.

2.2 ground-based batch training

After the 2D Legendre neural network is built, an algorithm is needed to adjust the weight of the neural network

The trained weights are error minimized from the polynomial coefficients W of distortion model equation (18). In this embodiment, a method for implementing geometric distortion correction on an orbit star map based on a two-dimensional legendre neural network is described, which is to begin with a training method of 2DLNN in ground calibration. When the algorithm is implemented on the ground, a star map can be captured from a random sky plot. Therefore, the position distribution of star points in the star map is more easily distributed in the whole star sensor field of view, and the global distortion model of the star map is favorably learned. Therefore, training the Legendre neural network in a ground experiment is a point-to-point training method, and the mapping relation between the distorted star point coordinates and the coordinate offset is learned from the whole star map data set.

The estimation error E is expressed as equation (21):

defining a loss function J _p Equation (22):

in this embodiment, a method for implementing geometric distortion correction on an orbit star map based on a two-dimensional legendre neural network uses a gradient descent algorithm [ see document: application of legacy neural network for solving organizational differential evaluation, applied Soft Computing,43:347-356, 2016.3.2]And updating the weight. According to the chain-type derivation rule, J _p Can be obtained by calculating the first partial differential of Jp, as shown in equation (23):

in this embodiment, a method for implementing geometric distortion correction on an orbital star map based on a two-dimensional legendre neural network is provided, and an Adam algorithm [ see literature: diederik P Kingma and Jimmy ba. A method for storing opti-hybridization. ArXiv preprinting arXiv:1412.6980 2014.3.2], adam incorporates AdaGrad [ see literature: john Duchi, elad Hazan, and Yoram Singer.Adaptive subset method for online learning and storage optimization. Journal of machine learning research,12 (7), 2011.3.2] and RMSProp [ see: geofrey Hinton, nitish Srivastava, and Kevin Swersky. Neural networks for machine learning choice 6a overview of mini-batch parameter decision. Cited on,14 (8): 2,2012.3.2 ] two optimization algorithms, the step length of gradient update is calculated by comprehensively considering the first moment and the second moment of the gradient, and the convergence is proved by a strict theory. And the Adam algorithm has little requirement on the memory, is simple to realize and is suitable for on-orbit use. The weight update for 2DLNN is thus represented as:

wherein,

wherein m represents an exponentially moving average of the gradient, β ₁ =0.9, controlling the movement of the first order gradient, representing the exponentially moving average of the square of the gradient, β ₂ =0.999, the influence of the square of the control gradient,

and

the results show that the influence of the variation on the initial training stage is reduced by correcting the gradient. η =0.0001 is a positive gain, representing the learning rate. E =10 ^-8 To correct the factor, the divisor is avoided to become 0. Equation (24) is the proposed weight training method, and the authors of Adam have demonstrated that,

will gradually decrease and remain in a stable state.

2.3 on-track based on-line training

Due to the limitation of the storage space of the in-orbit satellite, the star sensor cannot store a large amount of star maps and star point coordinate data, so that the point-to-point training method for the in-orbit star sensor is unrealistic. The on-orbit star sensor is orbiting the satellite, so this section first analyzes the coverage of a star point at a particular time. And then an online learning method for correcting the distortion of the star sensor is provided.

2.3.1 Star point coverage

Because the algorithm can not be directly verified on the orbit, the method for realizing the geometric distortion correction of the orbit star map based on the two-dimensional Legendre neural network simulates the state of the star sensor in the operation on the orbit. Considering that the process of on-orbit training of 2DLNN is performed frame by frame and sample by sample, all star points in a period of time need to cover most positions of a star map to ensure that the 2DLNN learns the distortion model of the whole focal plane. In this embodiment, a method for implementing geometric distortion correction on an orbit star map based on a two-dimensional legendre neural network analyzes a star coverage rate in a specific time interval, where the star coverage rate is expressed as: the proportion of the area covered by all the star points in the view field of the star sensor in the time t to the whole focal plane is expressed as follows:

in the formula,

represents the Area enclosed by the contours (non-convex hulls) of all the star points within the time interval t, area _fp Denotes the area of the focal plane, the unit of which is the square px of the pixel ² 。

The star sensor shoots the star map along the orbit, the geometric distortion correction method of the orbit star map is realized based on the two-dimensional Legendre neural network, the Monte Carlo method is used for calculating the average star point coverage rate in continuous time intervals t, and the result is shown in Table 1. The sampling interval of the star map is 1s, and the orbit used is Starlink (550km, 53 degrees) orbit, the right ascension declination of which is generated from the Systems Tool Kit (STK).

TABLE 1 Star coverage at different times

Time	1	50	500	2000
					Average coverage rate	42.267％	71.232％	98.262％	99.309％

And at different continuous sampling times, the star points in the field of view of the star sensor are superposed to generate a star point distribution diagram, the sampling starting point is determined by a Monte Carlo method and is acquired along a Starlink track, and scattered points with the same color represent the star maps from the same frame. The coverage area of the stars is the envelope of these superimposed stars, shown as a light green background outline. The star point coverage increases as the number of star maps increases. Although the star point coverage rate of 500 frames is high, there are places with obvious holes in the middle. The star point coverage rate of about 2000 frames is high, and basically covers the whole field of view.

When the satellite runs in orbit, the star point can be seen as being crossed in the field of view of the star sensor at a certain angular speed. In engineering applications, the greater the probability that a star point is correctly identified when it is moved to a less distorted position. And correctly identified stars can be tracked in real time. As the star point moves to a more distorted position, the tracked star point may continue to be used for distortion correction. As seen from the star point distribution diagram, star points enter the visual field from multiple directions, so that the 2DLNN can learn the star map distortion at different positions, and the global distortion correction of the star map is completed.

2.3.2 on-line training method

The geometric distortion correction of the on-orbit star sensor is carried out along the orbit frame by frame. The loss function is determined by the Root Mean Square Error (RMSE) of all available star points of each frame of the star map, and the loss function in the training of a single frame of the star map is expressed as equation (27):

in the formula, N represents the number of correctly identified star points in a single-frame star map, i represents the mass center coordinate of the ith measurement star point in the single-frame star map, and the value of i of each frame of star map in the online distortion correction is different.

The gradient of the loss function in the on-orbit training can also be obtained by the chain derivation rule, as shown in equation (28):

calculating the minimum gradient of the loss function to obtain the optimal solution W of the coefficient of the Legendre polynomial ^* ：

Similarly, on-line training the network updates the network's weights to obtain the optimal solution W, again using the Adam algorithm (equations (24) and (25)) ^* 。

2.4 optimal order of two-dimensional Legendre polynomial

When implementing 2DLNN, different network orders may have some effect on the result. The order of the two-dimensional Legendre polynomial determines the number of neurons of the neural network, and has direct influence on the distortion correction capability of the network. If the order is too small, the distortion model of the star map cannot be completely represented; if there are too many neurons, the network structure is large and the existing data is not sufficient to completely fit the network. Therefore, an appropriate polynomial order is required to optimize the distortion correction capability of the model.

The embodiment is a method for realizing geometric distortion correction on an orbit star map based on a two-dimensional Legendre neural network, and the influence of polynomial orders on a training result is analyzed. Taking radial distortion as an example, two-dimensional Legendre neural networks of 1 order to 10 orders are respectively trained, and the distortion correction capability of the corresponding networks on a test set is examined. And obtaining two-dimensional Legendre network training results of different orders, wherein the two-dimensional Legendre network training results comprise training results of a training set and the performance of the corresponding two-dimensional Legendre neural network on a test set. The comparison shows that: when the order is relatively small, the convergence speed of 2DLNN is low, and the convergence speed is not on the training set, and the error on the test set is large, which indicates that the 2DLNN of the low order is under-fitted. When the order is greater than or equal to 5, the error of the training set is kept to be minimum as a whole, and the performance on the test set is also the best. In practical applications, the optical distortion model uses 4 th order to 6 th order distortion, and the optimal legendre polynomial order proposed by the present embodiment is 5 in consideration of the temporal and spatial complexity of the calculation.

3. Experiments and analyses

Several groups of simulation experiments are designed to verify that the method for realizing the geometric distortion correction of the orbit star map based on the two-dimensional Legendre neural network is provided. The method comprises a ground verification experiment and an on-orbit simulation experiment. In the ground night star observation experiment, the star map can be obtained from a random day area or a continuous day area. The star map acquired in the random sky area has a large number of stars and is uniformly distributed, so that the random sky area is suitable for batch learning; the star maps acquired in the continuous sky region are generated along the satellite orbit and are suitable for frame-by-frame learning. In an in-orbit simulation experiment, a star sensor is simulated to generate a star map along a low-orbit satellite orbit, and the possibility of in-orbit operation of the method is analyzed.

The system parameters of the star sensor used in the experiment are shown in table 2. The capability of the method for correcting the geometric distortion of the orbital star chart based on the two-dimensional Legendre neural network to correct the distortion of an optical system (radial, tangential and thin prism distortion) and the distortion of an image (shearing and perspective projection transformation) is tested respectively. The parameters of the distortion model used in the experiment are shown in tables 3 and 4, and the distortion model used is described in section 1.2. The method of generation of the star atlas data set used in the experiment is presented in section 3.1.

TABLE 2 Star sensor parameters

Parameter(s)	Parameter value	Unit of
			Area of the detector	2048x2048	Pixel
Size of pixel	7.45	Micron meter
			Star sensitive field of view	20	Degree of rotation
Focal length	43.2	Millimeter
			Maximum sensitivity star, etc	6.0	Mv

TABLE 3 distortion parameters for optical systems

TABLE 4 distortion parameters of images

3.1 Star atlas training data set

Since real star maps are rarely passed down to the ground from on-orbit star sensors, it is impractical to directly use real star maps as training data sets. In the embodiment, the method for realizing geometric distortion correction of the on-orbit star map based on the two-dimensional Legendre neural network generates the star map according to system parameters (table 2) of a star sensor, and mixes star map data acquired by other methods in a data set. The star sensor parameters used in all the star map data sets are the same. The star map data set mainly comprises the following parts:

the star maps can be generated from the professional software Starry Night and digital simulation platform [ see literature: hao Zhang, yanxing Niu, jianzhen Lu, chengfen Zhang, and Yanqiang Yang.on-orbit simulation for star sensors with priority information. Optics express,25, 18393-18409,2017.1,4.1], which can obtain an asterogram for any day region;

a method for generating a ground simulation star map according to parameters of a real star sensor [ see literature: method, techniques and Algorithms, springer,2016.4.1, generates a simulated star map, and adds noise signals including shot noise, dark current noise, and the like to the star map;

star sensors of the same parameters, star maps shot by star experiments viewed on the ground at night.

And carrying out distortion processing on the star map according to the true distortion condition of the star sensor on the orbit, mainly the distortion caused by the change of optical system parameters. Using the star point extraction algorithm [ see literature 1, min-Song Wei, fei Xing, and Z young. A real-time detection and po-positioning method for small and week targets using a 1d morphology-based approach in 2d images. Light; 2. ting Sun, fei Xing, jingyu Bao, songsong Ji, and Jin Li. Supress-version of string light based on energy information development applied optics,57 (31): 9239-9245,2018.4; 3. chenguang Shi, rui Zhang, yong Yu, xingzhe Sun, and Xiiaodong Lin.A slic-dbscan based algorithm for extracting an effective skin region from a single stand image, 21 (17), 2021.4.1; 4. xiaoowei Wan, gangyi Wang, xinguo Wei, jian Li, and Guangjun Zhang. Odcc: A dynamic star spots extraction method for star sensors. IEEE Transactions on Instrumentation and Measurement,70: sun Xingzhe, zhang Rui, shi Chenguang, and Lin Xiaoodong.Star identi-indication algorithm based on dynamic angle matching.acta Optica Sinica,41 (16): 1610001,2021.4.1] the centroid coordinates of the star points are obtained from the distorted star map. Then, the attitude matrix of the sensor star is obtained using the QUEST algorithm [ Itzhack Y Bar-Itzhack. Request-a iterative request algorithm for sequence-real attitude determination. Journal of guide, control, and Dynamics,19 (5): 1034-1038,1996.4.1] or the TRIAD algorithm [ Malcomum David Shuster. Algorithms for determining optimal attitude solution-positions. Computer Sciences Corporation,1978.4.1 ]. And obtaining the theoretical coordinate of the measured star point through the navigation star library, the star sensor parameters and the coordinate conversion relation. And taking the difference value of the theoretical star point coordinates and the measured star point centroid coordinates as a training label of the 2DLNN, and taking the star point centroid coordinates identified in the distorted star map as training data. The star map data set is mainly divided into three parts: a ground random sky star map dataset (GRD), a terrestrial autorotation orbit star map dataset (GCD) and an in-orbit simulation star map dataset (OD).

3.2 simulation experiment based on ground calibration

The proposed method does not require the selection of a specific number of star points from the star map, and all identifiable star points in the star map can participate in the training of the neural network model. In the ground experiment, all available star points of the star map data set are combined into a complete point-to-point star point coordinate data set. The star point centroid coordinates obtained from the distorted star map are used as the input of the 2DLNN, the difference value of the theoretical star point coordinates and the measured star point centroid coordinates is used as a label of training data, and the error of the 2DLNN is converged to the minimum through training. All the star point coordinate data are randomly divided into a training data set and a testing data set according to the proportion of 8.

The hyper-parameters of the legendre neural network are set to batch _ size =128, learning \ rate =1x10 ^-4 . The order of the one-dimensional legendre polynomial N =5, so the number of neurons of the 2D legendre neural network is N _modes =21. This example simulates 6 star map distortions. The network structure is the same for different distortion models, only the training data and the network model weights (i.e., the coefficients of the legendre polynomial) are different. First, geometric distortion correction is performed on a star map of a random sky region. Followed byThe star points in the sky area are distributed more uniformly in the star map, and the learning of the global distortion of the star map is facilitated. In the training process of the star map of the random sky area, the training gradients of different distortion models are obtained, and the star map data set comes from the random sky area.

Geometric distortion correction is then performed on the star map generated along the orbit of the earth's rotation. The earth orbit star map data set is mainly a star map shot in a night star observation experiment. Similarly, point-to-point batch learning is performed on the earth orbit star map data set. In the training process of the earth orbit star map, training gradients of different distortion models are obtained, and a star map data set is from a sky area of the earth rotation orbit.

The initial weights of the network used to test the different distortion models are all the same. The initial estimation error is different due to the difference in distortion model. The initial weights of the network may be randomly generated or obtained by an intelligent optimization algorithm, such as the sparrow search algorithm SAA [ see literature: jiankai Xue and Bo Shen.A novel sweep interpolation optimization ap-reach: spark search algorithm.systems Science & Control Engineering,8 (1): 22-34,2020.4.2]. After the network is trained, the estimation error of the star point coordinates can be converged to 0.04 pixels. Considering the possibility of on-orbit implementation, this embodiment will discuss on-orbit star map distortion correction in section 3.3. The results of ground simulation experiments show that: the 2DLNN can fit different star map distortions and the star point position error is corrected to a small value. Meanwhile, the initial weight training process of distortion correction can be realized by a ground simulation experiment. During the launching process of the satellite, parameters of an optical system can be changed due to the influence of some external factors. The initial weights of the ground calibration cannot be completely fitted to the geometric distortion model of the on-orbit star map. On-track distortion correction is therefore a process of on-line continued learning.

3.3 simulation experiment for on-orbit correction

Based on the conclusion of section 2.3.1, an on-orbit simulation star map of one orbit period is generated as a training data set by using the data set generation method of section 3.1. Different from the ground simulation experiment, the star map shooting of the on-orbit star sensor is carried out frame by frame. The 2DLNN on-orbit training uses the equation (27) method. In the training process, the training gradients of different distortion models and star atlas data sets come from star chain orbits. It can be seen that approximately 2000 stars are required to achieve coarse geometric distortion correction. At least 2500 star maps are needed to achieve satisfactory correction. Taking radial distortion as an example, the average time required for training a single star map by using a CPU is 0.6ms, and the method is suitable for on-orbit execution.

Fig. 5 is a graph of the results of geometric distortion correction of a single star point taken from a radially distorted star map. As shown in FIG. 5, before calibration, the distance between the actual observation star point and the reference star point is 2.619x10 ^-3 x1024 is approximately equal to 2.683pixels, and after the correction of the algorithm of the embodiment, the distance between the correction star point and the reference star point is 4.751x10 ^-5 x1024 ≈ 0.048pixels. The relative error of the star point can be reduced by (2.683-0.048)/2.683x100% ≈ 98.18%. It is explained that the geometric distortion correction algorithm proposed by the present embodiment is effective and accurate.

And comparing the pixel distribution of the star image focal plane before correction with the pixel flow of the star image focal plane after correction, wherein the first line is the distortion of the star sensor focal plane, and the second line is a distortion model learned by using 2 DLNN. The corrected star point average error is shown in table 5. At the edges of the star map, the distortion caused by the optical system is about 2 pixels, while the distortion of the image itself is up to 3pixels at maximum. After the correction of the algorithm of the embodiment, the average position error of the star point can reach about 0.04 pixel, which indicates that the algorithm provided by the embodiment successfully predicts the distortion of the star map. Further, the present embodiment method may learn any type of distortion, without being limited to the six types of distortion analyzed by the present embodiment.

TABLE 5 mean position error of different models

	Barrel distortion	Distortion of pillow shape	Tangential distortion	Distortion of thin prism	Shear transformation	Perspective transformation
							x	0.02131	0.03172	0.04677	0.05288	0.03489	0.03171
y	0.03502	0.03051	0.04931	0.02662	0.03822	0.04632

The proposed distortion correction algorithm can be run on a high performance coprocessor, taking into account the computation time cost. The proposed network model is single-layer and high-precision, and can complete the learning of distortion in a single iteration without repeated learning of data. In the method proposed in this embodiment, a global distortion model of the star map, that is, a pixel distortion stream, is learned. Therefore, when the neural network is applied on the ground, the distorted star map can be corrected for geometric distortion by using a suitable resampling method (for example, refer to Xiaoyu Li, bo Zhang, pendro V Sander, and lacing Liao. Band geometric deviation correction in images through depth estimation in the IEEE/CVF Conference Computer Vision and Pattern Recognition, pages 4855-4864, 2019.4.3).

4. Conclusion

The star sensor is an attitude measuring instrument with the highest precision on a spacecraft, and an optical system is distorted due to the influences of lens processing errors, optical path assembly errors, on-orbit temperature alternation and the like. The optical lens distortion and the image distortion have certain influence on the accuracy of the star sensor. In order to improve the accuracy of the star sensor and the availability of the star map. In this embodiment, a method for implementing geometric distortion correction on an orbit star map based on a two-dimensional legendre neural network is provided, and geometric distortion correction of an optical system can be automatically implemented by a single-layer two-dimensional legendre neural network (2 DLNN). In the embodiment, the method for realizing geometric distortion correction of the on-orbit star map based on the two-dimensional Legendre neural network respectively designs an off-line training method based on batch star maps and a sequential on-line star map training algorithm based on single star maps, thereby realizing off-line and on-line correction of optical geometric distortion. The 2DLNN is a single-layer network, has high convergence speed, does not need an activation function, and is suitable for on-orbit learning. The method has the characteristics of autonomous learning and lifelong learning, and can adapt to complex distortion types. Simulation analysis was performed on 6 types of common optical system distortion and image distortion. The result shows that the geometric distortion correction precision of the on-orbit star map is high, and the star point position error can reach below 0.04 pixel. The distortion correction of a sub-pixel level is realized, and the attitude determination precision of the star sensor is effectively improved. The method for realizing the geometric distortion correction of the orbit star map based on the two-dimensional Legendre neural network has the potential of becoming a universal geometric distortion correction of the star map, and can be applied to image distortion correction of satellite loads and ground star observation experiments.

It will be understood by those skilled in the art that all or part of the steps of the foregoing embodiments may be implemented by hardware, or may be implemented by a program instructing relevant hardware, and the program may be stored in a computer-readable storage medium, where the storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like.

The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and additions can be made without departing from the principle of the present invention, and these modifications and additions should also be regarded as the protection scope of the present invention.

Claims

1. A method for realizing geometric distortion correction of an orbit star map based on a two-dimensional Legendre neural network comprises the following steps:

s1, shooting an image of a sky area through an optical lens, and obtaining a measurement star map through star point extraction;

s3, expressing a position mapping relation between an actual measurement star coordinate of the measurement star map and a reference star coordinate of the reference star map by using a common polynomial to obtain a pre-correction pixel stream, and optimizing to obtain an optimal solution of the common polynomial coefficient;

s4, fitting and measuring actual measurement star coordinates and reference star coordinates of the star map by using a pre-correction pixel stream, solving correction star coordinates of unidentified stars, and finally obtaining a corrected star map after distortion correction;

it is characterized in that step S3: expressing a position mapping relation between a distorted star point of a measurement star map and a reference star point of a reference star map by using a two-dimensional Legendre polynomial, and constructing a two-dimensional Legendre neural network to solve an optimal solution of a two-dimensional Legendre polynomial coefficient;

the two-dimensional Legendre polynomial is obtained by:

wherein,

Y _i ^mea is to measure the measured star coordinate of the ith observation star point in the star map,

Y _i ^ref is that the reference star coordinate of the reference star map corresponding to the ith observation star point is expressed as

Y _i ^ref Function D _j，X And D _j，Y Respectively representing the distortion of the X direction and the Y direction of the measured star map of the jth frame;

s32, an n-order Legendre polynomial P _n (x) Expressed as:

the two-dimensional distortion basis is expressed as:

the distortion mode is represented by its index m as:

s34, the mode of the two-dimensional Legendre polynomial is expressed as: b is a mixture of _m (x，y)＝L _n-k (x)×L _k (y) distortion D of i star points of the j-th frame star map _j，X And D _j，Y Expressed as:

wherein, ω is _i,m,X And ω _i,m,Y Coefficients of Legendre polynomials respectively representing two directional distortion modes;

wherein n is _i,X ，n _i,Y Indicating an observation error.

2. The method for realizing geometric distortion correction of an orbit star map based on the two-dimensional Legendre neural network according to claim 1, wherein the step S3: according to the equation

Constructing a single-layer two-dimensional Legendre neural network structure; the input of the two-dimensional Legendre neural network is the centroid coordinate of a star point of a measurement star map, namely the actually measured star coordinate X _mean ，Y _mea The output is the estimated value of the coordinate deviation of the actually measured star

3. The method for realizing geometric distortion correction on an orbit star map based on the two-dimensional Legendre neural network according to claim 2, wherein the step S3 is used for constructing the two-dimensional Legendre neural network, and the specific steps are as follows:

s301, equation

The abbreviation is:

the two-dimensional legendre network constructed is represented as:

in the formula,

s302, normalizing Legendre polynomial

Weight ω in _m Correspondingly, two sets of adjustable weights ω _mx ，ω _my Respectively representing polynomial coefficients of two directions, and obtaining ideal omega by updating a training algorithm _mx ，ω _my Weights, such that the trained weights ω _mx ，ω _my And two-dimensional Legendre polynomial coefficient estimation value

The error is minimal.

4. The method for realizing geometric distortion correction of the on-orbit star map based on the two-dimensional Legendre neural network according to claim 3, wherein the step S303 specifically comprises the following steps:

5. The method for realizing geometric distortion correction of an orbital star map based on a two-dimensional Legendre neural network as claimed in claim 4, wherein the step S3031: capturing a star map from a random sky area, distributing the positions of star points in the star map over the whole optical lens field of view, training a two-dimensional Legendre neural network by a point-to-point training method, and learning the mapping relation between distorted star point coordinates and reference coordinate offset from the whole star map data set;

the method specifically comprises the following steps:

s30311, the estimation error E is expressed as:

s30312, defining a loss function J _p Comprises the following steps:

s30313, updating the weight by using a gradient descent algorithm, and obtaining a chain derivation rule J _p By calculating J _p The first partial differential of (a) yields:

s30314, updating the weight value by using an Adam algorithm, comprehensively considering the first moment and the second moment of the gradient, and calculating the step length of updating the gradient, wherein the updating of the weight value of the two-dimensional Legendre neural network is represented as:

wherein,

m represents the exponentially moving average of the gradient, beta ₁ Controlling the movement of first order gradients, exponential moving means, beta, representing the square of the gradient ₂ The influence of the square of the gradient is controlled,

and

the results show that the influence of the deviation on the initial training stage is reduced by correcting the gradient.

6. The method for realizing geometric distortion correction of an orbital star map based on a two-dimensional Legendre neural network as claimed in claim 4, wherein the step S3032: the star points are considered to be drawn in the optical lens field of view at a certain angular speed; when the star point moves to a position with small distortion, the probability that the star point is correctly identified is higher, and the correctly identified star is tracked in real time; when the star point moves to a position with larger distortion, the tracked star point is continuously used for distortion correction; star points enter the field of view of the optical lens from multiple directions, and the two-dimensional Legendre neural network learns the star map distortion at different positions to complete the global distortion correction of the star map;

the method specifically comprises the following steps:

s30322, the gradient of the loss function during on-track on-line training is obtained by a chain type derivative method:

s30324, updating the weight value by using an Adam algorithm, comprehensively considering the first moment and the second moment of the gradient, and calculating the step length of updating the gradient, wherein the updating of the weight value of the two-dimensional Legendre neural network is represented as:

wherein,

and

7. The method of claim 6, wherein the method for correcting geometric distortion of the on-orbit star map based on the two-dimensional Legendre neural network comprises: the on-orbit online learning method is carried out frame by frame and sample by sample, all star points in a period of time need to cover most positions of a star map, and a two-dimensional Legendre neural network is guaranteed to learn a distortion model of the whole focal plane of an optical lens.

8. The method for realizing geometric distortion correction of an orbit star map based on the two-dimensional Legendre neural network according to claim 1, wherein: the two-dimensional Legendre polynomial has an order of 4 to 6.

9. The method for realizing geometric distortion correction on an orbit star map based on the two-dimensional Legendre neural network according to claim 1, wherein: the observation errors are represented by gaussian noise that is distributed independently.

10. A star sensor based on two-dimensional Legendre neural network for realizing geometric distortion correction of an orbit star map comprises an optical lens and a two-dimensional Legendre neural network, and is characterized in that: the method for implementing geometric distortion correction on an orbit star map based on the two-dimensional Legendre neural network is used for executing any claim from 1 to 9.