CN117351333A - Quick star image extraction method of star sensor - Google Patents

Abstract

The invention discloses a fast star image extraction method for a star sensor. The invention provides a star image extraction network-SSN suitable for star sensors, which can extract the area where the star image target is located in a star map full of stray light. ; Use the error compensation model SEC based on neural networks to reduce the star image centroid coordinate error obtained by the Gaussian surface fitting method in processing the area where the star image target is located. The invention can directly and accurately extract star image centroid coordinates from star charts interfered by strong stray light.

Description

A fast star image extraction method for star sensors

Technical field

The invention relates to the technical field of star sensor attitude measurement, in particular to a method for fast star image extraction of a star sensor.

Background technique

The star sensor provides attitude information with arc-second accuracy to the spacecraft by detecting stars at different locations on the celestial sphere. It is considered one of the most accurate attitude sensors. The main process of the star sensor measuring attitude includes starry sky imaging, star image extraction, star map recognition and attitude estimation. Starry sky imaging is to use a camera to take pictures of the starry sky to obtain a star map, and star image extraction is to process the star map to determine where the star image is. Position in the star map coordinate system. The accuracy of star image extraction directly affects the success or failure of star image recognition and attitude measurement performance. At the same time, star image extraction is the most time-consuming part of the star sensor attitude measurement process. Research on fast star image extraction methods is of great significance for the development of high-performance star sensors.

Early star sensor research only considered the starry sky imaging environment with high signal-to-noise ratio, and usually used the global threshold method for simple denoising to perform star image extraction. With the diversification of aircraft missions, the working environment of star sensors is becoming more and more complex, the influence of stray light is becoming more and more significant, and the accuracy requirements for star sensors are also getting higher and higher. However, it is difficult to obtain the accuracy of star sensors using traditional star image extraction algorithms. Satisfactory results. Researchers have conducted in-depth research on star image extraction algorithms that resist stray light interference. Ding et al. of the National University of Defense Technology realized real-time star image centroid extraction based on the parallel computing capabilities of FPGA. The extraction speed is only 5.2ms/frame, and the centroid accuracy is better than 0.01 pixels. This method uses Top-Hat morphological filters and has achieved a certain degree of resistance. Noise effect. Xing Fei and others from Tsinghua University aimed at the problem of attitude measurement of high-speed spinning satellites. By introducing the extended Kalman filter, they deeply integrated the data of the star sensor and the mems-gyroscope to reduce the impact of detector noise on the accuracy of star image extraction. The star point extraction error of this method is less than 0.2 pixels. The star image extraction algorithm based on gray gradient proposed by He Yiyang et al. uses an adaptive threshold segmentation algorithm to reduce star image noise and improve the performance of the star sensor against Gaussian white noise. The above algorithm has achieved good results in star map processing speed and star image extraction accuracy, but there is still room for further improvement in star map processing with high resolution and strong stray light. Therefore, research on fast and accurate anti-stray light star image extraction technology is an inevitable requirement for the development of high-performance star sensors.

Contents of the invention

In view of the problems existing in the prior art, the present invention provides a fast star image extraction method suitable for star sensors, which can extract the area where the star image target is located in a star map interfered by stray light; it uses an error based on a neural network The compensation model reduces the star image centroid coordinate error obtained by the Gaussian surface fitting method when processing the area where the star image target is located.

The object of the present invention is achieved through the following technical solutions.

A fast star image extraction method for a star sensor, including the following steps:

1) Divide the 64k×64k star image polluted by stray light into four sub-star images of 32k×32k size, and send the four sub-star images into the feature extraction backbone network of the star image extraction network;

2) Take each sub-star image with a size of 32k×32k and a channel number of 1 as input. After the first layer of two-dimensional convolution with a stride of 2 and an activation function of ReLU, the output is 16k×16k size and the number of channels is Feature map F1 of 8;

3) Send the feature map F1 in step 2) to the first residual module Res n, and obtain the feature map F2 with an output size of 16k×16k and a channel number of 8;

4) Send the feature map F2 in step 3) to the second residual module Res n, and obtain the feature map F3 with an output size of 8k×8k and a channel number of 8;

5) Send the feature map F3 in step 4) to the third residual module Res n, and obtain the feature map F4 with an output size of 4k×4k and a channel number of 16;

6) Send the feature map F4 in step 5) to the fourth residual module Res n to obtain the feature map F5 whose output is 2k×2k size and the number of channels is 16;

7) Send the feature map F5 in step 6) to the fifth residual module Res n, and obtain the feature map F6 whose output is k×k size and the number of channels is 16;

8) The feature map enters the feature fusion module for feature fusion. The F6 obtained in step 7) is processed by 5 CR modules in turn to obtain the feature map F7. After the upsampling operation, the channel superposition and addition operation is performed with the F5 obtained in step 5). Two feature map channels of the same size are spliced together to obtain F8. F8 is processed by 5 CR modules in turn to obtain the feature map F9. F9 is upsampled and F4 obtained in step 4) is subjected to a channel superposition and addition operation. The two Feature map channels of the same size are spliced together to obtain F10, which is then processed by 5 CR modules in sequence to obtain the final predicted feature map P;

9) Send the feature map P to the detection module for star image detection;

10) Output the prediction area coordinate data, that is, the area where the star image in the sub-star map is located;

11) Coordinate transformation of the prediction area coordinate data. The four sub-star maps processed in parallel by the network all belong to the same star map. The horizontal and vertical coordinates of the first sub-map remain unchanged; the abscissa of the second sub-map is multiplied by the sub-star map scaling ratio (the scaling ratio is the original image size/sub-image size). The vertical coordinate remains unchanged; the vertical coordinate of the third sub-image is multiplied by the scaling ratio of the sub-star chart, and the abscissa remains unchanged; the horizontal and vertical coordinates of the fourth sub-star chart are multiplied by the scaling ratio of the sub-star chart, and the star image in the sub-image can be obtained The original image area corresponding to the area where the area is located;

12) Output the star image area image in the original image;

13) Perform Gaussian surface fitting on the given star image area image to solve for the star image centroid. Center positioning is performed based on the energy distribution characteristics of the star image. Assume the initialization surface center is (x ₀ , y ₀ , I ₀ ), then the Gaussian surface model is as follows:

In the formula, (x ₀ , y ₀ ) is the center of the star image; I ₀ is the central star image energy, which is related to the magnitude and optical system; σ is the Gaussian dispersion radius, indicating the size of the star image spot; f (x _i , y _i ) is the energy of each pixel. Taking the logarithm of both sides of the Gaussian surface model and linearizing it, we get:

Based on the idea of least squares, the center of mass coordinates of the star image can be solved. The calculated star image centroid position has a large error with the actual star image position, and is sent to the error compensation neural network SEC to perform error compensation on the centroid coordinates.

The structure of the star image extraction network SSN includes a feature extraction backbone network, a feature fusion network and a detection network.

The feature extraction backbone network includes 5 residual modules Res n. The Res n module is composed of n residual structures (Res unit) and m two-dimensional convolution layers. The value of n is affected by the depth of the network layers. , the value is 1 or 2, the value of m is a fixed value 1; the size of each convolution kernel in the residual structure (Res unit) and the two-dimensional convolution layer is 3×3, and the activation function is the ReLU function; features The extraction backbone network is used to accurately extract the features of star images in star maps.

The feature fusion network includes a CR module, an upsampling operation and a channel superposition operation. The CR module is a standard convolution module, including a two-dimensional convolution layer, batch normalization, and ReLU activation function; the upsampling operation is performed through a bilinear inner The interpolation method increases the low-resolution image to a high resolution, so that the sizes of the feature maps of two different resolutions are restored to be consistent, and is used for channel overlay operations on feature maps of the same size; the feature fusion network is used to improve the feature map The amount of contextual information included.

The detection network includes a CR module and a convolutional layer, and the detection network is used to predict star image areas on feature maps.

The change of the feature map in a single residual structure (Res unit) includes the following process:

The input feature map x undergoes a 1×1 dimensionality reduction convolution operation to obtain the output feature map x’;

Perform a 3×3 convolution operation on the feature map x’ to obtain the output feature map x”;

Perform nonlinear mapping on each element of x" through the ReLU activation function to obtain the feature map z;

The feature map z is fed into the attention mechanism, and the feature map on each channel is compressed through the global average pooling operation to obtain the global context information of each channel. The compressed feature map is passed through a fully connected layer to generate For the weight vector of each channel, multiply the feature map by the weight vector of the corresponding channel, and perform weighted scaling on the feature map to enhance important features and weaken unimportant features to obtain the feature map z';

Add the feature map z and the feature map z’ to obtain the residual r, and then input the residual r to the next layer for convolution operation;

The residual r is passed through the ReLU activation function to perform nonlinear mapping and a 1×1 dimensionality-raising convolution operation on each element, and finally the output feature map y is obtained;

The above process is described as:

y=W ₂ BN(ReLU(BN(ReLU(W ₁ ·x))))+W _s ·x

Among them, W ₁ and W ₂ are the convolution filters used by each convolution layer respectively, W _s is a dimensional transformation, used to change the number of channels of the input feature map to the same as the number of channels of the output feature map, x is the input feature map, and y is the output feature map.

The neural network-based error compensation model SEC used to compensate for the centroid coordinate error obtained by the Gaussian surface fitting method includes five hidden layers F1-F5, one input layer and one output layer. The F1 and F5 hidden layers are each composed of five neural networks. Composed of neurons, the F2, F3, and F4 hidden layers are each composed of 7 neurons, and the activation function of each neuron is the ReLU function;

The error compensation model uses the mean square error loss function and the Adam optimizer. Suppose the output of the model is y and the true value is t. Then the formula of the mean square error of the loss function is as follows:

where n represents the number of predicted values and actual values. For a given sample, _yi represents the value predicted by the model, and t _i represents the actual value;

In each training iteration, data with errors is input into the model and the output result of the model is obtained; the mean square error between the output result and the real result is calculated and used as the loss value. Then, clear the gradient cache, perform backpropagation and update network parameters; repeat the above training process several times until the performance of the network meets the requirements;

By sending the star image centroid coordinates with errors into the trained error compensation model SEC, the error-corrected star image centroid coordinates can be obtained.

Compared with the existing technology, the advantage of the present invention is that the present invention provides a star image extraction network Star Sensor Net, referred to as SSN, suitable for star sensors, which can extract stars from star maps full of stray light. Image the area where the target is located; provide a neural network-based error compensation network Star Error Compensktion, referred to as SEC, to reduce the error of the Gaussian surface fitting method in calculating the center of mass coordinates of star images. The invention can directly and accurately extract star image centroid coordinates from star charts interfered by strong stray light. The invention can solve the technical problem that the existing technology cannot accurately and quickly extract the centroid of a star image from a star chart polluted by stray light.

Description of drawings

Figure 1 is a flow chart of fast star image extraction.

Figure 2 is a schematic diagram of the residual structure.

Figure 3 is a schematic diagram of the SSN star image extraction network.

Figure 4 is a stray light pollution star chart according to an embodiment.

Figure 5 is the sub-satellite diagram 1 after segmentation according to the embodiment.

Figure 6 is the sub-satellite diagram 2 after segmentation in the embodiment.

Figure 7 is the sub-satellite diagram 3 after segmentation according to the embodiment.

Figure 8 is the sub-satellite diagram 4 after segmentation in the embodiment.

Figure 9 shows the output result of sub-satellite image 1 processed by the SSN star image detection network according to the embodiment.

Figure 10 shows the output result of sub-satellite image 2 processed by the SSN star image detection network according to the embodiment.

Figure 11 shows the output result of sub-satellite image 3 processed by the SSN star image detection network according to the embodiment.

Figure 12 shows the output result of sub-satellite image 4 processed by the SSN star image detection network according to the embodiment.

Figure 13 is a diagram of the star image area with star image number 1 in the embodiment.

Figure 14 is a schematic diagram of the Gaussian surface fitting centroid in the star image number 1 region of the embodiment.

Figure 15 is a schematic diagram of the star image coordinate error compensation neural network SEC.

Figure 16 is an error diagram of the ordinate error of the centroid of all star images in the embodiment.

Figure 17 is an error diagram of the abscissa of the centroid of all star images in the embodiment.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

Example

Figure 1 shows the implementation process of the neural network-based fast star image extraction method provided by the embodiment of the present invention. The details are as follows:

The stray light star image that needs to be extracted in the embodiment is shown in Figure 4, and Figures 5, 6, 7, and 8 represent star image sub-images.

1. Divide the 1024×1024 star image contaminated by stray light into four sub-star images of 512×512 size, and send the four sub-star images to the feature extraction backbone network of SSN.

2. Take a sub-star image with a size of 512×512 and a channel number of 1 as input. After the first layer of two-dimensional convolution with a stride of 2 and an activation function of ReLU, output features with a size of 256×256 and a channel number of 8. Figure F1.

3. Send the feature map F1 in step 2 to the first residual module Res (a residual structure Res unit + a two-dimensional convolution), and obtain the feature map F2 with an output size of 256×256 and a channel number of 8.

4. Send the feature map F2 in step 3 to the second residual module Res (a residual structure Res unit + a two-dimensional convolution), and obtain the feature map F3 with an output size of 128×128 and a channel number of 8.

5. Send the feature map F3 in step 4 to the third residual module Res2 (two residual structures Res unit + one two-dimensional convolution), and obtain the feature map F4 with an output size of 64×64 and a channel number of 16. .

6. Send the feature map F4 in step 5 to the fourth residual module Res2 (two residual structures Res unit + one two-dimensional convolution), and obtain the feature map F5 with an output size of 32×32 and a channel number of 16. .

7. Send the feature map F5 in step 6 to the fifth residual module Res (a residual structure Res unit + a two-dimensional convolution), and obtain the feature map F6 with an output size of 16×16 and a channel number of 16.

8. The feature map enters the feature fusion module for feature fusion. The F6 obtained in step 7 is sent to the 5 CR modules to obtain the feature map F7. After the upsampling operation, the channel superposition and addition operation is performed with the F5 obtained in step 5. The two The channels of feature maps of the same size are spliced together to obtain F8. F8 is sent to 5 CR modules to obtain the feature map F9. After upsampling, F9 performs a channel superposition and addition operation with F4 obtained in step 4, and the two feature maps of the same size are combined. The channels are spliced together to obtain F10, and then five CR modules are used to obtain the final predicted feature map P.

9. Send the feature map P to the detection module for star image detection.

10. Output the prediction area coordinate data, that is, the area where the star image is located in the sub-star map, as shown in Figure 9, Figure 10, Figure 11, and Figure 12. The prediction area coordinates are shown in Table 1. (x ₁ , y ₁ ) is the prediction The coordinates of the upper left corner of the area, (x ₂ , y ₂ ) are the coordinates of the lower right corner of the prediction area.

Table 1 Predicted Area Coordinates DataTable.1Predicted Area Coordinates Data

11. Transform the prediction area coordinate data. The four sub-star maps processed in parallel by the network all belong to the same star map. The coordinates obtained by the first sub-map remain unchanged, and the abscissa of the second sub-map is multiplied by 2 (original image size/sub-image size). , the vertical coordinate remains unchanged, the vertical coordinate of the third sub-map is multiplied by 2, the horizontal coordinate remains unchanged, the horizontal and vertical coordinates of the fourth sub-star map are both multiplied by 2, and the original map area range coordinates corresponding to the sub-map area range coordinates can be obtained. The coordinates of the predicted area range after coordinate transformation are shown in Table 2.

Table 2 Transformed Predicted Region Coordinates DataTable.2Transformed Predicted RegionCoordinates Data

In order to further illustrate the calculation process, the present invention uses the prediction area range with star image serial number 1 as an example for illustration, and the other star image centroid extraction steps are the same.

12. Output the area image of star image 1 in the original image, as shown in Figure 13. The size of the area image is 25×25, and the position of the area image in the original image is (802, 50, 827, 75). Among them (802, 50) is the coordinate of the upper left corner, and (827, 75) is the coordinate of the upper right corner.

13. Perform Gaussian surface fitting on the given area image to solve for the star image centroid. Center positioning is performed based on the energy distribution characteristics of the star image. Assume the initialization surface center is (x ₀ , y ₀ , I ₀ ), then the Gaussian surface model is as follows:

In the formula, (x ₀ , y ₀ ) is the center of the star image; I ₀ is the central star image energy, which is related to the magnitude and optical system; σ is the Gaussian dispersion radius, indicating the size of the star image spot; f (x _i , y _i ) is the energy of each pixel. Taking the logarithm of both sides of the Gaussian surface model and linearizing it, we get:

Based on the idea of least squares, it can be calculated that the center coordinates of the regional image of star image number 1 are (13.326, 13.217), plus the coordinates of the upper left corner of the original image where the regional image is located (802, 50), that is, we get The star image centroid coordinates are (815.326, 63.217), which has a large error with the actual star image centroid coordinates (816.938, 64.376).

14. Affected by stray light, the center of mass position of the star image calculated by Gaussian surface fitting has a large error with the actual star image position. The error compensation neural network is sent to the error compensation neural network to compensate for the error of the center of mass coordinates. The corrected coordinates are (816.658, 64.686) , the error with the exact position coordinates (816.938, 64.376) is small.

Table 2 Star image extraction simulation experiment results (adding stray light interference)

Tab.2 Results of star extraction simulation(Add stray lightinterference)

As shown in Table 2, the present invention can extract the centroid coordinates of all star images in the star map, and after the error coordinates obtained by the Gaussian surface fitting method are sent to the error compensation neural network, the centroid coordinates of all star images obtained are the same as the accurate coordinates of the star images. There are small errors. The abscissa error is shown in Figure 10, and the column coordinate error is shown in Figure 11. The abscissa error and column coordinate error are about 0.03 pixels, and the distance error between the centroid position and the standard centroid position is 0.04 pixels. pixels. Therefore, the star image extraction algorithm provided by the present invention can well solve the problem of rapid star image extraction under strong stray light interference.

Claims (8)

1. A fast star image extraction method for a star sensor, which is characterized by including the following steps: 1) Divide the 64k×64k star image contaminated by stray light into four sub-star images of 32k×32k size, and send the four sub-star images into the feature extraction backbone network of the star image extraction network, where k is an integer; 2) Take each sub-star image with a size of 32k×32k and a channel number of 1 as input. After the first layer of two-dimensional convolution with a stride of 2 and an activation function of ReLU, the output is 16k×16k size and the number of channels is Feature map F1 of 8; 3) Send the feature map F1 in step 2) to the first residual module Res n, and obtain the feature map F2 with an output size of 16k×16k and a channel number of 8; 4) Send the feature map F2 in step 3) to the second residual module Res n, and obtain the feature map F3 with an output size of 8k×8k and a channel number of 8; 5) Send the feature map F3 in step 4) to the third residual module Res n, and obtain the feature map F4 with an output size of 4k×4k and a channel number of 16; 6) Send the feature map F4 in step 5) to the fourth residual module Res n to obtain the feature map F5 whose output is 2k×2k size and the number of channels is 16; 7) Send the feature map F5 in step 6) to the fifth residual module Res n, and obtain the feature map F6 whose output is k×k size and the number of channels is 16; 8) The feature map enters the feature fusion module for feature fusion. The F6 obtained in step 7) is sent to 5 CR modules to obtain the feature map F7. After the upsampling operation, the channel superposition and addition operation is performed with the F5 obtained in step 5). Two feature map channels of the same size are spliced together to obtain F8. F8 is sent to 5 CR modules to obtain the feature map F9. F9 is upsampled and F4 obtained in step 4) is subjected to a channel superposition and addition operation, and the two same-sized feature maps are combined. The feature map channels are spliced together to obtain F10, and then the final predicted feature map P is obtained through 5 CR modules; 9) Send the feature map P to the detection module for star image detection; 10) Output the prediction area coordinate data, that is, the area where the star image in the sub-star map is located; 11) Coordinate transformation of the prediction area coordinate data. The four sub-star maps processed in parallel by the network all belong to the same star map. The horizontal and vertical coordinates of the first sub-map remain unchanged; the abscissa of the second sub-map is multiplied by the sub-star map scaling ratio, and the vertical coordinates are The coordinates remain unchanged; the vertical coordinate of the third sub-image is multiplied by the scaling ratio of the sub-star chart, and the abscissa remains unchanged; the horizontal and vertical coordinates of the fourth sub-star chart are multiplied by the scaling ratio of the sub-star chart, and the location of the star image in the sub-image can be obtained The original image area range corresponding to the area range; 12) Output the star image area image in the original image; 13) Perform Gaussian surface fitting on the given star image area image, solve for the star image centroid, and locate the center based on the energy distribution characteristics of the star image. Suppose the initialization surface center is (x ₀ , y ₀ , I ₀ ), then the Gaussian surface The model is as follows: In the formula, (x ₀ , y ₀ ) is the center of the star image; I ₀ is the central star image energy, which is related to the magnitude and optical system; σ is the Gaussian dispersion radius, indicating the size of the star image spot; f (x _i , y _i ) is the energy of each pixel, linearize the logarithm on both sides of the Gaussian surface model, and get: Based on the idea of least squares, the centroid coordinates of the star image can be solved. The calculated centroid position of the star image has a large error with the actual star image position. The error compensation neural network is sent to the error compensation neural network to compensate for the error of the centroid coordinates, and the corrected centroid is obtained. coordinate. 2. A fast star image extraction method for a star sensor according to claim 1, characterized in that the structure of the star image extraction network SSN includes a feature extraction backbone network, a feature fusion network and a detection network. 3. A star sensor fast star image extraction method according to claim 2, characterized in that the feature extraction backbone network includes 5 residual modules Res n, and the Res n module includes n residual structures and m two-dimensional convolution layers, the value of n is affected by the depth of the network layer, the value is 1 or 2, the value of m is a fixed value 1; the residual structure and the size of each convolution kernel in the two-dimensional convolution layer The sizes are all 3×3, and the activation function is the ReLU function; the feature extraction backbone network is used to accurately extract the features of the star images in the star map. 4. A star sensor fast star image extraction method according to claim 2, characterized in that the feature fusion network includes a CR module, an upsampling operation and a channel superposition operation, and the CR module is a standard convolution module, including a Two-dimensional convolution layer, batch normalization, ReLU activation function; the upsampling operation increases the low-resolution image to high-resolution through bilinear interpolation, allowing the feature map size of two different resolutions to be restored Consistent, used for channel overlay operations on feature maps of the same size; feature fusion network is used to increase the amount of context information of feature maps. 5. A star sensor fast star image extraction method according to claim 2, characterized in that the detection network includes a CR module and a convolution layer, and the detection network is used to predict star image areas on feature maps. . 6. A star sensor fast star image extraction method according to claim 3, characterized in that the change of the feature map in a single residual structure includes the following process: The input feature map x undergoes a 1×1 dimensionality reduction convolution operation to obtain the output feature map x’; Perform a 3×3 convolution operation on the feature map x’ to obtain the output feature map x”; Perform nonlinear mapping on each element of x" through the ReLU activation function to obtain the feature map z; The feature map z is fed into the attention mechanism, and the feature map on each channel is compressed through the global average pooling operation to obtain the global context information of each channel. The compressed feature map is passed through a fully connected layer to generate For the weight vector of each channel, multiply the feature map by the weight vector of the corresponding channel, and perform weighted scaling on the feature map to enhance important features and weaken unimportant features to obtain the feature map z'; Add the feature map z and the feature map z’ to obtain the residual r, and then input the residual r to the next convolutional layer; The residual r is passed through the ReLU activation function to perform nonlinear mapping and a 1×1 dimensionality-raising convolution operation on each element, and finally the output feature map y is obtained; The above process is described as: y=W ₂ BN(ReLU(BN(ReLU(W ₁ ·x))))+W _s ·x Among them, W ₁ and W ₂ are the convolution filters used by each convolution layer respectively, W _s is a dimensional transformation, used to change the number of channels of the input feature map to the same as the number of channels of the output feature map, x is the input feature map, and y is the output feature map. 7. A fast star image extraction method for a star sensor according to claim 1, characterized by using an error compensation model SEC based on a neural network to perform error compensation on the centroid coordinates obtained by the Gaussian surface fitting method. 8. A star sensor fast star image extraction method according to claim 7, characterized in that the neural network-based error compensation model SEC includes five hidden layers F1-F5, one input layer and one output layer, The F1 and F5 hidden layers are each composed of 5 neurons, and the F2, F3, and F4 hidden layers are each composed of 7 neurons. The activation function of each neuron is the ReLU function; The error compensation model uses the mean square error loss function and the Adam optimizer. Suppose the output of the model is y and the true value is t. Then the formula of the mean square error of the loss function is as follows: where n represents the number of predicted values and actual values. For a given sample, _yi represents the value predicted by the model, and t _i represents the actual value; In each training iteration, data with errors is input into the model and the output result of the model is obtained; the mean square error between the output result and the real result is calculated and used as the loss value, and then the gradient cache is cleared. , perform backpropagation and update network parameters; repeat the above training process several times until the performance of the network meets the requirements; By sending the star image centroid coordinates with errors into the trained error compensation model SEC, the error-corrected star image centroid coordinates can be obtained.