Spacecraft attitude estimation method based on uncertainty

Abstract

The invention relates to the technical field of mode recognition, in particular to a spacecraft attitude estimation method based on uncertainty, which comprises the following steps: performing attitude prediction on each calibration sample in a calibration set based on a trained multi-attitude hypothesis regression network model, and outputting a plurality of attitude hypotheses and corresponding confidence scores; constructing a non-conformal function, calculating the non-conformity score of the network model for the predicted output of each calibration sample to the true value attitude, and calculating the quantile of the non-conformity score as a calibration parameter; inputting a test sample into the network model to obtain a multi-attitude hypothesis of the test sample, and constraining the multi-attitude hypothesis of the test sample by using the calibration parameter to obtain a prediction set; and extracting a final attitude estimation result from the prediction set, and quantifying the uncertainty of the estimation result. According to the method, attitude estimation can be carried out according to an uncertainty quantification result, and the precision and reliability of spacecraft attitude estimation are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of pattern recognition, and more particularly to a method for spacecraft attitude estimation based on uncertainty. Background Art

[0002] With the continuous increase of space missions, people's interest in tasks such as on-orbit service, debris removal, and formation flight is increasing, and related technologies are constantly developing. Among them, spacecraft attitude estimation is a very important task, which can obtain the relative attitude position between the target and itself, and play a series of roles such as assisting in close-range navigation and rendezvous and docking operations, providing initialization parameters for accurate attitude tracking, and providing target satellite attitude information in space-based surveillance.

[0003] In recent years, with the popularization and exponential growth of deep learning methods, deep learning-based methods have become the preferred solution for solving the problem of non-cooperative spacecraft attitude estimation. However, although these deep learning models usually perform excellently in terms of overall prediction accuracy, it is well known that they sometimes make unexpected, wrong, but overly confident predictions, especially in complex real-world environments. This can cause serious consequences in high-risk applications such as on-orbit service and space surveillance. In on-orbit missions, due to the complex space imaging conditions, imaging sensors are interfered by conditions such as light changes and space noise, and the imaging quality changes significantly, which will cause great interference to the attitude estimation task. In this regard, deep learning models should be aware of what they don't know to avoid overly confident predictions. For example, when encountering an uncertain attitude, it should assign a higher uncertainty to the predicted result of its output to warn technicians and avoid fatal errors.

[0004] "Understanding what a deep learning model doesn't know" boils down to placing appropriate uncertainty scores in its predictions, also known as uncertainty quantification (UQ). With the development of uncertainty quantification technology, the academic community has conducted many studies on the sources and modeling of uncertainty in deep models, and some methods have been produced, but few studies have applied them to the space target attitude estimation task.

[0005] Most deep learning-based spacecraft attitude estimation methods mainly emphasize accuracy and real-time performance, usually ignoring the uncertainties inherent in the predictions of deep models. However, spacecraft attitude estimation is closely related to safety-critical applications, so it is crucial to evaluate the reliability of attitude predictions. To address this issue, some existing techniques use the intersection over union (IOU) between the predicted bounding boxes and the ground truth boxes around predefined key points on the satellite as a measure of spatial uncertainty. However, this method only outputs a single value to represent the uncertainty of the key points and does not show the anisotropy of the key point uncertainties. Some technical solutions use Monte Carlo sampling techniques to convert the estimation results into a categorical distribution. However, for the space environment with limited resources, the increasing computational requirements brought by increasing the sampling are impractical. There are also technical solutions that use evidence regression to estimate the uncertainties of key points but do not consider the propagation of key point uncertainties to attitude uncertainties. Although the accuracy of attitude estimation is improved, there is no measure of attitude reliability. Generally speaking, the existing related technologies have problems such as high computational resource consumption, single uncertainty modeling, and no direct indicator of attitude reliability. Summary of the Invention

[0006] In view of this, the present invention provides an uncertainty-based spacecraft attitude estimation method, which can perform attitude estimation according to the quantization results of uncertainties, improving the accuracy and reliability of spacecraft attitude estimation.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] In a first aspect, the present invention provides an uncertainty-based spacecraft attitude estimation method, including the following steps:

[0009] Obtain satellite images and construct a training set, a calibration set, and a test set;

[0010] Use the training set to train a pre-constructed multi-attitude hypothesis regression network model;

[0011] Based on the trained multi-attitude hypothesis regression network model, perform attitude predictions on each calibration sample in the calibration set, and output multiple attitude hypotheses and corresponding confidence scores;

[0012] Construct a non-conformal function, calculate the non-conformity scores of the predicted outputs of the trained multi-attitude hypothesis regression network model for each calibration sample with respect to the true attitude, and calculate the quantiles of the non-conformity scores as calibration parameters;

[0013] Input the test samples in the test set into the trained multi-attitude hypothesis regression network model to obtain the multi-attitude hypotheses of the test samples, and use the calibration parameters to constrain the multi-attitude hypotheses of the test samples to obtain a prediction set;

[0014] The final pose estimation result is extracted from the prediction set, and the uncertainty of the estimation result is quantified.

[0015] Furthermore, the main body of the multi-pose hypothesis regression network model is divided into ResNet, followed by two multi-layer perceptrons as prediction heads to regress the rotation vector, translation vector and respective pose scores represented by six degrees of freedom; the regressed pose is supervised by distance loss, and the pose score is supervised by cross entropy loss.

[0016] Furthermore, the non-conformal function is used to capture the maximum deviation between the predicted pose hypothesis and the true value, and its expression is:

[0017]

[0018] in, represents the set of predicted pose hypotheses and their associated confidence scores for the input image x in the calibration set, h i represents the i-th pose hypothesis of the input image x, p i represents the confidence score corresponding to the i-th pose hypothesis of the input image x, n represents that the input image x contains a total of n pose hypotheses, and y represents the true value of the pose of the input image x.

[0019] Furthermore, the calculation steps of the calibration parameters include:

[0020] For each calibration sample (x j ,y j )∈D cal , select the top 3 posture hypotheses with the highest confidence scores to participate in the calibration process, and use the non-conformal function to calculate the non-conformity score of each calibration sample Among them, s j =max(p i ||h i -y||), represents the non-conformity score of the jth calibration sample; D cal represents the calibration set, n cal Indicates that a total of n cal Non-compliance score;

[0021] Sum up the nonconformity scores of all calibration samples and arrange them in ascending order;

[0022] Select coverage error ∈, calculate the score that does not meet Quantile, the non-compliance score corresponding to the calculated quantile is used as the calibration parameter α.

[0023] Furthermore, the steps of generating the prediction set include:

[0024] Input the test sample into the trained multi - pose hypothesis regression network model to obtain the multi - pose hypotheses of the test sample and the corresponding confidence scores, and select the top three pose hypotheses ranked by confidence scores to construct a prediction set, which is expressed as:

[0025]

[0026] where y represents the true pose of the test sample x N+1 and Y represents the set of true poses of the test sample, and h N+1,k represents the k - th pose hypothesis of the test sample x N+1 and p N+1,k represents the confidence score corresponding to the k - th pose hypothesis of the test sample x N+1 , α represents the calibration parameter, and k = 1, 2, 3.

[0027] Furthermore, for the test sample x N+1 , the probability that its true pose y N+1 is included in the prediction set is at least 1 - ∈. According to the data exchange hypothesis and the relevant properties of the Beta distribution, the coverage probability of the prediction set of the test sample x N+1 satisfies:

[0028]

[0029] where n cal represents the number of samples in the calibration set, which is the same as the number of non - conformity scores.

[0030] Furthermore, the final pose estimation result and its uncertainty quantification process include:

[0031] Sample the boundary points of the prediction set to obtain a discrete representation that can capture the shape and range of the prediction set;

[0032] Apply the Welzl algorithm to calculate the minimum enclosing ball of the sampled boundary points;

[0033] Designate the center of the enclosing ball as the final pose estimation result, and use the radius of the enclosing ball as a quantitative measure of the prediction uncertainty.

[0034] In a second aspect, the present invention provides an electronic device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor; when the processor executes the computer program, the steps of the method for spacecraft attitude estimation based on uncertainty as described above are implemented.

[0035] In a third aspect, the present invention provides a computer - readable storage medium, on which a computer program is stored, characterized in that when the computer program is executed by a processor, the steps of the method for spacecraft attitude estimation based on uncertainty as described above are implemented.

[0036] As can be seen from the above technical solutions, compared with the prior art, the present invention has the following beneficial effects:

[0037] First of all, the present invention uses a multi-pose hypothesis regression network based on CNN, which can directly regress multiple pose hypotheses of non-cooperative satellite targets, achieving a trade-off between efficiency and accuracy. Secondly, the present invention uses a non-conformal function to obtain a pose prediction set, which reflects the uncertainty of pose estimation and probabilistically covers the true pose. Finally, the present invention extracts the final pose estimation result from the prediction set and quantifies the uncertainty of the complex prediction set, and this uncertainty contributes to reliability assessment. All in all, the present invention ensures the inclusion of the true pose of the target with a certain probability, while considering the multiple possibilities of the target pose when including the true pose, providing a reliable and accurate pose estimation result, which helps to reduce the on-orbit risk. Description of the Drawings

[0038] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained according to the provided drawings.

[0039] Figure 1 It is a flowchart of the method for spacecraft attitude estimation based on uncertainty provided by the present invention;

[0040] Figure 2 It is a schematic diagram of the uncertainty distribution of the BSP1.0 dataset provided by the present invention;

[0041] Figure 3 It is a schematic diagram of the uncertainty distribution of the SPEED dataset provided by the present invention;

[0042] Figure 4 It is a schematic diagram for comparing the uncertainty distributions of the BSP1.0 dataset and the SPEED dataset provided by the present invention;

[0043] Figure 5 It is a schematic diagram of the visualization result of the boundary pose of the prediction set provided by the present invention. Detailed Embodiments

[0044] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0045] As Figure 1 shown, an embodiment of the present invention discloses a spacecraft attitude estimation method based on uncertainty, including the following steps:

[0046] S1. Obtain satellite images, construct a training set, a calibration set, and a test set; use the training set to train a pre-constructed multi-attitude hypothesis regression network model;

[0047] S2. Based on the trained multi-attitude hypothesis regression network model, perform attitude prediction on each calibration sample in the calibration set, and output multiple attitude hypotheses and corresponding confidence scores;

[0048] Construct a non-conformal function, calculate the non-conformity score of the predicted output of the trained multi-attitude hypothesis regression network model for each calibration sample with respect to the true attitude, and calculate the quantile of the non-conformity score as the calibration parameter;

[0049] S3. Input the test samples in the test set into the trained multi-attitude hypothesis regression network model to obtain the multi-attitude hypotheses of the test samples, and use the calibration parameter to constrain the multi-attitude hypotheses of the test samples to obtain a prediction set;

[0050] S4. Extract the final attitude estimation result from the prediction set and quantify the uncertainty of the estimation result.

[0051] The present invention is a spacecraft attitude estimation technology for monocular visible light images, which is applied to space target image analysis and space target attitude estimation. Generally speaking, the present invention processes satellite images through a multi-attitude hypothesis regression network model to generate multiple attitude hypotheses and their corresponding attitude scores. After completing the model training, a non-conformal function is designed to calibrate the model on the calibration set to obtain the calibration value. Subsequently, when a new image is received, the calibration value and the multi-attitude hypotheses output by the model are used to construct a prediction set, and the constructed prediction set can contain the true attitude of the target with a manually set probability. Finally, a sampling method is designed to extract the final pose estimation result from the prediction set and quantify the uncertainty of the estimation result. These designs ensure the inclusion of the true attitude of the target with a certain probability, and at the same time consider the multiple possibilities of the target attitude when including the true attitude, providing reliable and accurate attitude estimation results.

[0052] The following further explains the above steps.

[0053] S1. Construction of the multi - pose hypothesis regression network model and construction of the dataset.

[0054] Symmetry is a fundamental challenge in spacecraft attitude estimation because many spacecraft exhibit varying degrees of structural symmetry. This symmetry leads to visually similar or even identical appearances in different directions, thus complicating attitude estimation. To alleviate this problem, the present invention designs a multi - pose hypothesis regression network model as shown in Figure 1 . The backbone part of the model is ResNet, followed by two multi - layer perceptrons as prediction heads to regress the rotation vector, translation vector, and their respective attitude scores representing six degrees of freedom; the regressed attitudes are supervised by distance loss, and the attitude scores are supervised by cross - entropy loss. This strategy enables the network model to identify and represent all possible attitudes by assigning similar scores to multiple prediction results, rather than forcing the output of a single definite result. In this way, the model can effectively capture the inherent attitude uncertainty caused by symmetry.

[0055] After that, a satellite image dataset will be obtained and divided into a training set D train , a calibration set D cal and a test set D test . The training set is used to train the model, the calibration set is used to generate parameters regarding uncertainty, and the test set is used to test the performance of the method.

[0056] S2. Conformal calibration.

[0057] After completing the training of the multi - pose hypothesis regression network on the training set, a non - conformal function is designed to calibrate the inconsistency between the predictions of the trained model and the true attitudes. This non - conformal function is used to capture the maximum deviation between the predicted pose hypotheses and the true values, and its expression is:

[0058]

[0059] where represents the set of predicted pose hypotheses and their associated confidence scores for the input image x in the calibration set, h i represents the i - th pose hypothesis of the input image x, p i represents the confidence score corresponding to the i - th pose hypothesis of the input image x, n represents the total number of pose hypotheses contained in the input image x, and y represents the true attitude of the input image x.

[0060] During calibration, the confidence scores of each pose hypothesis are taken into account. The specific calibration process is as follows:

[0061] For each calibration sample (x j , y j ) ∈ D cal, select the top 3 pose hypotheses with the highest confidence scores to participate in the calibration process, and use a non-conformal function to calculate the nonconformity scores for each calibration sample, obtaining a total of n cal nonconformity scores, denoted as where s j = max(p i ||h i - y||), representing the nonconformity score of the j-th calibration sample; D cal represents the calibration set, and n cal indicates that a total of n cal nonconformity scores are obtained;

[0062] Aggregate the nonconformity scores of all calibration samples and sort them in ascending order;

[0063] Select the coverage error ∈ and calculate the quantile of the nonconformity scores, and use the nonconformity score corresponding to the calculated quantile as the calibration parameter α.

[0064] S3. Construction of the prediction set.

[0065] After determining the value of the quantile during the calibration process, use it together with the non-conformal function to construct the prediction set for the test images. Input the test samples into the trained multi-pose hypothesis regression network model to obtain the multi-pose hypotheses and corresponding confidence scores of the test samples, and the prediction set for the new data points is defined as follows:

[0066] S(x N+1 ) = {y ∈ Y|max(p N+1,k ||h N+1,k - y|| ≤ α)}

[0067] Further expansion gives:

[0068]

[0069] where y represents the true pose of the test sample x N+1 , Y represents the set of true poses of the test samples, h N+1,k represents the k-th pose hypothesis of the test sample x N+1 , p N+1,k represents the confidence score corresponding to the k-th pose hypothesis of the test sample x N+1 , and α represents the calibration parameter. Similar to the calibration process, when constructing the prediction set, also select the top three pose hypotheses with the highest confidence scores to construct the prediction set, i.e., k = 1, 2, 3.

[0070] For the test sample x N+1 , its true pose y N+1The probability of being included in the prediction set is at least 1 - ∈. According to the data exchangeability hypothesis, the distribution of the samples is invariant under any permutation. Then, the outlier scores of the new samples with true labels can be exchanged with the outlier scores of the calibrated samples, and thus may be located anywhere among all the scores. For the quantile, meanwhile, its conditional distribution on the calibration set is a Beta distribution Beta(n cal + 1)(1 - ∈), (n cal + 1)∈). According to the relevant properties of the Beta distribution, it has an expectation of 1 - ∈ and gradually converges to this value as the number of samples in the calibration set increases. Therefore, for the test sample x N+1 the coverage probability of the prediction set satisfies:

[0071]

[0072] where n cal represents the number of samples in the calibration set, which is the same as the number of outlier scores.

[0073] For a task such as spacecraft attitude estimation, the acquisition of images from each perspective in the dataset is independent, thus satisfying the exchangeability hypothesis. Therefore, the prediction set constructed in the present invention has a theoretically 1 - ∈ inclusion probability for the true attitude.

[0074] S4. Uncertainty quantification and attitude prediction.

[0075] Once the prediction set has obtained a probability guarantee of covering the true attitude, the next step is to extract the final attitude estimation value and quantify the uncertainty associated with the prediction. Intuitively, the size of the prediction set is a natural indicator of uncertainty because when the model is uncertain about a given input, the prediction set expands to include a wider range of possible attitudes to ensure the required coverage probability. Therefore, the larger the prediction set, the lower the confidence of the model in the estimated pose, and the smaller the prediction set, the higher the confidence. Therefore, the goal of uncertainty quantification is to estimate the size of the prediction set to directly measure the confidence of the model in its prediction. The present invention proposes a sampling and estimation strategy to simultaneously estimate the size of the prediction set and consider the information of the prediction set to generate the final attitude estimation result. The specific steps are as follows:

[0076] Sample the boundary points of the prediction set. The specific method is as follows: Initialize 20 random initial seeds within the prediction set using the random convex combination of the centers of the top 3 attitude hypotheses ranked by confidence scores. Subsequently, within the range of 2000 steps, for each random seed, randomly initialize the step size and direction at each step until all the random seeds reach the boundary of the prediction set and then stop. Due to the uniformity of the direction sampling, the random seeds can be evenly distributed on the boundary of the prediction set, thereby obtaining a discrete representation that can capture the shape and range of the prediction set;

[0077] Apply the Welzl algorithm to calculate the minimum enclosing sphere of the sampled boundary points; the specific objective is: given a point set, the goal is to find a smallest sphere that covers all points in it. Let be the "set of boundary points" that constitutes the enclosing sphere, then the Welzl algorithm proceeds with the following recursive process:

[0078] Randomly select a point from and then remove it from. Call the recursion on the remaining point set ′ = - {} to obtain a minimum sphere. If the point is inside or on the boundary of the sphere, return. If the point is outside the sphere: it means the sphere is not large enough and must contain, so add to the boundary point set, and continue the recursion with the processed and until is empty or the points in R can determine a sphere.

[0079] Designate the center of the enclosing sphere as the final attitude estimation result, and use the radius of the enclosing sphere as a quantitative measure of the prediction uncertainty. Since the prediction set forms a convex region, this enclosing sphere provides a reliable approximation of the size of the prediction set.

[0080] In other embodiments, the present invention also provides an electronic device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor; characterized in that when the processor executes the computer program, the steps of the above-mentioned uncertainty-based spacecraft attitude estimation method are implemented.

[0081] In some other embodiments, the present invention also provides a computer-readable storage medium, on which a computer program is stored, characterized in that when the computer program is executed by a processor, the steps of the above-mentioned uncertainty-based spacecraft attitude estimation method are implemented.

[0082] Next, in order to verify the advantages of the present invention, the publicly available spacecraft attitude estimation datasets SPEED and BSP1.0 were collected and trained on the training sets of the two datasets respectively, and the trained models were respectively experimented on the test sets.

[0083] The BSP1.0 dataset consists of simulated images, representing different orientations of five different satellite models, with a total of 56,656 attitude changes for each satellite model. The dataset consists of grayscale images with a resolution of 256×256, featuring weak texture and low resolution, and each satellite model is centered in a unified deep space background. The SPEED dataset consists of synthetic images and real images, capturing different attitudes of the Tango spacecraft. Compared with BSP1.0, it has a higher resolution and richer texture, but its background is complex and there is strong interference. Due to the relatively complementary characteristics of these two datasets, combining these two datasets can comprehensively test the comprehensive performance of this method.

[0084] First, the true value coverage of the prediction set of the method of the present invention was tested on two datasets, and the test results are shown in Table 1. The statistical results show that for these two datasets, when ∈ = 0.01, the coverage rate reaches approximately 99%. Such a high coverage rate indicates that the prediction set effectively encompasses the true poses with a high confidence, thus affirming the reliability of this method in the pose estimation task. For other ∈ values, the observed coverage rates generally conform to the expected theoretical trends stipulated by the 1 - ∈ rule, further demonstrating the rationality of the prediction set in this method.

[0085] Table 1 True value coverage rates under different specified coverage errors

[0086] dataset ∈＝0.4 ∈＝0.2 ∈＝0.1 ∈＝0.05 ∈＝0.01 BSP 1.0 60.44％ 80.35％ 90.02％ 95.06％ 99.10％ SPEED 54.30％ 79.58％ 88.82％ 93.58％ 97.97％

[0087] Subsequently, the errors and inference times of the single-point predictions generated from the prediction set by this method were tested on two datasets, and the test results are shown in Tables 2 and 3.

[0088] Table 2 Test results of the BSP1.0 dataset

[0089]

[0090] Table 3 Test results of the SPEED dataset

[0091]

[0092]

[0093] It can be seen from the statistical results that after considering the uncertainty information, the Euler angle error and E Euler , the rotation matrix error E rotation and the translation error E translation of the method of the present invention have all decreased significantly, which shows the feasibility and importance of adding uncertainty information to the pose estimation method. At the same time, the part adding uncertainty quantification does not significantly slow down the speed of pose estimation, and the entire method can still achieve real-time performance. The excellent performance on the two datasets also shows that this method can simultaneously handle well the two challenging situations of low texture resolution and complex background.

[0094] Furthermore, the cumulative distribution function of the uncertainty predicted by the model was visualized, and the results are as Figures 2 - 4As shown. From the cumulative distribution function graph of uncertainty, it can be seen that the uncertainty distribution curves quantified by this method all have relatively steep regions, indicating that the uncertainty is relatively concentrated in these regions. For intervals with larger uncertainty, the curve is slightly flatter, indicating that the uncertainty is less distributed in these intervals. This characteristic simultaneously provides an index for measuring the reliability of the pose estimation results. For example, for the BSP1.0 dataset, when the predicted uncertainty is higher than 3 degrees, it can be considered that the prediction is unreliable. This measurement of reliability is very precious for high-risk applications in orbit. At the same time, from the comparison of uncertainty distributions, it can be seen that the predicted uncertainty of the SPEED dataset is greater than that of the BSP1.0 dataset, which indicates that it is more challenging for the model to perform pose estimation on images with more complex backgrounds. This also provides an indication for the deployment of the model in real-world scenarios.

[0095] Finally, the single-point pose predicted by the method of the present invention and some sampled boundary poses in the prediction set are visualized. The predicted pose is visualized using red, green, and blue colors to represent the satellite body coordinate axes, while the boundary poses are assigned random colors. The results are as Figure 5 shown. From Figure 5 it can be seen that the boundary poses sampled in the prediction set always perturb around the predicted pose, and the more difficult the estimation is, the more obvious the perturbation range. This shows that the prediction set can reflect the uncertainty of pose estimation and the final predicted pose fully considers this uncertainty.

[0096] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. The same or similar parts among the various embodiments can be referred to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple. For the relevant parts, reference can be made to the description in the method section.

[0097] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the broadest scope consistent with the principles and novel features disclosed herein.

Claims

1. A spacecraft attitude estimation method based on uncertainty, characterized in that The following steps are involved: Obtain satellite images and construct training sets, calibration sets, and test sets; Use the training set to train the pre-built multi-pose hypothesis regression network model; Based on the trained multi-pose hypothesis regression network model, the pose of each calibration sample in the calibration set is predicted, and multiple pose hypotheses and corresponding confidence scores are output; Construct a non-conformal function, calculate the non-conformity score of the predicted output of the trained multi-pose hypothesis regression network model for each calibration sample with respect to the true pose, and calculate the quantile of the non-conformity score as the calibration parameter; The test samples in the test set are input into the trained multi-pose hypothesis regression network model to obtain the multi-pose hypothesis of the test samples, and the multi-pose hypothesis of the test samples is constrained by the calibration parameters to obtain the prediction set; The final pose estimation result is extracted from the prediction set, and the uncertainty of the estimation result is quantified.

2. The method for estimating the attitude of a spacecraft based on uncertainty according to claim 1, characterized in that The main body of the multi-pose hypothesis regression network model is divided into ResNet, followed by two multi-layer perceptrons as prediction heads to regress the rotation vector, translation vector and respective pose scores represented by six degrees of freedom; the regressed pose is supervised by distance loss, and the pose score is supervised by cross entropy loss.

3. The method for spacecraft attitude estimation based on uncertainty according to claim 1, characterized in that The non-conformal function is used to capture the maximum deviation between the predicted pose hypothesis and the true value, and its expression is: Among them, represents the set of predicted pose hypotheses of the input image x in the calibration set and their associated confidence scores, h i represents the i-th pose hypothesis of the input image x, p i represents the confidence score corresponding to the i-th pose hypothesis of the input image x. n represents that the input image x contains n pose hypotheses in total, and y represents the ground truth pose of the input image x.

4. The method for estimating the attitude of a spacecraft based on uncertainty according to claim 3, wherein The calculation steps of the calibration parameters include: For each calibration sample (x j , y j ) ∈ D cal , select the top 3 pose hypotheses with the highest confidence scores to participate in the calibration process, and use a non-conformal function to calculate the nonconformity score for each calibration sample where s j = max(p i ||h i - y||) represents the nonconformity score of the j-th calibration sample; D cal represents the calibration set, and n cal means that a total of n cal nonconformity scores are obtained; Sum up the nonconformity scores of all calibration samples and arrange them in ascending order; Select the coverage error ∈ and calculate the non-compliance score quantile, and use the non-compliance score corresponding to the calculated quantile as the calibration parameter α.

5. The method for spacecraft attitude estimation based on uncertainty according to claim 1, wherein The steps to generate the prediction set include: The test sample is input into the trained multi-pose hypothesis regression network model to obtain the multi-pose hypothesis of the test sample and the corresponding confidence score, and the top three pose hypotheses with the highest confidence scores are selected to construct the prediction set. The prediction set is expressed as: where y represents the true pose of the test sample x N+1 , Y represents the set of true poses of the test samples, and h N+1,k represents the k-th pose hypothesis of the test sample x N+1 , p N+1,k represents the confidence score corresponding to the k-th pose hypothesis of the test sample x N+1 , α represents the calibration parameter, and k = 1, 2, 3.

6. The method for spacecraft attitude estimation based on uncertainty according to claim 5, wherein, For the test sample x N+1 , its true pose y N+1 is included in the prediction set with a probability of at least 1 - ∈. According to the data exchangeability hypothesis and the relevant properties of the Beta distribution, the test sample x N+1 The coverage probability of the prediction set satisfies: where n cal represents the number of samples in the calibration set, which is the same as the number of nonconformity scores.

7. The method for spacecraft attitude estimation based on uncertainty according to claim 1, characterized in that The final attitude estimation result and its uncertainty quantification process include: Sampling boundary points of the prediction set to obtain a discrete representation that captures the shape and range of the prediction set; Apply the Welzl algorithm to calculate the minimum bounding sphere of the sampling boundary points; The center of the bounding sphere is assigned as the final pose estimation result, and the radius of the bounding sphere is used as a quantitative measure of the prediction uncertainty.

8. An electronic device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor; wherein when the processor executes the computer program, the steps of the uncertainty-based spacecraft attitude estimation method as described in any one of claims 1 to 7 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, the steps of the uncertainty-based spacecraft attitude estimation method as described in any one of claims 1 to 7 are implemented.

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