A space variant PSF low-dimensional manifold modeling and online template generation method for large aberration star sensor

Abstract

The present application relates to a kind of space variation PSF low-dimensional manifold modeling and online template generation method for large aberration star sensor, it is related to star sensor imaging and photoelectric measurement technical field, with as small as possible storage and calculation cost, high-fidelity modeling and online template generation are carried out to full field of view space variation PSF.The method includes the following steps: the star sensor or its front end simplified optical system to be measured is modeled, and the mapping relationship of image plane coordinates and field of view radial coordinates is established;Along preset meridian plane, offline acquisition reference PSF sample is carried out at high-resolution radial step.The present application is directed to the specific technical problem of large aberration, strong asymmetric, full field of view space variation PSF, constructs the modeling scheme combined with coaxial rotation symmetry prior and low-dimensional feature space representation, avoids the mismatch of traditional center symmetry model, and by one-dimensional radial sampling replaces two-dimensional full field of view point-by-point sampling, significantly reduces offline sample quantity and template library size.

Description

Technical Field

[0001] This invention relates to the field of star sensor imaging and photoelectric measurement technology, and in particular to a method for low-dimensional manifold modeling and online template generation of spatial variation PSF for star sensors with large aberrations. Background Technology

[0002] Star sensors are crucial payloads for attitude measurement in spacecraft and near-space vehicles. Their core task is to stably extract the centroid of stars from stellar images and perform high-precision attitude reference measurements. With the increasing demands for lightweight, miniaturized, and low-power payloads from platforms such as microsatellites, high-altitude long-endurance UAVs, and near-space vehicles, simplification of the star sensor's front-end optical system is often necessary. Common engineering practices include reducing the number of lenses, shrinking the structural size, and lowering system complexity. However, these simplifications typically weaken the aberration correction capabilities of the optical system, leading to severe asymmetric stretching, tailing, and topological distortion of the point spread function in the off-axis field of view. This, in turn, causes significant systematic biases in traditional centroid-based methods or Gaussian fitting methods that rely on centrosymmetry assumptions.

[0003] There are three main categories of existing technical approaches that are similar to this invention. The first category consists of traditional star point extraction and localization methods, such as the gray-scale centroid method, region growing method, and two-dimensional Gaussian fitting method. These methods are simple to implement and have low computational burden, but they typically rely on the near-central symmetry of star point morphology, making them prone to localization errors when dealing with strongly asymmetric star spots under conditions of large aberrations. The second category consists of systematic error correction methods, such as calibration compensation schemes for S-curve errors in star sensors or distortion introduced by image intensifiers. These methods focus on reducing systematic bias through empirical calibration or error models, but they typically do not directly handle PSFs (point spread functions) with highly irregular morphologies and spatial variations across the entire field of view. The third category consists of spatially variable PSF modeling methods. In the broader field of astronomical imaging, existing work has used principal component analysis (PCA) to construct PSF libraries, reconstructing position-dependent PSFs with a small number of principal components. These methods demonstrate the feasibility of representing complex PSFs with a low-dimensional feature space, but they are mainly geared towards astronomical observation image correction and are not typically specifically designed for the efficiency of online template retrieval for star sensors with large aberrations or the subsequent real-time localization requirements.

[0004] Compared to existing solutions, this invention addresses a more specific engineering problem: how to perform high-fidelity modeling and online template generation of spatially variable star spots across the entire field of view (PSF) with minimal storage and computational cost, given a significantly simplified front-end optical system, severe off-axis aberrations, and the need for online matching for star spot localization. Existing methods either rely on analytical symmetry models, making them ill-suited for the continuous evolution of spatially variable star spots due to principal axis rotation, enhanced tailing, and energy eccentricity under lightweight front-end conditions; or, while employing low-dimensional feature representations, they fail to incorporate the one-dimensional radial sampling characteristics of coaxial rotationally symmetric systems and lack a complete template generation mechanism for online matching. Summary of the Invention

[0005] This invention aims to address the technical problem in the prior art of how to perform high-fidelity modeling and online template generation of spatially variable PSFs across the entire field of view with minimal storage and computational cost, under conditions where the front-end optical system is significantly simplified, off-axis aberrations are severe, and star point positioning requires online matching and retrieval. It provides a method for low-dimensional manifold modeling and online template generation of spatially variable PSFs for star sensors with large aberrations.

[0006] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: A method for low-dimensional manifold modeling and online template generation of spatial variation PSF for star sensors with large aberrations includes the following steps: Step 1: Model the star sensor under test or its simplified front-end optical system to confirm that it belongs to a coaxial rotationally symmetric imaging system, and establish the mapping relationship between the image plane coordinates and the radial coordinates of the field of view; Step 2: Acquire reference PSF samples offline along the preset meridional plane at a high-resolution radial step size, and extend them to any field of view azimuth angle through azimuth rotation relationship; Step 3: Normalize the total energy of all offline PSF samples, calculate the centroid of the top percentile pixels in brightness and force center alignment to eliminate the interference of absolute light intensity difference and translation drift on feature extraction; Step 4: Flatten the aligned 2D PSF samples into vectors, construct the mean-removed sample matrix, and obtain the intrinsic PSF basis through principal component analysis or equivalent singular value decomposition. Step 5: Select the number of principal components according to the cumulative energy retention rate criterion to obtain the low-dimensional intrinsic subspace, and project each offline sample into the corresponding low-dimensional coefficient vector; Step 6: Construct a continuous one-dimensional coefficient manifold lookup table with radial field coordinates as independent variables and projection coefficients of each principal component as dependent variables; Step 7: During online operation, for any target star point, interpolation is performed in the lookup table based on its radial position in the field of view to recover the principal component coefficient vector at that position, and then linearly combined with the average PSF and each intrinsic PSF to generate a static position correlation template. Step 8: When the system can obtain angular velocity information, the static template is convolved with the motion blur kernel to generate a dynamic position-related template for subsequent matching or positioning algorithms.

[0007] In the above technical solution, step 3 specifically includes: First, perform total energy normalization on each sample. Then, extract the high signal-to-noise ratio pixels with the highest brightness in the sample according to a preset ratio. Use these pixels to calculate the weighted centroid and use it as the anchor center. Then, forcibly translate each sample to a unified reference coordinate center.

[0008] In the above technical solution, step 4 specifically includes: Each 2D PSF sample is flattened into a column vector, and after subtracting the mean shape, a continuous mean-free sample matrix is ​​constructed. ; By analyzing the matrix Perform singular value decomposition to obtain the orthogonal subspace of aberration evolution: In the formula, For the mean-removed sample matrix An orthogonal matrix composed of the right singular vectors is used to characterize the relative combination relationship of different offline PSF samples on each singular component; T This represents the matrix transpose operation; It is an orthogonal matrix; It is a diagonal matrix.

[0009] In the above technical solution, step 5 specifically includes: For each offline sampling radius location, project its original sample onto... Within the eigenvalue subspace, the corresponding... A vector of coefficients.

[0010] In the above technical solution, step 7 specifically includes: During system operation, the radial position of the target star point in the field of view is first calculated based on the image plane coordinates of the target star point. Subsequently, in the coefficient manifold lookup table The system retrieves neighboring sampling nodes and performs linear interpolation to obtain the estimated coefficient vector for the current position. : Then from the average template With each intrinsic template Perform a weighted linear combination to generate a static position-related template. : Finally, apply the azimuth angle to it. Rotation Operator This yields a position-related template that matches the observed star point.

[0011] In the above technical solution, step 8 specifically includes: If the star sensor system also has angular velocity information provided by the inertial sensor A motion blur kernel is constructed based on the two-dimensional displacement during the exposure time. and related templates for the above static positions Perform spatial convolution Generate dynamic location-related templates : .

[0012] The present invention has the following beneficial effects: The present invention provides a low-dimensional manifold modeling and online template generation method for spatially variability PSF of star sensors with large aberrations. It addresses the specific technical problems of large aberration, strong asymmetry, and full-field spatial variability PSF by constructing a modeling scheme that combines coaxial rotational symmetry priors with low-dimensional feature space representation. This avoids the mismatch of traditional centrosymmetric models and significantly reduces the number of offline samples and the size of the template library by replacing two-dimensional full-field point-by-point sampling with one-dimensional radial sampling.

[0013] The present invention provides a low-dimensional manifold modeling and online template generation method for spatial variation PSF of star sensors with large aberrations. Through high signal-to-noise ratio anchoring alignment and energy normalization, the principal components more centrally express the evolution of light spot morphology rather than translation or intensity differences, thereby improving the physical interpretability of the intrinsic subspace.

[0014] The present invention provides a low-dimensional manifold modeling and online template generation method for spatial variation PSF of star sensors with large aberrations. By replacing high-order explicit fitting with coefficient manifold lookup tables, the method reduces the computational complexity during online calls while ensuring reconstruction accuracy, making it more suitable for embedded star sensor implementation.

[0015] The present invention provides a method for low-dimensional manifold modeling and online template generation of spatial variation PSF for star sensors with large aberrations. The generated location-related physical templates can be called online and can directly provide a unified prior for subsequent matching, segmentation and localization algorithms. The present invention provides a method for low-dimensional manifold modeling and online template generation of spatial variation PSF for star sensors with large aberrations. Under dynamic conditions, this method can be naturally extended to motion blur template generation, providing a foundation for template matching in highly dynamic scenes. Attached Figure Description

[0016] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0017] Figure 1 A flowchart is provided for the overall process of offline modeling and online template generation. The process includes steps such as coaxial rotationally symmetric system modeling, radial PSF sampling, sample normalization and alignment, intrinsic subspace extraction, coefficient manifold lookup table construction, and online static / dynamic template generation.

[0018] Figure 2 This is an example of the optical system used in this invention, showing a simplified optical path diagram of the three-cement lens system and the PSF spot morphology at different fields of view. As the field of view increases, the PSF gradually degenerates from an approximately symmetrical dot pattern to an asymmetrical stretched and trailing shape.

[0019] Figure 3 This is a schematic diagram of one-dimensional radial sampling and azimuth rotation recovery. In a coaxial rotationally symmetric system, a template with an arbitrary azimuth position can be recovered by planar rotation simply by sampling along the meridional plane.

[0020] Figure 4 This is a schematic diagram illustrating the principle of PCA for extracting intrinsic PSF subspaces. As shown in the figure, which simplifies the feature space, PCA finds the direction that maximizes the data variance in the original high-dimensional data space (PC1) and sequentially constructs mutually orthogonal basis vectors. By projecting the observed data onto these principal component axes and discarding the secondary dimensions that carry local residuals or noise (PC2), a refined mapping from high-dimensional data to a low-dimensional space can be achieved while retaining most of the structural information.

[0021] Figure 5 This is a graph showing the relationship between energy retention rate and the number of principal components. Taking the simplified triplex lens used in this invention as an example, the number of principal components is selected based on the cumulative variance contribution rate.

[0022] Figure 6 This is a schematic diagram of dynamic template expansion. (a) Static manifold template (b) Motion blur kernel (c) Dynamic template. A dynamic PSF template can be generated by convolving a static template with a motion blur kernel.

[0023] Figure 7 The reconstruction results and similarity statistics of feature point templates for typical mid-field and meridional planes are shown. (a) Reconstructed PSF template (b) True PSF (c) Absolute residual distribution (d) Cross-sectional profile comparison Figure 8 The reconstruction results of the edge field point template and their similarity statistics are shown. (a) Reconstructed PSF template (b) True PSF (c) Absolute residual distribution (d) Cross-sectional profile comparison.

[0024] Figure 9 The results show the DMD dot matrix imaging under different field-of-view partitions.

[0025] Figure 10 Comparison of cropped images (top) and reconstructed images (bottom) of the central field of view, intermediate field of view, and edge field of view. Detailed Implementation

[0026] The inventive concept of this invention is as follows: The method of this invention, without increasing the complexity of the front-end optical system, utilizes techniques such as coaxial rotational symmetry prior, one-dimensional radial sampling strategy, sample normalization and anchoring alignment, principal component analysis dimensionality reduction, and coefficient manifold lookup table to establish a position-related PSF template generation mechanism that can be quickly invoked online, thereby providing a unified high-fidelity physical prior for the accurate matching, segmentation, and positioning of complex star spots.

[0027] The present invention will now be described in detail with reference to the accompanying drawings.

[0028] Figure 1 A comprehensive workflow framework from offline modeling to online template generation is presented. For example... Figure 1 As shown, the basic process of the spatial variation PSF low-dimensional manifold modeling and online template generation method for large aberration star sensors of the present invention is as follows: Step 1: Model the star sensor under test or its simplified front-end optical system to confirm that it belongs to a coaxial rotationally symmetric imaging system, and establish the mapping relationship between the image plane coordinates and the radial coordinates of the field of view; Step 2: Acquire reference PSF samples offline along the preset meridional plane at a high-resolution radial step size, and extend them to any field of view azimuth angle through azimuth rotation relationship; Step 3: Normalize the total energy of all offline PSF samples, calculate the centroid of the top percentile pixels in brightness and force center alignment to eliminate the interference of absolute light intensity difference and translation drift on feature extraction; Step 4: Flatten the aligned 2D PSF samples into vectors, construct the mean-removed sample matrix, and obtain the intrinsic PSF basis through principal component analysis or equivalent singular value decomposition. Step 5: Select the number of principal components according to the cumulative energy retention rate criterion to obtain the low-dimensional intrinsic subspace, and project each offline sample into the corresponding low-dimensional coefficient vector; Step 6: Construct a continuous one-dimensional coefficient manifold lookup table with radial field coordinates as independent variables and projection coefficients of each principal component as dependent variables; Step 7: During online operation, for any target star point, interpolation is performed in the lookup table based on its radial position in the field of view to recover the principal component coefficient vector at that position, and then linearly combined with the average PSF and each intrinsic PSF to generate a static position correlation template. Step 8: When the system can obtain angular velocity information, the static template is convolved with the motion blur kernel to generate a dynamic position-related template for subsequent matching or positioning algorithms.

[0029] The core of this invention lies in addressing the specific technical problem of large aberration star sensors by combining coaxial rotational symmetric sampling, one-dimensional coefficient manifold lookup tables, and online template generation mechanisms to form a complete technical solution for real-time invocation.

[0030] The following explanation focuses on three aspects: offline sampling and low-dimensional modeling, online position-related template generation, and dynamic template expansion. To facilitate understanding of the imaging scenarios of large aberration star sensors and the basic manifestations of spatially variable PSFs addressed in this invention, the imaging characteristics are first explained using a simplified optical system. Figure 2 An example of the triple-cemented optical system used in this invention is presented, along with the variation of the PSF spot morphology at different field-of-view positions. Figure 2 As can be seen, with the increase of the field of view radius, the PSF gradually evolves from approximately symmetrical spot patterns in the paraxial region into complex star patterns with obvious asymmetric stretching and trailing characteristics. Therefore, it is necessary to perform high-fidelity characterization of its PSF morphology in order to provide a reliable basis for subsequent extraction and localization.

[0031] i. Spatial Variance PSF Sampling under Coaxial Rotationally Symmetric Prior Constraints (Step 1) Most compact star sensor front-end optical systems are coaxial rotationally symmetric systems. In these systems, the strength of off-axis aberration is mainly determined by the radial distance from the field point to the optical axis, while the azimuth angle change is mainly manifested as the rotation of the image spot in the two-dimensional coordinate system.

[0032] (Step 2) Therefore, this invention does not employ point-by-point sampling across the entire two-dimensional field of view, but instead acquires a series of benchmark PSF samples along a fixed meridional plane with a high-resolution step size. The specific illustration is as follows: Figure 3 As shown. When the algorithm runs online, regardless of the angle at which the target star falls within the field of view, it only needs to find the reference sample with the corresponding radius and apply a coordinate rotation operator to it. This allows us to reconstruct the true shape of the light spot at that location, namely: This technique compresses the original sampling complexity of the template library from two-dimensional grid sampling to one-dimensional radial sampling, reducing the size of the original data while maintaining high sampling density, thus laying a lightweight foundation for subsequent high-precision modeling.

[0033] ii. Sample normalization and high signal-to-noise ratio anchoring alignment (Step 3) If dimensionality reduction is directly performed on the original PSF image, non-morphological information related to target position drift and total energy difference will be mixed into the principal components, affecting the physical purity of the intrinsic subspace. Therefore, this invention first performs total energy normalization on each sample, and then extracts the top 5% (preferably the top 5%) of high signal-to-noise ratio pixels by brightness from the samples. These pixels are used to calculate the weighted centroid, which is then used as the anchor center. Subsequently, each sample is forcibly translated to a unified reference coordinate center. This method significantly reduces the interference of energy center drift of large aberration star spots on the subsequent dimensionality reduction results, ensuring that the extracted principal components primarily reflect the spatial evolution of the true shape of the light spots.

[0034] iii. Intrinsic PSF subspace extraction (Step 4) After completing sample normalization and center alignment, flatten each two-dimensional PSF sample into a column vector, and after subtracting the mean shape, construct a continuous mean-free sample matrix. By performing singular value decomposition on this matrix, the orthogonal subspace of aberration evolution can be obtained: In the formula, For the mean-removed sample matrix An orthogonal matrix composed of the right singular vectors is used to characterize the relative combination relationship of different offline PSF samples on each singular component; T This represents the matrix transpose operation; It is an orthogonal matrix; It is a diagonal matrix.

[0035] orthogonal matrix The column vectors form the "intrinsic PSF" basis describing morphological variations; while the diagonal matrix The singular values ​​in the model quantify the variance weights carried by each intrinsic component. To explain the extraction mechanism of the intrinsic PSF subspace in this invention, Figure 4 A schematic diagram of the PCA dimensionality reduction process is given. By projecting high-dimensional PSF samples onto at least a few dominant orthogonal directions, a low-dimensional and compact representation of spatially variable PSFs can be achieved while preserving the main morphological evolution information.

[0036] To achieve a balance between template compression rate and reconstruction fidelity, the cumulative variance (energy) retention rate criterion is used. Before choosing Each principal component, such as a threshold that can be set. : In the formula, For the first A singular value, The total number of principal components. Figure 5 This diagram illustrates the relationship between the energy retention rate of the example optical system of this invention and the number of principal components, thereby determining the minimum number of principal components required to satisfy the preset cumulative variance contribution rate. Through the above steps, the complex aberration patterns originally dispersed in the high-dimensional pixel space are refined into a few dominant modes with clear physical interpretations.

[0037] iv. Construction of coefficient manifold lookup table (Step 5) For each offline sampling radius location, project its original sample onto the above... Within the eigenvalue subspace, the corresponding... A coefficient vector. As the field of view radius increases... These coefficient vectors, changing continuously, form a smooth one-dimensional manifold curve in the feature space. The low-dimensional reconstruction at any radial position can be approximated as: In the formula, The average PSF shape of all samples. For the first An intrinsic PSF substrate, Radial position The corresponding projection coefficients.

[0038] (Step 6) Construct a continuous one-dimensional coefficient manifold lookup table using the radial field-of-view coordinates as the independent variable and the projection coefficients of each principal component as the dependent variable. In this invention, instead of using explicit fitting with high-order polynomials, a non-parametric offline lookup table is established between the discrete radius positions and the corresponding coefficient vectors. This avoids the oscillations that high-order fitting may cause at the edge of the field of view, and also allows the coefficients to be quickly recovered in the online stage simply by looking up the table and using low-order interpolation.

[0039] v. Online location-related template generation (Step 7) During the system operation phase, first calculate the corresponding radial position of the field of view based on the image plane coordinates of the target star. Then, in the above coefficient manifold lookup table... The system retrieves neighboring sampling nodes and performs linear interpolation to obtain the estimated coefficient vector for the current position. : Then from the average template With each intrinsic template Perform a weighted linear combination to generate a static position-related template. : Finally, apply the azimuth angle to it. Rotation Operator This will give you a position-related template that matches the observed star point.

[0040] vi. Dynamic template extension (Step 8) In dynamic observation scenarios, static position-related templates can be further expanded into dynamic templates by combining platform motion information. Figure 6 The generation process from a static manifold template and a motion blur kernel to a dynamic template is illustrated. This is relevant if the star sensor system also possesses angular velocity information provided by an inertial sensor. Then, a motion blur kernel can be further constructed based on the two-dimensional displacement during the exposure time. and related templates for the above static positions Perform spatial convolution Generate dynamic location-related templates : The low-dimensional manifold framework of this invention can be extended to high-dynamic motion blur scenes including pitch, yaw, or roll.

[0041] To quantitatively evaluate the proposed intrinsic PSF manifold model's ability to reconstruct large aberration spots, typical feature points were selected across the entire field of view, and sub-pixel-level registration and comparison analysis was performed between the model-generated PSF and ground truth data. The evaluation metrics used were normalized cross-correlation coefficients to characterize morphological similarity and peak difference to characterize photometric consistency.

[0042] In the discrete field-of-view sampling grid, the mid-field test point (5,5) and the meridional feature field-of-view point (0,7) are selected. The reconstructed PSF closely matches the true value, as shown below. Figure 7 As shown, the NCC values ​​are as high as 0.9967 and 0.9956, respectively, and the peak intensity error is controlled within 0.5% (0.45% and 0.15%, respectively). This indicates that the PCA principal component effectively captures the optical features of the region, and the rotation reconstruction strategy does not introduce obvious interpolation artifacts.

[0043] Even at the edge of the field of view, the manifold model maintains a high topological similarity of 0.9743, such as... Figure 8 As shown. Although the peak intensity error at this point increases slightly (to 8.19%), this is mainly due to the truncation effect of PCA dimensionality reduction on the extremely high frequency residual energy. For star point extraction and localization applications based on subsequent morphological matching or correlation measurement, this magnitude of local peak deviation usually does not significantly disrupt the dominant morphological consistency between the template and the actual star spots, so its impact on the subsequent geometric positioning accuracy remains within an acceptable range.

[0044] In addition to simulation verification, the practicality of this invention was also verified through semi-physical experiments. For example... Figure 9As shown, a partitioned scanning experimental platform was built based on a DMD star simulator, collimator, three-connected TIR prism, a PSF lens for spatial variation under test, and auxiliary adjustment mechanisms. Measured PSF samples were acquired at different field-of-view positions, and a radial coefficient manifold was constructed along the meridional plane. This radial model was then rotated and generalized to non-radial positions for verification. The DMD lattice imaging results acquired at different field-of-view positions are shown below. Figure 9 As shown. Reference points were selected from the non-radial acquisition locations and divided into paraxial, intermediate, and edge field-of-view regions. Five reference points were selected from each region for statistical analysis. The results show that the average core region NCC of representative non-radial specks in the paraxial, intermediate, and edge field-of-view regions reached 0.9839, 0.9698, and 0.9681, respectively. Figure 10 Representative measured spot patterns and reconstruction results are presented at three different field-of-view locations. It can be seen that as the off-axis degree increases, the local detail differences between the model and the measured star spots increase, but the NCC in the core region remains at a high level, indicating that the radial PSF manifold model can well preserve the main lobe structure, principal scale information, and energy diffusion range of the measured star spots.

[0045] In other specific implementations: (1) The coaxial rotationally symmetric optical system described in this invention is not limited to a three-colloidal lens, but can also be extended to other refractive, reflective or catadioptric approximately rotationally symmetric compact imaging systems.

[0046] (2) Offline sampling is not limited to a single meridional plane; when there is a slight non-ideal assembly error in the system, multi-meridian joint sampling can be used to construct a segmented lookup table or a multi-branch manifold model.

[0047] (3) In the high signal-to-noise ratio anchoring strategy used for sample alignment, the brightness screening ratio is not limited to the top 5%, but can be selected from the top 1% to 20% of high confidence pixels according to the sensor noise level and target shape.

[0048] (4) Principal component extraction can be achieved by singular value decomposition, which is equivalent to PCA; other low-dimensional orthogonal decomposition or constrained feature decomposition methods can also be used without changing the core idea of ​​"low-dimensional feature space expression + online template generation".

[0049] (5) In addition to linear interpolation, the online calling methods for coefficient manifolds can also be piecewise spline interpolation, nearest neighbor interpolation, or local regression.

[0050] (6) Static templates can be further combined with different types of motion blur kernels, image shift kernels or time integration kernels to generate online templates suitable for dynamic observation scenarios.

[0051] (7) In addition to star sensors, the present invention can also be extended to other optical measurement or navigation imaging systems that require compact modeling and real-time calling of the response of spatially variable point targets.

[0052] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for low-dimensional manifold modeling and online template generation of spatially variability PSF for star sensors with large aberrations, characterized in that, Includes the following steps: Step 1: Model the star sensor under test or its simplified front-end optical system to confirm that it belongs to a coaxial rotationally symmetric imaging system, and establish the mapping relationship between the image plane coordinates and the radial coordinates of the field of view; Step 2: Acquire reference PSF samples offline along the preset meridional plane at a high-resolution radial step size, and extend them to any field of view azimuth angle through azimuth rotation relationship; Step 3: Normalize the total energy of all offline PSF samples, calculate the centroid of the top percentile pixels in brightness and force center alignment to eliminate the interference of absolute light intensity difference and translation drift on feature extraction; Step 4: Flatten the aligned 2D PSF samples into vectors, construct the mean-removed sample matrix, and obtain the intrinsic PSF basis through principal component analysis or equivalent singular value decomposition. Step 5: Select the number of principal components according to the cumulative energy retention rate criterion to obtain the low-dimensional intrinsic subspace, and project each offline sample into the corresponding low-dimensional coefficient vector; Step 6: Construct a continuous one-dimensional coefficient manifold lookup table with radial field coordinates as independent variables and projection coefficients of each principal component as dependent variables; Step 7: During online operation, for any target star point, interpolation is performed in the lookup table based on its radial position in the field of view to recover the principal component coefficient vector at that position, and then linearly combined with the average PSF and each intrinsic PSF to generate a static position correlation template. Step 8: When the system can obtain angular velocity information, the static template is convolved with the motion blur kernel to generate a dynamic position-related template for subsequent matching or positioning algorithms.

2. The method for low-dimensional manifold modeling and online template generation of spatial variation PSF for star sensors with large aberrations according to claim 1, characterized in that, Step 3 specifically involves: First, perform total energy normalization on each sample. Then, extract the high signal-to-noise ratio pixels with the highest brightness in the sample according to a preset ratio. Use these pixels to calculate the weighted centroid and use it as the anchor center. Then, forcibly translate each sample to a unified reference coordinate center.

3. The method for low-dimensional manifold modeling and online template generation of spatial variation PSF for star sensors with large aberrations according to claim 1, characterized in that, Step 4 is as follows: Each 2D PSF sample is flattened into a column vector, and after subtracting the mean shape, a continuous mean-free sample matrix is ​​constructed. ; By analyzing the matrix Perform singular value decomposition to obtain the orthogonal subspace of aberration evolution: In the formula, For the mean-removed sample matrix An orthogonal matrix composed of the right singular vectors is used to characterize the relative combination relationship of different offline PSF samples on each singular component; T This represents the matrix transpose operation; It is an orthogonal matrix; It is a diagonal matrix.

4. The method for low-dimensional manifold modeling and online template generation of spatial variation PSF for star sensors with large aberrations according to claim 1, characterized in that, Step 5 specifically involves: For each offline sampling radius location, project its original sample onto... Within the eigenvalue subspace, the corresponding... A vector of coefficients.

5. The method for low-dimensional manifold modeling and online template generation of spatial variation PSF for star sensors with large aberrations according to claim 1, characterized in that, Step 7 specifically includes: During system operation, the radial position of the target star point in the field of view is first calculated based on the image plane coordinates of the target star point. ; Then, in the coefficient manifold lookup table The system retrieves neighboring sampling nodes and performs linear interpolation to obtain the estimated coefficient vector for the current position. : Then from the average template With each intrinsic template Perform a weighted linear combination to generate a static position-related template. : Finally, apply the azimuth angle to it. Rotation Operator This yields a position-related template that matches the observed star point.

6. The method for low-dimensional manifold modeling and online template generation of spatial variation PSF for star sensors with large aberrations according to claim 1, characterized in that, Step 8 specifically includes: If the star sensor system also has angular velocity information provided by the inertial sensor A motion blur kernel is constructed based on the two-dimensional displacement during the exposure time. and related templates for the above static positions Perform spatial convolution Generate dynamic location-related templates : 。

Images