Dark space target detection and initial orbit determination method and related equipment

Abstract

The invention discloses a dark space target detection and initial orbit determination method and related equipment, and relates to the technical field of space target optical detection and space situation awareness, and the method comprises the steps: constructing a dynamic point spread function model covering a full field of view, and determining the initial orbit based on the dynamic point spread function model; the method comprises the steps of generating an enhanced image for detecting a dark space target, generating a track signal profile sequence of each candidate point source, judging whether each candidate point source is the dark space target or not according to the track signal profile sequence of each candidate point source, obtaining the position of each dark space target and a corresponding timestamp, and determining whether the position of each candidate point source is the dark space target or not. And constructing an objective function containing orbit physical constraints and solving the objective function to obtain initial orbit state parameters of the dark space target. According to the method, the initial orbit state parameters can be rapidly and stably calculated under the extremely short observation arc section, the success rate and timeliness of short arc orbit determination are greatly improved, and the application requirements of rapid cataloguing and real-time response are met.

Description

A method and related equipment for target detection and initial trajectory determination in dimly lit spaces Technical Field

[0001] This invention relates to the field of optical detection of space targets and space situational awareness technology, and in particular to a method and related equipment for detecting and determining the initial orbit of a faint space target. Background Technology

[0002] Utilizing small- and medium-aperture ground-based optical telescopes for the detection and initial orbit determination of faint space targets is a cost-effective and important method in the field of space target surveying and cataloging, but it faces a series of severe technical challenges. These challenges are specifically reflected in three closely related stages: In the weak signal detection stage, faint space targets have extremely low signal-to-noise ratios in single-frame images, rendering traditional image processing methods ineffective; in the target identification stage, dynamic point spread function variations caused by large field-of-view optical systems result in severe stellar interference, making traditional stellar removal methods unreliable; and in the orbit determination stage, the extremely short observation arc leads to a high failure rate for traditional initial orbit determination methods, making it difficult to meet the requirements of rapid response. Therefore, there is an urgent need for a comprehensive technical solution that can collaboratively solve the challenges throughout the entire process from image processing and target identification to orbit calculation.

[0003] To address the aforementioned challenges, existing technologies offer several partial solutions. At the detection level, there are deep learning-based spatial target detection methods and moving target detection methods based on inter-frame difference. At the image preprocessing level, traditional methods employ single or fixed point spread function models for matched filtering to enhance the signal. At the trajectory determination level, traditional methods rely on classic algorithms such as the Laplacian method or the Gaussian method, or on long observation arcs and complex dynamic models. These techniques attempt to address some of the difficulties in processing faint targets from different perspectives.

[0004] However, these existing technologies all have significant limitations and cannot effectively address the aforementioned systemic challenges. Deep learning-based methods rely on massive amounts of labeled data and have poor model generalization ability; inter-frame difference methods further reduce the signal-to-noise ratio (SNR) when dealing with faint targets with a SNR below 3, leading to missed detections. Traditional point spread function (PSF) modeling methods cannot adapt to dynamic PSFs that change significantly with the field of view in large fields of view, resulting in poor matched filtering performance. Traditional initial orbit determination methods suffer from high failure rates or huge errors when dealing with extremely short observation arcs and very limited observation data, failing to meet the real-time requirements of rapid cataloging and collision warning. Existing technologies often handle detection or orbit determination problems in isolation, lacking an integrated solution that deeply integrates image preprocessing, target detection, and initial orbit determination based on the characteristics of the observation data.

[0005] In summary, existing technologies struggle to achieve highly sensitive detection of faint space targets with a signal-to-noise ratio below 3 and rapid, high-success-rate initial orbit determination based on extremely short arc segments when using small-to-medium aperture ground-based optical telescopes with small pixel sizes and large fields of view. Therefore, there is an urgent need for an innovative method specifically optimized for the optical and observational characteristics of such telescopes, capable of synergistically improving detection and orbit determination performance. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to address the shortcomings of the prior art. Specifically, it provides a method and related equipment for detecting and determining the initial orbit of targets in dark space, as follows: 1) In a first aspect, the present invention provides a method for detecting and determining the initial orbit of targets in dark space, the specific technical solution of which is as follows: Based on the sequence images of the observed area of ​​the targets in dark space, a dynamic point spread function model covering the entire field of view is constructed; based on the dynamic point spread function model, the position of each pixel in the sequence image is processed to generate an enhanced image for detecting targets in dark space; multiple candidate point sources of targets in dark space are extracted from the enhanced image, and a trajectory signal profile sequence of each candidate point source is generated; based on the trajectory signal profile sequence of each candidate point source, it is determined whether each candidate point source is a target in dark space, and the position and corresponding timestamp of each target in dark space are obtained; using the position and timestamp of the targets in dark space as observations, an objective function containing orbital physical constraints is constructed and solved to obtain the initial orbital state parameters of the targets in dark space.

[0007] The beneficial effects of the faint space target detection and initial orbit determination method provided by this invention are as follows: By constructing a dynamic point spread function model covering the entire field of view and performing position-aware matched filtering, this method effectively overcomes the problem of star point morphology changes caused by large field-of-view aberrations, significantly improving the detection capability of faint space targets with a signal-to-noise ratio below 3. Using trajectory signal profile sequences for moving target confirmation fundamentally avoids the complex and unreliable star removal steps, preventing the risk of falsely removing real targets and simplifying the processing flow. By using the position and timestamp of the faint space target as observations and constructing an objective function containing orbital physical constraints for solution, this method transforms the classic initial orbit determination problem into a single-parameter search for the initial geocentric distance. Combined with an adaptive optimization algorithm, it can achieve fast and stable initial orbit state parameter calculation in extremely short observation arcs, greatly improving the success rate and timeliness of short-arc orbit determination, and meeting the application requirements of rapid cataloging and real-time response.

[0008] 2) In a second aspect, the present invention also provides a system for detecting and determining the initial orbit of a target in dim space, the specific technical solution of which is as follows: It includes a model building module, an enhanced image generation module, a trajectory signal profile sequence generation module, a position timestamp acquisition module, and an initial orbit state parameter acquisition module; the model building module is used to: construct a dynamic point spread function model covering the entire field of view based on the sequence images of the observed area of ​​the dim space target; the enhanced image generation module is used to: process the position of each pixel in the sequence image based on the dynamic point spread function model to generate an enhanced image for detecting dim space targets; the trajectory signal profile sequence generation module is used to: extract multiple candidate point sources of dim space targets from the enhanced image and generate a trajectory signal profile sequence for each candidate point source; the position timestamp acquisition module is used to: determine whether each candidate point source is a dim space target based on the trajectory signal profile sequence of each candidate point source, and obtain the position and corresponding timestamp of each dim space target; the initial orbit state parameter acquisition module is used to: use the position and timestamp of the dim space target as observations, construct an objective function containing orbital physical constraints and solve it to obtain the initial orbit state parameters of the dim space target.

[0009] 3) In a third aspect, the present invention also provides an electronic device, the electronic device including a processor coupled to a memory, the memory storing at least one computer program, the at least one computer program being loaded and executed by the processor, so that the electronic device implements any of the above-mentioned methods for detecting targets in dim space and determining initial orbits.

[0010] 4) In a fourth aspect, the present invention also provides a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements any of the above-described methods for detecting targets in dim space and determining initial orbits.

[0011] It should be noted that the beneficial effects of the technical solutions of the second to fourth aspects of the present invention and their corresponding possible implementations can be found in the above description of the technical effects of the first aspect and its corresponding possible implementations, and will not be repeated here. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments of the present invention will be briefly introduced below: Figure 1 is a flowchart of a method for detecting targets in dim space and determining initial orbits according to an embodiment of the present invention; Figure 2 is a structural diagram of a system for detecting targets in dim space and determining initial orbits according to an embodiment of the present invention. Detailed Implementation

[0013] The principles and features of the present invention are described below. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0014] The technical solution of the present invention and how the technical solution of the present invention solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of the present invention will now be described with reference to the accompanying drawings.

[0015] As shown in Figure 1, an embodiment of the present invention provides a method for detecting and determining the initial orbit of a faint space target, comprising the following steps: S1. Based on the acquired sequence of images of the faint space target observation area, a dynamic point spread function model covering the entire field of view is constructed. Specifically, from the sequence of images of the faint space target observation area acquired by a ground-based optical telescope, multiple isolated stars distributed at different field-of-view positions are selected. Point spread function fitting is performed on each isolated star, and the morphological parameters of the point spread function of each isolated star are extracted. Based on the field-of-view coordinates of each isolated star and the corresponding morphological parameters of the point spread function, a dynamic point spread function model covering the entire field of view is constructed. By directly utilizing the isolated star data in the observation sequence images, a dynamic point spread function model related to the field of view position is constructed, effectively solving the problem of the point spread function morphology changing with the field of view position in a large field-of-view optical system. The model established based on the mapping relationship between the field of view coordinates and the point spread function morphological parameters can accurately describe and predict the point spread function morphology at any position within the entire field of view. This provides an accurate basis for subsequent position-aware matched filtering, thereby significantly enhancing the ability to extract dark and weak point signals with consistent morphology and overcoming the shortcomings of traditional single models that cannot adapt to the entire field of view.

[0016] The specific implementation process of S1 is as follows: S10. Select sample stars for modeling from the sequence of images of the space target observation area acquired by the ground-based optical telescope. Usually, the first frame of the image sequence or the frame with the highest signal-to-noise ratio is selected as the source image. On this image, at least twenty isolated stars distributed at different positions in the field of view are identified and selected through an automatic star detection algorithm or in combination with star catalog assistance. When selecting, it is necessary to ensure that these isolated stars are relatively uniformly distributed in the entire field of view, covering representative areas such as the center, edge, and four corners of the field of view, and covering different brightness levels from brighter to darker, so as to ensure that the sampling can fully reflect the changing trend of the point spread function morphology with the field of view position and signal intensity.

[0017] S11. For each isolated star, a sufficiently large sub-image region is extracted, centered on its estimated centroid position in the image. A pre-defined mathematical model, such as a two-dimensional elliptic Gaussian function or the Moffat function, is used to fit the surface distribution of pixel gray values ​​within this sub-image region. The fitting process employs optimization algorithms such as nonlinear least squares to adjust the model parameters, ensuring the function surface best matches the actual pixel gray values ​​of the star image point, thereby obtaining a precise mathematical expression describing the morphology of the star's spread function.

[0018] S12. For cases where a two-dimensional elliptic Gaussian function is used for fitting, the morphological parameters can be directly calculated from the fitted function parameters. These morphological parameters typically include the full width at half maximum (FWHM), ellipticity, and principal axis direction. The FWHM describes the concentration and magnitude of the energy distribution of the star image on the two-dimensional plane; the ellipticity describes the flattening of the star image and is a dimensionless quantity; the principal axis direction describes the pointing angle of the major axis of the star image ellipse in the image plane. These parameters collectively quantify the specific morphological characteristics of the point spread function at a particular field of view location.

[0019] S13. Record the field-of-view coordinates for each isolated star used for modeling. Field-of-view coordinates refer to the position coordinates of the star's image point on the detector plane, usually represented by pixel coordinates, but can also be converted into normalized angular coordinates with the center of the field of view as the origin. These coordinates precisely mark the specific position of each sample star in the telescope's full field of view, forming a one-to-one correspondence with the morphological parameters of the point spread function extracted from that star, providing input data for subsequent construction of models of spatial variations.

[0020] S14. Based on the field-of-view coordinates of all sample points and the corresponding point spread function (PSF) morphological parameters, a dynamic PSF model covering the entire field of view is constructed. This step employs spatial interpolation or regression methods. Specifically, the field-of-view coordinates of each sample point are used as the independent variable, and the PSF morphological parameters are used as the dependent variable. For example, independent interpolation models can be established for the three morphological parameters: full width at half maximum (FWHM), ellipticity, and principal axis direction. Thin-plate spline interpolation or polynomial regression methods are used to learn the mapping relationship from any field-of-view coordinate to the morphological parameters at that coordinate. The final dynamic PSF model is a mathematical function or a set of functions. Inputting the coordinates of any position within the field of view, the model can output the predicted PSF morphological parameters at that position, thus describing the dynamic changes of the PSF morphology with the field of view position.

[0021] The faint space target observation area refers to the region of the sky that a ground-based optical telescope points to and images from at a specific time. This area is the target sky region of the observation plan, expected to contain space targets with extremely weak signals that need to be detected, such as geostationary orbit debris or low-Earth orbit debris. By adjusting its pointing, the telescope images the light from this region onto the detector, forming a sequence of images.

[0022] The field of view (FOP) refers to the specific location of a particular point within the sky region observed by the telescope, or on a single frame of an image. It describes the spatial relationship of a point target relative to the entire observable range and is typically represented using two-dimensional coordinates. In an image, each pixel corresponds to a unique FOP.

[0023] Isolated stars refer to stellar images in a single frame of astronomical imagery that are relatively bright and free from interference from other nearby stars of similar brightness or other point light sources within their point spread function's influence range. Selecting isolated stars ensures the acquisition of pure point spread function samples unaffected by nearby light sources, thereby guaranteeing the accuracy of the extracted morphological parameters.

[0024] The point spread function (PSF) is the brightness distribution function of an optical imaging system image of an ideal point light source. It describes how the light energy of a point light source diffuses across the imaging plane due to the combined effects of optical system aberrations, diffraction, and atmospheric turbulence. The shape of the PSF determines the size, shape, and brightness distribution characteristics of the star image.

[0025] The morphological parameters of the point spread function (PSF) are a set of numerical indicators used to quantitatively describe the specific shape and size of the PSF. These parameters typically include full width at half maximum (FWHM), ellipticity, and principal axis orientation. They mathematically characterize the spatial distribution of the PSF and are key to quantitatively expressing its morphology.

[0026] Field-of-view coordinates are a set of values ​​used to precisely determine the position of the field of view. In digital images, the row and column numbers of pixels are usually used as field-of-view coordinates. Alternatively, based on the telescope's calibration parameters, pixel coordinates can be converted to celestial coordinates in arcseconds or degrees, relative to the center of the field of view or a reference point.

[0027] The full field of view (FLP) refers to the complete area of ​​the sky that can be observed in a single exposure by a ground-based optical telescope using a specific detector. It is a two-dimensional angular concept; for example, the FLP is greater than or equal to 2.6° multiplied by 2.6°. The FLP encompasses the sky area corresponding to all pixels in an image.

[0028] The dynamic point spread function (PSF) model is a mathematical model that describes how the morphological parameters of the PSF continuously change with the field of view. This model establishes a mapping relationship that can predict the PSF morphology at any unknown location within the entire field of view by learning from a finite number of PSF morphological parameter samples at known field of view locations. This solves the problem of inconsistent PSF morphology in large field-of-view optical systems.

[0029] S2. Based on a dynamic point spread function (PSF) model, each pixel in the image sequence is processed to generate an enhanced image for detecting weak spatial targets. Specifically, based on the dynamic PSF model, a corresponding PSF matched filter kernel is dynamically generated for each pixel in the image sequence and convolutional filtering is performed to obtain a matched-filtered image sequence. Then, background subtraction and image registration are performed on each frame of the matched-filtered image sequence, and the registered multi-frame images are superimposed to form an enhanced image for detecting weak spatial targets. By dynamically generating a matched filter kernel for each pixel, optimal matching with the locally varying PSF morphology is achieved, thereby maximizing the enhancement of weak point signals with consistent morphology across the entire field of view during convolutional filtering. Background subtraction and image registration on the filtered image sequence eliminate non-target background and correct inter-frame displacement, creating conditions for signal superposition. The final multi-frame image superposition effectively suppresses random noise, accumulates and highlights the signal of weak spatial targets, and ultimately generates an enhanced image with a significantly improved signal-to-noise ratio, laying a solid foundation for subsequent reliable detection.

[0030] The specific implementation process of S2 is as follows: S20. Based on the dynamic point spread function model, a point spread function matching filter kernel is dynamically generated for each pixel position in the sequence image. Specifically, for each frame of the input image sequence, each pixel position is traversed. Based on the field coordinates of the pixel, the previously constructed dynamic point spread function model is queried. After receiving the field coordinate input, the dynamic point spread function model outputs the predicted morphological parameters of the point spread function applicable to that position, mainly including the full width at half maximum (FWHM), ellipticity, and principal axis direction. Using these morphological parameters, a discrete two-dimensional digital matrix can be constructed as the point spread function matching filter kernel. This filter kernel matches the ideal point spread function predicted locally in terms of morphology, and its value is usually normalized so that the convolution operation can enhance the point signal with the same morphology as the local point spread function.

[0031] S21. For each pixel in the image, a point spread function matched filter kernel specifically generated for its location is used to perform a two-dimensional convolution operation within a local neighborhood centered on that pixel. The convolution calculation multiplies the value of the filter kernel by the gray value of the corresponding pixel and sums the results, which serve as the new gray value of that pixel in the output image. This operation is performed pixel by pixel in the entire frame, generating an image that has undergone position-aware matched filtering. This process is performed independently for each frame of the original image in the sequence, ultimately resulting in a matched-filtered image sequence with the same number of frames as the original sequence.

[0032] S22. Background subtraction is performed on each frame of the matched-filtered image sequence. In addition to point source signals such as stars and space objects, astronomical images also contain a non-uniform background composed of sky background light, detector dark current, and bias. For each frame of the matched-filtered image, a background estimation algorithm is used to estimate this background value. A common method involves using a large-sized filtering window to traverse the image, calculating the median or mean of the pixels within the window as the background estimate for the window's center point, thus generating a background estimation map with the same size as the original image. Finally, the corresponding background estimation map is subtracted from the matched-filtered image to obtain the background-subtracted image, making the point source signals more prominent.

[0033] S23. Due to telescope tracking errors or minute variations in atmospheric refraction, the positions of stars in each frame of a sequence may drift at the sub-pixel level. The purpose of image registration is to correct this inter-frame displacement, aligning the star positions in all images of the sequence. One frame is selected as a reference frame, and a spatial transformation model is calculated for each frame to be registered. By matching multiple identical star points in two frames, transformation parameters representing translation, rotation, or more complex deformations can be calculated. These transformation parameters are then used to resample or transform the coordinates of each frame, ensuring that the stars in all images are precisely aligned to the coordinates of the reference frame, generating a registered image sequence.

[0034] S24. All corresponding pixels in the registered image sequence are numerically synthesized. To effectively suppress random noise and preserve the true signal, a 3σ cropped mean method is used for superposition. For each output pixel position in the superimposed image, the average and standard deviation of the pixel values ​​at that position across all frames in the registered sequence are calculated. Outlier frames whose pixel values ​​exceed the average by ±3 times the standard deviation are removed. Then, the average value is recalculated using the pixel values ​​of the remaining frames at that position, and this recalculated value is used as the output value of the final superimposed image at that pixel. This process iterates through all pixel positions, ultimately forming an enhanced image with a significantly improved signal-to-noise ratio, suitable for detecting targets in dimly lit spaces.

[0035] The filter kernel is a small two-dimensional numerical matrix used for image convolution operations. In image processing, the convolution operation achieves effects such as image filtering, enhancement, or feature extraction by sliding the filter kernel across the image and performing a weighted sum with local pixels. In this invention, the point spread function matching filter kernel is generated based on the predicted morphological parameters of the point spread function. Its shape and numerical distribution are designed to match the local ideal point spread function, thus serving as a matching template to enhance point-like target signals with similar morphologies.

[0036] Background subtraction is a digital image processing step that removes background or non-target signal components from astronomical images. These background components mainly originate from light pollution from night sky light, dark current in detectors, and electronic bias. Background subtraction is achieved by estimating the background value at each pixel location in the image and subtracting this estimate from the original pixel value. After background subtraction, the remaining signals in the image mainly correspond to celestial objects such as stars and space targets, as well as random noise, which is beneficial for subsequent detection and measurement of point source targets.

[0037] Image registration refers to the process of geometrically aligning two or more images of the same scene acquired at different times, from different perspectives, or by different sensors. In astronomical image processing, image registration is often used to correct minor shifts in the positions of the same star between frames caused by imperfect telescope tracking, atmospheric disturbances, or instrument distortion. By calculating and applying a spatial coordinate transformation, image registration aligns all star points in a sequence of images to the same reference coordinate system, providing an accurate data basis for subsequent image overlay or change detection.

[0038] S3. Extract multiple candidate point sources of faint space targets from the enhanced image, and generate a trajectory signal profile sequence for each candidate point source. Specifically, extract multiple candidate point sources of faint space targets from the enhanced image. For each candidate point source, set multiple velocity assumptions of uniform linear motion. For each velocity assumption, extract signal values ​​along the trajectory corresponding to that velocity assumption in the matched-filtered image sequence to generate the trajectory signal profile sequence for that candidate point source. By setting multiple velocity assumptions for each candidate point source and extracting trajectory signal values ​​from the matched-filtered image sequence to generate the trajectory signal profile sequence, the target detection process is directly correlated with its motion characteristics. This method does not rely on external star catalogs for complex star matching and elimination, but extracts signals directly from the raw data based on motion trajectory assumptions. For real space moving targets, the sequence extracted under the correct velocity assumption will exhibit periodic high signals; for stationary stars, any sequence under a non-zero velocity assumption will appear as noise. This achieves highly reliable confirmation of faint moving targets against a strong stellar background.

[0039] The specific implementation process of S3 is as follows: S30, Extract candidate point sources of multiple weak spatial targets from the enhanced image. The enhanced image is a single image with a high signal-to-noise ratio formed after dynamic point spread function matched filtering, background subtraction, image registration, and overlay processing. On this enhanced image, digital image processing algorithms are used to identify all potential point signals. A common method is local peak search, which involves scanning the entire image and marking pixels with gray values ​​higher than all pixels in their surrounding neighborhood as candidates. Another method is connected component analysis, which involves binarizing the image by setting a low gray threshold, marking interconnected pixel regions as objects, and calculating the centroid of each object as the position of the candidate point source. Regardless of the method used, the precise pixel coordinates of each nominated candidate point source in the enhanced image need to be recorded as the initial position for subsequent processing steps.

[0040] S31. For each extracted candidate point source, set multiple velocity assumptions for uniform linear motion. Each velocity assumption is a two-dimensional vector representing the number of pixels the point source moves per frame along the x and y axes in the image plane. The setting of velocity assumptions needs to be based on the actual observation conditions. Consider the telescope's tracking mode, such as in star tracking mode where the background stars are stationary while the space target moves. Determine a reasonable velocity search range based on the telescope's maximum tracking speed and the possible orbital types of the observed space target. For example, for a geostationary orbit target, its angular velocity is relatively small, and the corresponding image plane velocity range may be between ±1.2 pixels per frame. Within this velocity range, perform systematic sampling with a certain step size, or randomly sample in the velocity space, to generate a series of discrete velocity assumptions. For each candidate point source, this same set of velocity assumptions will be traversed, assuming that it may be moving at a uniform linear velocity at each of these speeds.

[0041] S32. For each candidate point source and its velocity hypothesis, extract signal values ​​from the matched-filtered image sequence to construct a trajectory. Here, we use an unstacked image sequence that has only undergone dynamic point spread function matched filtering and background subtraction. For a given candidate point source and its velocity hypothesis, the hypothetical position of the point source in each frame can be deduced. The deduction method uses the coordinates of the candidate point in the enhanced image as its starting position in a reference frame, and calculates its expected position in each of the remaining frames based on the hypothetical velocity vector and the inter-frame time interval. For each frame in the sequence, extract pixel grayscale values ​​within a fixed-size region centered on the hypothetical position coordinates of that frame. This region can be 3×3 pixels. The extracted pixel values ​​can be the sum or average of the pixel grayscale values ​​within this region, serving as a scalar representing the signal strength of that frame. This extraction operation is repeated for each frame of the image sequence.

[0042] S33. Generate the trajectory signal profile sequence of the candidate point source under the assumed velocity. The signal values ​​extracted from each frame of the image sequence are arranged chronologically to form a one-dimensional sequence, which is the trajectory signal profile sequence. It describes the change in signal intensity over time along the trajectory of a point source moving at the currently assumed velocity, on the un-superimposed original filtered image sequence. For a real spatial target, if the assumed velocity is close to its actual velocity, the extracted signal value will be higher in the frames traversed by its actual trajectory, and will have a certain degree of matching with the locally predicted point spread function shape; while in other frames, the extracted signal value will be close to the background noise level. For false candidate points caused by stars or noise, under any non-zero velocity assumption, its trajectory signal profile sequence will appear as random noise, without any periodic peaks related to the motion trajectory. By generating such a trajectory signal profile sequence for each velocity assumption of each candidate point source, basic data is provided for subsequent trajectory likelihood determination.

[0043] Candidate point sources are potential target signal locations with point-like morphological features identified by automatic algorithms during the image enhancement processing stage. These locations may be real spatial targets, or they may be residual noise fluctuations, incompletely subtracted stellar side lobes, or image defects. The purpose of extracting candidate point sources is to provide an initial list of targets that needs further verification for subsequent, more refined motion analysis, avoiding the omission of any possible targets.

[0044] The velocity hypothesis is a conjecture about the velocity of a candidate point source within the image plane, proposed to test whether it is a moving spatial object. Each velocity hypothesis is a specific two-dimensional motion vector. By setting a series of velocity hypotheses covering the possible range of motion for each candidate point source, the signal performance of the candidate point under different motion modes is systematically tested, thereby distinguishing moving objects from stationary stars.

[0045] The trajectory signal profile sequence refers to the signal intensity sequence extracted frame by frame from the original image sequence after matched filtering, along the motion trajectory determined by the velocity assumption, for a specific candidate point source and a specific velocity assumption. The morphological characteristics of this sequence are the key basis for determining the authenticity of the candidate point source and measuring its true velocity. The trajectory signal profile sequence generated by a real moving target under its correct velocity assumption will show periodic high signal segments.

[0046] In this context, the signal value refers to a numerical value extracted from a specific region of a digital image to characterize the signal intensity of that region. Specifically, in the context of this invention, the signal value refers to a representative value calculated from a small region (e.g., 3×3 pixels) centered on an imaginary trajectory point in a matched-filtered image sequence; for example, the sum or average of the grayscale values ​​of all pixels within that region. This value reflects the intensity level of point source signals that may exist in the image at that location and time.

[0047] S4. Based on the trajectory signal profile sequence of each candidate point source, determine whether each candidate point source is a target in a dark space, and obtain the position and corresponding timestamp of each target. Specifically, for each candidate point source, based on the trajectory signal profile sequence corresponding to each velocity assumption, calculate the matching degree and average signal-to-noise ratio between each trajectory signal profile sequence and the locally predicted point spread function shape. Determine the maximum trajectory likelihood and its corresponding velocity vector based on a weighted sum. If the maximum trajectory likelihood exceeds a preset threshold, the candidate point source is confirmed as a target in a dark space, and the position and corresponding timestamp of the target in each frame of the original image are output. By comprehensively evaluating the matching degree and average signal-to-noise ratio between the trajectory signal profile sequence and the locally predicted point spread function shape, and calculating the maximum trajectory likelihood by weighting, an objective and quantitative judgment on whether a candidate point source is a real target in a dark space is achieved. Making a confirmation decision based on whether the maximum trajectory likelihood exceeds a preset threshold ensures the controllability and reliability of the target confirmation process. For the confirmed target, its precise position and corresponding timestamp in each frame of the original image are output synchronously, providing direct and accurate observations for subsequent initial trajectory determination and avoiding the introduction of additional errors in intermediate steps.

[0048] The specific implementation process of S4 is as follows: S40. For a specific velocity assumption of a candidate point source, calculate the matching degree between its trajectory signal profile sequence and the locally predicted point spread function shape. The locally predicted point spread function shape is given by the dynamic point spread function model at each point of the trajectory. For a trajectory signal profile sequence, the signal value in each frame comes from a 3×3 pixel region centered on the hypothetical position of that frame. To evaluate the consistency between the signal distribution in this region and the locally predicted shape, an ideal point spread function template that matches the predicted shape parameters can be constructed. This template is similar to the kernel used for matched filtering. Then, the normalized cross-correlation coefficient between the actual pixel gray value distribution of the 3×3 region and this ideal template is calculated. The higher the correlation coefficient, the better the extracted signal shape matches the locally predicted point spread function shape. For all frames in this trajectory signal profile sequence (except for frames that are completely noisy), the correlation coefficient is calculated and the average value is taken as the overall matching degree index of the trajectory signal profile sequence under this velocity assumption.

[0049] S41. Calculate the average signal-to-noise ratio (SNR) of the same trajectory signal profile sequence. For each frame in the sequence, the signal value is taken from the sum or mean of the pixel grayscale values ​​of a 3×3 region. The local background noise level of this region needs to be estimated, which can be obtained by calculating the standard deviation of the pixels in the annular background region near the target area in that frame. Therefore, the SNR of that frame can be defined as the signal value minus the local background mean, divided by the local background noise standard deviation. By traversing all frames in the trajectory signal profile sequence and averaging the SNR of all frames, the average SNR of the trajectory signal profile sequence under this velocity assumption is obtained. The average SNR reflects the overall level of signal strength extracted along the assumed trajectory relative to the noise.

[0050] S42. Determine the trajectory likelihood for each velocity hypothesis based on a weighted sum. For each velocity hypothesis, two evaluation metrics are now available: the degree of matching between the sequence and the locally predicted point spread function morphology, and the average signal-to-noise ratio (SNR) of the sequence. The trajectory likelihood is a single score combining these two metrics, calculated as follows: Trajectory likelihood equals the matching degree multiplied by a weighting coefficient A plus the average SNR multiplied by a weighting coefficient B. Weighting coefficients A and B are pre-set positive numbers used to balance the relative importance of morphology matching and signal strength in the discrimination. Through this weighted calculation, a trajectory likelihood value is assigned to each velocity hypothesis of the candidate point source.

[0051] S43. Traverse all velocity hypotheses and determine the maximum trajectory likelihood and its corresponding velocity vector. Each velocity hypothesis for a candidate point source corresponds to a calculated trajectory likelihood value. Search for and find the maximum value among these values; this maximum value is the maximum trajectory likelihood. Record the velocity hypothesis used to reach this maximum trajectory likelihood; the two-dimensional motion vector defined by this velocity hypothesis is the corresponding velocity vector. This velocity vector represents the velocity conjecture within the image plane that makes the extracted signal sequence most resemble the actual point source trajectory.

[0052] S44. Target confirmation based on maximum trajectory likelihood. A preset threshold, determined through experiments or simulations, is set. The obtained maximum trajectory likelihood is compared with this preset threshold. If the maximum trajectory likelihood exceeds the preset threshold, the candidate point source is determined to be a real, faint spatial target. This is because only real spatial targets, under the assumption of approaching their true velocity, will simultaneously produce high morphological matching and average signal-to-noise ratio, thus causing the trajectory likelihood to exceed the discrimination threshold. Conversely, if the maximum trajectory likelihood does not exceed the preset threshold, the candidate point source is determined to be noise or a false detection and is discarded.

[0053] S45. Output the position and corresponding timestamp of the confirmed faint spatial target in each frame of the original image. For a confirmed target, its corresponding velocity vector is considered the best estimate of its planar motion velocity in the measured image. Using this velocity vector and the initial candidate point source position of the target in the enhanced image, its precise centroid position in each frame of the unprocessed original image can be calculated backtrackingly. The transformation parameters of image registration are considered during the calculation, and the position is uniformly backtracked to the original image coordinate system. At the same time, the midpoint time of the exposure of each frame is recorded as the corresponding timestamp. The final output is a set of position coordinates and a set of precise timestamps for the target in each frame of the observation sequence. These data will be used as the observations for the next step of initial trajectory determination.

[0054] The locally predicted point spread function morphology refers to the specific shape and size characteristics that the point spread function should have at a specific pixel location in an image sequence, as predicted by the dynamic point spread function model. This prediction is described by morphological parameters calculated by an interpolation model based on the field-of-view coordinates at that location. It represents the theoretical brightness distribution pattern that an ideal point source should have after imaging at that location, and serves as a standard template for evaluating whether the actual extracted signal originates from a point source.

[0055] The maximum trajectory likelihood refers to the highest trajectory likelihood score obtained by calculating the weighted sum of the matching degree of the trajectory signal profile sequence and the average signal-to-noise ratio under all tested velocity assumptions for a candidate point source. This maximum value comprehensively reflects the degree to which the signal performance of the candidate point source matches the characteristics of the real moving point source under the optimal motion velocity assumption, and is the core numerical indicator for distinguishing between real and false targets.

[0056] Here, the velocity vector specifically refers to the velocity hypothesis that maximizes the trajectory likelihood of the candidate point source. It is a two-dimensional vector containing velocity components along the x and y axes of the image plane, typically in pixels per frame. This velocity vector is considered the closest estimate of the motion of the target in a dark space and is used for subsequent target location backtracking calculations.

[0057] Among them, faint space targets refer to space objects whose signals are extremely weak and whose signal-to-noise ratio is less than 3 in a single frame of optical observation image, such as small geostationary orbit debris or low orbit debris. The optical signals of such targets are easily drowned out by the noise of the detector, making them difficult to detect and identify directly using traditional image processing methods.

[0058] In this context, the position and corresponding timestamp of a faint spatial target in each frame of the original image refer to the target's precise two-dimensional coordinates on each frame of the original image without any geometric correction within the observation time series, along with the absolute time information corresponding to the exposure of that frame. Position coordinates are typically expressed in pixels and can be converted to celestial coordinates (right ascension and declination) using the telescope's calibration parameters. Timestamps are usually in International Standard Time (UST). This set of position and timestamp data constitutes the most basic measurement of the target's angular motion on the celestial sphere and is the direct input required for initial orbit determination.

[0059] S5. Using the position and timestamp of the faint space target as observations, an objective function incorporating orbital physical constraints is constructed and solved to obtain the initial orbital state parameters of the faint space target. Specifically, using the position and timestamp of the faint space target as observations, and based on the conservation of angular momentum and the orbital energy equation, the orbit determination is parameterized into a single-parameter search problem for the initial geocentric distance. An objective function incorporating orbital physical constraints is constructed, and an adaptive moment estimation algorithm is used to optimize and solve the objective function to obtain the initial orbital state parameters of the faint space target. By utilizing the conservation of angular momentum and the orbital energy equation to parameterize the complex orbit determination problem into a single-parameter search for the initial geocentric distance, the dimensionality and complexity of the solution are significantly reduced. Constructing an objective function incorporating orbital physical constraints ensures the physical rationality of the solution. The use of an adaptive moment estimation algorithm for efficient optimization enables rapid and stable convergence to the optimal solution under conditions of extremely short observation arcs and limited computational resources, thereby reliably obtaining the initial orbital state parameters of the faint space target and effectively improving the success rate and timeliness of short-arc orbit determination.

[0060] The specific implementation process of S5 is as follows: S50, Prepare the observations and establish the error model. The input data is the position and corresponding timestamp of the faint spatial target in each frame of the original image output from the previous processing stage. These positions need to be converted from pixel coordinates to right ascension and declination angles with the geocentric inertial frame as the reference, based on the telescope's optical system and detector parameters. Each observation time corresponds to a set of right ascension and declination, constituting the basic angular position observations. At the same time, reasonable error weights need to be assigned to these observations. Using the telescope's known pointing accuracy better than 10 arcseconds and repeatability better than 30 arcseconds, a measurement error standard deviation can be estimated for each angular observation value, forming an error covariance matrix, which is used to measure the reliability of different observation data in subsequent optimization.

[0061] S51. Based on physical laws, the six-parameter orbit determination problem is simplified to a single-parameter search for the initial geocentric distance. Traditional initial orbit determination requires solving for six orbital elements, but for extremely short observation arcs, observational information is severely insufficient. Here, we utilize the approximately invariant geometric properties of the orbital surface within short arcs, combined with the principle of conservation of angular momentum and the orbital energy equation expressed by the Vis-viva equation. Specific derivation shows that, under given angular observation conditions, the position and velocity vectors of the target at the beginning of the observation arc can be determined by observation geometry, except for a common scale factor. This key scale factor is the initial geocentric distance, i.e., the radial distance of the target relative to the Earth's center at the initial observation time. By setting the initial geocentric distance as the only free parameter to be searched, the complete three-dimensional position vector at the beginning of observation and the velocity vector constrained by physical laws can both be expressed as functions of this initial geocentric distance parameter.

[0062] S52. Construct an objective function that incorporates orbital physics constraints. The objective function evaluates the quality of a hypothetical initial geocentric distance value. For a test initial geocentric distance value, first calculate the corresponding initial position and velocity vector, i.e., a complete orbital state. Then, starting from this initial state, use a simple two-body orbital dynamics model to predict the theoretical right ascension and declination of the target at subsequent observation times. Next, calculate the residuals between these theoretical predictions and actual observations, and weight them using the error covariance matrix established in step one to obtain a fitting residual term. In addition to the fitting residuals, the objective function must also incorporate orbital physics constraints. These constraints include: the total orbital energy must be negative to ensure an elliptical orbit around the Earth; the perigee altitude calculated from this orbital state must be greater than the Earth's radius to avoid unreasonable collision trajectories. Test solutions that violate these physical constraints will be subject to a very large penalty term. Finally, the objective function is the sum of the observation fitting residuals and the physical constraint penalty term, and the goal is to minimize this function value.

[0063] S53. The adaptive moment estimation algorithm is used to optimize the objective function. The adaptive moment estimation algorithm is an iterative optimization algorithm for function minimization. The optimization process begins with a randomly selected initial geocentric distance guess, or one set based on prior information. In each iteration, the algorithm calculates the gradient of the objective function at the current parameter value and dynamically adjusts the learning step size of each parameter using the first and second moment estimates of the gradient. This adaptive step size mechanism allows the algorithm to efficiently search different regions of the parameter space. The optimization process continues until the change in the function value is less than a certain tolerance or the preset maximum number of iterations is reached. The initial geocentric distance parameter value corresponding to the final convergence is the optimal solution that minimizes the objective function.

[0064] S54. Calculate the complete initial orbital state parameters from the optimal parameters. After the adaptive moment estimation algorithm finds the optimal initial geocentric distance that minimizes the objective function, substitute this optimal value into the formula in step S52 to directly calculate the precise position and velocity vectors of the target in the geocentric inertial coordinate system at the initial observation time. This set of position and velocity vectors constitutes the determined initial orbital state. If necessary, these rectangular coordinate state parameters can be converted into standard Keplerian orbital elements, including the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of perigee, and mean perigee. These initial orbital state parameters serve as the final output of the method of this invention and can be used for target cataloging or collision warning analysis.

[0065] Among them, the conservation of angular momentum and the orbital energy equation are two fundamental physical laws describing the motion of objects in Earth's orbit. The law of conservation of angular momentum states that in an ideal two-body system acted upon only by the central gravitational force, the orbital angular momentum vector of an object remains constant. The orbital energy equation, also known as the Vis-viva equation, establishes the mathematical relationship between the velocity at any point on the orbit, the distance of the current position from the Earth's center, and the semi-major axis of the orbit. These two laws together form the theoretical foundation connecting short-arc observation geometry with orbital dynamics.

[0066] The initial geocentric distance refers to the straight-line distance between the observed faint space target and the Earth's center of mass at the beginning of the observation arc. This is a scalar value, usually measured in kilometers. In the geometric model of short-arc orbit determination, the initial geocentric distance is a key unknown scale parameter that determines the target's absolute position in three-dimensional space, not just its angle along the line of sight.

[0067] The single-parameter search problem for the initial geocentric distance refers to reformulating the multi-dimensional parameter optimization problem of determining the complete initial orbit into a mathematical problem that searches and optimizes only a single parameter, namely the initial geocentric distance, through physical and geometric relationships. This parameterization significantly reduces the dimensionality of the problem, making it more suitable for the characteristics of limited observation data in extremely short arc segments, and improving the stability and efficiency of the solution.

[0068] Orbital physical constraints refer to the fundamental physical and geometric conditions that any real Earth orbit must satisfy. These constraints include the requirement that the total orbital energy must be negative, ensuring that the orbit is elliptical rather than parabolic or hyperbolic; and the requirement that the perigee altitude must be greater than the Earth's radius, ensuring that the object will not be on an impossible orbit intersecting with the solid portion of the Earth. These constraints exclude physically impossible solutions from the mathematical solution space.

[0069] The objective function, which incorporates orbital physical constraints, is a mathematical function used to evaluate the quality of the orbital solution. It combines the goodness of fit to the observed data with the degree to which the orbital physical constraints are satisfied. The smaller the function value, the better the corresponding orbital assumption fits the observed angular data, and it is also a physically realistic and reasonable orbit. The goal of the optimization process is to find the parameters that minimize this function value.

[0070] The adaptive moment estimation algorithm is a first-order iterative optimization algorithm, particularly suitable for parameter space searches involving noisy or non-stationary objective functions. This algorithm adaptively adjusts the learning rate for each parameter by calculating the exponential moving average of the first and second moments of the gradient, thus achieving fast and relatively robust convergence. In this invention, it is used to efficiently minimize a complex objective function with respect to the initial geocentric distance.

[0071] The initial orbital state parameters refer to a set of parameters that can completely describe the orbital motion of a faint space target at a specific epoch. It can typically be represented as the position and velocity vectors at that epoch, or equivalently, a set of six Keplerian orbital elements. These parameters are the final output of the orbit determination process, providing the foundation for subsequent target tracking, orbit improvement, and space situation analysis.

[0072] The technical solution of the present invention will be further described through another embodiment. The core of the present invention is: to construct a dynamic point spread function model using the observation data of the device itself to cope with the characteristics of the optical system, to bypass the star removal step through the correlation strategy of trajectory assumption and signal extraction, and to establish a simplified physical model that matches short-arc observation for rapid orbit determination. Specifically, it includes the following steps: S101, based on the sequence images of the acquired faint space target observation area, construct a dynamic point spread function model covering the entire field of view, and fully utilize the observation sequence data itself to construct a point spread function model library strongly correlated with the field of view position to solve the problem of star morphology changes caused by large field of view aberrations. Specifically, it includes: 1) Dynamic point spread function sampling and modeling: from the first frame or the frame with a high signal-to-noise ratio of the image sequence, automatically select no less than 20 isolated stars in different field of view areas and different brightness levels. For each star, use a two-dimensional elliptical Gaussian function or Moffat function to perform surface fitting, and accurately extract the morphological parameters of its point spread function, including full width at half maximum (FWHM), ellipticity, and principal axis direction.

[0073] 2) Constructing a spatial variation model of the point spread function: Using the field-of-view coordinates of the above sampling points and the fitted point spread function morphological parameters as input, a point spread function morphological parameter interpolation model covering the entire field of view is established using thin-plate splines or polynomial regression methods. This model can predict the ideal point spread function morphology at any location within the field of view.

[0074] S102. Based on the dynamic point spread function model, each pixel position in the image sequence is processed to generate an enhanced image for detecting targets in dim space. This step specifically includes: 1) Position-aware matched filtering: For each frame in the sequence, based on the field of view position of each pixel, a corresponding point spread function matched filter kernel is dynamically generated from the above interpolation model and used as a matched filter for convolution operation at that position. This operation can maximize the enhancement of all point signals and suppress noise that does not match the shape of the local point spread function, obtaining an image sequence after matched filtering.

[0075] 2) Background Estimation and Sequence Stacking: Accurate astronomical background estimation and subtraction are performed on each frame of the matched-filtered image. Subsequently, subpixel-precision image registration and alignment are performed using stars as references. Finally, the registered multi-frame images are stacked using a 3σ cropping mean to further suppress random noise and highlight the accumulated signal of faint targets, thus forming an enhanced image for detecting faint space targets.

[0076] S103. Extract candidate point sources of multiple faint spatial targets from the enhanced image and generate a trajectory signal profile sequence for each candidate point source. This step combines detection and motion confirmation, extracting signals directly from the original sequence using assumed trajectories, thus avoiding unreliable segmentation on low signal-to-noise ratio superimposed images. Specifically, this includes: 1) Candidate target nomination: On the obtained enhanced image, use connected component analysis or local peak finding to extract all potential candidate point sources and record their initial positions.

[0077] 2) Multiple Hypothesis Trajectory Signal Extraction: For each candidate point source, it is assumed that it may move at different uniform linear speeds in the image sequence. A reasonable velocity search space is set based on the telescope's tracking mode and maximum tracking speed or acceleration. For each velocity hypothesis, a signal value of a 3×3 pixel region centered on the trajectory point is extracted directly from the unstacked image sequence after the matched filtering process in step S2, along the hypothetical trajectory path, forming a trajectory signal profile sequence corresponding to that velocity hypothesis for that candidate point source.

[0078] S104. Based on the trajectory signal profile sequence of each candidate point source, determine whether each candidate point source is a faint spatial target, and obtain the position and corresponding timestamp of each faint spatial target. Specifically: calculate the matching degree and average signal-to-noise ratio of each trajectory signal profile sequence with the morphology predicted by the local dynamic point spread function model. For a real spatial target, under the assumption of its real motion velocity, its trajectory signal profile sequence will exhibit periodic signal peaks highly correlated with the point spread function morphology; while for stars, under all non-zero velocity assumptions, their trajectory signal profile sequences are all noise. By traversing the velocity space, find the velocity vector that maximizes the trajectory likelihood, where the trajectory likelihood is a weighted sum of the signal-to-noise ratio and the matching degree. This velocity vector is the image planar motion velocity of the target, and based on this, confirm that it is a real spatial target, while recording its precise centroid position and corresponding timestamp in each frame of the original image.

[0079] S105. Using the position and timestamp of the faint space target as observations, construct and solve an objective function that includes orbital physical constraints to obtain the initial orbital state parameters of the faint space target. This step deeply integrates the geometric characteristics of short-arc observations with orbital mechanical constraints, transforming the high-dimensional search problem into a robust low-dimensional search under the guarantee of equipment pointing accuracy. Specifically, this includes: 1) Observation preparation and error modeling: Using the precise position and corresponding timestamp of the target in the image sequence output in step S4 as observations. At the same time, using the telescope's pointing accuracy and repeatability information, a reasonable error covariance matrix is ​​established for the observations.

[0080] 2) Energy-Constrained Single-Parameter Orbit Modeling: For Earth orbit targets, under the coplanar approximation of short-arc observations, the classic six-parameter orbit determination problem is transformed into a search problem for the core parameter of initial geocentric distance by utilizing the conservation of angular momentum and the Vis-viva energy equation. Other initial state variables can be expressed as functions of this distance parameter and angular observations.

[0081] 3) Constructing a robust objective function: The objective function is defined as the degree of deviation between the orbital state calculated from observations and physical constraints under different initial distance assumptions. Constraints include: the orbital energy must be negative, the perigee altitude must be greater than the Earth's radius, and the residuals between the predicted orbital value and a small number of subsequent observations.

[0082] 4) Adaptive Gradient Optimization: An adaptive moment estimation optimizer is used to minimize the objective function. The adaptive moment estimation optimizer utilizes the gradient information of the objective function to quickly and purposefully search within the parameter space, typically converging to the global optimum within tens to hundreds of iterations. This determines the most probable initial distance and the corresponding set of orbital elements, i.e., the initial orbital state parameters. This method is particularly suitable for rapid orbit determination in field environments with limited computational resources.

[0083] The invention is further illustrated through an example of "GEO faint debris detection and orbit determination," specifically including: 1) using a 36cm Schmidt telescope, aimed at a region of the sky in the geosynchronous orbit zone. Using star-tracking mode, with an exposure time set to 15 seconds, 20 frames of images were continuously acquired, resulting in a total effective observation arc of approximately 5 minutes. The telescope's pointing accuracy, better than 10 arcseconds, ensured the stability of the image sequence.

[0084] 2) Based on the acquired image sequence, 25 evenly distributed isolated stars are selected from the first frame for point spread function (PFD) fitting to establish a dynamic PFD model covering the entire field of view. Based on this model, position-aware matched filtering, background subtraction, and image registration are performed on all 20 frames of the image sequence. A 3σ cropping and averaging process is then applied to create an enhanced image for detecting faint spatial targets. Twelve candidate point sources are extracted from this enhanced image. For each candidate point source, 200 velocity assumptions of uniform linear motion are sampled within the image plane velocity range (±1.2 pixels / frame) corresponding to the geosynchronous orbit target. For each velocity assumption, signal values ​​are extracted along the trajectory corresponding to that velocity assumption in the matched-filtered image sequence to generate a trajectory signal profile sequence for each candidate point source. For each candidate point source, based on its trajectory signal profile sequence corresponding to each velocity assumption, the matching degree and average signal-to-noise ratio between each sequence and the locally predicted PFD shape are calculated. The maximum trajectory likelihood and its corresponding velocity vector are determined based on a weighted sum. By using a preset threshold, three candidate point sources were successfully identified as real spatial targets with a signal-to-noise ratio between 1.8 and 2.5. The speed of their planar motion in the image was accurately measured, and the positions and corresponding timestamps of these three faint spatial targets in each frame of the original image were output.

[0085] 3) Initial Orbit Determination: Using the positions and timestamps of the three faint space targets as observations, and based on the conservation of angular momentum and the orbital energy equation, orbit determination is parameterized as a single-parameter search problem for the initial geocentric distance, constructing an objective function that includes orbital physical constraints. An adaptive moment estimation algorithm is used to optimize the objective function, searching within the initial geocentric distance range of 36,000 km to 42,000 km, converging on average within 80 iterations. The initial orbital state parameters of the three targets were successfully calculated. Subsequent comparison with the precise orbits published by the US Space Monitoring Network showed that the semi-major axis errors determined by the method of this invention were 65 km, 98 km, and 210 km, respectively, fully meeting the accuracy requirements for cataloging geosynchronous orbit targets.

[0086] The technical effects of this invention are as follows: This invention relates to the field of space target optical detection and space situational awareness technology, and particularly to a method for high-sensitivity detection of faint space targets (such as geostationary orbit debris and low orbit debris) with a signal-to-noise ratio (SNR) below 3 using small-to-medium aperture ground-based optical telescopes, and for achieving high-success-rate initial orbit determination using an extremely short observation arc (typically 2-5 minutes). The purpose of this invention is to overcome the shortcomings of existing technologies and provide a faint space target processing scheme specifically adapted to small-to-medium aperture ground-based optical telescopes with small pixel sizes and large fields of view. This invention can effectively improve the detection capability of faint space targets with a SNR below 3 in large-field-of-view optical systems with strong noise and significant aberrations; without relying on external star catalogs, it utilizes the differences in motion characteristics between space targets and stars in image sequences to achieve highly reliable target separation and confirmation; and it utilizes limited measurement data acquired within an extremely short observation arc (2-5 minutes) to achieve rapid, stable, and high-precision initial orbit determination. Compared with the prior art, the present invention has the following beneficial effects: 1) Detection sensitivity breaks through the limit of equipment: By constructing a dynamic point spread function model covering the entire field of view for position-aware matching filtering, and combining the extraction and discrimination of trajectory signal profile sequence, this method can stably detect faint spatial targets with a signal-to-noise ratio as low as 1.5. Compared with the traditional inter-frame difference or simple superposition method, the detection rate is improved by more than 50% under the same observation conditions.

[0087] 2) Fundamentally avoid stellar interference: The innovative trajectory hypothesis testing method confirms the target by generating and evaluating trajectory signal profile sequences. It eliminates the need for star catalog matching and star removal steps, which not only simplifies the process but also completely avoids the false removal of real targets due to star point overlap or inaccurate star catalogs. It is particularly suitable for observation areas with complex star field backgrounds.

[0088] 3) High success rate and efficiency in short-arc orbit determination: By parameterizing orbit determination as a single-parameter search problem for the initial geocentric distance, and using an adaptive moment estimation algorithm to optimize the objective function containing physical constraints, the success rate of initial orbit determination (half-major axis error less than 300 km) is increased from about 50-60% in traditional methods to over 92%, while the computation time is reduced by an order of magnitude, meeting the requirements of real-time and near-real-time applications. For example, in the embodiment, orbit determination can be successfully completed within a 5-minute arc segment.

[0089] 4) Deeply aligned with equipment characteristics, forming a technological barrier: The methodology of this invention is closely designed around the optical characteristics, mechanical performance, and pointing accuracy of the 36cm Schmidt telescope and sCMOS detector. From dynamic point spread function modeling to trajectory velocity search range setting, and then to using pointing accuracy to build an error model, the performance potential of this level of equipment is maximized. The resulting technical solution has the best effect on this specific equipment combination and is not easy to be easily reproduced.

[0090] In the above embodiments, although the steps are numbered S1, S2, etc., they are only specific embodiments given by the present invention. Those skilled in the art can adjust the execution order of S1, S2, etc. according to the actual situation. The scheme after adjusting the order is also within the protection scope of the present invention. It can be understood that in some embodiments, some or all of the above embodiments may be included.

[0091] As shown in Figure 2, a faint space target detection and initial trajectory determination system 200 according to an embodiment of the present invention includes a model building module 201, an enhanced image generation module 202, a trajectory signal profile sequence generation module 203, a position determination timestamp acquisition module 204, and an initial trajectory state parameter acquisition module 205. The model building module 201 is used to: construct a dynamic point spread function model covering the entire field of view based on the acquired sequence images of the faint space target observation area; the enhanced image generation module 202 is used to: process the position of each pixel in the sequence images based on the dynamic point spread function model to generate an enhanced image for detecting faint space targets. The enhanced image; trajectory signal profile sequence generation module 203 is used to: extract multiple candidate point sources of faint spatial targets from the enhanced image, and generate a trajectory signal profile sequence for each candidate point source; the position and timestamp acquisition module 204 is used to: determine whether each candidate point source is a faint spatial target based on the trajectory signal profile sequence of each candidate point source, and obtain the position and corresponding timestamp of each faint spatial target; the initial orbital state parameter acquisition module 205 is used to: construct an objective function containing orbital physical constraints and solve it using the position and timestamp of the faint spatial target as observations, and obtain the initial orbital state parameters of the faint spatial target.

[0092] Optionally, in the above technical solution, the model building module 201 is specifically used to: select multiple isolated stars distributed at different field-of-view positions from the sequence images of the faint space target observation area obtained by the ground-based optical telescope, perform point spread function fitting on each isolated star, extract the morphological parameters of the point spread function of each isolated star, and construct a dynamic point spread function model covering the entire field of view based on the field-of-view coordinates of each isolated star and the corresponding morphological parameters of the point spread function.

[0093] Optionally, in the above technical solution, the enhanced image generation module 202 is specifically used to: dynamically generate a corresponding point spread function matched filter kernel for each pixel position in the sequence image based on the dynamic point spread function model and perform convolution filtering to obtain the image sequence after matched filtering; then perform background subtraction and image registration on each frame of the image sequence after matched filtering, and superimpose the registered multi-frame images to form an enhanced image for detecting targets in dark spaces.

[0094] Optionally, in the above technical solution, the trajectory signal profile sequence generation module 203 is specifically used to: extract multiple candidate point sources of dark and weak spatial targets from the enhanced image; set multiple velocity assumptions for each candidate point source with uniform linear motion; and extract signal values ​​along the trajectory corresponding to the velocity assumption in the image sequence after matched filtering for each velocity assumption, thereby generating the trajectory signal profile sequence of the candidate point source.

[0095] Optionally, in the above technical solution, the location timestamp acquisition module 204 is specifically used to: for each candidate point source, calculate the matching degree and average signal-to-noise ratio of each trajectory signal profile sequence with the locally predicted point spread function shape according to the trajectory signal profile sequence corresponding to each velocity assumption, determine the maximum trajectory likelihood and its corresponding velocity vector based on the weighted sum, and if the maximum trajectory likelihood exceeds a preset threshold, confirm that the candidate point source is a faint spatial target, and output the position and corresponding timestamp of the faint spatial target in each frame of the original image.

[0096] Optionally, in the above technical solution, the initial orbital state parameter acquisition module 205 is specifically used to: take the position and timestamp of the faint space target as observations, and based on the conservation of angular momentum and the orbital energy equation, parameterize the orbit determination into a single-parameter search problem for the initial geocentric distance, construct an objective function containing orbital physical constraints, and use an adaptive moment estimation algorithm to optimize and solve the objective function to obtain the initial orbital state parameters of the faint space target.

[0097] It should be noted that the beneficial effects of the low-light space target detection and initial trajectory determination system 200 provided in the above embodiments are the same as those of the low-light space target detection and initial trajectory determination method described above, and will not be repeated here. Furthermore, the system provided in the above embodiments is only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the system can be divided into different functional modules according to the actual situation to complete all or part of the functions described above. In addition, the system and method embodiments provided in the above embodiments belong to the same concept, and their specific implementation process is detailed in the method embodiments, and will not be repeated here.

[0098] An electronic device according to an embodiment of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements any of the above-mentioned methods for detecting targets in dim space and determining initial trajectories.

[0099] An embodiment of the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements any of the above-described methods for detecting targets in dimly lit spaces and determining initial trajectories.

[0100] The above description is merely a preferred embodiment of the present invention and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of disclosure in this invention is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-disclosed concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this invention.

[0101] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for target detection and initial trajectory determination in dimly lit space, characterized in that, include: Based on the sequence of images of the target observation area in the dim space, a dynamic point spread function model covering the entire field of view is constructed; Based on the dynamic point spread function model, each pixel position in the sequence image is processed to generate an enhanced image for detecting targets in dark spaces; From the enhanced image, candidate point sources of multiple faint spatial targets are extracted, and a trajectory signal profile sequence of each candidate point source is generated; Based on the trajectory signal profile sequence of each candidate point source, determine whether each candidate point source is a faint spatial target, and obtain the position and corresponding timestamp of each faint spatial target; Using the position and timestamp of the faint space target as observations, an objective function containing orbital physical constraints is constructed and solved to obtain the initial orbital state parameters of the faint space target.

2. The method for detecting targets and determining initial orbits in dimly lit spaces according to claim 1, characterized in that, Based on the sequence of images of the faint space target observation area obtained from the ground-based optical telescope, a dynamic point spread function model covering the entire field of view is constructed. This includes: selecting multiple isolated stars distributed at different field positions from the sequence of images of the faint space target observation area obtained from the ground-based optical telescope; performing point spread function fitting on each isolated star; extracting the morphological parameters of the point spread function of each isolated star; and constructing a dynamic point spread function model covering the entire field of view based on the field coordinates of each isolated star and the corresponding morphological parameters of the point spread function.

3. The method for detecting targets and determining initial orbits in dimly lit spaces according to claim 2, characterized in that, Based on the dynamic point spread function model, each pixel position in the sequence of images is processed to generate an enhanced image for detecting targets in dim space. This includes: dynamically generating a corresponding point spread function matched filter kernel for each pixel position in the sequence of images based on the dynamic point spread function model and performing convolution filtering to obtain a matched-filtered image sequence; then performing background subtraction and image registration on each frame of the matched-filtered image sequence; and finally superimposing the registered multi-frame images to form an enhanced image for detecting targets in dim space.

4. The method for detecting targets and determining initial orbits in dimly lit spaces according to claim 3, characterized in that, Extracting multiple candidate point sources of faint spatial targets from the enhanced image and generating a trajectory signal profile sequence for each candidate point source includes: extracting multiple candidate point sources of faint spatial targets from the enhanced image; setting multiple velocity assumptions for each candidate point source based on uniform linear motion; and extracting signal values ​​along the trajectory corresponding to the velocity assumption in the matched-filtered image sequence for each velocity assumption, thereby generating a trajectory signal profile sequence for the candidate point source.

5. The method for detecting targets and determining initial orbits in dimly lit spaces according to claim 4, characterized in that, Based on the trajectory signal profile sequence of each candidate point source, determine whether each candidate point source is a faint spatial target and obtain the position and corresponding timestamp of each faint spatial target. This includes: for each candidate point source, based on the trajectory signal profile sequence corresponding to each velocity assumption, calculate the matching degree and average signal-to-noise ratio of each trajectory signal profile sequence with the locally predicted point spread function shape, determine the maximum trajectory likelihood and its corresponding velocity vector based on weighted sum, and if the maximum trajectory likelihood exceeds a preset threshold, confirm that the candidate point source is a faint spatial target and output the position and corresponding timestamp of the faint spatial target in each frame of the original image.

6. The method for detecting targets and determining initial orbits in dimly lit spaces according to claim 5, characterized in that, Using the position and timestamp of the faint space target as observations, an objective function containing orbital physical constraints is constructed and solved to obtain the initial orbital state parameters of the faint space target. This includes: using the position and timestamp of the faint space target as observations, based on the conservation of angular momentum and the orbital energy equation, parameterizing the orbit determination into a single-parameter search problem for the initial geocentric distance, constructing an objective function containing orbital physical constraints, and using an adaptive moment estimation algorithm to optimize and solve the objective function to obtain the initial orbital state parameters of the faint space target.

7. A system for detecting and determining the initial trajectory of a target in low-light space, characterized in that, The system includes a model building module, an enhanced image generation module, a trajectory signal profile sequence generation module, a position determination timestamp acquisition module, and an initial trajectory state parameter acquisition module. The model building module is used to: construct a dynamic point spread function model covering the entire field of view based on the acquired sequence images of the observed area of ​​the faint spatial target; the enhanced image generation module is used to: process the position of each pixel in the sequence images based on the dynamic point spread function model to generate an enhanced image for detecting faint spatial targets; the trajectory signal profile sequence generation module is used to: extract multiple candidate point sources of faint spatial targets from the enhanced image and generate a trajectory signal profile sequence for each candidate point source; the position determination timestamp acquisition module is used to: determine whether each candidate point source is a faint spatial target based on the trajectory signal profile sequence of each candidate point source, and obtain the position and corresponding timestamp of each faint spatial target. The initial orbital state parameter acquisition module is used to: use the position and timestamp of the faint space target as observations, construct an objective function containing orbital physical constraints and solve it to obtain the initial orbital state parameters of the faint space target.

8. The system for detecting and determining initial orbits of targets in dimly lit spaces according to claim 7, characterized in that, The model building module is specifically used to: select multiple isolated stars distributed at different field-of-view positions from the sequence of images of the faint space target observation area obtained by the ground-based optical telescope; fit the point spread function for each isolated star; extract the morphological parameters of the point spread function of each isolated star; and construct a dynamic point spread function model covering the entire field of view based on the field-of-view coordinates of each isolated star and the corresponding morphological parameters of the point spread function.

9. An electronic device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the method for detecting targets in dim space and determining initial trajectories as described in any one of claims 1 to 6.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the method for detecting targets in dim space and determining initial orbits as described in any one of claims 1 to 6.

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