Spacecraft maneuver detection method based on TLE data and kernel density estimation

Abstract

The invention relates to a spacecraft maneuver detection method based on TLE data and kernel density estimation. The invention relates to the technical field of spacecraft maneuver detection. The method comprises the following steps: acquiring and inputting satellite historical TLE data; gaussian filtering denoising is carried out on the input data; based on the de-noised data, propagation forecasting is carried out through an SGP4 model; constructing a joint residual sequence, and carrying out error distribution modeling and sample scoring; determining a maneuvering threshold value, and judging to obtain abnormal data; and aggregating abnormal data and carrying out maneuvering identification. The method can still realize accurate and stable track maneuver automatic detection under the constraint conditions of unstable TLE data, complex error distribution, no external auxiliary data and the like. The method has good adaptability, robustness and interpretability, and is a track anomaly detection technical scheme which is complete in structure, rigorous in logic and capable of achieving engineering landing.

Description

Technical Field

[0001] This invention relates to the field of spacecraft maneuver detection technology, and is a spacecraft maneuver detection method based on TLE data and kernel density estimation. Background Technology

[0002] As the number of low Earth orbit satellites continues to grow, satellites are maneuvering more frequently to avoid collisions, maintain altitude, or adjust phase. If maneuvers can be identified promptly using only publicly available TLE data without incurring additional observation costs, the efficiency of collision avoidance warnings and mission scheduling will be significantly improved.

[0003] Time-Like Errors (TLEs) are characterized by discrete updates, limited accuracy, and a lack of confidence level labeling. They are also affected by spatial environment and data catalog maintenance, often exhibiting "sudden jumps or slow drifts." Under these conditions, traditional judgments based on fixed thresholds are prone to false alarms or false negatives, and struggle to balance timeliness and robustness. Therefore, it is necessary to introduce statistical modeling and adaptive threshold mechanisms oriented towards error sequences to improve the reliability and generalization of detection. Summary of the Invention

[0004] To address the problems of high false alarm rate, insensitivity to small maneuvers, difficulty in unifying thresholds, and difficulty in balancing timeliness and robustness when relying solely on TLE data for maneuver detection, this invention proposes a spacecraft maneuver detection method based on TLE data and kernel density estimation. This method identifies historical maneuver moments using historical TLE data from satellites without relying on precise orbit determination.

[0005] This invention provides the following technical solutions: A spacecraft maneuver detection method based on TLE data and kernel density estimation, the method comprising the following steps: Step 1: Obtain and input historical TLE data from satellites; Step 2: Perform Gaussian filtering on the input data to remove noise; Step 3: Based on the denoised data, propagation prediction is performed using the SGP4 model; Step 4: Construct the joint residual sequence and perform error distribution modeling and sample scoring; Step 5: Determine the maneuver threshold and identify abnormal data; Step 6: Aggregate abnormal data and perform motion identification.

[0006] Step 1 specifically involves: The input is a time-incrementing TLE history set containing three repeated lines in the format of "name row + row 1 + row 2". The task is to read multiple TLEs within a preset time period, remove and filter out different TLE data with the same time, and mark obviously abnormal rows. The six orbital numbers are obtained through analytical calculation. Epoch t, ​​average motion n, and orbital period T.

[0007] Preferably, step 2 specifically comprises: For angular elements i, Ω, ω, M, phase unwrap on the time axis to avoid 359°. A 1° jump is applied to each element sequence using a one-dimensional Gaussian filter:

[0008] in, For smooth strength, The cutoff radius is [value].

[0009] Preferably, step 3 specifically comprises: Based on the i-th TLE, it is advanced to the subsequent i-th TLE according to the propagation model. TLE's epoch w is automatically estimated based on the daily update frequency of TLE, and kept between 5 and 30. The propagation model is selected as the SGP4 model to adapt to TLE data.

[0010] Preferably, step 4 specifically comprises: By comparing the filtered cataloging elements and the baseline propagation elements at the same time, a series of residual samples are obtained:

[0011] To fit the probability distribution of these residuals Kernel density estimation (KDE) is used. The KDE method is constructed as follows:

[0012] in, The kernel is a multidimensional Gaussian kernel, and h is the bandwidth; After modeling is completed, for any residual sample Calculate its log-likelihood score under the model:

[0013] The log-likelihood values ​​of all samples form a set. .

[0014] Preferably, step 5 specifically comprises: To convert continuous log-likelihood fractions Mapped to binary labels indicating "abnormality": setting most residuals From "normal operation" status If a data point follows a stable distribution, then according to statistical laws, in a one-dimensional Gaussian distribution:

[0015] Correspondingly, the threshold is set as follows:

[0016] in Represents the p-th quantile; Each baseline TLE i can slide backward w times to predict and generate w values. .

[0017] Preferably, step 6 specifically comprises: Step 6.1: For each baseline TLEi, count the number of instances marked as anomalies in the w sliding windows following it, defined as:

[0018] Obtain discrete counting sequence ; Step 6.2: Apply a slight one-dimensional Gaussian filter to ID(i) to obtain a smoothed version. ; Search for all non-zero intervals and calculate the mean of each interval. If it is less than the empirical threshold If so, the entire segment will be cleared and considered a "false trigger segment"; Step 6.3: For the retained non-zero segments, select the index of the maximum value point of each segment as the representative point for movement; Set display threshold Only outputs at specific times, ensuring that the results are sparse and interpretable; The final output includes: TLE index i, corresponding UTC time, and score ID (i).

[0019] A spacecraft maneuver detection system based on TLE data and kernel density estimation, the system comprising: The data acquisition module acquires and inputs historical TLE data from the satellite. A noise reduction module performs Gaussian filtering on the input data to reduce noise. The propagation module performs propagation prediction based on the denoised data using the SGP4 model. A sequence construction module, which constructs a joint residual sequence and performs error distribution modeling and sample scoring; An anomaly detection module determines a dynamic threshold and identifies abnormal data. A motion identification module, which aggregates abnormal data and performs motion identification.

[0020] A computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement a spacecraft maneuver detection method based on TLE data and kernel density estimation.

[0021] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement a spacecraft maneuver detection method based on TLE data and kernel density estimation.

[0022] The present invention has the following beneficial effects: The present invention provides a spacecraft maneuver detection method based on Time-Loop (TLE) data, extrapolated residual Gaussian filtering, and kernel density estimation, comprising: acquiring multiple TLEs of the target within a preset time period; performing time alignment or extrapolation comparison on two adjacent TLEs to construct an error sequence; applying a one-dimensional Gaussian filter to the error sequence for noise reduction and smoothing (the filter standard deviation or window length can be adaptively set according to the TLE update frequency); establishing a probabilistic model on the smoothed error using a kernel density estimation algorithm; generating amplitude interval thresholds according to the nP rule and calculating the (logarithmic) probability density of the samples to form a density threshold; marking samples as anomalies when they meet the triggering conditions of the amplitude domain and / or density domain, and performing connected grouping to obtain maneuver events, forming a structured event record for use in orbit prediction correction and collision avoidance assessment.

[0023] This invention achieves accurate and stable automatic detection of orbital maneuvers even under constraints such as unstable TLE data, complex error distribution, and lack of external auxiliary data. It exhibits good adaptability, robustness, and interpretability, and represents a structurally complete, logically rigorous, and engineeringally feasible orbital anomaly detection technology. This method can be widely applied in fields such as space situational awareness, satellite operation monitoring, and orbital safety analysis. It provides low-cost, highly stable orbital behavior recognition capabilities, supporting avoidance strategy evaluation, anomaly behavior review, and orbital drift trend analysis. Attached Figure Description

[0024] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0025] Figure 1 The diagram shows a schematic flow of the spacecraft maneuver detection method based on TLE data and kernel density estimation according to the present invention. Figure 2 The graph shows the joint log-likelihood distribution and outlier threshold verification based on KDE of the present invention. Figure 3 The data analysis diagram shown is from the present invention. Figure 4 The graph shown is a log-likelihood score of the KDE of this invention; Figure 5 The diagram shows the results of the maneuver. Detailed Implementation

[0026] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] The present invention will be described in detail below with reference to specific embodiments. Specific Implementation Example 1: according to Figures 1 to 5 As shown, the specific optimized technical solution adopted by the present invention to solve the above-mentioned technical problems is: The present invention relates to a spacecraft maneuver detection method based on TLE data and kernel density estimation.

[0029] This invention provides a spacecraft maneuver detection method based on TLE data and kernel density estimation, the method comprising the following steps: The method includes the following steps: Step 1: Obtain and input historical TLE data from satellites; Step 1 specifically involves: The input is a time-incrementing TLE history set containing three repeated lines in the format of "name row + row 1 + row 2". The task is to read multiple TLEs within a preset time period, remove and filter out different TLE data with the same time, and mark obviously abnormal rows. The six orbital numbers are obtained through analytical calculation. Epoch t, ​​average motion n, and orbital period T.

[0030] Step 2: Perform Gaussian filtering on the input data to remove noise; Step 2 specifically involves: For angular elements i, Ω, ω, M, phase unwrap on the time axis to avoid 359°. A 1° jump is applied to each element sequence using a one-dimensional Gaussian filter:

[0031] in, For smooth strength, The cutoff radius is [value].

[0032] Step 3: Based on the denoised data, propagation prediction is performed using the SGP4 model; Step 3 specifically involves: Based on the i-th TLE, it is advanced to the subsequent i-th TLE according to the propagation model. TLE's epoch w is automatically estimated based on the daily update frequency of TLE, and kept between 5 and 30. The propagation model is selected as the SGP4 model to adapt to TLE data.

[0033] Step 4: Construct the joint residual sequence and perform error distribution modeling and sample scoring; Step 4 specifically involves: By comparing the filtered cataloging elements and the baseline propagation elements at the same time, a series of residual samples are obtained:

[0034] To fit the probability distribution of these residuals Kernel density estimation (KDE) is used. The KDE method is constructed as follows:

[0035] in, The kernel is a multidimensional Gaussian kernel, and h is the bandwidth; After modeling is completed, for any residual sample Calculate its log-likelihood score under the model:

[0036] The log-likelihood values ​​of all samples form a set. .

[0037] Step 5: Determine the maneuver threshold and identify abnormal data; Step 5 specifically involves: To convert continuous log-likelihood fractions Mapped to binary labels indicating "abnormality": setting most residuals From "normal operation" status If a data point follows a stable distribution, then according to statistical laws, in a one-dimensional Gaussian distribution:

[0038] Correspondingly, the threshold is set as follows:

[0039] in Represents the p-th quantile; Each baseline TLE i can slide backward w times to predict and generate w values. .

[0040] Step 6: Aggregate abnormal data and perform motion identification.

[0041] Step 6 specifically involves: Step 6.1: For each baseline TLEi, count the number of instances marked as anomalies in the w sliding windows following it, defined as:

[0042] Obtain discrete counting sequence ; Step 6.2: Apply a slight one-dimensional Gaussian filter to ID(i) to obtain a smoothed version. ; Search for all non-zero intervals and calculate the mean of each interval. If it is less than the empirical threshold If so, the entire segment will be cleared and considered a "false trigger segment"; Step 6.3: For the retained non-zero segments, select the index of the maximum value point of each segment as the representative point for movement; Set display threshold Only outputs at specific times, ensuring that the results are sparse and interpretable; The final output includes: TLE index i, corresponding UTC time, and score ID (i).

[0043] The present invention also provides a spacecraft maneuver detection system based on TLE data and kernel density estimation, the system comprising: The data acquisition module acquires and inputs historical TLE data from the satellite. A noise reduction module performs Gaussian filtering on the input data to reduce noise. The propagation module performs propagation prediction based on the denoised data using the SGP4 model. A sequence construction module, which constructs a joint residual sequence and performs error distribution modeling and sample scoring; An anomaly detection module determines a dynamic threshold and identifies abnormal data. A motion identification module, which aggregates abnormal data and performs motion identification.

[0044] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement a spacecraft maneuver detection system method based on TLE data and kernel density estimation.

[0045] The present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement a spacecraft maneuver detection system method based on TLE data and kernel density estimation. Specific Implementation Example 2: The only difference between Embodiment 2 and Embodiment 1 of this application is that: The purpose of this invention is to address the problems of high false alarm rate, insensitivity to small maneuvers, difficulty in unifying thresholds, and difficulty in balancing timeliness and robustness when relying solely on TLE data for maneuver detection. This invention proposes a maneuver detection framework that combines multi-parameter joint residuals, KDE distribution, nP rule, and Gaussian smoothing. This framework identifies historical maneuver moments using historical TLE data from satellites without relying on precise orbit determination.

[0047] The specific technical solution of the spacecraft maneuver detection method, apparatus, equipment, and medium based on TLE data and kernel density estimation of the present invention is as follows: S1. Data Acquisition and Processing: The input is a time-sequential TLE history set, containing three repeated lines in the format "name row + row 1 + row 2". The program reads multiple TLEs within a preset time period, filters out TLEs with the same time interval, and marks obviously abnormal lines. The program then calculates the number of track six elements. Epoch t, ​​average motion n, and orbital period T.

[0048] S2. Gaussian filtering for noise reduction: The aim is to reduce the interference of catalog jitter and outlier time-limited extensions (TLEs) on subsequent detection at the source. Angular features i, Ω, ω, M are unwrapped on the time axis to avoid 359°. A 1° jump. Apply a one-dimensional Gaussian filter to each element sequence:

[0049] in, For smoothing, the strength is typically set between 0.3 and 1.5. , where is the cutoff radius. Filtering of angular elements is performed at the unfolded angle, ultimately returning to .

[0050] S3. Baseline Propagation: Using the i-th TLE as the baseline, propagate it to subsequent TLEs according to the propagation model. TLE's epoch w is automatically estimated based on the daily update frequency of TLE, and maintained between 5 and 30. The propagation model selected is the SGP4 model, which can be well adapted to TLE data.

[0051] S4. Joint Residual Construction Compare the filtered catalog elements and the baseline propagation elements at the same time. A series of residual samples are obtained.

[0052]

[0053] S5. Error Distribution Modeling and Sample Scoring This step aims to learn the natural distribution pattern of the joint residual vector under non-maneuvering conditions by statistically modeling it, and to define an "anomaly score" based on this, laying a probabilistic foundation for subsequent maneuver identification.

[0054] To fit the probability distribution of these residuals Kernel density estimation (KDE) was selected.

[0055] The KDE method is constructed as follows:

[0056] in, The kernel is a multidimensional Gaussian kernel, and h is the bandwidth. It is usually automatically selected using Silverman's rule. This method is suitable for scenarios with dense data points and low dimensionality, and can well characterize non-Gaussian and multimodal features.

[0057] After modeling is completed, for any residual sample Its log-likelihood score under the model can be calculated:

[0058] The lower the value, the greater the deviation from the training data distribution; it is a direct quantitative indicator of "anomaly." The log-likelihood values ​​of all samples constitute a set. .

[0059] S6. Threshold Determination and Anomaly Detection To convert continuous log-likelihood fractions Mapped to binary labels indicating "abnormality," this step designs a robust and statistically meaningful thresholding strategy. The method includes the following two optional paths: nP rule (n-sigma principle): Assume that most residuals From "normal operation" status If a data point follows a stable distribution, then according to statistical laws, in a one-dimensional Gaussian distribution:

[0060] Correspondingly, the threshold is set as follows:

[0061] in Let p represent the p-th quantile.

[0062] Each baseline TLE i can slide backward w times to predict and generate w values. The more anomalies occur, the more likely that moment is a trigger point for a maneuver. Note that the sliding window width w can be dynamically estimated based on the TLE frequency to ensure a balance between timeliness and coverage.

[0063] Step 7: Anomaly Counting, Smoothing, and Motion Extraction Because residual scoring is susceptible to noise disturbances or small TLE errors, directly using a scoring point below the threshold may generate too many fragmented false alarms. This step designs a counting-smoothing-peak extraction process to construct the final mobile detection result: 1. Anomaly Count (ID Vector): For each baseline TLEi, count the number of instances marked as anomalies in the w sliding windows following it, defined as:

[0064] Obtain discrete counting sequence The larger the value, the more likely it is to be the starting point of a maneuver.

[0065] 2. Smoothing and noise suppression: Apply a slight one-dimensional Gaussian filter to ID(i) (e.g.) ), to get a smooth version ; Search for all non-zero segments and calculate the mean of each segment. If it is less than the empirical threshold (like If the condition is true, the entire segment will be cleared and considered a "false trigger segment".

[0066] 3. Motorized extraction: For the retained non-zero segments, the index of the maximum value point (peak value) of each segment is selected as the representative point for the maneuver; Set display threshold Only outputs at specific times, ensuring that the results are sparse and interpretable; The final output includes: TLE index i, corresponding UTC time, and score ID (i).

[0067] Compared to traditional point-by-point identification, this method provides clear event-level maneuver detection results, which can be further used for downstream spatial data applications such as automatic task scheduling, strategy updates, and map correction.

[0068] The present invention provides a spacecraft maneuver detection method based on Time-Loop (TLE) data, extrapolated residual Gaussian filtering, and kernel density estimation, comprising: acquiring multiple TLEs of the target within a preset time period; performing time alignment or extrapolation comparison on two adjacent TLEs to construct an error sequence; applying a one-dimensional Gaussian filter to the error sequence for noise reduction and smoothing (the filter standard deviation or window length can be adaptively set according to the TLE update frequency); establishing a probabilistic model on the smoothed error using a kernel density estimation algorithm; generating amplitude interval thresholds according to the nP rule and calculating the (logarithmic) probability density of the samples to form a density threshold; marking samples as anomalies when they meet the triggering conditions of the amplitude domain and / or density domain, and performing connected grouping to obtain maneuver events, forming a structured event record for use in orbit prediction correction and collision avoidance assessment.

[0069]

[0070] First, this method possesses excellent data adaptability and spatiotemporal universality. Since it relies entirely on TLE orbital element data, it is applicable to various orbital types, including low Earth orbit, medium Earth orbit, and geostationary orbit. Furthermore, it can transcend different satellite types, mission contexts, and data release frequencies, requiring no external dynamic models or onboard telemetry data, thus exhibiting high versatility.

[0071] In the preprocessing stage, the method introduces various filtering and denoising mechanisms to effectively improve data stability. These include a Gaussian filter: low-pass smoothing of the orbital six-root time series to suppress high-frequency measurement noise; at the modeling level, this method uses kernel density estimation (KDE) to fit the distribution of prediction errors. This method does not rely on any specific distribution assumptions, and by introducing a smoothing kernel function to weight and sum local probabilities in the sample space, it can adaptively reconstruct the true probability density of the error. KDE can naturally characterize complex distribution features such as multimodal, skewed, and long-tailed distributions, thus more comprehensively reflecting the statistical differences in TLE errors under non-maneuvering and maneuvering conditions.

[0072] Compared to Gaussian mixture models or fixed threshold methods, KDE does not require preset component numbers and parameter initialization, avoiding the convergence instability and overfitting problems of the EM algorithm; at the same time, its non-parametric characteristics enable the model to flexibly adapt to the residual shape changes under different time periods and different satellite types.

[0073] When dealing with non-Gaussian noise, multi-source disturbances, slow drift, and sudden jumps, KDE exhibits higher robustness and generalization ability, enabling it to more accurately identify track anomalies and minor maneuvering events. For anomaly detection, this method constructs an anomaly intensity index through probability density inversion and confidence interval extraction, thereby identifying error values ​​that are extremely difficult to occur under statistical models. Combined with this, a sliding window extreme value search and soft threshold strategy are further introduced to avoid false alarms triggered by single-point disturbances, improving overall detection stability.

[0074] The final output not only includes the time and location of the identified maneuvering events, but also labels the anomaly score, error dimension distribution, original TLE fragment index and other multi-dimensional information, which facilitates subsequent verification and analysis.

[0075] Overall, this method demonstrates significant technical advantages in terms of low data dependence, wide applicability, strong model interpretability, and good false alarm control, making it particularly suitable for orbital behavior analysis tasks lacking prior dynamic conditions or involving heterogeneous satellite types. It exhibits high adaptability and practical value for scenarios such as space situation analysis, orbital monitoring experiments, and TLE quality assessment. Furthermore, the method provided by this invention maintains clear interpretability throughout the entire process. All input and output variables have explicit physical meanings (such as orbital six roots, propagation error, confidence probability, etc.), and intermediate calculation results are highly visualized, facilitating subsequent analysis, review, and verification. Unlike "black box" solutions that rely on complex neural network models, this method maintains a transparent inference chain during maneuver detection, making it suitable for scenarios requiring rigorous analysis and accurate positioning.

[0076] In summary, this method achieves accurate and stable automatic detection of orbital maneuvers even under constraints such as unstable TLE data, complex error distribution, and lack of external auxiliary data. It exhibits good adaptability, robustness, and interpretability, making it a structurally complete, logically rigorous, and engineeringally feasible orbital anomaly detection technology. This method can be widely applied in fields such as space situational awareness, satellite operation monitoring, and orbital safety analysis. It provides low-cost, highly stable orbital behavior recognition capabilities, supporting avoidance strategy evaluation, anomaly behavior review, and orbital drift trend analysis.

[0077] Figure 2 This section displays the joint log-likelihood (loglik) distribution of all orbital prediction residual samples. The horizontal axis represents the log-likelihood value of the sample; a smaller value indicates a greater deviation from the KDE-modeled distribution, meaning a higher probability of orbital parameter anomalies. The vertical axis represents the probability density corresponding to that value. The red vertical line represents the anomaly threshold calculated according to the n-P rule, used to distinguish between normal and anomalous samples. By observing the density of samples to the left of the threshold, the rationality of the anomaly judgment standard can be verified: if anomalous samples are highly concentrated to the left of the threshold, the current threshold setting is relatively reasonable; if there are a large number of normal points or obvious overlapping distributions near the threshold, the bandwidth or confidence level parameters need to be readjusted to optimize detection performance.

[0078] according to Figures 3-5As shown in the figure, the blue curve represents the original monitoring data, which exhibits obvious fluctuations and local abrupt changes; the red curve represents the result after filtering the original data, which is smoother than the original blue curve, successfully filtering out noise in the original data and presenting the overall change pattern of the data more intuitively.

[0079] Data from the first 120 days of 2023 for satellite ID 49962 was selected for analysis, and the final maneuver results are as follows: Figure 5 As shown, during the period from February 2nd to March 7th, 2023, a total of 13 abnormal data points were detected. Adjacent data points were merged into the same maneuver (abnormal points 4 and 5 in the box, and abnormal points 11 and 12), resulting in a total of 11 maneuvers. Compared to the actual data, there was one false alarm, but no missed detections, indicating a good actual test result.

[0080] The above description is merely a preferred embodiment of a spacecraft maneuver detection method based on TLE data and kernel density estimation. The scope of protection for such a method is not limited to the above embodiments; all technical solutions falling within this conceptual framework are within the scope of protection of this invention. It should be noted that for those skilled in the art, any improvements and variations made without departing from the principles of this invention should also be considered within the scope of protection of this invention.

Claims

1. A spacecraft maneuver detection method based on TLE data and kernel density estimation, characterized by: The method includes the following steps: Step 1: Obtain and input historical TLE data from satellites; Step 2: Perform Gaussian filtering on the input data to remove noise; Step 3: Based on the denoised data, propagation prediction is performed using the SGP4 model; Step 4: Construct the joint residual sequence and perform error distribution modeling and sample scoring; Step 5: Determine the maneuver threshold and identify abnormal data; Step 6: Aggregate abnormal data and perform motion identification.

2. The method according to claim 1, characterized in that: Step 1 specifically involves: The input is a time-incrementing TLE history set containing three repeated lines in the format of "name row + row 1 + row 2". The task is to read multiple TLEs within a preset time period, remove and filter out different TLE data with the same time, and mark obviously abnormal rows. The six orbital numbers are obtained through analytical calculation. Epoch t, ​​average motion n, and orbital period T.

3. The method according to claim 2, characterized in that: Step 2 specifically involves: Phase expansion of angular elements i, Ω, ω, M on the time axis to avoid 359° A 1° jump is applied to each element sequence using a one-dimensional Gaussian filter: in, For smooth strength, The cutoff radius is [value].

4. The method according to claim 3, characterized in that: Step 3 specifically involves: Based on the i-th TLE, it is advanced to the subsequent i-th TLE according to the propagation model. TLE's epoch w is automatically estimated based on the daily update frequency of TLE, and kept between 5 and 30. The propagation model is selected as the SGP4 model to adapt to TLE data.

5. The method according to claim 4, characterized in that: Step 4 specifically involves: By comparing the filtered cataloging elements and the baseline propagation elements at the same time, a series of residual samples are obtained: To fit the probability distribution of these residuals Kernel density estimation (KDE) is used. The KDE method is constructed as follows: in, The kernel is a multidimensional Gaussian kernel, and h is the bandwidth; After modeling is completed, for any residual sample Calculate its log-likelihood score under the model: The log-likelihood values ​​of all samples form a set. .

6. The method according to claim 5, characterized in that: Step 5 specifically involves: To convert continuous log-likelihood fractions Mapped to binary labels indicating "abnormality": setting most residuals From "normal operation" status If a data point follows a stable distribution, then according to statistical laws, in a one-dimensional Gaussian distribution: Correspondingly, the threshold is set as follows: in Represents the p-th quantile; Each baseline TLE i can slide backward w times to predict and generate w values. .

7. The method according to claim 6, characterized in that: Step 6 specifically involves: Step 6.1: For each baseline TLEi, count the number of instances marked as anomalies in the w sliding windows following it, defined as: Obtain discrete counting sequence ; Step 6.2: Apply a slight one-dimensional Gaussian filter to ID(i) to obtain a smoothed version. ; Search for all non-zero intervals and calculate the mean of each interval. If it is less than the empirical threshold If so, the entire segment will be cleared and considered a "false trigger segment"; Step 6.3: For the retained non-zero segments, select the index of the maximum value point of each segment as the representative point for movement; Set display threshold Only outputs at specific times, ensuring that the results are sparse and interpretable; The final output includes: TLE index i, corresponding UTC time, and score ID (i).

8. A spacecraft maneuver detection system based on TLE data and kernel density estimation, characterized in that: The system includes: The data acquisition module acquires and inputs historical TLE data from the satellite. A noise reduction module performs Gaussian filtering on the input data to reduce noise. The propagation module performs propagation prediction based on the denoised data using the SGP4 model. A sequence construction module, which constructs a joint residual sequence and performs error distribution modeling and sample scoring; An anomaly detection module determines a dynamic threshold and identifies abnormal data. A motion identification module, which aggregates abnormal data and performs motion identification.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the method as claimed in any one of claims 1-7.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the method of any one of claims 1-7.

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