Satellite irregular telemetry data adaptive reconstruction method for continuous time modeling

Abstract

The invention provides a satellite irregular telemetry data self-adaptive reconstruction method for continuous time modeling, belongs to the technical field of aerospace, and aims to solve the problems that the precision of nonlinear data reconstruction is reduced, the output dimension is fixed, and the reconstruction precision is low due to the fact that detailed information of data change is easy to lose in traditional satellite telemetry data reconstruction. The method comprises the following steps: calculating an abnormal threshold value of the telemetry data based on the telemetry data; constructing a satellite telemetry data adaptive reconstruction window based on the abnormal threshold, and recording a missing position and missing time; dividing the telemetry data into a training data set and a test data set according to a missing detection result, and establishing a satellite telemetry data reconstruction model based on NODE; inputting the test data set, the missing position and the missing time into the trained satellite telemetry data reconstruction model for data adaptive reconstruction to obtain normally sampled satellite telemetry data; and the calculation is repeated until the maximum number of iterations is reached, and a reconstructed data set of the satellite telemetry data is obtained.

Description

Technical Field

[0001] The invention relates to a continuous-time modeling method for adaptively reconstructing satellite irregular telemetry data, and belongs to the technical field of aerospace. Background Art

[0002] With the rapid advancement of electronic and mechanical launch technologies, China's satellite industry has entered a new phase of rapid development and intensive launches, placing higher demands on satellite on-orbit status assessment and operational support. As the primary means of obtaining the operational status of critical satellite systems, satellite telemetry data, collected by sensors, is transmitted to a ground-based long-tube system via a satellite-to-ground telemetry link, providing data support for satellite status assessment and control. However, due to factors such as interference from the complex space environment, sensor performance degradation, and unstable satellite-to-ground communication links, telemetry data transmitted back from satellites often exhibits time drift, missing data, or redundancy, leading to data anomalies such as sampling irregularities, phase deviations, and localized amplitude-frequency variations. These data quality issues not only reduce the accuracy and real-time nature of satellite assessments but, in extreme cases, can also lead to misjudgments by ground personnel, potentially impacting the normal performance of satellite missions. Therefore, reconstructing the time series of irregularly sampled telemetry data and restoring its regularity can significantly improve the accuracy of satellite status assessment, laying a critical foundation for precise satellite operation and reliable control.

[0003] At present, the adaptive reconstruction methods for irregularly sampled telemetry data are mainly based on the analysis of the global or local change characteristics of the data to construct a data continuous reconstruction model, thereby realizing the estimation of missing data. Existing methods usually adopt global data reconstruction or local data reconstruction strategies. These methods have been widely used in data reconstruction tasks in large-scale communication systems, medical texts, industrial process control and other fields. However, since satellites have fixed working modes and are affected by random spatial interference and communication link fluctuations, the missing or resampling of their telemetry data often presents small-scale and highly random characteristics, which brings significant challenges to the reconstruction of irregular telemetry data. The current telemetry data reconstruction methods have the following shortcomings: (1) Satellites are typical dynamic systems, and their working modes and operating states are continuous and complex, resulting in telemetry data showing highly nonlinear continuous change characteristics. Most existing methods are based on discretization assumptions for modeling, which easily loses detailed information about data changes, thereby reducing the accuracy of nonlinear data reconstruction. (2) Due to factors such as random interference of space particles, instability of satellite-to-ground communication links, and sensor timestamp drift, the missing points of satellite telemetry data are often highly random. However, current modeling-based reconstruction methods usually require fixed output dimensions and are difficult to flexibly adapt to different missing situations, limiting their applicability in dynamic environments. Summary of the Invention

[0004] In order to solve the problems that traditional satellite telemetry data reconstruction easily loses detailed information of data changes, thereby reducing the accuracy of nonlinear data reconstruction and the output dimension is fixed, making it difficult to adapt to different missing situations, the present invention proposes an adaptive reconstruction method for irregular satellite telemetry data based on continuous time modeling.

[0005] The technical solution adopted by the present invention to solve the above problems is: the present invention comprises the following steps:

[0006] Step 1: Obtain telemetry data of a typical satellite system and calculate the threshold value TH of the telemetry data that generates anomalies based on the telemetry data;

[0007] Step 2: Construct an adaptive reconstruction window for satellite telemetry data based on the anomaly threshold, perform data missing detection based on the adaptive reconstruction window for satellite telemetry data, and record the missing position L and missing time Δt;

[0008] Step 3: Divide the telemetry data of the typical satellite system into a training dataset Y with normal data in proportion according to the missing detection results. train and the test dataset Y with missing data test , and establish a continuous reconstruction model of satellite telemetry data based on NODE, where NODE is a neural ordinary differential equation;

[0009] Step 4: Based on the training dataset Y train The satellite telemetry data continuous reconstruction model is trained and the test data set Y test , missing position L and missing time Δt are input into the trained satellite telemetry data continuous reconstruction model to adaptively reconstruct the missing data and obtain normally sampled satellite telemetry data;

[0010] Step 5: Repeat step 4 until the maximum number of iterations is reached to obtain the satellite telemetry data reconstruction dataset Y′ test , and evaluate the accuracy of the continuous reconstruction model of satellite telemetry data until the accuracy of the continuous reconstruction model of satellite telemetry data meets expectations.

[0011] Furthermore, step 1 specifically includes:

[0012] Step 1.1: Obtain telemetry data Y = [y1, y2, y3, ..., y T ], where the telemetry data sampling interval is Sa, and T is the total number of sampling points of the telemetry data;

[0013] Step 1.2: Calculate the mean and variance of the acquired satellite telemetry data, and calculate the threshold TH for generating anomalies based on the mean and variance of the satellite telemetry data;

[0014] The calculation formula for the abnormal threshold TH of satellite telemetry data is:

[0015]

[0016] In formula (1), is the mean value of satellite telemetry data, is a constant obtained by looking up a table, and Var is the variance of satellite telemetry data.

[0017] Furthermore, step 2 specifically includes:

[0018] Calculate the difference Δy between the satellite telemetry data and the mean value of satellite telemetry data at each moment, i and compare the difference Δy i with the threshold TH. If Δy i ≥TH, it means that there is data missing at the corresponding moment. If Δy i <TH, it means that the satellite telemetry data at the corresponding moment is normal. Record the positions of data missing L = [l1, l2,..., l m and the continuous data missing time ΔT = [Δt1, Δt2,..., Δt m , and construct a data reconstruction window at each data missing position, where m is the number of satellite telemetry data adaptive reconstruction windows;

[0019] The difference Δy between the satellite telemetry data and the mean value of satellite telemetry data is calculated by the formula: i The calculation formula is:

[0020]

[0021] Furthermore, the expression of the telemetry data continuous reconstruction model established in step 3 is:

[0022]

[0023] In formula (3), f(·) is the NODE model, and θ is the sampling moment of satellite telemetry data.

[0024] Furthermore, step 4 specifically includes:

[0025] Based on the training dataset Y train , Y train = [y1, y2,..., y T×0.8 , construct the training input Y train-in of the telemetry data continuous reconstruction model and the training label Y train-label of the model, and train the telemetry data continuous reconstruction model. During the training process, use the numerical solver of the differential equation to solve formula (6) to obtain the adaptive reconstruction result Y′ of the satellite telemetry data train,Y′ train =[y′1,y′2,y′3,...,y′ T×0.8 ], and the loss function L(θ) is used to optimize the parameters of the continuous reconstruction model of telemetry data;

[0026] Training input Y train-in With training labels Y train-label The expression is:

[0027]

[0028] The expression of the loss function L(θ) is:

[0029]

[0030] The expression for solving the adaptive reconstruction result is:

[0031]

[0032] Furthermore, in step 4, the test data set Y test The expression for reconstructing the satellite telemetry data in is:

[0033]

[0034] In formula (7), L is the missing position and Δt is the missing time.

[0035] Furthermore, the accuracy evaluation of the continuous reconstruction model of satellite telemetry data in step 5 specifically includes:

[0036] Repeat step 4 until the number of iterations i = m, and calculate the satellite telemetry data reconstructed data Y′ test If the error is not less than the preset value, the parameters of the telemetry data continuous reconstruction model are adjusted and the telemetry data continuous reconstruction model is retrained until the error is less than the preset value, and the final reconstructed satellite telemetry data is output;

[0037] The formula for calculating the mean square error is:

[0038]

[0039] The formula for calculating the root mean square error is:

[0040]

[0041] In formulas (8) and (9), y i ′ is the satellite telemetry data reconstruction data output by the current iteration training, y i is the real satellite telemetry data, and N is the current training round.

[0042] The beneficial effects of the present invention are:

[0043] (1) This invention dynamically slides an analysis window over time-series telemetry data, calculates the deviation of the data within the window from the mean in real time, and compares it with a preset threshold, thereby identifying data anomaly areas and constructing an adaptive reconstruction window. This design ensures that each window contains a typical missing anomaly pattern, effectively delineating the reconstruction range and significantly improving the algorithm's execution efficiency.

[0044] (2) This invention innovatively applies the NODE model to the field of irregular reconstruction of satellite telemetry data. This method uses differential equations to accurately characterize the gradient characteristics of data changes, achieves data reconstruction at any time through integral operations, and establishes a continuous time series model of the telemetry data change state. This continuous modeling approach is suitable for capturing local short-term nonlinear changes, significantly improving the modeling accuracy of the nonlinear characteristics of irregular satellite telemetry data and enhancing the adaptability of the reconstruction algorithm.

[0045] (3) The present invention uses satellite temperature sensor telemetry data for experiments. The experimental results show that the present invention can achieve high-precision reconstruction of irregular sampling data with high accuracy: MSE = 0.11%, RMSE = 0.97%, which is much higher than the traditional satellite telemetry data reconstruction method. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A schematic flow chart of a method for adaptively reconstructing irregular satellite telemetry data using continuous-time modeling provided by the present invention;

[0047] Figure 2 A schematic diagram of a NODE-based continuous reconstruction model for satellite telemetry data provided by the present invention;

[0048] Figure 3 This is a schematic diagram of the reconstruction results of the satellite telemetry data continuous reconstruction model provided by the present invention when 10 sampling points are missing;

[0049] Figure 4 This is a schematic diagram of the reconstruction results of the satellite telemetry data continuous reconstruction model provided by the present invention when 5 sampling points are missing;

[0050] Figure 5 This is a schematic diagram of the reconstruction results of the satellite telemetry data continuous reconstruction model provided by the present invention when three sampling points are missing;

[0051] Figure 6 This is a schematic diagram of the reconstruction results of the satellite telemetry data continuous reconstruction model provided by the present invention when one sampling point is missing. DETAILED DESCRIPTION

[0052] Specific implementation method 1: Combination Figure 1-6This embodiment is described as follows. Figure 1 As shown, the steps of the method for adaptively reconstructing satellite irregular telemetry data based on continuous time modeling described in this embodiment include:

[0053] S1: Acquire telemetry data of typical satellite systems;

[0054] This embodiment uses satellite temperature sensor telemetry data as an example to study the temporal variation characteristics of the data and further verify the effectiveness of the method proposed in the present invention. The satellite temperature sensor telemetry data contains a total of T = 20000s of data, and the sampling interval of the satellite temperature sensor telemetry data is Sa = 1s. The temperature sensor telemetry data is Y = [y1, y2, y3, ..., y 20000 ].

[0055] S2: Calculate the threshold value of generating anomaly of telemetry data based on the telemetry data;

[0056] S201: Calculate the mean of the satellite temperature sensor telemetry data, as shown in formula (1), and calculate the variance of the satellite temperature sensor telemetry data, as shown in formula (2). The mean of the satellite temperature sensor telemetry data is obtained by calculation. The variance of the temperature sensor telemetry data is Var = 0.24;

[0057]

[0058] S202: Calculate the threshold TH for abnormal telemetry data based on the mean and variance of the satellite temperature sensor telemetry data, as shown in formula (3):

[0059]

[0060] In formula (3), is the mean value of satellite telemetry data, is a constant obtained by looking up a table, and Var is the variance of the satellite telemetry data.

[0061] S3: Build an adaptive reconstruction window for satellite telemetry data based on the abnormal threshold, perform data missing detection based on the adaptive reconstruction window for satellite telemetry data, and record the missing location and missing time;

[0062] Calculate satellite telemetry data and satellite telemetry data mean by time The difference Δy i , and the difference Δy i Compare with the threshold TH, if Δy i ≥TH, it means that there is data missing at the corresponding moment. If Δy i<TH, it indicates that the satellite telemetry data at the corresponding moment is normal, record the positions L = [l1, l2,..., l m and the continuous data missing time ΔT = [Δt1, Δt2,..., Δt m , and construct a data reconstruction window at each data missing position, where m = 30, representing the number of satellite telemetry data adaptive reconstruction windows;

[0063] In this invention, by dynamically sliding an analysis window on the sequential telemetry data, calculating the deviation between the data within the window and the mean value in real time, and comparing it with a preset threshold, the data abnormal area is identified and an adaptive reconstruction window is constructed. This design ensures that each window contains a typical missing abnormal pattern, effectively delimits the reconstruction range, and significantly improves the execution efficiency of the algorithm.

[0064] Satellite telemetry data and the mean value of satellite telemetry data The difference Δy i The calculation formula is:

[0065]

[0066] S4: Divide the telemetry data of the satellite typical system into a training data set with normal data and a test data set containing data missing according to a proportion according to the missing detection result, and establish a continuous reconstruction model of satellite telemetry data based on NODE;

[0067] S401: Divide the satellite telemetry data set into a training data set Y train = [y1, y2,..., y 16000 and a test data set Y test = [y 16001 , y 16002 ,..., y 20000 according to the ratio of 8:2, where the data in the training data is normal and the test data contains data missing;

[0068] The training input Y train-in and the training label Y train-label The expressions are:

[0069]

[0070] S402: The established continuous reconstruction model of telemetry data is as Figure 2 shown, and its expression is:

[0071]

[0072] In formula (5), f(·) is the NODE model, and θ is the sampling moment of satellite telemetry data.

[0073] S5: Training the satellite telemetry data continuous reconstruction model based on the training dataset;

[0074] During the training process, the numerical solver of differential equations is used to solve formula (8) to obtain the adaptive reconstruction result Y′ of satellite telemetry data. train =[y′1,y′2,y′3,...,y′ 16000 ], and the loss function L(θ) is used to optimize the parameters of the continuous reconstruction model of telemetry data;

[0075] The expression of the loss function L(θ) is:

[0076]

[0077] The expression for solving the adaptive reconstruction result is:

[0078]

[0079] This method uses differential equations to accurately characterize the gradient characteristics of data changes, and through integral operations, it reconstructs data at any moment, establishing a continuous time series model of the telemetry data's changing state. This continuous modeling approach is suitable for capturing local, short-term nonlinear changes, significantly improving the accuracy of modeling the nonlinear characteristics of irregular satellite telemetry data. It also significantly increases the accuracy of reconstructing the satellite telemetry data to be reconstructed.

[0080] S6: Input the test set, missing locations, and missing times into the trained satellite telemetry data continuous reconstruction model to adaptively reconstruct the missing data and obtain normally sampled satellite telemetry data;

[0081] The test data set Y test L and ΔT are injected into the adaptive reconstruction model, and the missing satellite telemetry data are reconstructed using formula (9):

[0082]

[0083] In formula (9), L is the missing position and Δt is the missing time.

[0084] S7: Repeat S6 until the maximum number of iterations is reached, obtain a satellite telemetry data reconstruction dataset, and evaluate the accuracy of the satellite telemetry data continuous reconstruction model until the accuracy of the satellite telemetry data continuous reconstruction model meets a preset threshold;

[0085] Repeat S6 until the number of iterations i = 30, and calculate the satellite telemetry data reconstructed data Y′ testIf the error is not less than the preset value, the parameters of the telemetry data continuous reconstruction model are adjusted and the telemetry data continuous reconstruction model is retrained until the error is less than the preset value, and the final reconstructed satellite telemetry data is output;

[0086] The formula for calculating the mean square error is:

[0087]

[0088] The formula for calculating the root mean square error is:

[0089]

[0090] In formulas (10) and (11), y i ′ is the satellite telemetry data reconstruction data output by the current iteration training, y i is the real satellite telemetry data, and N is the current training round.

[0091] In this embodiment, when 10 sampling points, 5 sampling points, 3 sampling points and 1 sampling point are missing, the reconstruction results of the satellite telemetry data continuous reconstruction model are as follows: Figure 3 、 Figure 4 、 Figure 5 and Figure 6 As shown in Table 1, when 10 sampling points, 5 sampling points, 3 sampling points and 1 sampling point are missing, the mean square error and root mean square error of the satellite telemetry data reconstructed by the present invention and the reconstructed data by the existing method are as follows:

[0092] Table 1

[0093]

[0094] It can be seen from Table 1 that the method proposed in the present invention has the highest average accuracy and can achieve high-precision reconstruction of irregularly sampled data.

[0095] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the present profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical content disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement of the above embodiments made according to the technical essence of the present invention, within the spirit and principles of the present invention, without departing from the content of the technical solution of the present invention, shall still fall within the scope of protection of the technical solution of the present invention.

Claims

1. A method for adaptive reconstruction of satellite irregular telemetry data based on continuous time modeling, characterized in that: include: Step 1: Obtain telemetry data of a typical satellite system and calculate the threshold value when the telemetry data is abnormal based on the telemetry data; Step 2: Construct an adaptive reconstruction window for satellite telemetry data based on the anomaly threshold, perform data missing detection based on the adaptive reconstruction window for satellite telemetry data, and record the missing position L and missing time Δt; Step 3: Divide the telemetry data of the typical satellite system into a training dataset Y with normal data in proportion according to the missing detection results. train and the test dataset Y containing missing data test , and establish a continuous reconstruction model of satellite telemetry data based on NODE, where NODE is a neural ordinary differential equation; Step 4: Based on the training dataset Y train The satellite telemetry data continuous reconstruction model is trained and the test data set Y test , missing position L and missing time Δt are input into the trained satellite telemetry data continuous reconstruction model to adaptively reconstruct the missing data and obtain normally sampled satellite telemetry data; Step 5: Repeat step 4 until the maximum number of iterations is reached to obtain the satellite telemetry data reconstruction dataset Y′ test , and evaluate the accuracy of the continuous reconstruction model of satellite telemetry data until the accuracy of the continuous reconstruction model of satellite telemetry data meets expectations.

2. The method for adaptive reconstruction of satellite irregular telemetry data based on continuous time modeling according to claim 1, characterized in that: Step 1 specifically includes: Step 1.1: Obtain telemetry data Y = [y1, y2, y3, ..., y T ], where the telemetry data sampling interval is Sa, and T is the total number of sampling points of the telemetry data; Step 1.2: Calculate the mean and variance of the acquired satellite telemetry data, and calculate the threshold TH for generating anomalies based on the mean and variance of the satellite telemetry data; The calculation formula for the abnormal threshold TH of satellite telemetry data is: In formula (1), is the mean value of satellite telemetry data, is a constant obtained by looking up a table, and Var is the variance of the satellite telemetry data.

3. The method for adaptive reconstruction of satellite irregular telemetry data based on continuous time modeling according to claim 2, characterized in that: Step 2 specifically includes: Calculate the difference Δy between the satellite telemetry data at each moment and the mean value y of the satellite telemetry data i , and compare the difference Δy i with the threshold TH. If Δy i ≥ TH, it indicates that there is data missing at the corresponding moment. If Δy i < TH, it indicates that the satellite telemetry data at the corresponding moment is normal. Record the positions L = [l1, l2,..., l m where data is missing and the continuous data missing time ΔT = [Δt1, Δt2,..., Δt m , and construct a data reconstruction window at each data missing position. Here, m is the number of satellite telemetry data adaptive reconstruction windows; Satellite telemetry data and satellite telemetry data mean The difference Δy i The calculation formula is:

4. The method for adaptive reconstruction of satellite irregular telemetry data based on continuous time modeling according to claim 1, characterized in that: The expression of the telemetry data continuous reconstruction model established in step 3 is: In formula (3), f(·) is the NODE model, and θ is the sampling time of satellite telemetry data.

5. The method for adaptive reconstruction of satellite irregular telemetry data based on continuous time modeling according to claim 1, characterized in that: Step 4 specifically includes: Based on the training dataset Y train ,Y train =[y1,y2,...,y T×0.8 ]Construct the training input Y of the telemetry data continuous reconstruction model train-in and the model's training labels Y train-label , the telemetry data continuous reconstruction model is trained. During the training process, the numerical solver of the differential equation is used to solve formula (6) to obtain the adaptive reconstruction result Y′ of the satellite telemetry data train ,Y′ train =[y′1,y′2,y′3,...,y′ T×0.8 ], and the loss function L(θ) is used to optimize the parameters of the continuous reconstruction model of telemetry data; Training input Y train-in With training labels Y train-label The expression is: The expression of the loss function L(θ) is: The expression for solving the adaptive reconstruction result is:

6. The method for adaptive reconstruction of satellite irregular telemetry data based on continuous time modeling according to claim 1, characterized in that: Test dataset Y in step 4 test The expression for reconstructing the satellite telemetry data in is: In formula (7), L is the missing position and Δt is the missing time.

7. The method for adaptive reconstruction of satellite irregular telemetry data based on continuous time modeling according to claim 1, characterized in that: The accuracy evaluation of the continuous reconstruction model of satellite telemetry data in step 5 specifically includes: Repeat step 4 until the number of iterations i = m, and calculate the satellite telemetry data reconstructed data Y′ test If the error is not less than the preset value, the parameters of the telemetry data continuous reconstruction model are adjusted and the telemetry data continuous reconstruction model is retrained until the error is less than the preset value, and the final reconstructed satellite telemetry data is output; The formula for calculating the mean square error is: The formula for calculating the root mean square error is: In formulas (8) and (9), y i ′ is the satellite telemetry data reconstruction data output by the current iteration training, y i is the real satellite telemetry data, and N is the current training round.

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