Satellite attitude and orbit control sensor missing value supplement method based on angular momentum conservation

Abstract

The invention discloses a satellite attitude and orbit control sensor missing value supplement method based on angular momentum conservation, and relates to a satellite attitude and orbit control sensor missing value supplement method. The invention aims to solve the problem that in the prior art, a specific physical constraint mechanism of a satellite cannot be effectively fused, so that obvious limitation exists in missing data filling. According to the method, the continuous evolution process of sensor data is modeled through a differential equation, self-adaptive filling at any time point is achieved through numerical integration, the problem of gradient information loss caused by discrete sampling in a traditional method is effectively solved, and the missing data filling precision under the high-dynamic working condition is remarkably improved. The invention belongs to the technical field of satellite attitude and orbit control.

Description

Technical Field

[0001] The present invention relates to a method for supplementing missing values ​​of a satellite attitude and orbit control sensor, and belongs to the technical field of satellite attitude and orbit control. Background Art

[0002] As the core control system for spacecraft on-orbit operations, the satellite attitude and orbit control system (AOC) is responsible for maintaining orbital accuracy, stabilizing attitude and pointing, and executing maneuvers. This system collects key state information, such as satellite attitude angles, angular velocities, and orbital parameters, in real time through a multi-source sensor network. Based on this data, the system collaborates with the ground-based control center to implement closed-loop control. However, during actual on-orbit operations, sensor data acquisition faces multiple challenges. On one hand, the extreme space environment (such as high-energy particle radiation and drastic temperature fluctuations) can lead to sensor performance degradation and increased measurement errors. On the other hand, limited onboard resources can cause incomplete data sampling and transmission delays, while asynchrony between the satellite and ground clocks can lead to missing sensor data and timestamp drift. These factors collectively lead to problems such as decreased sensor data accuracy, time sequence disruption, and missing data, severely impacting the state assessment and control decisions of the ground-based control center. This is particularly prominent in mission scenarios such as high-precision Earth observation and formation flying. Therefore, developing effective methods to fill missing sensor values ​​is of great engineering value for improving satellite control accuracy and mission reliability.

[0003] Currently, sensor missing value filling methods typically analyze the variation patterns of sparse data and use known observations to estimate unsampled data. These methods are widely used in the field of image and video missing data filling. However, these methods face special difficulties when processing satellite attitude and orbit control system data. Due to the influence of orbital periodic motion and maneuvering missions, sensor data exhibits significant nonlinear characteristics. At the same time, interference from the space environment causes sampling time drift. More importantly, existing technologies fail to effectively integrate the satellite's unique physical constraint mechanism, resulting in obvious limitations in missing data filling. Specific challenges include:

[0004] (1) The satellite orbital motion presents the composite characteristics of Kepler periodicity and perturbation, which, combined with the sudden maneuvering requirements of the attitude and orbit control system, leads to significant nonlinear characteristics in the sensor data, which brings challenges to the construction of an accurate sensor missing value filling model.

[0005] (2) Factors such as radiation interference, temperature fluctuations, and communication link fluctuations in the space environment not only affect sensor performance, but also cause sensor data time base drift and sampling interval anomalies. This non-uniform sampling characteristic directly restricts the training effect of the model.

[0006] (3) Satellite motion must strictly adhere to physical laws such as orbital dynamics and attitude kinematics. The output of any sensor missing value filling model must satisfy basic physical constraints such as conservation of angular momentum. Existing methods lack modeling of these space-specific physical laws, making it difficult to ensure the physical rationality of the results. Summary of the Invention

[0007] In order to solve the problem that the existing technology fails to effectively integrate the satellite's unique physical constraint mechanism, resulting in obvious limitations in filling missing data, the present invention proposes a method for supplementing missing values ​​of satellite attitude and orbit control sensors based on the conservation of angular momentum.

[0008] The technical solution adopted by the present invention to solve the above problems is: the steps of the present invention include:

[0009] Step 1: Collect satellite attitude and orbit control system sensor data;

[0010] Step 2: Calculate the intermediate parameters of the satellite attitude and orbit control system;

[0011] Step 3: Divide the dataset into τ, where the first 80% is the training dataset and does not contain missing values: The last 20% of the data with irregular sampling intervals is the test data set, which contains missing values:

[0012] Step 4: Construct a training set for the satellite attitude and orbit control system sensor data missing value filling model;

[0013] Step 5: Establish a missing value filling model for satellite attitude and orbit control system sensor data based on NCDE, and use τ′ train Conduct model training;

[0014] Step 6: Use the commonly used numerical solution method for integral equations;

[0015] Step 7: A decoder consisting of an L-layer fully connected network is used to map the hidden state of the sensor at time t to the output of the sensor;

[0016] Step 8: Obtain the output data of the missing value filling model of the satellite attitude and orbit control system sensor;

[0017] Step 9: Calculate the loss function;

[0018] Step 10: Introduce the MAP framework and add regularization restrictions during training to optimize the training process;

[0019] Step 11: Introduce the conservation of angular momentum as a physical constraint to guide the training process;

[0020] Step 12: Calculate the loss function of the satellite attitude and orbit control system sensor data missing value filling model and obtain the optimal satellite sensor data missing value filling model;

[0021] Step 13: Inject the sensor test data set into the satellite attitude and orbit control system sensor missing value filling model, and obtain the satellite attitude and orbit control system sensor missing value interpolation data;

[0022] Step 14: Use the mean square error and root mean square error to evaluate the accuracy of the missing value filling model for the satellite attitude and orbit control system sensor data.

[0023] Furthermore, the satellite attitude and orbit control system sensor data in step 1 Where M represents the total number of sampling points of sensor data, and the sampling frequency of the sensor is fixed at Sa;

[0024] Calculate the intermediate parameters of the satellite attitude and orbit control system in step 2 The formula is:

[0025]

[0026] In formula (1), I represents the physical constant of the satellite attitude and orbit control system;

[0027] In step 4 is the training input of the model, is the training label of the model, is the test input of the model, is the test label of the model.

[0028] Furthermore, in step 5, τ′ is used train To train the model, the specific formula is:

[0029]

[0030] In formula (2), Represents sensor data at t i The hidden state at the moment, θ represents the parameters of the model;

[0031] The solution process in step 6 is:

[0032]

[0033] In step 7, a decoder consisting of an L-layer fully connected network is used to map the hidden state of the sensor at time t to the output of the sensor. The specific formula is:

[0034]

[0035] Furthermore, in step 8, Formula (2) to Formula (4) are repeated M×0.8-1 times, and the output data of the missing value filling model of the satellite attitude and orbit control system sensor is obtained:

[0036]

[0037] Furthermore, the formula for calculating the loss function in step 9 is:

[0038]

[0039] Furthermore, the optimization training process in step 10 is:

[0040]

[0041] In formula (6), σ represents the weight and θ represents the model parameter.

[0042] Furthermore, in step 11, the conservation of angular momentum is introduced as a physical constraint, and the formula guiding the training process is:

[0043]

[0044] In formula (7), λ represents the weight, and I represents the moment of inertia of the satellite attitude and orbit control system.

[0045] Furthermore, in step 12, formulas (5) to (7) are integrated to calculate the loss function of the satellite attitude and orbit control system sensor data missing value filling model, and the optimal satellite sensor data missing value filling model is obtained:

[0046]

[0047] Furthermore, in step 13, the sensor test dataset Inject it into the missing value filling model of the satellite attitude and orbit control system sensor and obtain the data after the missing value interpolation of the satellite attitude and orbit control system sensor

[0048] Furthermore, in step 14, the accuracy of the missing value filling model of the satellite attitude and orbit control system sensor data is evaluated using the mean square error and root mean square error:

[0049]

[0050] The beneficial effects of the present invention are:

[0051] 1. This invention uses differential equations to model the continuous evolution of sensor data and numerical integration to achieve adaptive filling at any time point. This effectively solves the problem of gradient information loss caused by discrete sampling in traditional methods and significantly improves the accuracy of missing data filling under highly dynamic conditions.

[0052] 2. During the model training process, the present invention innovatively introduces the MAP framework. By designing a loss function with a regularization term, the training process is optimized, model convergence is accelerated, and the probability of obtaining the optimal sensor anomaly data to fill the model is greatly improved;

[0053] 3. This invention incorporates the conservation of angular momentum as a physical constraint into model training. This innovation ensures that the model output strictly follows the laws of satellite dynamics, enhancing the interpretability of the results and ensuring the physical rationality of the missing data filling results.

[0054] 4. The present invention uses actual observation data from the flywheel sensor of the satellite attitude and orbit control system to conduct experiments. The experimental results show that the MSE of the model output result is 20%, and the RMSE is 4.47%, which has a high accuracy in filling abnormal data. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a block diagram of the overall solution of the present invention;

[0056] Figure 2 This is a schematic diagram of the missing value filling model for satellite attitude and orbit control system sensor data based on NCDE;

[0057] Figure 3 It is a comparative schematic diagram of the present invention and other technologies. DETAILED DESCRIPTION

[0058] Specific implementation method 1: Figures 1 to 3 As shown, a method for supplementing missing values ​​of satellite attitude and orbit control sensors based on conservation of angular momentum includes the following steps:

[0059] This paper takes the observation data of the flywheel sensor of the satellite attitude and orbit control system as an example to verify the effectiveness of the method proposed in the present invention in the field of filling missing values ​​in the satellite attitude and orbit control system data.

[0060] Step 1: The acquired flywheel sensor data has a total of M = 20,000 sampling points, and the sampling frequency of the sensor is fixed at 1 Sa / min. The torque of the satellite attitude and orbit control system flywheel is calculated using formula (1-1): τ = [τ1, τ2,…, τ 20000 ], where I = 160000.

[0061] Step 2: Divide the dataset into τ, where the first 80% is the training dataset (excluding missing values): τ train =[τ1,τ2,…,τ 16000 ], the last 20% of the data with irregular sampling intervals is the test data set (including missing values): τ test =[τ 16001 ,τ 16002 ,…,τ20000 ].

[0062] Step 3: Construct a training set for the satellite attitude and orbit control system sensor data missing value filling model, where τ′ train =[τ1,τ2,…,τ 15999 ] is the training input of the model, τ″ train =[τ2,τ3,…,τ 16000 ] is the training label of the model, τ′ test =[τ 16001 ,τ 16002 ,…,τ 19999 ] is the test input of the model, τ′ test =[τ 16002 ,τ 16003 ,…,τ 20000 ] is the test label of the model.

[0063] Step 4: Establish a missing value filling model for satellite attitude and orbit control system sensor data based on NCDE (such as Figure 2 As shown in formula (1-2). And the fourth-order Runge-Kutta method is used to solve (1-2), as shown in formula (1-3).

[0064] Step 5: Use a decoder consisting of a fully connected network of L=3 layers to map the hidden state of the sensor at time t to the output of the sensor, as shown in formula (1-4).

[0065] Step 6: Repeat (1-2) to (1-4) 15999 times and obtain the output data of the satellite attitude and orbit control system sensor abnormal data filling model:

[0066] Step 7. Use formula (1-11) to calculate the loss function.

[0067]

[0068] Step 8. Introduce the MAP framework and add regularization restrictions during training to optimize the training process, as shown in (1-12), where θ represents the model parameters.

[0069]

[0070] Step 9: Introduce the conservation of angular momentum as a physical constraint to guide the training process, as shown in formula (1-13).

[0071]

[0072] Step 10. Finally, integrate (1-11) to (1-13) to calculate the loss function of the satellite attitude and orbit control system sensor data missing value filling model, as shown in formula (1-14), and obtain the optimal satellite sensor data missing value filling model.

[0073]

[0074] Step 11: Transform the sensor test data set τ′ test =[τ 16001 ,τ 16002 ,…,τ 19999 ] is injected into the satellite attitude and orbit control sensor data missing value filling model, and the satellite attitude and orbit control system sensor data after filling is obtained

[0075] Step 12. Finally, the present invention uses the mean square error (MSE) and root mean square error (RMSE) to evaluate the accuracy of the missing value filling model of the satellite attitude and orbit control system sensor data, as shown in formulas (1-15) and (1-16).

[0076]

[0077] Step 13. Finally, the method proposed in the present invention is compared with the currently advanced data missing value filling methods (Physics-Informed neural networks Neural Ordinary Differential Equation (PINODE) ​​and Physics-Informed neural networks Convolutional Neural Network (PICNN)), and the accuracy of the model is calculated using formulas (1-15) and (1-16), as shown in Table 1 and Figure 3 As shown in the figure, the method proposed by the present invention has the highest accuracy.

[0078] Table 1 Comparison of method accuracy

[0079]

[0080] 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 supplementing missing values ​​of satellite attitude and orbit control sensors based on conservation of angular momentum, characterized in that: The specific steps include: Step 1: Collect satellite attitude and orbit control system sensor data; Step 2: Calculate the intermediate parameters of the satellite attitude and orbit control system; Step 3: Divide the dataset into τ, where the first 80% is the training dataset and does not contain missing values: The last 20% of the data with irregular sampling intervals is the test data set, which contains missing values: Step 4: Construct a training set for the satellite attitude and orbit control system sensor data missing value filling model; Step 5: Establish a missing value filling model for satellite attitude and orbit control system sensor data based on NCDE, and use τ′ train Conduct model training; Step 6: Use the commonly used numerical solution method for integral equations; Step 7: A decoder consisting of an L-layer fully connected network is used to map the hidden state of the sensor at time t to the output of the sensor; Step 8: Obtain the output data of the missing value filling model of the satellite attitude and orbit control system sensor; Step 9: Calculate the loss function; Step 10: Introduce the MAP framework and add regularization restrictions during training to optimize the training process; Step 11: Introduce the conservation of angular momentum as a physical constraint to guide the training process; Step 12: Calculate the loss function of the satellite attitude and orbit control system sensor data missing value filling model and obtain the optimal satellite sensor data missing value filling model; Step 13: Inject the sensor test data set into the satellite attitude and orbit control system sensor missing value filling model, and obtain the satellite attitude and orbit control system sensor missing value interpolation data; Step 14: Use the mean square error and root mean square error to evaluate the accuracy of the missing value filling model for the satellite attitude and orbit control system sensor data.

2. A method for supplementing missing values ​​of satellite attitude and orbit control sensors based on conservation of angular momentum according to claim 1, characterized in that: Satellite attitude and orbit control system sensor data in step 1 Where M represents the total number of sampling points of sensor data, and the sampling frequency of the sensor is fixed at Sa; Calculate the intermediate parameters of the satellite attitude and orbit control system in step 2 The formula is: In formula (1), I represents the physical constant of the satellite attitude and orbit control system; In step 4 is the training input of the model, is the training label of the model, is the test input of the model, is the test label of the model.

3. The method for supplementing missing values ​​of satellite attitude and orbit control sensors based on conservation of angular momentum according to claim 1, characterized in that: In step 5, we use τ′ train To train the model, the specific formula is: In formula (2), Represents sensor data at t i The hidden state at the moment, θ represents the parameters of the model; The solution process in step 6 is: In step 7, a decoder consisting of an L-layer fully connected network is used to map the hidden state of the sensor at time t to the output of the sensor. The specific formula is:

4. A method for supplementing missing values ​​of satellite attitude and orbit control sensors based on conservation of angular momentum according to claim 1 or 3, characterized in that: In step 8, repeat formula (2) to formula (4) M×0.8-1 times, and obtain the output data of the missing value filling model of the satellite attitude and orbit control system sensor:

5. The method for supplementing missing values ​​of satellite attitude and orbit control sensors based on conservation of angular momentum according to claim 1, characterized in that: The formula for calculating the loss function in step 9 is:

6. The method for supplementing missing values ​​of satellite attitude and orbit control sensors based on conservation of angular momentum according to claim 1, characterized in that: The optimization training process in step 10 is: In formula (6), σ represents the weight and θ represents the model parameter.

7. The method for supplementing missing values ​​of satellite attitude and orbit control sensors based on conservation of angular momentum according to claim 1, characterized in that: In step 11, the conservation of angular momentum is introduced as a physical constraint, and the formula guiding the training process is: In formula (7), λ represents the weight, and I represents the moment of inertia of the satellite attitude and orbit control system.

8. A method for supplementing missing values ​​of satellite attitude and orbit control sensors based on conservation of angular momentum according to claim 1, 4, 5 or 6, characterized in that: In step 12, formulas (5) to (7) are integrated to calculate the loss function of the satellite attitude and orbit control system sensor data missing value filling model, and the optimal satellite sensor data missing value filling model is obtained:

9. The method for supplementing missing values ​​of satellite attitude and orbit control sensors based on conservation of angular momentum according to claim 1, characterized in that: In step 13, the sensor test dataset Inject it into the missing value filling model of the satellite attitude and orbit control system sensor and obtain the data after the missing value interpolation of the satellite attitude and orbit control system sensor 10. The method for supplementing missing values ​​of satellite attitude and orbit control sensors based on conservation of angular momentum according to claim 1, characterized in that: In step 14, the accuracy of the missing value filling model of the satellite attitude and orbit control system sensor data is evaluated using the mean square error and root mean square error:

Images