A Modeling and Compensation Method for On-Orbit Errors of Star Sensors Based on LSTM

Abstract

The present invention discloses a method for modeling and compensating the on-orbit error of a star sensor based on LSTM, which includes: the ground station receives multi-track measurement data transmitted back from the satellite as the input of the sample set; constructing a low-frequency error analytical model; estimating the low-frequency error of the star sensor based on the combined attitude determination filter composed of the star sensor and the gyroscope as the expected output of the sample set; using the input and expected output of the sample set to perform offline training on a pre-constructed LSTM network; the ground station uploads the trained low-frequency error model to the satellite; the satellite uses the trained low-frequency error model to online estimate the low-frequency error of the star sensor; and using the online estimated low-frequency error to perform error compensation on the measurement output of the star sensor. In the modeling process of the present invention, the influence of environmental factors changing with time and space on the measurement accuracy of the star sensor is comprehensively considered, which can improve the accuracy, stability and adaptability to interference of the model.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite attitude sensor measurement, and more specifically, to a method for modeling and compensating the on-orbit error of a star sensor based on LSTM. Background Art

[0002] With the improvement of the complexity of spaceborne missions such as telemetry and remote sensing, the demand for the accuracy of satellite attitude determination by people is getting higher and higher. Improving the measurement accuracy of the attitude determination sensor is one of the most important methods to achieve high-precision satellite attitude determination.

[0003] The star sensor has the characteristics of high attitude measurement accuracy, long life, low power consumption, and flexible working mode, and is widely used in the spacecraft navigation and control system. When using the star sensor to measure the attitude of a satellite in orbit, since the satellite is at different spatial positions at different times, not only the star sensor is affected by the alternating solar radiation field, but also the navigation stars periodically enter and exit its field of view. Under the influence of such comprehensive factors of time and space, a low-frequency error is generated in the output of the star sensor, and it shows the characteristics of periodic variation with multiple frequency points over time. Therefore, the star sensor is affected by its own factors and complex space environments such as the temperature field and magnetic field, generating measurement errors mainly composed of low-frequency errors, which affect the on-orbit attitude measurement accuracy. In order to meet the urgent need for high-precision attitude in applications such as satellite telemetry and remote sensing, it is necessary to effectively compensate the measurement errors of the star sensor to ensure the attitude accuracy.

[0004] At present, a large amount of research work has been carried out on the modeling, estimation, and compensation methods for the measurement errors of star sensors. The main idea is to establish an analytical model describing the errors according to the signal characteristics of error components such as low-frequency errors, and then use the method of state augmentation filtering to estimate the parameters of the error model and determine the error components. Obviously, only by establishing a model adapted to the actual errors existing in the system and ensuring the accuracy of the model structure and parameters can the effective estimation and compensation of the error terms be achieved. However, the complexity and uncertainty of the operating environment of the satellite attitude system increase the difficulty and complexity of establishing an accurate analytical model, which to a certain extent limits the application performance of such methods.

[0005] Therefore, how to provide a method for modeling and compensating the on-orbit error of a star sensor based on LSTM, which can improve the accuracy of the star sensor by improving the accuracy, stability, and adaptability to interference of the error model, is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a method for modeling and compensating the on-orbit error of a star sensor based on LSTM, comprehensively considering the influence of low-frequency errors caused by the variation of environmental factors over time and space on the measurement accuracy. By using an LSTM network with good time series modeling ability and generalization ability, the on-orbit measurement error of the star sensor is modeled offline, estimated online, and compensated, which can improve the accuracy, stability, and adaptability to interference of the model, and further improve the use accuracy of the star sensor.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] A method for modeling and compensating the on-orbit error of a star sensor based on LSTM, comprising:

[0009] Receiving the measurement data of the star sensor and gyroscope and the orbit data of multiple orbit periods transmitted back from the satellite through the ground station to generate the input of the sample set;

[0010] Constructing a low-frequency error analytical model based on an analytical method;

[0011] Based on the low-frequency error analytical model, constructing a combined attitude determination filter composed of a star sensor and a gyroscope to estimate the low-frequency error of the star sensor as the expected output of the sample set;

[0012] Using the input and expected output of the sample set to perform offline training on a pre-constructed LSTM network to obtain a final low-frequency error model;

[0013] Uploading the trained low-frequency error model to the satellite through the ground station;

[0014] On the satellite, using the trained low-frequency error model to estimate the low-frequency error of the star sensor online;

[0015] Using the online estimated low-frequency error to compensate the measurement output of the star sensor.

[0016] As can be seen from the above technical solutions, compared with the prior art, in the ground station, through offline processing of a large number of on-orbit continuous measurement data of the star sensor and gyroscope transmitted from the satellite, a sample set of measurement errors of the star sensor varying with time and space is obtained. During the process of constructing the training sample set, in view of the actual situation that the true values of the attitude and low-frequency error components in the on-orbit measurement data of the star sensor are unknown, in the ground station, an offline processing method is adopted, with the aid of the attitude measurement information provided by the gyroscope, and the data processing method of star sensor / gyroscope combined attitude determination is used to obtain the estimated values of the on-orbit low-frequency errors at different times and spaces, which are used to generate the sample set required for constructing the error model based on LSTM. The sample set is used to perform offline training on the long short-term memory network (LSTM) deep network model, and an on-orbit attitude measurement error model of the star sensor mainly composed of low-frequency errors is established; the nonlinear modeling ability and generalization ability of the LSTM network model are fully utilized, so that the established model has stronger adaptability to the influence brought by uncertain factors such as the environment.

[0017] The final low-frequency error model of the star sensor measurement based on deep network structures such as LSTM obtained by training is uploaded to the on-board processor; on the satellite, the established final low-frequency error model is used to estimate the low-frequency error of the star sensor on orbit, and the measurement error of the star sensor is compensated to improve its on-orbit use accuracy, providing technical support for realizing applications based on high-precision satellite attitude. During the process of applying the error model on orbit, when in the working state of star sensor / gyroscope combined attitude determination and when the computing power of the on-board processor is sufficient, the reference information provided by the gyroscope can be used to update the established error model online to improve the adaptability of the model.

[0018] Generally speaking, the low-frequency error model of the star sensor provided by the present invention reduces the dependence on parameters such as the frequency and number of low-frequency error components, and has robustness to measurement noise; the low-frequency error compensation method provided by the present invention comprehensively considers the time and space characteristics of the low-frequency error to realize the modeling and compensation of the measurement error of the star sensor, and can reduce the demand for the measurement information of the gyroscope when applied;

[0019] Further, in the above method for modeling and compensating the on-orbit error of the star sensor based on LSTM, the measurement data and orbit data of the star sensor and gyroscope transmitted back from the satellite received by the ground station include: the current time t k and the relative time Δt with the initial moment t of the satellite operation 0 = t k - t k 、the argument of latitude θ of the satellite orbit 0 、the attitude quaternions k and output by the star sensor for two adjacent times and the [t calculated according to the gyro measurementk-1 ,t k Attitude change quaternion in the interval

[0020] Furthermore, in the above method for modeling and compensating the on-orbit error of a star sensor based on LSTM, the construction of the low-frequency error analytical model based on the analytical method includes:

[0021] Describe the satellite attitude Q measured by the star sensor using the following formula st :

[0022]

[0023] Where is the true satellite attitude in quaternion form; Q λ =[λ 0 (λ p ) T T , Q ξ =[ξ 0 (ξ) T T represent the low-frequency error and random measurement error of the star sensor respectively, and the superscript T represents the transpose of the vector matrix; λ 0 ≈1, ξ 0 ≈1, represent the scalar parts respectively; λ p and ξ represent the vector parts respectively;

[0024] Use the Fourier expansion to model the low-frequency error component Q st with certain periodicity in the satellite attitude Q measured by the star sensor; let the vector part λ λ =[λ p λ 1 λ 2 λ 3 T , where λ i (i = 1, 2, 3) has periodic variation characteristics and is expressed in Fourier expansion form as follows:

[0025]

[0026] Where n represents the serial number of the Fourier expansion component; N represents the order of the Fourier series; and represent the coefficients corresponding to the nth order Fourier series of the ith component; Ω n represents the angular frequency corresponding to the nth order Fourier series; t represents time;

[0027] Express the vector part of the low-frequency error in matrix form as:

[0028] λ​​​p = Φκ

[0029] Wherein, Φ represents a matrix composed of the sine and cosine trigonometric function values of each frequency point; κ is a vector of low-frequency error parameters to be estimated.

[0030] Furthermore, in the above method for modeling and compensating the on-orbit error of a star sensor based on LSTM, the construction of the low-frequency error analytical model based on the analytical method further includes:

[0031] Analyze the spectrum of the star sensor measurement data, and take multiple frequency points to model the low-frequency error.

[0032] Furthermore, in the above method for modeling and compensating the on-orbit error of a star sensor based on LSTM, the estimation of the low-frequency error of the star sensor by the combined attitude determination filter composed of the star sensor and the gyroscope includes:

[0033] Take the parameters of the low-frequency error analytical model as part of the state vector of the combined attitude determination filter composed of the star sensor and the gyroscope, and use the state estimation method to obtain the estimated values of the parameters of the low-frequency error analytical model;

[0034] Use the estimated values of the parameters of the low-frequency error analytical model to calculate the estimated value sequence of the low-frequency error of the star sensor;

[0035] Take the calculated estimated value sequence of the low-frequency error of the star sensor as the expected output of the sample set.

[0036] Furthermore, in the above method for modeling and compensating the on-orbit error of a star sensor based on LSTM, the construction of the combined attitude determination filter composed of the star sensor and the gyroscope includes:

[0037] Establish the state equation of the combined attitude determination filter for gyro-assisted estimation of the parameters of the low-frequency error model of the star sensor, and the expression is:

[0038]

[0039]

[0040] Wherein, δq represents the vector part of the error quaternion ΔQ between the satellite attitude Q obtained by integrating the angular velocity ω measured by the gyroscope g and the true attitude, and κ is the parameter vector of the low-frequency error model to be estimated; w g and the true attitude and κ is the parameter vector of the low-frequency error model to be estimated; w g is the random measurement noise of the gyroscope;

[0041] According to the satellite attitude Q measured by the star sensor st and the satellite attitude Q obtained by gyro measurement and calculation g, construct the measurement equation of the combined attitude determination filter composed of a star sensor and a gyroscope, and the expression is:

[0042]

[0043] Take the vector part of the above formula to establish the measurement equation of the combined attitude determination filter at time t k , and the expression is:

[0044]

[0045] where the subscript k represents time t k ; H k = [I 3×3 Φ k , representing the measurement matrix, and I 3×3 represents the 3-order identity matrix; Q g represents the satellite inertial attitude obtained by integrating the angular velocity measured by the gyroscope; δq k represents δq at time t k ; Φ k represents the matrix composed of the sine and cosine trigonometric function values corresponding to each frequency point at time t k ; X k = [δq k T κ k T T is the state vector of the combined attitude determination filter at time t k .

[0046] Further, in the above method for modeling and compensating the on-orbit error of a star sensor based on LSTM, the step of obtaining the estimated values of the parameters of the low-frequency error analysis model by using a state estimation method includes:

[0047] Use the Kalman filtering and smoothing algorithm to perform state estimation on the filtering equation of the combined attitude determination filter at time t k , and obtain the estimated values of the parameters of the low-frequency error analysis model:

[0048]

[0049] where, represents the estimated value of δq k ; represents the estimated value of κ.

[0050] Further, in the above method for modeling and compensating the on-orbit error of a star sensor based on LSTM, the calculation formula for the estimated value of the low-frequency error of the star sensor at time t k is:

[0051]

[0052] Among them, represents the vector part of calculating the low-frequency error according to the state estimation at time t k in the moment state estimation Calculate the vector part of the low-frequency error; represents the quaternion estimation corresponding to the low-frequency error at time t k moment.

[0053] Furthermore, in the above method for modeling and compensating the on-orbit error of a star sensor based on LSTM, the pre-constructed low-frequency error model based on the LSTM network is offline trained using the input and expected output of the sample set, including:

[0054] Perform standardization processing on the sample set;

[0055] Take the root mean square error of the quaternion after standardization as the loss function for training the low-frequency error model;

[0056] Perform inverse standardization on the components corresponding to the low-frequency error quaternion vector output by the LSTM network to obtain the corresponding components of the low-frequency error estimated by the low-frequency error model based on the LSTM network;

[0057] Calculate the loss between the expected output of the standardized sample set and the corresponding components of the low-frequency error before inverse standardization estimated by the LSTM-based low-frequency error model, and iteratively update the LSTM network parameters until the loss function reaches the minimum to obtain the final low-frequency error model.

[0058] Furthermore, in the above method for modeling and compensating the on-orbit error of a star sensor based on LSTM, during the process of compensating the measurement output of the star sensor using the online estimated low-frequency error, ignoring the random error, the attitude quaternion measured by the compensated star sensor is approximately obtained as:

[0059]

[0060] Among them, represents the attitude of the star sensor after compensation at time t k ; represents the actual measured attitude of the star sensor at time t k ; represents the low-frequency error of the star sensor estimated using the final low-frequency error model at time t k . Description of the Drawings

[0061] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on the provided drawings.

[0062] Figure 1 It is a flowchart of the method for modeling and compensating the on-orbit error of a star sensor based on LSTM provided by the present invention;

[0063] Figure 2 It is a schematic diagram of offline training of a low-frequency error model based on the LSTM network provided by the present invention;

[0064] Figure 3 It is a schematic structural diagram of a low-frequency error model based on the LSTM network provided by the present invention;

[0065] Figure 4(a) is a schematic diagram of the fitting result of LSTM1 provided by the present invention;

[0066] Figure 4(b) is a schematic diagram of the fitting result of LSTM2 provided by the present invention;

[0067] Figure 5(a) is a curve graph of the modeling error of LSTM1 provided by the present invention;

[0068] Figure 5(b) is a curve graph of the modeling error of LSTM2 provided by the present invention;

[0069] Figure 6 It is a curve graph of the attitude measurement error before the measurement output compensation of the star sensor;

[0070] Figure 7 It is a curve graph of the attitude measurement error after the measurement output compensation of the star sensor. Specific embodiments

[0071] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0072] As Figure 1 shown, the embodiments of the present invention disclose a method for modeling and compensating the on-orbit error of a star sensor based on LSTM, including:

[0073] S1. Receive the measurement data of star sensors and gyroscopes and orbit data for multiple orbital periods transmitted back from the satellite by the ground station, and generate the input of the sample set;

[0074] S2. Construct a low-frequency error analytical model based on an analytical method;

[0075] S3. Based on the low-frequency error analytical model, construct a combined attitude determination filter composed of star sensors and gyroscopes, and estimate the low-frequency error of the star sensor as the expected output of the sample set;

[0076] S4. Use the input and expected output of the sample set to perform offline training on a pre-constructed low-frequency error model based on the LSTM network;

[0077] S5. Upload the trained low-frequency error model parameters to the satellite through the ground station;

[0078] S6. On the satellite, use the trained low-frequency error model to estimate the low-frequency error of the star sensor online;

[0079] S7. Use the online estimated low-frequency error to compensate the measurement output of the star sensor.

[0080] The specific implementation process of the present invention mainly includes two stages: offline training and on-orbit application. Offline training includes S1 - S4, and on-orbit application includes S6 - S7.

[0081] Specifically, in S1, the measurement data of the attitude sensors for multiple consecutive orbits obtained on the satellite is transmitted to the ground station. For a geostationary satellite that starts orbiting at time t 0 , the time, satellite orbit argument of latitude, measurement data of star sensors and gyroscopes are extracted from these transmitted data. Accordingly, the input of the sample set is generated. The input corresponding to time t k includes the relative time Δt k = t k - t 0 , the satellite orbit argument of latitude θ k , the attitude quaternions of two adjacent measurements of the star sensor and and the attitude change quaternion k-1 ,t k interval obtained by gyro measurement solution

[0082] Ideally, the expected output of the sample set should adopt the true value of the low-frequency error in the actual system Obviously, this parameter is difficult to obtain directly. The present invention uses the angular velocity measurement information provided by the gyroscope for assistance. On the basis of establishing an analytical model of the low-frequency error, the error model parameters are taken as part of the state and methods such as Kalman filtering are used for offline estimation, and then the estimation of the low-frequency error of the star sensor is obtained. to replace it with used to construct the expected output of the sample set.

[0083] In S2 - S4, through offline training, a low-frequency error model of the on-orbit star sensor based on LSTM is established.

[0084] When using the LSTM network to establish a low-frequency error model, in order to make the established model have accuracy, stability and generalization ability, generating a sufficient sample set related to the low-frequency error is an essential link for training, validating and testing the model. Since the true attitude of the satellite during on-orbit operation is unknown, certain technical means need to be taken to extract the error term mainly composed of low-frequency error from the on-orbit measurement data of the star sensor.

[0085] In the current satellite attitude determination system, the gyroscope has become one of the basic configurations. The attitude calculated from the angular velocity measured by it is almost not affected by low-frequency error. Therefore, using the attitude information obtained by the two sensors, the low-frequency error can be extracted from it to construct a sample set. When using the state augmentation method based on error model parameters to estimate the low-frequency error of the star sensor, on the one hand, due to the limited on-board processing capacity, it is difficult to use an error model with a complex structure and many parameters; on the other hand, on-board tasks generally require real-time acquisition of high-precision attitude information, so it is difficult to apply the post-processing method based on the smoothing idea to further improve the accuracy of model parameter estimation. Therefore, the present invention adopts an offline modeling method to ensure the estimation accuracy of the measurement error of the star sensor. Here, through the offline processing of the on-orbit measurement data of the attitude sensor, a sample data set is constructed, and then on this basis, the low-frequency error model of the on-orbit star sensor based on LSTM is trained, and then optimized model parameters are obtained.

[0086] Taking into account the alternating characteristics of the low-frequency error with time and space, the input of the LSTM model consists of the current time t k and the relative time Δt 0 with the initial time t k of the satellite operation k = t 0 - t k , the satellite orbit argument of latitude θ and the attitude quaternions of two adjacent outputs of the star sensor k-1 and k and the attitude change quaternion in the interval t k-1 , t k calculated from the gyro measurement Composition; the output is t represented in quaternion form k Low-frequency error at a moment

[0087] Specifically, in S2, the construction process of the low-frequency error analysis model is as follows:

[0088] The influences of the low-frequency error and the random measurement error of the star sensor on the measurement output are regarded as rotations relative to the true attitude, and are respectively represented in quaternion form as Q λ =[λ 0 (λ p ) T T and Q ξ =[ξ 0 (ξ) T T , where the superscript T represents the transpose of the vector matrix. Since the error magnitude is small, the scalar parts respectively satisfy λ 0 ≈1 and ξ 0 ≈1, and the vector parts are respectively λ p and ξ. Furthermore, the satellite attitude Q st measured by the star sensor can be expressed as:

[0089]

[0090] where, is the true attitude.

[0091] The Fourier expansion is used to model the low-frequency error component Q λ with a certain periodicity. Let the vector part λ p =[λ 1 λ 2 λ 3 T , where λ i (i = 1, 2, 3) has periodic variation characteristics, and is expressed in Fourier expansion form as follows:

[0092]

[0093] where, n represents the serial number of the Fourier expansion component; N is the order of the Fourier series; and are the coefficients corresponding to the nth-order Fourier series of the ith component; let the period of the nth frequency point be T n , then its angular frequency is Ω n = 2π / T n ; Ω n represents the angular frequency corresponding to the nth-order Fourier series; t represents time.

[0094] ​​​The vector part of the low-frequency error is expressed in matrix form as follows:

[0095] λ p = Φκ (3)

[0096] where κ = [(κ 1 ) T … (κ N ) T T ,

[0097] Φ = [Φ 1 … Φ N ,

[0098] Here, Φ represents a matrix composed of the sine and cosine trigonometric function values at each frequency point; κ is the vector of low-frequency error parameters to be estimated; κ n represents the parameter vector composed of the corresponding coefficients of each order of Fourier series; cΩ nt = cos(Ω n t), sΩ nt = sin(Ω n t); n = 1,…, N. The determination of N needs to comprehensively consider the requirements of the on-board system for model accuracy, complexity, and computational load. For the application requirement of constructing an error model training sample set based on the on-orbit measurement data of star sensors and gyros, accuracy becomes the primary consideration factor. The low-frequency error can be modeled by taking multiple frequency points according to the spectral analysis of the star sensor measurement data. In the embodiments of the present invention, N = 3 is temporarily taken.

[0099] The following further describes the calculation process of the estimated value Figure 2 of the low-frequency error of the star sensor in S3 .

[0100] S31. Take the parameters of the low-frequency error analysis model as part of the state vector of the combined attitude determination filter composed of the star sensor and the gyro, and use the state estimation method to obtain the estimated value of the low-frequency error analysis model parameters. The combined attitude determination filter composed of the star sensor and the gyro is also called an extended filter.

[0101] Specifically, in order to ensure the estimation accuracy of the low-frequency error, the gyro measurement after error compensation is used to assist in estimating the on-orbit low-frequency error. Here, considering the random error, the measurement model of the gyro is established as follows:

[0102] ω g = ω b + w g (4)

[0103] where ω g ​The angular velocity measured by the gyroscope is ω b The projection of the rotation speed of the satellite's body frame relative to the inertial frame in the body frame is w g is the random measurement noise of the gyroscope.

[0104] Let the satellite inertial attitude obtained by integrating the angular velocity measured by the gyroscope be Q g , and the error between it and the true attitude is defined as the error quaternion:

[0105]

[0106] Taking the derivative of the above equation, we can get:

[0107]

[0108] From it can be deduced that:

[0109]

[0110] The attitude kinematic equation of the satellite can be written in the form of quaternion multiplication as follows:

[0111]

[0112] Among them, represents the quaternion form of ω b Substituting Equation (7) and Equation (8) into Equation (6), it can be deduced that:

[0113]

[0114] Among them, represents the quaternion form of ω g Substituting Equation (4) into Equation (9), according to the quaternion operation rules, ignoring the quadratic terms, we can get

[0115]

[0116] Among them, represents the quaternion form of w g δq is the vector part of ΔQ, and [a×] represents the skew-symmetric matrix formed by the vector a. Taking out the vector part of ΔQ in the above equation, we can get:

[0117]

[0118] According to Equation (3), the low-frequency error at time t k can be expressed as

[0119]

[0120] Among them, Φ k is a matrix composed of the sine and cosine trigonometric function values of each frequency point at time t k ; κ is the vector of low-frequency error parameters to be estimated, satisfying

[0121]

[0122] Take the state vector as X = [δq T κ T T . The system state equation for gyro-assisted estimation of the low-frequency error model parameters of the star sensor is formed by equations (11) and (13). Discretizing this continuous state equation gives:

[0123] X k+1 = A k+1|k X k + Γ k W k (14)

[0124] In the formula, assuming the discrete time step is Δt, then the subscript k represents time t k .

[0125] Establish the state equation of the combined attitude determination filter for gyro-assisted estimation of the low-frequency error model parameters of the star sensor, and the expression is:

[0126]

[0127]

[0128] Among them, δq represents the vector part of the error quaternion ΔQ between the satellite attitude Q g obtained by integrating the angular velocity ω g measured by the gyro and the true attitude ; κ is the parameter vector of the low-frequency error model to be estimated; w g is the random measurement noise of the gyro;

[0129] From the satellite attitudes Q st and Q g obtained from the star sensor and gyro measurements respectively, the measurement equation of the combined attitude determination filter composed of the star sensor and the gyro can be derived:

[0130]

[0131] Take the vector part of the above formula and establish the measurement equation of the combined attitude determination filter at time t k as follows:

[0132] ​

[0133] Among them, H k = [I 3×3 Φ k , where H k represents the measurement matrix; I 3×3 represents the 3x3 identity matrix; X k represents the state vector at time t k .

[0134] Equations (14) and (16) constitute the filtering equation for the attitude estimation of the star sensor / gyroscope combination containing the low-frequency error model parameters. For this linear equation, state estimation algorithms such as Kalman filtering and smoothing can be used to obtain the state estimation value at time t k . Among them, represents the estimated value of δq k ; represents the estimated value of κ at time t k .

[0135] S32. Use the estimated values of the low-frequency error analysis model parameters to calculate the estimated value sequence of the low-frequency error of the star sensor.

[0136] After the estimation error of the system state converges stably, use the k in the state estimation at time t to calculate the vector part of the low-frequency error as follows:

[0137]

[0138] Thus, the quaternion estimation corresponding to the low-frequency error at time t k can be further determined as:

[0139]

[0140] S33. Use to replace the true value for generating the output of the sample set of the low-frequency error analysis model established based on LSTM.

[0141] During the on-orbit application of star sensors, the periodic changes in the thermal field and field of view caused by the spatial position changes of the satellite relative to celestial bodies such as the Earth and the Sun are the main causes of the low-frequency errors. Therefore, when conditions permit, on-orbit data with as large a time and space span as possible should be used to generate the sample set. Only in this way can the constructed sample set comprehensively reflect the relationship between the low-frequency errors of the star sensor and factors such as time and space. On this basis, based on the LSTM network model, through in-depth mining of the data in the sample set, deep features related to factors such as time and space can be effectively extracted, and then a low-frequency error model with sufficient accuracy, stability, and generalization ability can be established.

[0142] The following combines Figure 3 to further illustrate the process of offline training of the pre-constructed low-frequency error model based on the LSTM network using the input and expected output of the sample set in S4.

[0143] S41. Standardize the sample set.

[0144] As can be seen from the low-frequency error model of the star sensor established based on the LSTM network, the input x k of this model is composed of components such as space-time parameters and the attitude quaternion measured by the star sensor; the output y k is the estimated value of the low-frequency error obtained based on the extended Kalman filter estimation According to the generation mechanism of the low-frequency error, its existence is mainly related to the on-orbit operating environment of the star sensor and does not actually depend on the gyroscope. However, according to the angular velocity measured by the gyroscope, information reflecting the attitude change can be obtained as a supplement to improve the accuracy of the model. Therefore, different LSTM-based low-frequency error models are established according to whether the gyroscope-solved attitude change quaternion is included or not in the input vector to meet the application requirements in different situations.

[0145] The low-frequency error model of the star sensor established based on the LSTM network is simplified and represented by a function as:

[0146] y k = F LSTM (x k ) (19)

[0147] Obviously, the physical units of the components included in the input x k and the output y k are different, and the corresponding value ranges also vary greatly. When directly using the original data to establish the loss function, the prediction error of the component with a large value will have a greater impact on the loss function. Therefore, by standardizing the components in the input and output, their influence on the loss function during the training process can be made as similar as possible.

[0148] Without loss of generality, represent the time series of a certain one-dimensional component in the input and output data of the LSTM network as \(u = \{u 1 , u 2 , \cdots, u m \}\), where \(m\) is the sequence length. Then, the standardized sequence \(u'=\{u' 1 , u' 2 , \cdots, u' m \}\) satisfies:

[0149]

[0150] where, \(\mu u \) represents the mean of \(u\); \(\sigma u \) represents the standard deviation of \(u\).

[0151] When training the LSTM network, use the standardized data to calculate the loss value and optimize the model parameters.

[0152] S42. Use the root mean square error of the standardized quaternion as the loss function for training the low-frequency error model based on the LSTM network.

[0153] Select the root mean square error of the standardized quaternion as the loss function for training the model, that is:

[0154]

[0155] where \(m\) is the total number of training samples; is the standardized value of the low-frequency error vector part estimated by the low-frequency error model based on the LSTM network under the input of the \(k\)-th sample; is the standardized value of the low-frequency error vector part corresponding to the output of the \(k\)-th sample, which is the expected output value of the low-frequency error analysis model based on the LSTM network.

[0156] S43. Perform inverse standardization on the components corresponding to the low-frequency error quaternion vector output by the LSTM network to obtain the corresponding components of the low-frequency error estimated by the low-frequency error model based on the LSTM network.

[0157] After obtaining the quaternion vector output by the low-frequency error model based on the LSTM network, it is necessary to perform inverse standardization on it to obtain the low-frequency error estimated value required for actual application

[0158] Output from the sample set The time series formed by a certain - dimensional component of the vector part is represented as \(v = \{v 1 ,v 2 ,\cdots,v m \}\); It represents the output value of the corresponding component of the low - frequency error model at the \(k\) - th moment; is the value after is de - normalized. The formula for de - normalization is:

[0159]

[0160] In the formula, \(\mu v represents the mean value of \(v\); \(\sigma v represents the standard deviation of \(v\).

[0161] Using the obtained by de - normalization, the corresponding component of the low - frequency error estimate value obtained based on the LSTM network model can be obtained.

[0162] S44. Calculate the loss between the expected output of the normalized sample set and the corresponding component of the low - frequency error before de - normalization estimated by the LSTM - based low - frequency error model, and iteratively update the LSTM network parameters until the loss function reaches the minimum to obtain the final low - frequency error model.

[0163] Since the structure of the neural network is complex and large - scale, it is impossible to directly obtain the optimal solution by establishing an analytical expression. The present invention uses the gradient - descent method, along the direction that makes the loss function decrease, that is, along the direction opposite to the gradient, to continuously iteratively update the network parameters, approaching the optimal solution step by step at a relatively fast speed, so that the loss function reaches the minimum.

[0164] In the embodiment of the present invention, Adam is selected as the optimizer for training the LSTM. By calculating the adaptive learning rate and introducing the historical gradient, the occurrence of oscillation is suppressed while ensuring the convergence speed. In practical applications, other optimization methods can be used to optimize the parameters of the LSTM network model according to the training effect.

[0165] S5. The ground station uploads the parameters of the final low - frequency error model based on the LSTM network established to the satellite.

[0166] In S6, the specific process of on - satellite online estimating the low - frequency error of the star sensor is as follows:

[0167] Through the ground station, inject the parameters of the final low - frequency error model based on the LSTM into the satellite to update the on - satellite LSTM - based star sensor in - orbit error model. On this basis, according to the input parameter \(\Delta t\) obtained onlinek , θ k , The estimated value of the low-frequency error obtained by using this model is as follows:

[0168]

[0169] In S7, the in-orbit compensation process of the low-frequency error is as follows:

[0170] Due to the random error Q ξ being very small, the attitude of the star sensor after compensation is approximately obtained as:

[0171]

[0172] wherein, represents the attitude of the star sensor after compensation at time t k ; represents the attitude actually measured by the star sensor at time t k ; represents the low-frequency error of the star sensor estimated by using the final low-frequency error model at time t k .

[0173] In a specific application, the present invention takes a three-axis stabilized earth-oriented satellite with an orbital period of about 6000 s as an example. The sampling frequencies of the gyroscope and the star sensor are both 8 Hz. The parameters of the low-frequency error of the star sensor are listed in Table 1, and the random measurement noise is 1″. The random measurement noise of the gyroscope is 0.05° / h.

[0174] Table 1 Low-frequency error parameters of the star sensor

[0175] Frequency point Period X-axis (") Y-axis (") Z-axis (") 1 6000 5 6 4 2 3000 0.5 0.4 0.5 3 1500 0.5 0.8 0.1

[0176] Take the initial state of the filter for estimating the low-frequency error model parameters as and its state error covariance matrix is:

[0177] P 0 = diag([(10″) 2 I 3×3 (10″) 2 I 6×6 (1″) 2 I 6×6 (1″) 2 I 6×6 )

[0178] According to the measurement performances of the gyroscope and the star sensor, the system noise matrix and the measurement noise matrix are determined respectively as: Q k =(0.05° / h) 2 I 3×3 and R k=(1″) 2 I 3×3 。

[0179] For the measurement data of the attitude sensors in 15 orbit periods obtained from the simulation, data sample sets for method verification are obtained through processing. Among them, the state components corresponding to the low-frequency error parameters estimated by the combined attitude filtering in the 1st to 3rd orbit periods have not fully entered the stable convergence state, and this part of the data will not be used as part of the sample set; the data of 12 orbit periods from the 4th to 15th orbit periods are used to form the sample data set. The sample set is divided into a training set and a test set according to a ratio of 10:2.

[0180] Parameter settings of the LSTM network: The number of hidden nodes is set to 29, and 300 rounds of training are carried out. To prevent gradient explosion, the gradient threshold is set to 1, and the initial learning rate η 0 =0.01, and after 150 rounds, the learning rate is reduced to η = 0.2η 0 . The input of the LSTM network model respectively adopts an input vector containing the quaternion of the attitude change solved by the gyro and an input vector not containing the quaternion of the attitude change solved by the gyro. After training, the low-frequency error models LSTM1 and LSTM2 can be obtained.

[0181] As Figure 4(a) and 4(b) shown, it is a comparison chart of the true value of the low-frequency error, the estimated value (expected value) in the data sample set, and the low-frequency error estimated values (predicted values) obtained based on the models LSTM1 and LSTM2 respectively. It can be seen from the figure that the low-frequency errors estimated based on the models LSTM1 and LSTM2 basically coincide with the estimated values and the true values of the low-frequency errors in the data sample set, indicating that the established models can well reflect the spatio-temporal variation characteristics of the low-frequency errors. As Figure 5(a) and 5(b) shown, it is a curve chart of the errors (the difference between the expected value and the predicted value) of estimating the low-frequency error using the models LSTM1 and LSTM2 networks respectively. It can be seen from the figure that relevant information measured by the gyro is introduced into the input of the LSTM1 model. Affected by the random measurement error of the gyro, there is a certain amount of high-frequency noise in the estimated error of the low-frequency error, while the LSTM2 model does not rely on gyro measurement, and the estimated error of the obtained low-frequency error is relatively smooth.

[0182] Table 2 statistics the mean error and mean square error of the low-frequency error estimated by LSTM1 and LSTM2 respectively. It can be seen from Table 2 that the residuals of LSTM1 and LSTM2 for estimating the low-frequency error are about 10% of the original low-frequency error. Compared with LSTM1, the estimation accuracy of LSTM2 for the low-frequency error decreases slightly, but this model still has a strong low-frequency error estimation ability, and the error is within an acceptable range. The above shows that the low-frequency error model established based on the LSTM network model effectively extracts and models the spatio-temporal variation characteristics in the low-frequency error sample set, and has good low-frequency error estimation ability.

[0183] Table 2 Modeling Error Statistics of Low-Frequency Error Based on LSTM

[0184]

[0185] When applied in orbit, if gyro measurements are available, model LSTM1 can be adopted. If gyro measurements are not available and only rely on spatio-temporal information and star sensor measurements to estimate and compensate for the low-frequency error, model LSTM2 can be adopted.

[0186] Figure 6 and Figure 7 The figure shows the attitude measurement error curves before and after estimating and compensating the low-frequency error in the star sensor measurement using the trained LSTM1 network model. It can be seen that after estimating and compensating the low-frequency error using the LSTM-based low-frequency error model, the amplitude of the attitude measurement error is significantly reduced, and the periodic component therein is significantly reduced.

[0187] Table 3 lists the statistical results of the star sensor attitude measurement error before and after compensation. It can be seen that both the mean and mean square error of the attitude measurement error after compensation have decreased significantly. Thus, when a model of the low-frequency error of the star sensor varying with time and space is established based on LSTM, this model can be used to effectively estimate and compensate for the low-frequency error of the star sensor, improving the in-orbit use accuracy of the star sensor.

[0188] Table 3 Error Statistics of Low-Frequency Error Before and After Compensation Based on LSTM Model

[0189]

[0190] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the embodiments, reference can be made to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and reference can be made to the description in the method part for the relevant parts.

[0191] The foregoing description of the disclosed embodiments enables those skilled in the art to practice or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for modeling and compensating the on-orbit error of a star sensor based on LSTM, characterized in that, it includes: Receiving the measurement data of the star sensor and gyroscope and the orbit data of multiple orbit periods transmitted back from the satellite through the ground station to generate the input of the sample set; Constructing a low-frequency error analytical model based on an analytical method; Based on the low-frequency error analytical model, constructing a combined attitude determination filter composed of a star sensor and a gyroscope to estimate the low-frequency error of the star sensor as the expected output of the sample set; Using the input and expected output of the sample set to perform offline training on a pre-constructed low-frequency error model based on the LSTM network; Uploading the trained low-frequency error model to the satellite through the ground station; On the satellite, using the trained low-frequency error model to online estimate the low-frequency error of the star sensor; Using the online estimated low-frequency error to compensate the measurement output of the star sensor; The constructing of the low-frequency error analytical model based on the analytical method includes: The satellite attitude Q measured by the star sensor is described by the following formula st :[[]]END]] Among them, is the true satellite attitude in quaternion form; Q λ = [λ 0 (λ p ) T T , Q ξ = [ξ 0 (ξ) T T , respectively representing the low-frequency error and random measurement error of the star sensor. The superscript T represents the transpose of the vector matrix; λ 0 ≈1, ξ 0 ≈1, respectively representing the scalar parts; λ p and ξ respectively represent the vector parts;​​ The satellite attitude Q measured by the star sensor is modeled using the Fourier expansion for the low-frequency error component Q with a certain periodicity st in Q; let the vector part λ λ be defined as follows: p λ 1 λ 2 λ 3 where λ T has a periodic variation characteristic, i = 1, 2, 3, and λ i is expressed in the form of Fourier expansion as follows: i ​ Among them, n represents the serial number of the Fourier expansion component; N represents the order of the Fourier series; a i n and b i n represents the coefficient corresponding to the nth-order Fourier series of the ith component; Ω n represents the angular frequency corresponding to the nth-order Fourier series; t represents time; Representing the vector part of the low-frequency error in matrix form as: λ p = Φκ where, Φ represents a matrix composed of the sine and cosine trigonometric function values of each frequency point; κ is a vector of low-frequency error parameters to be estimated.

2. The method for modeling and compensating the on-orbit error of a star sensor based on LSTM according to claim 1, characterized in that, The measurement data of the star sensor and gyroscope and the orbit data transmitted back from the satellite received by the ground station include: the current time t k and the initial moment t of the satellite operation 0 the relative time Δt k = t k - t 0 the argument of latitude θ of the satellite orbit k the attitude quaternions output by the star sensor for two adjacent times and and the attitude change quaternion in the interval [[t k-1 , t k calculated from the gyro measurement 3. The method for modeling and compensating the on-orbit error of a star sensor based on LSTM according to claim 1, characterized in that, The constructing of the low-frequency error analytical model based on the analytical method further includes: Analyzing the spectrum of the star sensor measurement data and taking multiple frequency points to model the low-frequency error.

4. The method for modeling and compensating the on-orbit error of a star sensor based on LSTM according to claim 1, characterized in that, The estimating of the low-frequency error of the star sensor by the combined attitude determination filter composed of the star sensor and the gyroscope includes: Taking the low-frequency error analytical model parameters as a part of the state vector of the combined attitude determination filter composed of the star sensor and the gyroscope, and using the state estimation method to obtain the estimated values of the low-frequency error analytical model parameters; Using the estimated values of the low-frequency error analytical model parameters to calculate the estimated value sequence of the low-frequency error of the star sensor; Taking the calculated estimated value sequence of the low-frequency error of the star sensor as the expected output of the sample set.

5. The method for modeling and compensating the on-orbit error of a star sensor based on LSTM according to claim 4, characterized in that, The construction of the combined attitude determination filter composed of the star sensor and the gyroscope includes: Establishing the state equation of the combined attitude determination filter for estimating the low-frequency error model parameters of the star sensor assisted by the gyroscope, and the expression is: where δq represents the angular velocity ω measured by the gyroscope g the satellite attitude Q obtained through integral calculation g and the true attitude the vector part of the error quaternion ΔQ between them, κ is the vector of low-frequency error parameters to be estimated, w g the random measurement noise of the gyroscope; Based on the satellite attitude Q measured by the star sensor st and the satellite attitude Q obtained by gyro measurement and solution g , construct the measurement equation of the combined attitude determination filter composed of the star sensor and the gyro, and the expression is: Take the vector part of the above equation to establish the measurement equation of the combined attitude determination filter at time t k The expression is as follows: where the subscript k represents time t k ; H k = [I 3×3 Φ k , representing the measurement matrix, and I 3×3 represents the 3-order identity matrix; δq k represents δq at time t k ; Φ k represents the matrix composed of the sine and cosine trigonometric function values corresponding to each frequency point at time t k ; X k = [δq k T κ k T T represents the state vector of the combined attitude determination filter at time t k .​ 6. The method for modeling and compensating the on-orbit error of a star sensor based on LSTM according to claim 5, characterized in that, The obtaining of the estimated values of the low-frequency error analytical model parameters by using the state estimation method includes: Use the Kalman filtering and smoothing algorithm to perform state estimation on the filtering equation of the combined attitude determination filter at time t k to obtain the estimated values of the parameters of the low-frequency error analysis model: Among them, represents the estimated value of δq k ; represents the estimated value of κ.

7. The method for modeling and compensating the on-orbit error of a star sensor based on LSTM according to claim 5, characterized in that, t k The calculation formula for the estimated value of the low-frequency error of the moment star sensor is as follows: Among them, represents the calculation of the vector part of the low-frequency error in the state estimation according to t k in the moment state estimation; Calculate the vector part of the low-frequency error; represents the quaternion estimation corresponding to the low-frequency error at time t k instant.

8. The method for modeling and compensating the on-orbit error of a star sensor based on LSTM according to claim 1, characterized in that, Offline training of a pre - constructed low - frequency error model based on the LSTM network using the input and expected output of the sample set, including: Performing normalization processing on the sample set; Taking the root - mean - square error of the normalized quaternion as the loss function for training the low - frequency error model based on the LSTM network; Performing denormalization processing on the components corresponding to the low - frequency error quaternion vector output by the LSTM network to obtain the corresponding components of the low - frequency error estimated by the low - frequency error model based on the LSTM network; Calculating the loss between the expected output of the normalized sample set and the corresponding components of the low - frequency error before denormalization estimated by the LSTM - based low - frequency error model, and iteratively updating the LSTM network parameters until the loss function reaches the minimum to obtain the final low - frequency error model.

9. A method for modeling and compensating the on - orbit error of a star sensor based on LSTM according to claim 1, characterized in that, During the process of compensating the measurement output of the star sensor using the online - estimated low - frequency error, ignoring the random error, the attitude quaternion measured by the compensated star sensor is approximately obtained as: Among them, represents the attitude of the star sensor after compensation at time t; k represents the attitude actually measured by the star sensor at time t; k represents the low-frequency error of the star sensor estimated using the final low-frequency error model at time t. represents t k The low-frequency error of the star sensor estimated using the final low-frequency error model at the moment.

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