Method, device and equipment for controlling satellite-borne atomic clock and storage medium

Abstract

The invention relates to the field of pulsar timing navigation and the field of autonomous time keeping of spacecrafts, and discloses a method, device and equipment for controlling a satellite-borne atomic clock and a storage medium. The method comprises the following steps: calculating a clock difference observation value of a target atomic clock carried by a satellite based on observation data of electromagnetic waves emitted by the satellite to a target pulsar; constructing a Gaussian process model based on the clock difference characteristic of the atomic clock; training the Gaussian process model based on the clock difference observation value of the target atomic clock; estimating the clock error of the target atomic clock by using the trained Gaussian process model; and performing clock difference compensation on the target atomic clock based on the clock difference of the target atomic clock. By adopting the method, real-time and high-precision clock error control of the satellite-borne atomic clock can be realized.

Description

Technical Field

[0001] The present application relates to the fields of pulsar timing navigation and spacecraft autonomous timekeeping, and particularly to a method, device, equipment, and storage medium for controlling an on-board atomic clock. Background Art

[0002] Currently, the time information of spacecraft mainly relies on the on-board atomic clocks carried by themselves. Due to factors such as the aging of the atomic clocks themselves and the influence of the space environment, the on-board atomic clocks will drift during use. Therefore, it is necessary to regularly correct the clock error of the atomic clocks relying on an external time reference.

[0003] A pulsar is a kind of neutron star with a high-speed rotation, and its long-term rotation stability is excellent. Since the radiation signals of pulsars cover multiple bands such as radio and X-rays, spacecraft can receive the X-ray signals radiated by pulsars by carrying miniaturized X-ray detectors. By observing the X-ray signals of pulsars, the clock error of the on-board atomic clocks can be calibrated. The clock error control of related on-board atomic clocks mostly uses a linear fitting method to calibrate the frequency of the on-board atomic clocks. However, this method has low fitting accuracy, resulting in insufficient clock error calibration accuracy. And the insufficient clock error control accuracy will affect the overall performance of the satellite system. Therefore, it is necessary to find a high-precision method for controlling the clock error of on-board atomic clocks. Summary of the Invention

[0004] In view of this, the present application aims to propose a method, device, equipment, and storage medium for controlling an on-board atomic clock to achieve efficient and high-precision control of the clock error of on-board atomic clocks.

[0005] To achieve the above object, the technical solution of the present application is as follows:

[0006] The first aspect of the embodiments of the present application provides a method for controlling an on-board atomic clock, the method including:

[0007] Based on the observation data of the electromagnetic waves emitted by a target pulsar by a satellite, calculating an observed value of the clock error of the target atomic clock carried by the satellite;

[0008] Based on the clock error characteristics of the atomic clock, constructing a Gaussian process model;

[0009] Based on the observed value of the clock error of the target atomic clock, training the Gaussian process model;

[0010] Using the trained Gaussian process model to estimate the clock error of the target atomic clock;

[0011] Based on the clock error of the target atomic clock, performing clock error compensation on the target atomic clock.

[0012] Optionally, constructing a Gaussian process model based on the clock error characteristics of the atomic clock, including:

[0013] Construct the mean function \(m(t)\) of the Gaussian process model using a quadratic polynomial:

[0014] Based on the power spectrum characteristics of the clock offset of the atomic clock, construct the covariance function \(k(t, t T ) of the Gaussian process model using fractional Brownian motion;

[0015] Construct a Gaussian process model according to the mean function and the covariance function:

[0016] \(x(t)\sim GP(m(t), k(t, t T ))

[0017] Optionally, the mean function \(m(t)\) of the Gaussian process model is as follows:

[0018]

[0019] where \(t 0 represents the starting time of the operation of the atomic clock; \(a 0 is the clock offset of the atomic clock at time \(t 0 ; \(a 1 is the frequency deviation of the atomic clock at time \(t 0 ; \(a 2 is the frequency drift deviation of the atomic clock at time \(t 0 ;

[0020] The covariance function \(k(t, t T ) of the Gaussian process model is as follows:

[0021] \(k(t, s) = (\sigma 2 / 2)(t 2H + s 2H - |t - s| 2H )

[0022] where \(t\) and \(s\) are any two times, and \(\sigma 2 = k(0, 0)\) represents the clock offset variance at time 0.

[0023] Optionally, based on the clock offset observation values of the target atomic clock, train the Gaussian process model, including:

[0024] Continuously obtain \(N\) clock offset observation values and construct an observation sequence based on all clock offset observation values; where \(N\) is not less than 5;

[0025] Use the observation sequence to train the Gaussian process model, specifically including:

[0026] Construct the likelihood function of the observation sequence:

[0027]

[0028] Among them, y is the observation sequence, including N clock error observations; P represents the noise variance matrix of the observation sequence, and its expression is:

[0029]

[0030] Among them,

[0031] Among them, T 50 is the semi-flux density duration of the pulsar, T b is the time resolution of the detector carried by the satellite, A is the effective area of the detector, Δt k is the duration of the k-th segment of the satellite observing the pulsar, η s and η b respectively represent the flux of the pulsar and the background noise;

[0032] Σ represents the covariance matrix of the observation sequence, and its expression is:

[0033]

[0034] Based on the likelihood function, the parameters θ = [a 0 , a 1 , a 2 , H, σ 2 of the Gaussian process model are solved by the maximum likelihood method to complete the training of the Gaussian process model:

[0035]

[0036] Optionally, the method for controlling the spaceborne atomic clock further includes:

[0037] Determine the number N of clock error observations according to the clock error estimation accuracy requirement;

[0038] When the number of the obtained clock error observations is greater than N, delete the clock error observations with earlier acquisition times so that the number of clock error observations in the observation sequence is N, and update the observation sequence;

[0039] Based on the updated observation sequence, adjust the Gaussian process model;

[0040] Based on the adjusted Gaussian process model, re-estimate the clock error of the target atomic clock.

[0041] Optionally, using the trained Gaussian process model to estimate the clock error of the target atomic clock includes:

[0042] Obtain a joint Gaussian distribution based on the observation sequence y:

[0043]

[0044] where y * represents the clock error of the target atomic clock at the to-be-estimated time t * ; y is the observation sequence, including N clock error observation values; P represents the noise variance matrix of the observation sequence; Σ represents the covariance matrix of the observation sequence; μ = m(t) represents the mean of the clock errors in the observation sequence; μ * = m(t * ) represents the mean of the clock error at the to-be-estimated time; Σ * = [k(t 1 , t * ) k(t 2 , t * ) … k(t N , t * )] T represents the covariance between the clock error at the to-be-estimated time t * and the clock errors in the observation sequence; is the transpose of Σ * ; Σ ** = k(t * , t * ) represents the variance of the clock error at the to-be-estimated time;

[0045] Calculate y that follows the following Gaussian distribution * :

[0046]

[0047] Determine the expected value of y * as the estimated value of the clock error of the target atomic clock:

[0048]

[0049] Optionally, based on the observation data of the electromagnetic wave emitted by the satellite to the target pulsar, calculate the clock error observation value of the target atomic clock carried by the satellite, including:

[0050] Obtain the first arrival time of the X-ray photons radiated by the target pulsar reaching the satellite, and convert the first arrival time to the solar system barycenter to obtain the phase observation value;

[0051] Based on the time-phase model of the target pulsar, the spatial position of the satellite, and the direction vector of the target pulsar, obtain the phase prediction value;

[0052] Based on the phase observation value, the phase prediction value, and the frequency of the target pulsar, calculate the clock error observation value of the target atomic clock.

[0053] According to the second aspect of the embodiments of the present application, there is provided a device for controlling an on-board atomic clock, which is used to implement the steps in the method provided in the first aspect of the embodiments of the present application. The device includes:

[0054] An observation data processing module, configured to calculate a clock error observation value of a target atomic clock carried by the satellite based on the observation data of the electromagnetic wave emitted by the target pulsar by the satellite;

[0055] A training module, configured to construct a Gaussian process model based on the clock error characteristics of the atomic clock; and train the Gaussian process model based on the clock error observation value of the target atomic clock;

[0056] A calibration module, configured to estimate the clock error of the target atomic clock by using the trained Gaussian process model; and perform clock error compensation on the target atomic clock based on the clock error of the target atomic clock.

[0057] According to the third aspect of the embodiments of the present application, there is provided a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps in the method provided in the first aspect of the embodiments of the present application are implemented.

[0058] According to the fourth aspect of the embodiments of the present application, there is provided an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the computer program is executed by the processor, the steps in the method provided in the first aspect of the embodiments of the present application are implemented.

[0059] By using the method for controlling an on-board atomic clock provided by the present application, the observation data of the electromagnetic wave emitted by the target pulsar by the satellite is obtained, and the clock error observation value of the target atomic clock carried by the satellite is calculated based on the observation data. A Gaussian process model is constructed based on the clock error characteristics of the atomic clock, and the model is trained by using the clock error observation value of the target atomic clock, so as to determine the parameters of the Gaussian process model. The clock error of the target atomic clock is estimated by using the trained Gaussian process model to obtain a high-precision clock error estimation value, and then the clock error compensation of the target atomic clock is realized according to the clock error estimation value.

[0060] This solution makes use of the high stability characteristics of pulsars, obtains accurate clock difference observation values by using the electromagnetic waves radiated by pulsars, models the clock difference of the spaceborne atomic clock as a high-precision Gaussian process model, and trains the Gaussian process model using the clock difference observation values of the atomic clock. The traditional linear fitting method for clock difference control can only obtain the estimated frequency deviation and cannot directly obtain the clock difference estimate. If the clock difference is to be obtained, it still needs to be obtained through calculation and conversion. However, the Gaussian process model completed through training in this solution can directly obtain high-precision clock difference estimates, simplifies the conversion steps, and improves the efficiency of clock difference calibration. Moreover, the Gaussian process model adopted in this solution has higher precision than the traditional fitting polynomial and can achieve real-time control of the atomic clock. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the accompanying drawings required for the description of the embodiments of the present application will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other accompanying drawings can be obtained based on these drawings without creative efforts.

[0062] Figure 1 is a flowchart of a method for controlling a spaceborne atomic clock proposed in an embodiment of the present application;

[0063] Figure 2 is a schematic diagram of a device for controlling a spaceborne atomic clock proposed in an embodiment of the present application;

[0064] Figure 3 is a schematic diagram of an electronic device proposed in an embodiment of the present application;

[0065] Figure 4 is a graph of the clock difference error comparison results of the atomic clock in an embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0066] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are some, but not all, of the embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts fall within the scope of protection of the present application.

[0067] It should be understood that the "one embodiment" or "an embodiment" mentioned throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of the present application. Therefore, the appearances of "in one embodiment" or "in an embodiment" throughout the specification do not necessarily refer to the same embodiment. In addition, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments.

[0068] In various embodiments of the present application, it should be understood that the magnitudes of the serial numbers of the following processes do not imply the order of execution, and the order of execution of each process should be determined by its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of the present application.

[0069] Here, exemplary embodiments will be described in detail, and the examples are shown in the accompanying drawings. When the following description refers to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. On the contrary, they are merely examples of devices and methods consistent with some aspects detailed in the present application.

[0070] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments may be combined with each other.

[0071] Traditional on-board atomic clock calibration is to calibrate the on-board atomic clock by communicating with the ground control center and using the ground reference time. However, in this way, the ground signal needs to pass through the atmosphere and the ionosphere, and may be interfered during the transmission process, and it is highly dependent on the ground. In related technologies, pulsars with extremely high long-term rotation stability are used to calibrate the on-board atomic clock. By fitting a large amount of pulsar observation data, the frequency deviation of the on-board atomic clock is obtained, and then the frequency deviation of the atomic clock obtained by fitting is compensated to achieve frequency control and get rid of the dependence on the ground. However, this method has low accuracy and cannot directly give the clock error of the on-board atomic clock. During calibration, the frequency deviation needs to be converted, and the steps are cumbersome, reducing the calibration efficiency and unable to achieve real-time control of the atomic clock.

[0072] The method provided in this embodiment uses the electromagnetic waves radiated by pulsars to control the on-board atomic clock in orbit. The clock error of the on-board atomic clock is modeled as a high-precision Gaussian process model. The clock error observation value of the on-board atomic clock is calculated through pulsar observation data, and the Gaussian process is trained using the clock error observation value, so as to obtain a high-precision clock error estimation value of the atomic clock and achieve real-time on-orbit control of the on-board atomic clock.

[0073] The present application will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0074] Figure 1 is a flowchart of a method for controlling an on-board atomic clock proposed in an embodiment of the present application. As Figure 1 shown, the method includes:

[0075] S1: Calculate the clock error observation value of the target atomic clock carried by the satellite based on the observation data of the electromagnetic waves emitted by the target pulsar by the satellite;

[0076] S2: Based on the clock error characteristics of the atomic clock, construct a Gaussian process model;

[0077] S3: Based on the clock error observation values of the target atomic clock, train the Gaussian process model;

[0078] S4: Use the trained Gaussian process model to estimate the clock error of the target atomic clock;

[0079] S5: Based on the clock error of the target atomic clock, perform clock error compensation on the target atomic clock.

[0080] In this embodiment, through the observation data of the electromagnetic waves emitted by the target pulsar by the satellite, the clock error observation values of the atomic clock carried by the satellite are calculated, and the Gaussian process model is trained using the clock error observation values, so as to obtain the high-precision clock error of the atomic clock. The electromagnetic wave signals radiated by pulsars cover multiple bands such as radio and X-rays. In view of the smaller size of X-ray detectors, they are easier to deploy on satellites. Therefore, in this embodiment, the case where the satellite carries an X-ray detector is taken as an example to illustrate the clock error control of the spaceborne atomic clock.

[0081] First, the X-ray detector carried on the satellite continuously receives the X-ray photons radiated by the target pulsar to observe the target pulsar. By performing relevant processing on the received X-ray photons, the clock error observation values of the current target atomic clock are obtained. In order to accurately estimate the clock error of the spaceborne atomic clock, in this embodiment, a high-precision Gaussian process model is constructed based on the clock error characteristics of the atomic clock. By obtaining the clock error observation values of the target atomic clock, the Gaussian process model is trained using the clock error observation values to solve its parameters, so as to achieve the accurate estimation of the clock error of the target atomic clock. Furthermore, according to the high-precision clock error estimation value, the output of the target atomic clock is compensated to achieve the calibration of the spaceborne atomic clock.

[0082] Compared with the traditional scheme of realizing clock error control by linear fitting, the traditional scheme can only obtain the estimated frequency deviation through linear fitting and cannot directly obtain the clock error estimation value. If the clock error needs to be obtained, it still needs to be calculated and converted. However, in this scheme, the trained Gaussian process model can directly obtain the high-precision clock error estimation value, which simplifies the conversion steps and improves the efficiency of clock error calibration. Moreover, the Gaussian process model adopted in this scheme has higher precision than the traditional fitting polynomial and can realize the real-time control of the atomic clock.

[0083] As an implementation manner of the present application, based on the observation data of the electromagnetic waves emitted by the target pulsar by the satellite, calculating the clock error observation values of the target atomic clock carried by the satellite includes:

[0084] Obtain the first arrival time when the X-ray photons radiated by the target pulsar reach the satellite, and convert the first arrival time to the solar system barycenter to obtain a phase observation value;

[0085] Based on the time-phase model of the target pulsar, the spatial position of the satellite, and the direction vector of the target pulsar, obtain a phase prediction value;

[0086] Based on the phase observation value, the phase prediction value, and the frequency of the target pulsar, calculate the clock error observation value of the target atomic clock.

[0087] In this embodiment, the X-ray photons radiated by the target pulsar are received by the X-ray detector carried by the satellite, and the on-board atomic clock (target atomic clock) carried by the satellite is used to record the photon arrival time (i.e., the first arrival time). Then, based on the spatial position information of the satellite (i.e., the relative position of the satellite with respect to the solar system barycenter), the first arrival time is converted to the solar system barycenter, and thus the phase observation value of the target pulsar is obtained.

[0088] Using the pulsar time-phase model based on the solar system barycenter, the spatial position information of the satellite, and the direction vector of the target pulsar, which are pre-constructed through a large amount of observation data of the target pulsar, calculate the phase prediction value of the target pulsar.

[0089] Furthermore, subtract the phase prediction value from the phase observation value of the target pulsar and divide by the frequency of the target pulsar to obtain the clock error observation value of the target atomic clock.

[0090] In one embodiment, in order to ensure the accuracy of the clock error observation value of the target atomic clock, during the process of receiving the signal radiated by the target pulsar by the X-ray detector, calculate the signal-to-noise ratio of the currently received photon signal at the first time interval, and compare the current signal-to-noise ratio with the first threshold. When the current signal-to-noise ratio is greater than or equal to the first threshold, record the current timestamp and control the X-ray detector to re-accumulate X-ray photons. This step is because the photons received by the detector are discrete and the energy of a single photon is weak. If the signal-to-noise ratio of the signal is low, it will affect the accuracy of the clock error observation value. Therefore, continuously receive the photons emitted by the target pulsar and calculate the signal-to-noise ratio at a fixed time interval during the photon accumulation process. When the signal-to-noise ratio reaches the first threshold, record the timestamp at the current moment. Based on the previous timestamp and the current timestamp, determine the first arrival time corresponding to the current clock error observation value. Ensure the accuracy of the clock error observation value by calculating the signal-to-noise ratio, and thus ensure the accuracy of the output result of the subsequent Gaussian process model.

[0091] As an implementation manner of the present application, based on the clock error characteristics of the atomic clock, construct a Gaussian process model, including:

[0092] Construct the mean function \(m(t)\) of the Gaussian process model using a quadratic polynomial:

[0093] Based on the power spectrum characteristics of the clock offset of the atomic clock, use fractional Brownian motion to construct the covariance function \(k(t,t T )\) of the Gaussian process model;

[0094] Construct a Gaussian process model according to the mean function and the covariance function:

[0095] \(x(t)\sim GP(m(t),k(t,t T ))\).

[0096] The Gaussian process model can be uniquely described by its mean function and covariance function. When constructing the Gaussian process model, it is first necessary to determine its mean function and covariance function. In one embodiment, a quadratic polynomial is selected as the mean function \(m(t)\) of the Gaussian process model, and fractional Brownian motion (FBM) is used to construct the covariance function \(k(t,t T )\) of the Gaussian process model. Based on the mean function and the covariance function, construct a Gaussian process model:

[0097] \(x(t)\sim GP(m(t),k(t,t T ))\).

[0098] When selecting the covariance function of the Gaussian process model, considering that the clock offset of the atomic clock is a non-stationary random process and its power spectral density is proportional to \(1 / f β ,\beta\gt0\) (\(f\) represents frequency, \(\beta\) represents its exponent). And fractional Brownian motion has similar power spectrum characteristics to the clock offset of the atomic clock. Therefore, according to the power spectrum characteristics of the atomic clock offset, modeling the covariance function of the Gaussian process model as a covariance function based on fractional Brownian motion can accurately reflect the change of the covariance of the clock offset with frequency, effectively characterize the characteristics of the random term in the atomic clock offset, and effectively improve the estimation accuracy of the model for the clock offset. Furthermore, by training the Gaussian process model, high-precision clock offset estimation can be achieved.

[0099] As an implementation manner of the present application, the mean function \(n(t)\) of the Gaussian process model is as follows:

[0100]

[0101] where \(t 0 \) represents the starting time of the operation of the atomic clock; \(a 0 \) is the clock offset of the atomic clock at time \(t 0 \); \(a 1 \) is the frequency deviation of the atomic clock at time \(t 0 \); \(a 2is the frequency drift deviation of the atomic clock at time t 0 at time

[0102] The covariance function k(t, t T ) of the Gaussian process model is as follows:

[0103] k(t, s) = (σ 2 / 2)(t 2H + s 2H - |t - s| 2H );

[0104] where t and s are any two times, and σ 2 = k(0, 0) represents the clock error variance at time 0.

[0105] In this embodiment, the mean function of the Gaussian process is constructed as the following quadratic polynomial:

[0106]

[0107] where t 0 represents the starting time of the atomic clock operation; a 0 is the clock error of the atomic clock at time t 0 ; a 1 is the frequency deviation of the atomic clock at time t 0 ; a 2 is the frequency drift deviation of the atomic clock at time t 0 at time

[0108] The power spectrum of the fractional Brownian motion is proportional to 1 / f 2H+1 , and the covariance function constructed based on the fractional Brownian motion is as follows:

[0109] k(t, s) = (σ 2 / 2)(t 2H + s 2H - |t - s| 2H );

[0110] where H represents the Hurst exponent, t and s are any two times, and σ 2 = k(0, 0) represents the clock error variance at time 0.

[0111] As an implementation manner of this application, training the Gaussian process model based on the clock error observation values of the target atomic clock includes:

[0112] Continuously obtaining N clock error observation values and constructing an observation sequence based on all the clock error observation values; where N is not less than 5;

[0113] Using the observation sequence to train the Gaussian process model, specifically including:

[0114] Construct the likelihood function of the observation sequence:

[0115]

[0116] where y is the observation sequence, including N clock difference observations; P represents the noise variance matrix of the observation sequence, and its expression is:

[0117]

[0118] where

[0119] where T 50 is the semi-flux density duration of the pulsar, T b is the time resolution of the detector carried by the satellite, A is the effective area of the detector, Δt k is the duration of the k-th segment of satellite observation of the pulsar, η s and η b represent the flux and background noise of the pulsar respectively;

[0120] Σ represents the covariance matrix of the observation sequence, and its expression is:

[0121]

[0122] Based on the likelihood function, solve the parameters θ = [a 0 , a 1 , a 2 , H, σ 2 of the Gaussian process model by the maximum likelihood method to complete the training of the Gaussian process model:

[0123]

[0124] In one embodiment, continuously obtain multiple clock difference observations of the target pulsar by the satellite to form an observation sequence, and use the observation sequence to train the Gaussian process model to determine the parameters of the model. Since the Gaussian process model is constructed based on the clock difference, the observation sequence composed of the clock difference follows a joint Gaussian distribution, and the following likelihood function can be obtained:

[0125]

[0126] where y is the observation sequence, including N clock difference observations; P represents the noise variance matrix of the observation sequence, and its expression is:

[0127]

[0128] where

[0129] where T50 is the semi-flux density duration of the pulsar, T b is the time resolution of the detector carried by the satellite, A is the effective area of the detector, and Δt k is the duration of the k-th satellite observation of the pulsar, η s and η b represent the flux of the pulsar and the background noise respectively;

[0130] Σ represents the covariance matrix of the observation sequence, and its expression is:

[0131]

[0132] According to the above likelihood function, the model parameters θ = [a 0 , a 1 , a 2 , H, σ 2 can be estimated by the maximum likelihood method which is expressed as:

[0133]

[0134] The model parameters θ include three parameters a 0 , a 1 , a 2 of the mean function, and two parameters H, σ 2 of the covariance function. In view of this, as long as no less than 5 clock offset observations are obtained, all parameters of the Gaussian process model can be determined. That is, based on the continuously obtained no less than 5 clock offset observations, an observation sequence is constructed, and this clock offset observation sequence is used to train the Gaussian process. By solving the maximum value of the likelihood function, the solution of the Gaussian process parameters can be realized, thus completing the Gaussian process training.

[0135] When constructing the clock offset observation sequence, the more clock offset observations in the sequence, the higher the accuracy of the trained Gaussian process model. However, it will also increase the computational amount and reduce the training efficiency of the model. Since the clock offset of the spaceborne atomic clock is dynamically changing, in order to ensure that the spaceborne atomic clock can be controlled in real time, according to the accuracy requirements, as few clock offset observations as possible can be used to construct the observation sequence for model training. In the actual application process, the number of clock offset observations in the observation sequence can be set according to the accuracy requirements, and this is not limited in this embodiment.

[0136] In this embodiment, the clock offset of the atomic clock is modeled as a Gaussian process. The clock offset observations are obtained through pulsar observation data. The Gaussian process is trained using a small number of clock offset observations and the clock offset of the atomic clock is estimated. It is possible to calibrate the clock offset of the atomic clock with a minimum of only 5 accumulated clock offset observations, and the effect of real-time clock offset estimation and control can be achieved.

[0137] As an implementation manner of the present application, using the trained Gaussian process model to estimate the clock offset of the target atomic clock includes:

[0138] Based on the observation sequence y, obtain a joint Gaussian distribution:

[0139]

[0140] where y * represents the clock offset of the target atomic clock at the to-be-estimated moment t * ; y is the observation sequence, including N clock offset observation values; P represents the noise variance matrix of the observation sequence; Σ represents the covariance matrix of the observation sequence; μ = m(t) represents the mean of the clock offsets in the observation sequence; μ * = m(t * ) represents the mean of the clock offset at the to-be-estimated moment; Σ * = [k(t 1 , t * ) k(t 2 , t * ) … k(t N , t * )] T represents the covariance between the clock offset at the to-be-estimated moment t * and the clock offsets in the observation sequence; is the transpose of Σ * ; Σ ** = k(t * , t * ) represents the variance of the clock offset at the to-be-estimated moment;

[0141] Calculate y * that follows the following Gaussian distribution:

[0142]

[0143] Determine the expected value of y * as the estimated value of the clock offset of the target atomic clock:

[0144]

[0145] In this embodiment, calculate the estimated value of the clock offset of the target atomic clock according to the trained Gaussian process model. According to the properties of the Gaussian process model, in the case where the clock offset observation sequence y has been obtained, the following joint Gaussian distribution can be obtained:

[0146]

[0147] where y * represents the clock offset of the target atomic clock at the to-be-estimated moment t *The clock error of the target atomic clock at that time; P represents the noise variance matrix of the observation sequence; Σ represents the covariance matrix of the observation sequence; μ = m(t) represents the mean of the clock error in the observation sequence; μ * = m(t * ) represents the mean of the clock error at the time to be estimated; Σ * = [k(t 1 , t * ) k(t 2 , t * ) … k(t N , t * )] T represents the covariance between the clock error at the time to be estimated t * and the clock error in the observation sequence; is the transpose of Σ * ; Σ ** = k(t * , t * ) represents the variance of the clock error at the time to be estimated;

[0148] That is,

[0149] In the above formula, μ, Σ, μ * , Σ * , Σ ** These parameters can all be calculated using the parameters θ = [a 0 , a 1 , a 2 , H, σ 2 of the already determined Gaussian process model according to the mean function and covariance function of the model.

[0150] Furthermore, taking the expectation of y * as the clock error estimate value, that is, the clock error estimate value obtained according to the trained Gaussian process model is:

[0151]

[0152] After obtaining the clock error estimate value of the target atomic clock, clock error compensation is performed on the output of the atomic clock based on this clock error estimate value, so as to realize the control of the spaceborne atomic clock. Specifically, on the basis of the time output by the target atomic clock, subtracting the clock error estimate value output by the Gaussian process model, the accurate atomic clock time can be obtained.

[0153] As an implementation manner of this application, the method for controlling the spaceborne atomic clock further includes:

[0154] Determine the number of clock error observation values N according to the clock error estimation accuracy requirement;

[0155] When the number of obtained clock error observations is greater than N, delete the clock error observations with earlier acquisition times so that the number of clock error observations in the observation sequence is N, and update the observation sequence;

[0156] Based on the updated observation sequence, adjust the Gaussian process model;

[0157] Based on the adjusted Gaussian process model, re-estimate the clock error of the target atomic clock.

[0158] Since the clock error of the atomic clock changes over time, it is necessary to dynamically update the Gaussian process model according to the clock error observations of the pulsar to ensure the accuracy requirements of clock error control. In one embodiment, the satellite continuously obtains the phase observations of the target pulsar, calculates the new clock error observations based on the phase observations and the phase prediction values, and updates the observation sequence according to the newly obtained clock error observations. The number N of clock error observations in the observation sequence is determined based on the accuracy requirements of clock error estimation. The higher the accuracy requirement, the larger the value of N of the required clock error observations, which will correspondingly increase the calculation amount. When updating the observation sequence subsequently, keep the number of clock error observations in the observation sequence as N, and delete the corresponding number of clock error observations with earlier acquisition times in the observation sequence according to the number of new clock error observations. That is, starting from the clock error observation with the farthest acquisition time from the current time, delete the corresponding number of clock error observations in order of acquisition time from far to near.

[0159] For example, when N is 5, if 2 new clock error observations are obtained, they are added to the observation sequence, and 2 clock error observations with the farthest acquisition time from the current time are deleted from the observation sequence to ensure that the total number of clock error observations in the observation sequence remains unchanged.

[0160] By dynamically updating the observation sequence and using the updated observation sequence to retrain the Gaussian process model and adjust the model parameters, the accuracy of the output result of the Gaussian process model is ensured to meet the high-precision requirements of real-time clock error control.

[0161] In addition, this embodiment also uses the measured data of the PSR B1937+21 pulsar of the American NICER detector and the clock error data of the on-board atomic clock of satellite G07 in the GPS satellite navigation system released by the IGS Center of Wuhan University to calculate and verify the clock error accuracy of this solution. The time spans of the above two groups of data are both from June 13 to July 23, 2018.

[0162] Figure 4 It is a diagram of the comparison result of the clock error of the atomic clock in an embodiment of the present application. Figure 4The clock error situations of two clock error control methods based on the Gaussian process model and based on Kalman filtering are shown. In the figure, the vertical axis is the clock error of the atomic clock (unit: second), the horizontal axis is time (unit: Julian day), and the points on the horizontal axis represent the comparison time value points of the two clock error control schemes. Figure 4 The solid line (GP) in the figure is the clock error estimation error of using the present scheme to train the Gaussian process model for clock error control, and the dashed line (KF) is the clock error estimation error of the clock error control method based on Kalman filtering. It can be seen that for the method of clock error control based on Gaussian process adopted in the present scheme, the output clock error value is smaller, that is, the clock error estimation accuracy is higher.

[0163] Based on the same inventive concept, an embodiment of the present application provides a device for controlling an on-board atomic clock. Refer to Figure 2 , Figure 2 is a schematic diagram of a device 200 for controlling an on-board atomic clock proposed in an embodiment of the present application. As shown in Figure 2 , the device includes:

[0164] An observation data processing module 201, configured to calculate a clock error observation value of a target atomic clock carried by the satellite based on observation data of electromagnetic waves emitted by the satellite to a target pulsar;

[0165] A training module 202, configured to construct a Gaussian process model based on the clock error characteristics of the atomic clock; and train the Gaussian process model based on the clock error observation value of the target atomic clock;

[0166] A calibration module 203, configured to estimate the clock error of the target atomic clock by using the trained Gaussian process model; and perform clock error compensation on the target atomic clock based on the clock error of the target atomic clock.

[0167] As an implementation manner of the present application, the training module 202, configured to construct a Gaussian process model based on the clock error characteristics of the atomic clock, specifically includes:

[0168] Use a quadratic polynomial to construct the mean function m(t) of the Gaussian process model:

[0169] Based on the clock error power spectrum characteristics of the atomic clock, use fractional Brownian motion to construct the covariance function k(t, t T );

[0170] Construct a Gaussian process model according to the mean function and the covariance function:

[0171] x(t) ∼ GP(m(t), k(t, t T ));

[0172] As an implementation manner of the present application, the training module 202 is configured to train the Gaussian process model based on the clock difference observation value of the target atomic clock, including:

[0173] Continuously obtain N clock difference observation values, and construct an observation sequence based on all the clock difference observation values; where N is not less than 5;

[0174] Use the observation sequence to train the Gaussian process model, specifically including:

[0175] Construct the likelihood function of the observation sequence:

[0176]

[0177] where y is the observation sequence, including N clock difference observation values; P represents the noise variance matrix of the observation sequence, and its expression is:

[0178]

[0179] where,

[0180] where T 50 is the semi-flux density duration of the pulsar, T b is the time resolution of the detector carried by the satellite, A is the effective area of the detector, Δt k is the duration of the k-th satellite observation of the pulsar, η s and η b respectively represent the flux and background noise of the pulsar;

[0181] Σ represents the covariance matrix of the observation sequence, and its expression is:

[0182]

[0183] Based on the likelihood function, solve the parameters θ = [a 0 , a 1 , a 2 , H, σ 2 of the Gaussian process model by the maximum likelihood method to complete the training of the Gaussian process model:

[0184]

[0185] As an implementation manner of the present application, the training module 202 is further configured to execute the following steps:

[0186] Determine the number N of clock difference observation values according to the clock difference estimation accuracy requirement;

[0187] When the number of acquired clock difference observations is greater than N, delete the clock difference observations with earlier acquisition times so that the number of clock difference observations in the observation sequence is N, and update the observation sequence;

[0188] Based on the updated observation sequence, adjust the Gaussian process model;

[0189] Based on the adjusted Gaussian process model, re-estimate the clock difference of the target atomic clock.

[0190] As an implementation manner of the present application, the calibration module 203 is configured to estimate the clock difference of the target atomic clock using the trained Gaussian process model, specifically including:

[0191] Obtain a joint Gaussian distribution based on the observation sequence y:

[0192]

[0193] where y * represents the clock difference of the target atomic clock at the moment t * to be estimated; y is the observation sequence, including N clock difference observations; P represents the noise variance matrix of the observation sequence; Σ represents the covariance matrix of the observation sequence; μ = m(t) represents the mean of the clock differences in the observation sequence; μ * = m(t * ) represents the mean of the clock difference at the moment to be estimated; Σ * = [k(t 1 , t * ) k(t 2 , t * ) … k(t N , t * )] T represents the covariance between the clock difference at the moment t * to be estimated and the clock differences in the observation sequence; is the transpose of Σ * ; Σ ** = k(t * , t * ) represents the variance of the clock difference at the moment to be estimated;

[0194] Calculate y * that follows the following Gaussian distribution:

[0195]

[0196] Determine the expected value of y * as the estimated value of the clock difference of the target atomic clock:

[0197]

[0198] As an implementation manner of the present application, the observation data processing module 201 is configured to calculate the clock error observation value of the target atomic clock carried by the satellite based on the observation data of the electromagnetic wave emitted by the target pulsar by the satellite, specifically including:

[0199] Obtain the first arrival time when the X-ray photons radiated by the target pulsar reach the satellite, and convert the first arrival time to the solar system barycenter to obtain the phase observation value;

[0200] Based on the time-phase model of the target pulsar, the spatial position of the satellite, and the direction vector of the target pulsar, obtain the phase prediction value;

[0201] Based on the phase observation value, the phase prediction value, and the frequency of the target pulsar, calculate the clock error observation value of the target atomic clock.

[0202] Based on the same inventive concept, an embodiment of the present application provides a computer program product. The computer program product includes a computer program, and when the computer program is executed by a processor, it implements the steps in the method for controlling an on-board atomic clock as described in any one of the above embodiments of the present application.

[0203] Based on the same inventive concept, an embodiment of the present application provides a readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the steps in the method for controlling an on-board atomic clock as described in any one of the above embodiments of the present application.

[0204] Based on the same inventive concept, an embodiment of the present application provides an electronic device. Refer to Figure 3 , Figure 3 is a schematic diagram of an electronic device proposed in an embodiment of the present application. The electronic device includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the computer program is executed by the processor, it implements the steps in the method for controlling an on-board atomic clock as described in any one of the above embodiments of the present application.

[0205] Regarding the device in the above embodiments, the specific manner in which each module performs operations has been described in detail in the embodiments related to the method, and will not be elaborated in detail here.

[0206] The above are only the preferred embodiments of the present application, and are not intended to limit the present application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

[0207] For method embodiments, for simplicity of description, they are all expressed as a series of combinations of actions. However, those skilled in the art should understand that this application is not limited by the described order of actions, because according to this application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also understand that the embodiments described in the specification are all preferred embodiments, and the actions and components involved are not necessarily essential to this application.

[0208] Those skilled in the art should understand that the embodiments of this application can be provided as methods, devices, or computer program products. Therefore, the embodiments of this application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the embodiments of this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0209] The embodiments of this application are described with reference to the flowcharts and / or block diagrams of methods, terminal devices (systems), and computer program products according to the embodiments of this application. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing terminal devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing terminal devices generate a device for implementing the functions specified in Figure 1 one or more of the flows Figure 1 or multiple flows and / or blocks

[0210] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing terminal device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device that implements the functions specified in Figure 1 one or more of the flows Figure 1 or multiple flows and / or blocks

[0211] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal device, such that a series of operation steps are performed on the computer or other programmable terminal device to generate a computer-implemented process, so that the instructions executed on the computer or other programmable terminal device provide steps for implementing the functions specified in Figure 1 one or more of the flows Figure 1 or multiple flows and / or blocks

[0212] Although the preferred embodiments of the embodiments of the present application have been described, those skilled in the art can make additional changes and modifications to these embodiments once they know the basic creative concept. Therefore, the present application is interpreted to include the preferred embodiments and all changes and modifications that fall within the scope of the embodiments of the present application.

[0213] Finally, it should also be noted that in this text, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or terminal device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or elements inherent to such process, method, article or terminal device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the process, method, article or terminal device comprising the element.

[0214] The method, apparatus, device and storage medium for controlling an on-board atomic clock provided by the present application have been introduced in detail above. Specific examples are used in this text to elaborate on the principle and implementation manner of the present application. The description of the above embodiments is only used to help understand the method and its core idea of the present application; at the same time, for those of ordinary skill in the art, according to the idea of the present application, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present application.

Claims

1. A method for driving a satellite-borne atomic clock, characterized in that: include: Calculating a clock error observation value of a target atomic clock carried by the satellite based on observation data of electromagnetic waves emitted by a target pulsar by the satellite; Based on the clock error characteristics of atomic clocks, a Gaussian process model is constructed; Training the Gaussian process model based on the clock error observation value of the target atomic clock; Using the trained Gaussian process model, estimating the clock error of the target atomic clock; Based on the clock error of the target atomic clock, the clock error of the target atomic clock is compensated.

2. The method for driving a satellite-borne atomic clock according to claim 1, characterized in that: Based on the clock error characteristics of the atomic clock, a Gaussian process model is constructed, including: The mean function m(t) of the Gaussian process model is constructed using a quadratic polynomial: Based on the clock error power spectrum characteristics of the atomic clock, the covariance function k(t,t T ); According to the mean function and the covariance function, a Gaussian process model is constructed: x(t)~GP(m(t),k(t,t T ))。 3. The method for driving a satellite-borne atomic clock according to claim 2, characterized in that: The mean function m(t) of the Gaussian process model is as follows: Where t0 represents the starting time of the atomic clock; a0 is the clock error of the atomic clock at time t0; a1 is the frequency deviation of the atomic clock at time t0; a2 is the frequency drift deviation of the atomic clock at time t0; The covariance function k(t,t T )as follows: k(t,s)=(σ 2 / 2)(t 2H +s 2H -|t-s| 2H ); Among them, t and s are any two moments, σ 2 =k(0,0) represents the clock error variance at time 0.

4. The method for driving a satellite-borne atomic clock according to claim 1, characterized in that: Training the Gaussian process model based on the clock error observation value of the target atomic clock includes: Continuously obtain N clock difference observations and construct an observation sequence based on all clock difference observations; where N is not less than 5; Using the observation sequence to train the Gaussian process model specifically includes: Construct the likelihood function of the observation sequence: Where y is the observation sequence, which contains N clock error observations; P represents the noise variance matrix of the observation sequence, which is expressed as: in, Among them, T 50 is the half-flux density duration of the pulsar, T b is the time resolution of the detector carried by the satellite, A is the effective area of ​​the detector, Δt k is the duration of the kth satellite observation of the pulsar, η s and η b denote the pulsar flux and background noise respectively; Σ represents the covariance matrix of the observation sequence, which is expressed as: Based on the likelihood function, the parameters of the Gaussian process model are solved by the maximum likelihood method. 2 ] to complete the training of the Gaussian process model:

5. The method for driving a satellite-borne atomic clock according to claim 4, characterized in that: Also includes: According to the accuracy requirement of clock error estimation, determine the number of clock error observation values ​​N; When the number of acquired clock difference observations is greater than N, delete the clock difference observations acquired earlier, so that the number of clock difference observations in the observation sequence is N, and update the observation sequence; Adjusting the Gaussian process model based on the updated observation sequence; Based on the adjusted Gaussian process model, the clock error of the target atomic clock is re-estimated.

6. The method for driving a satellite-borne atomic clock according to claim 1, characterized in that: Using the trained Gaussian process model, estimating the clock error of the target atomic clock includes: Based on the observation sequence y, a joint Gaussian distribution is obtained: Among them, y * represents the estimated time t * The clock error of the target atomic clock at time t; y is the observation sequence, which contains N clock error observations; P represents the noise variance matrix of the observation sequence; Σ represents the covariance matrix of the observation sequence; μ = m(t) represents the mean of the clock error in the observation sequence; μ * =m(t * ) represents the mean value of the clock difference to be estimated; Σ * =[k(t1,t * ) k(t2,t * ) … k(t N ,t * )] T represents the estimated time t * The covariance of the clock error with the clock error in the observation sequence; =Σ * The transpose of Σ ** = k(t * ,t * ) represents the variance of the clock error at the time to be estimated; Calculate y that follows the following Gaussian distribution * : y * The expected value of is determined as the estimated value of the clock error of the target atomic clock:

7. The method for driving a satellite-borne atomic clock according to claim 1, characterized in that: Based on the observation data of the electromagnetic waves emitted by the satellite to the target pulsar, the clock error observation value of the target atomic clock carried by the satellite is calculated, including: Obtaining the first arrival time of X-ray photons radiated by the target pulsar to the satellite, and converting the first arrival time to the center of mass of the solar system to obtain a phase observation value; Obtaining a phase prediction value based on the time phase model of the target pulsar, the spatial position of the satellite and the direction vector of the target pulsar; Based on the phase observation value, the phase prediction value and the frequency of the target pulsar, the clock error observation value of the target atomic clock is calculated.

8. A device for driving a satellite-borne atomic clock, characterized in that: Used to implement the method according to any one of claims 1 to 7, comprising: An observation data processing module is configured to calculate a clock error observation value of a target atomic clock carried by the satellite based on observation data of electromagnetic waves emitted by the satellite to the target pulsar; A training module is configured to construct a Gaussian process model based on the clock error characteristics of the atomic clock; and train the Gaussian process model based on the clock error observation value of the target atomic clock; The calibration module is configured to estimate the clock error of the target atomic clock using the trained Gaussian process model; and perform clock error compensation on the target atomic clock based on the clock error of the target atomic clock.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps in the method according to any one of claims 1 to 7 are implemented.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps in the method according to any one of claims 1 to 7 are implemented.

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