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

Abstract

This application relates to the fields of pulsar timing navigation and autonomous spacecraft timekeeping, and discloses a method, apparatus, device, and storage medium for steering a satellite-borne atomic clock. The method includes: calculating clock error observations of a target atomic clock carried by a satellite based on observation data of electromagnetic waves emitted by a target pulsar; constructing a Gaussian process model based on the clock error characteristics of the atomic clock; training the Gaussian process model based on the clock error observations of the target atomic clock; estimating the clock error of the target atomic clock using the trained Gaussian process model; and compensating the target atomic clock for its clock error based on the clock error of the target atomic clock. This method enables real-time, high-precision steering of satellite-borne atomic clocks.

Description

Technical Field

[0001] The present application relates to the field of pulsar timing and navigation and the field of autonomous timekeeping of spacecraft, and in particular to a method, apparatus, device and storage medium for controlling a satellite-borne atomic clock. Background Art

[0002] At present, the time information of spacecraft is mainly provided by the onboard atomic clocks they carry. Due to factors such as the aging of the atomic clocks themselves and the influence of the space environment, the onboard atomic clocks will drift during use. Therefore, it is necessary to regularly rely on external time standards to correct the clock errors of the atomic clocks.

[0003] Pulsars are rapidly rotating neutron stars with excellent long-term rotational stability. Because pulsar radiation signals cover multiple bands, including radio and X-rays, spacecraft can carry miniaturized X-ray detectors to receive these X-ray signals. By observing these X-ray signals, the clock errors of onboard atomic clocks can be calibrated. Conventional clock error control for spaceborne atomic clocks often uses linear fitting to calibrate the frequency of the onboard atomic clocks. However, this method suffers from low fitting accuracy, resulting in insufficient clock error calibration precision. Insufficient clock error control accuracy can affect the overall performance of satellite systems. Therefore, a high-precision clock error control method for spaceborne atomic clocks is needed. Summary of the Invention

[0004] In view of this, the present application aims to propose a method, apparatus, device and storage medium for controlling a satellite-borne atomic clock, so as to achieve efficient and high-precision clock error control of a satellite-borne atomic clock.

[0005] To achieve the above objectives, the technical solutions of this application are as follows:

[0006] A first aspect of an embodiment of the present application provides a method for driving a satellite-borne atomic clock, the method comprising:

[0007] Calculating a clock error observation value of a target atomic clock carried by the satellite based on observation data of electromagnetic waves emitted by the target pulsar by the satellite;

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

[0009] Training the Gaussian process model based on the clock error observation value of the target atomic clock;

[0010] Using the trained Gaussian process model, estimating the clock error of the target atomic clock;

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

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

[0013] The mean function m(t) of the Gaussian process model is constructed using a quadratic polynomial:

[0014] Based on the clock error power spectrum characteristics of the atomic clock, the covariance function k(t,t T );

[0015] According to the mean function and the covariance function, a Gaussian process model is constructed:

[0016] x(t)~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 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;

[0020] The covariance function k(t,t T )as follows:

[0021] k(t,s)=(σ 2 / 2)(t 2H +s 2H -|ts| 2H );

[0022] Among them, t and s are any two moments, σ 2 =k(0,0) represents the clock error variance at time 0.

[0023] Optionally, training the Gaussian process model based on the clock error observation value of the target atomic clock includes:

[0024] Continuously obtain N clock difference observations and construct an observation sequence based on all clock difference observations; where N is not less than 5;

[0025] Training the Gaussian process model using the observation sequence specifically includes:

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

[0027]

[0028] 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:

[0029]

[0030] in,

[0031] 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;

[0032] Σ represents the covariance matrix of the observation sequence, which is expressed as:

[0033]

[0034] 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:

[0035]

[0036] Optionally, the method for driving a satellite-borne atomic clock further includes:

[0037] Determine the number of clock error observations N based on the accuracy requirements of the clock error estimation;

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

[0039] Adjusting the Gaussian process model based on the updated observation sequence;

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

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

[0042] Based on the observation sequence y, a joint Gaussian distribution is obtained:

[0043]

[0044] Among them, y * Represents the time to be estimated 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 errors in the observation sequence; μ * =m(t * ) represents the mean of the clock difference to be estimated; Σ * =[k(t1,t * ) k(t2,t * ) … k(t N ,t * )] T Represents the time to be estimated t * The covariance of the clock error and 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;

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

[0046]

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

[0048]

[0049] Optionally, 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 includes:

[0050] Obtaining the first arrival time of X-ray photons emitted by the target pulsar at the satellite, and converting the first arrival time to the center of mass of the solar system to obtain a phase observation value;

[0051] Obtaining a phase prediction value based on a time phase model of the target pulsar, a spatial position of the satellite, and a direction vector of the target pulsar;

[0052] 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.

[0053] According to a second aspect of an embodiment of the present application, a device for driving a satellite-borne atomic clock is provided, for implementing the steps of the method provided in the first aspect of the embodiment of the present application, the device comprising:

[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 observation data of electromagnetic waves emitted by the satellite to the target pulsar;

[0055] 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;

[0056] The calibration module is configured to use the trained Gaussian process model to estimate the clock error of the target atomic clock; and perform clock error compensation on the target atomic clock based on the clock error of the target atomic clock.

[0057] According to a third aspect of an embodiment of the present application, a computer-readable storage medium is provided, 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 embodiment of the present application are implemented.

[0058] According to the fourth aspect of the embodiments of the present application, an electronic device is provided, comprising a memory, a processor, and a computer program stored in the memory and runnable 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] Using the method for controlling a satellite-borne atomic clock provided in this application, observational data from a satellite based on electromagnetic waves emitted by a target pulsar is obtained, and the clock error observations of the target atomic clock carried by the satellite are calculated based on this observational data. A Gaussian process model is constructed based on the clock error characteristics of the atomic clock, and the model is trained using the clock error observations of the target atomic clock to determine the parameters of the Gaussian process model. The trained Gaussian process model is used to estimate the clock error of the target atomic clock, obtaining a high-precision clock error estimate, which is then used to compensate for the clock error of the target atomic clock.

[0060] This approach leverages the high stability of pulsars, using the electromagnetic waves emitted by pulsars to obtain accurate clock error observations. The clock error of the satellite-borne atomic clock is modeled as a high-precision Gaussian process model, which is then trained using the atomic clock clock error observations. Traditional linear fitting methods for clock error steering only yield estimated frequency deviations, but cannot directly obtain clock error estimates. Obtaining the clock error requires computational conversion. However, this approach uses a trained Gaussian process model to directly obtain high-precision clock error estimates, simplifying the conversion process and improving the efficiency of clock error calibration. Furthermore, the Gaussian process model employed in this approach offers higher precision than traditional fitting polynomials, enabling real-time steering of atomic clocks. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments of the present application. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0062] Figure 1 This is a flow chart of a method for controlling a satellite-borne atomic clock proposed in one embodiment of the present application;

[0063] Figure 2 1 is a schematic diagram of a device for controlling a satellite-borne atomic clock according to an embodiment of the present application;

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

[0065] Figure 4 This is a diagram showing the comparison results of the clock error of the atomic clock in one embodiment of the present application. DETAILED DESCRIPTION

[0066] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0067] It should be understood that references throughout this specification to "one embodiment" or "an embodiment" mean that a particular feature, structure, or characteristic associated with 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 this specification do not necessarily refer to the same embodiment. Furthermore, these particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

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

[0069] Exemplary embodiments will be described in detail herein, with examples illustrated in the accompanying drawings. When the following description refers to the drawings, identical numerals in different figures represent identical or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments are not intended to represent all embodiments consistent with the present application. Rather, they are merely examples of apparatuses and methods consistent with certain aspects as detailed herein.

[0070] It should be noted that, unless there is any conflict, the embodiments and features in the embodiments of this application can be combined with each other.

[0071] Traditionally, satellite-borne atomic clocks are calibrated by communicating with a ground control center and using ground-based reference time. However, this method requires ground signals to pass through the atmosphere and ionosphere, which may be interfered with during transmission, and is heavily dependent on the ground. In related technologies, pulsars with extremely high long-term rotational stability are used to calibrate satellite-borne atomic clocks. A large amount of pulsar observation data is used for fitting to obtain the frequency deviation of the satellite-borne atomic clock, and the fitted atomic clock frequency deviation is then compensated to achieve frequency control and get rid of dependence on the ground. However, this method is not very accurate and cannot directly provide the clock error of the satellite-borne atomic clock. The frequency deviation also needs to be converted during calibration. The cumbersome steps reduce calibration efficiency and cannot achieve real-time control of the atomic clock.

[0072] The method provided in this embodiment utilizes electromagnetic waves emitted by pulsars to steer an on-orbit atomic clock. The clock error of the on-orbit atomic clock is modeled as a high-precision Gaussian process. Observed clock error values ​​are calculated using pulsar observation data. The Gaussian process is then trained using these observed clock error values ​​to obtain a high-precision clock error estimate, enabling real-time on-orbit atomic clock steering.

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

[0074] Figure 1 This is a flow chart of a method for controlling a satellite-borne atomic clock according to an embodiment of the present application. Figure 1 As shown, the method includes:

[0075] S1: Calculating 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: Construct a Gaussian process model based on the clock error characteristics of atomic clocks;

[0077] S3: training the Gaussian process model based on the clock error observation value of the target atomic clock;

[0078] S4: using 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 example, satellite observations of electromagnetic waves emitted by a target pulsar are used to calculate the clock error of an atomic clock onboard the satellite. This clock error observation is then used to train a Gaussian process model, resulting in high-precision clock errors. Pulsars emit electromagnetic signals across multiple bands, including radio and X-rays. Given the small size of X-ray detectors, which are easier to deploy on satellites, this example uses a satellite-mounted X-ray detector as an example to illustrate clock error control for a space-borne atomic clock.

[0081] First, the target pulsar is observed by continuously receiving X-ray photons emitted by an X-ray detector onboard the satellite. Correlation processing is performed on the received X-ray photons to obtain the clock error observation value of the current target atomic clock. To accurately estimate the clock error of the onboard atomic clock, this embodiment constructs a high-precision Gaussian process model based on the clock error characteristics of the atomic clock. By obtaining the clock error observation value of the target atomic clock, the Gaussian process model is trained using the clock error observation value and its parameters are solved, thereby achieving a precise estimation of the clock error of the target atomic clock. Furthermore, the output of the target atomic clock is compensated based on the high-precision clock error estimate to achieve calibration of the onboard atomic clock.

[0082] Compared to traditional linear fitting schemes for clock error control, which only estimate the frequency deviation but cannot directly obtain the clock error estimate through linear fitting, and require computational conversion to obtain the clock error, this scheme directly obtains high-precision clock error estimates through the trained Gaussian process model, simplifying the conversion process and improving the efficiency of clock error calibration. Furthermore, the Gaussian process model used in this scheme has higher accuracy than traditional fitting polynomials, enabling real-time control of atomic clocks.

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

[0084] Obtaining the first arrival time of X-ray photons emitted by the target pulsar at the satellite, and converting the first arrival time to the center of mass of the solar system to obtain a phase observation value;

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

[0086] 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.

[0087] In this embodiment, X-ray photons emitted by a target pulsar are received by a satellite-borne X-ray detector, and the arrival time of the photons (i.e., the first arrival time) is recorded using the satellite's onboard atomic clock (the target atomic clock). This first arrival time is then converted to the solar system's center of mass based on the satellite's spatial position (i.e., the satellite's relative position relative to the solar system's center of mass), thereby obtaining the phase observation value of the target pulsar.

[0088] The phase prediction value of the target pulsar is calculated using the pulsar time phase model based on the solar system center of mass, which is constructed in advance through a large amount of observation data of the target pulsar, the spatial position information of the satellite and the direction vector of the target pulsar.

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

[0090] In one embodiment, to ensure the accuracy of the target atomic clock's clock error observation, during the process of receiving signals emitted by the target pulsar via an X-ray detector, the signal-to-noise ratio (SNR) of the currently received photon signal is calculated at a first time interval and compared with a first threshold. If the current SNR is greater than or equal to the first threshold, the current timestamp is recorded and the X-ray detector is controlled to re-accumulate X-ray photons. This step is because the photons received by the detector are discrete, and the energy of individual photons is relatively weak. If the signal-to-noise ratio of the signal is low, the accuracy of the clock error observation will be affected. Therefore, photons emitted by the target pulsar are continuously received and the SNR is calculated at fixed time intervals during the photon accumulation process. When the SNR reaches the first threshold, the current timestamp is recorded. Based on the previous timestamp and the current timestamp, the first arrival time corresponding to the current clock error observation is determined. By calculating the SNR, the accuracy of the clock error observation is ensured, thereby ensuring the accuracy of the subsequent Gaussian process model output results.

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

[0092] The mean function m(t) of the Gaussian process model is constructed using a quadratic polynomial:

[0093] Based on the clock error power spectrum characteristics of the atomic clock, the covariance function k(t,t T );

[0094] According to the mean function and the covariance function, a Gaussian process model is constructed:

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

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

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

[0098] When selecting the covariance function of the Gaussian process model, it is considered that the clock error of the atomic clock is a non-stationary random process, and its power spectral density is proportional to 1 / f β ,β>0 (f represents frequency, β represents its exponent). Fractional Brownian motion and atomic clock errors have similar power spectrum characteristics. Therefore, based on the power spectrum characteristics of atomic clock errors, the covariance function of the Gaussian process model is modeled as a covariance function based on fractional Brownian motion. This accurately reflects the frequency-dependent covariance of the clock error, effectively characterizing the properties of the random terms in the atomic clock error, and significantly improving the accuracy of the model's clock error estimation. Furthermore, by training the Gaussian process model, high-precision clock error 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 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;

[0102] The covariance function k(t,t T )as follows:

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

[0104] Among them, t and s are any two moments, 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] Among them, 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.

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

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

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

[0111] As an embodiment of the present application, training the Gaussian process model based on the clock error observation value of the target atomic clock includes:

[0112] Continuously obtain N clock difference observations and construct an observation sequence based on all clock difference observations; where N is not less than 5;

[0113] Training the Gaussian process model using the observation sequence specifically includes:

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

[0115]

[0116] 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:

[0117]

[0118] in,

[0119] 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;

[0120] Σ represents the covariance matrix of the observation sequence, which is expressed as:

[0121]

[0122] 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:

[0123]

[0124] In one embodiment, multiple clock error observations of a target pulsar are continuously acquired from a satellite to form an observation sequence. This observation sequence is then used to train a Gaussian process model to determine the model parameters. Since the Gaussian process model is constructed based on clock errors, the following likelihood function can be obtained from the joint Gaussian distribution of the observation sequence composed of clock errors:

[0125]

[0126] 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:

[0127]

[0128] in,

[0129] 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;

[0130] Σ represents the covariance matrix of the observation sequence, which is expressed as:

[0131]

[0132] According to the above likelihood function, the model parameters θ=[a0,a1,a2,H,σ 2 ] Expressed as:

[0133]

[0134] The model parameters θ include the three parameters a0, a1, a2 of the mean function and the two parameters H, σ of the covariance function. 2Given this, all parameters of the Gaussian process model can be determined by obtaining at least five clock difference observations. That is, an observation sequence is constructed based on at least five continuously acquired clock difference observations. This clock difference observation sequence is used to train the Gaussian process. By finding the maximum value of the likelihood function, the Gaussian process parameters can be solved, thus completing the Gaussian process training.

[0135] When constructing a clock error observation sequence, the more clock error observations in the sequence, the higher the accuracy of the trained Gaussian process model. However, this also increases the computational effort and reduces the model's training efficiency. Since the clock error of a satellite-borne atomic clock changes dynamically, to ensure real-time control of the satellite-borne atomic clock, the observation sequence can be constructed using as few clock error observations as possible for model training based on accuracy requirements. In actual applications, the number of clock error observations in the observation sequence can be set based on the accuracy requirements, and this is not limited in this embodiment.

[0136] In this embodiment, the atomic clock clock error is modeled as a Gaussian process, and clock error observations are obtained through pulsar observation data. A small number of clock error observations are used to train the Gaussian process and estimate the clock error of the atomic clock. At least five clock error observations need to be accumulated to calibrate the atomic clock error, which can achieve the effect of real-time clock error estimation and control.

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

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

[0139]

[0140] Among them, y * Represents the time to be estimated 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 errors in the observation sequence; μ * =m(t * ) represents the mean of the clock difference to be estimated; Σ * =[k(t1,t * ) k(t2,t * ) … k(t N ,t * )] T Represents the time to be estimated t * The covariance of the clock error and 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;

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

[0142]

[0143] y * The expected value of is determined as the estimated value of the clock error of the target atomic clock:

[0144]

[0145] In this embodiment, the clock error estimate of the target atomic clock is calculated based on the trained Gaussian process model. According to the properties of the Gaussian process model, when the clock error observation sequence y is obtained, the following joint Gaussian distribution can be obtained:

[0146]

[0147] Among them, y * Represents the time to be estimated t * The clock error of the target atomic clock at time t; 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 difference to be estimated; Σ * =[k(t1,t * ) k(t2,t * ) … k(t N ,t * )] T Represents the time to be estimated t * The covariance of the clock error and 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;

[0148] Right now,

[0149] In the above formula, μ, Σ, μ * ,Σ * , Σ ** These parameters can all be used to determine the parameters of the Gaussian process model θ = [a0, a1, a2, H, σ 2 ], calculated based on the mean function and covariance function of the model.

[0150] Further, take y* The expectation of is the estimated value of the clock error, that is, the estimated value of the clock error obtained according to the trained Gaussian process model is:

[0151]

[0152] After obtaining the target atomic clock's clock error estimate, the atomic clock's output is compensated for the error based on this estimate, thereby achieving onboard atomic clock steering. Specifically, the clock error estimate output by the Gaussian process model is subtracted from the target atomic clock's output to obtain the precise atomic clock time.

[0153] As an embodiment of the present application, the method for driving a satellite-borne atomic clock further includes:

[0154] Determine the number of clock error observations N based on the accuracy requirements of the clock error estimation;

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

[0156] Adjusting the Gaussian process model based on the updated observation sequence;

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

[0158] Because the clock error of an atomic clock changes over time, the Gaussian process model needs to be dynamically updated based on the pulsar clock error observations to ensure the required accuracy of clock error control. In one embodiment, the satellite continuously acquires phase observations of the target pulsar, calculates new clock error observations based on the phase observations and phase predictions, and updates the observation sequence based on the newly acquired clock error observations. The number of clock error observations N in the observation sequence is determined based on the accuracy requirements of the clock error estimation. Higher accuracy requirements require larger values ​​for N, which increases the computational complexity. When subsequently updating the observation sequence, the number of clock error observations in the observation sequence is maintained at N, and a corresponding number of clock error observations acquired earlier in the observation sequence are deleted based on the number of new clock error observations. That is, starting with the clock error observation acquired the furthest from the current time, a corresponding number of clock error observations are deleted in descending order of acquisition time.

[0159] For example, when N is 5, if two new clock difference observations are obtained, they are added to the observation sequence, and the two clock difference observations whose acquisition time is farthest from the current time are deleted from the observation sequence to ensure that the total number of clock difference 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 results of the Gaussian process model is ensured, meeting the high-precision requirements of real-time clock error control.

[0161] This example also uses data from the PSR B1937+21 pulsar observed by the US NICER spacecraft and clock error data from the onboard atomic clock of GPS satellite G07, released by the IGS Center of Wuhan University, to verify the clock error accuracy of this solution. Both sets of data cover the period from June 13 to July 23, 2018.

[0162] Figure 4 This is a diagram showing the comparison results of the clock error of the atomic clock in one embodiment of the present application. Figure 4 The figure shows the clock error of two clock error control methods based on Gaussian process model and Kalman filter. The vertical axis in the figure 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 points of the two clock error control schemes. Figure 4 The solid line (GP) in the middle represents the clock error estimation error when the Gaussian process model is trained for clock error control using this scheme, and the dotted line (KF) represents the clock error estimation error when the clock error control method based on Kalman filtering is used. It can be seen that the clock error error value output by the Gaussian process-based clock error control method used in this scheme 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 a satellite-borne atomic clock. Figure 2 , Figure 2 FIG. 2 is a schematic diagram of a device 200 for controlling a satellite-borne atomic clock according to an embodiment of the present application. Figure 2 As shown, the device includes:

[0164] 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 waves emitted by the satellite to the target pulsar;

[0165] The training module 202 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 observations of the target atomic clock;

[0166] The calibration module 203 is configured to use the trained Gaussian process model to estimate the clock error of the target atomic clock; and perform clock error compensation on the target atomic clock based on the clock error of the target atomic clock.

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

[0168] The mean function m(t) of the Gaussian process model is constructed using a quadratic polynomial:

[0169] Based on the clock error power spectrum characteristics of the atomic clock, the covariance function k(t,t T );

[0170] According to the mean function and the covariance function, a Gaussian process model is constructed:

[0171] x(t)~GP(m(t),k(t,t T )).

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

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

[0174] Training the Gaussian process model using the observation sequence specifically includes:

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

[0176]

[0177] 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:

[0178]

[0179] in,

[0180] 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;

[0181] Σ represents the covariance matrix of the observation sequence, which is expressed as:

[0182]

[0183] 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:

[0184]

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

[0186] Determine the number of clock error observations N based on the accuracy requirements of the clock error estimation;

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

[0188] Adjusting the Gaussian process model based on the updated observation sequence;

[0189] Based on the adjusted Gaussian process model, the clock error of the target atomic clock is re-estimated.

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

[0191] Based on the observation sequence y, a joint Gaussian distribution is obtained:

[0192]

[0193] Among them, y * Represents the time to be estimated 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 errors in the observation sequence; μ * =m(t * ) represents the mean of the clock difference to be estimated; Σ * =[k(t1,t * ) k(t2,t * ) … k(t N ,t * )] T Represents the time to be estimated t * The covariance of the clock error and 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;

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

[0195]

[0196] y * The expected value of is determined as the estimated value of the clock error of the target atomic clock:

[0197]

[0198] As an embodiment 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 waves emitted by the satellite to the target pulsar, specifically including:

[0199] Obtaining the first arrival time of X-ray photons emitted by the target pulsar at the satellite, and converting the first arrival time to the center of mass of the solar system to obtain a phase observation value;

[0200] Obtaining a phase prediction value based on a time phase model of the target pulsar, a spatial position of the satellite, and a direction vector of the target pulsar;

[0201] 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.

[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, which, when executed by a processor, implements the steps of the method for controlling a satellite-borne atomic clock as described in any 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. When the computer program is executed by a processor, the steps in the method of driving a satellite-borne atomic clock as described in any of the above embodiments of the present application are implemented.

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

[0205] Regarding the apparatus in the above embodiment, the specific manner in which each module performs operations has been described in detail in the embodiment of the method, and will not be elaborated here.

[0206] The above description is only a preferred embodiment of the present application and is 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 scope of protection of the present application.

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

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

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

[0210] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing terminal device to operate in a specific manner, so that the instructions stored in the computer readable memory produce a manufactured product including an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0211] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal device so that a series of operating steps are executed on the computer or other programmable terminal device to produce a computer-implemented process, thereby providing instructions for executing on the computer or other programmable terminal device to implement the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0212] Although preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they become aware of the underlying inventive concepts. Therefore, this application is intended to include the preferred embodiments and all changes and modifications that fall within the scope of the embodiments of the present invention.

[0213] Finally, it should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that includes a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or terminal device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or terminal device that includes the element.

[0214] The above is a detailed introduction to the method, device, equipment and storage medium for controlling the satellite-borne atomic clock provided by the present application. Specific examples are used in this article to illustrate the principles and implementation methods of the present application. The description of the above embodiments is only used to help understand the method of the present application and its core idea; at the same time, for general technical personnel in this field, based on the ideas of the present application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on 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 the 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, clock error compensation is performed on the target atomic clock.

2. The method for driving a satellite-borne atomic clock according to claim 1, wherein: 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 controlling a satellite-borne atomic clock according to claim 2, wherein: 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, wherein: 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; Training the Gaussian process model using the observation sequence 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: Determine the number of clock error observations N based on the accuracy requirements of the clock error estimation; When the number of clock difference observations obtained is greater than N, delete the clock difference observations obtained 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, wherein: 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 time to be estimated 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 errors in the observation sequence; μ * =m(t * ) represents the mean of the clock difference to be estimated; Σ * =[k(t1,t * ) k(t2,t * ) … k(t N ,t * )] T Represents the time to be estimated t * The covariance of the clock error and 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, wherein: Calculating a clock error observation value of a target atomic clock carried by the satellite based on observation data of electromagnetic waves emitted by the target pulsar by the satellite includes: Obtaining the first arrival time of X-ray photons emitted by the target pulsar at 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 a time phase model of the target pulsar, a spatial position of the satellite, and a 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 controlling 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 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 use the trained Gaussian process model to estimate the clock error of the target atomic clock; 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, wherein: 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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