Satellite-borne atomic clock remote discontinuous frequency control method

Abstract

The invention provides a satellite-borne atomic clock remote discontinuous frequency control method. The method comprises the following steps: acquiring a clock difference between a controlled satellite-borne atomic clock and a space reference clock; performing state estimation on the state quantity of the clock correction by taking the clock correction as input through a Kalman filtering algorithm; according to the clock difference state quantity output by the Kalman filtering algorithm, calculating an optimal frequency control value through an LQR control algorithm; and inputting the optimal frequency control value into the controlled satellite-borne atomic clock to realize frequency control. In this way, the problems that in the spaceborne atomic clock frequency control process, measurement noise is large, and control reference is discontinuous can be solved.

Description

Technical Field

[0001] The present invention relates to the field of time and frequency technology, and in particular to a remote discontinuous frequency control method for a satellite-borne atomic clock. Background Art

[0002] With the development of science and technology, the requirements for time accuracy are getting higher and higher, and the means of measuring and maintaining time have also developed from the initial mechanical measurement to high-precision optical measurement. In the field of space applications, there has always been a widespread and urgent demand for high-precision satellite time in the fields of satellite navigation system performance improvement, satellite high-speed laser communication, astronomical and deep space exploration, and verification of general relativity.

[0003] Cesium clocks, rubidium clocks and hydrogen clocks are the most widely used satellite atomic clocks in orbit. However, they all have certain frequency drift during orbital operation, resulting in deterioration of long-term frequency stability. The frequency stability of high-precision space clocks represented by optical clocks has reached 10 -18 The level has far exceeded the current second definition reference cesium fountain clock. However, considering factors such as technology maturity, engineering construction costs, and satellite replacement speed, the comprehensive application of high-performance space clocks is difficult to achieve overnight. At this time, based on the high-precision inter-satellite time and frequency transmission link, the low-frequency drift rate and high-frequency stability of mercury ion microwave clocks or optical clocks can be used to remotely control the frequency of low-performance satellite-borne atomic clocks such as cesium clocks, rubidium clocks, and hydrogen clocks, which can effectively improve the performance of satellite-borne atomic clock time and frequency signals.

[0004] At present, the research on atomic clock frequency control methods is mainly focused on ground-based timekeeping systems, and some frequency control schemes have been proposed. However, compared with ground-based timekeeping systems, the frequency control process of satellite-borne atomic clocks has the characteristics of large measurement noise and discontinuous control reference, and the existing frequency control methods are not applicable.

[0005] Therefore, a method that can solve the problems existing in the prior art is urgently needed. Summary of the invention

[0006] The purpose of the present invention is to provide a remote discontinuous frequency steering method for a satellite-borne atomic clock, which is used to solve the problems of satellite-borne scenario application and the problems of large measurement noise and discontinuous steering reference during the frequency steering of the satellite-borne atomic clock.

[0007] In order to achieve the above object, the present invention provides a method for remote discontinuous frequency steering of a satellite-borne atomic clock, comprising the steps of:

[0008] Obtain the clock difference between the steered satellite-borne atomic clock and the space reference clock;

[0009] Using the clock error as input, the clock error state quantity is estimated through a Kalman filtering algorithm;

[0010] Calculate the optimal frequency control value through the LQR control algorithm according to the clock error state quantity output by the Kalman filter algorithm;

[0011] The optimal frequency steering value is input into the steered satellite-borne atomic clock to achieve frequency steering.

[0012] Further, obtaining the clock difference between the steered satellite-borne atomic clock and the space reference clock includes:

[0013] The clock difference between the onboard atomic clock of the piloted satellite and the space reference clock is obtained through the inter-satellite comparison measurement link.

[0014] Furthermore, the estimating the clock error state quantity by using the clock error as input through the Kalman filtering algorithm includes:

[0015] The clock error state quantity is predicted with one-step control quantity through Kalman filter algorithm;

[0016] Based on the clock error, the clock error state quantity of the one-step prediction is updated and corrected using a Kalman filtering algorithm.

[0017] Furthermore, the state equation of the Kalman filter algorithm in performing one-step prediction of the clock error state quantity with the control quantity is:

[0018] x(k+1|k)=φ(τ)x(k)+b(τ)u(k)+w(k);

[0019] Where x is the clock error state vector of the system; k is the discrete time; φ(τ) is the state transfer matrix; τ is the discrete time interval; b(τ) is the propagation term; u(k) is the frequency control value; w(k) is the atomic clock noise, and satisfies w(k)~~N(0,Q R );

[0020] The state transfer matrix φ(τ) is:

[0021]

[0022] The propagation term b(τ) is:

[0023]

[0024] The mean square error of the Kalman filter algorithm in one-step prediction of the clock error state quantity with control quantity is:

[0025] P(k+1|k)=φ(τ)P(k)φ T (τ)+Q R .

[0026] Furthermore, the equation for correcting the clock error state quantity predicted in one step based on the clock error is:

[0027] x(k+1)=x(k+1|k)+Kk +1 (z(k+1)-Hx(k+1|k));

[0028] Wherein, z is the measured value of the clock error; H is the measurement matrix; K k+1 is the filter gain;

[0029] The filter gain K k+1 for:

[0030] K k+1 =P(k+1|k)H T (HP(k+1|k)H T +R) -1 ;

[0031] The measurement equation of the Kalman filter algorithm is:

[0032] z(k+1)=Hx(k+1)+v(k+1);

[0033] H =

[100] ;

[0034] Wherein, v(k+1) is the measurement noise and satisfies v(k+1)~N(0,R).

[0035] Furthermore, the optimal frequency control value is calculated by the LQR control algorithm based on the following formula:

[0036] u(k)=-G o x(k);

[0037] Among them, G0 is the gain matrix;

[0038] The gain matrix G0 is:

[0039] G0=(B T K0B+W R ) -1 B T K0φ(τ);

[0040] Wherein, K0 is a linear quadratic regulator; and the linear quadratic regulator is calculated based on the steady-state Ricatti equation:

[0041] K0=φ T (τ)K0φ(τ)+W Q -φ T (τ)K0B(B T K0B+W R ) -1 BT K0φ(τ).

[0042] The satellite-borne atomic clock remote discontinuous frequency steering method disclosed in the present invention adopts the Kalman filtering algorithm as the minimum mean square error estimation method, which is responsible for estimating the state, reduces the requirements for measurement accuracy and continuity of the measurement value, and is applicable to the satellite-borne atomic clock frequency steering scene with large measurement noise and discontinuous steering reference; the LQR algorithm is also adopted as a controller design method based on state feedback, which is responsible for designing the controller, and the optimal frequency steering value is obtained by optimizing a quadratic cost function, and different steering speeds can be achieved by adjusting the relative size relationship of the parameters; the present invention combines the Kalman algorithm and the LQR algorithm, suppresses the system error through state feedback, and minimizes the steady-state deviation and control cost of the system, thereby ensuring the stability and robustness of the system; only the system output needs to be measured, and all state variables do not need to be accurately measured, so that the optimal control of the system can be achieved in the presence of state estimation errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 A flowchart of the steps of the remote non-continuous frequency steering method of a satellite-borne atomic clock provided in one embodiment of the present invention;

[0044] Figure 2 A schematic diagram of the remote discontinuous frequency steering method of a satellite-borne atomic clock provided in one embodiment of the present invention;

[0045] Figure 3 The figure is a schematic diagram of the frequency steering effect under different phase measurement accuracies using the satellite-borne atomic clock remote discontinuous frequency steering method of the present invention. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0047] It should be noted that references to "one embodiment", "embodiment", "example embodiment", etc. in this specification refer to the embodiment described, which may include specific features, structures or characteristics, but not every embodiment must include these specific features, structures or characteristics. In addition, such expressions do not refer to the same embodiment. Furthermore, when describing specific features, structures or characteristics in conjunction with an embodiment, whether or not there is an explicit description, it has been shown that it is within the knowledge of those skilled in the art to combine such features, structures or characteristics into other embodiments.

[0048] In addition, certain words are used in the specification and subsequent claims to refer to specific components or parts. Those with ordinary knowledge in the relevant field should understand that manufacturers can use different nouns or terms to refer to the same component or part. This specification and subsequent claims do not use differences in names as a way to distinguish components or parts, but use differences in the functions of components or parts as the criteria for distinction. "Including" and "including" mentioned throughout the specification and subsequent claims are open-ended terms and should be interpreted as "including but not limited to". In addition, the word "connected" here includes any direct and indirect electrical connection means. Indirect electrical connection means include connection through other devices.

[0049] Figure 1 A method for remote discontinuous frequency steering of a satellite-borne atomic clock provided by an embodiment of the present invention is shown, comprising the following steps:

[0050] S101: Obtain the clock difference between the atomic clock on the piloted satellite and the space reference clock; the space reference clock is used to provide an extremely accurate time standard to ensure the accuracy of time synchronization in space missions; the clock difference obtained in this step specifically refers to the clock difference between the atomic clock on the piloted satellite and the space reference clock.

[0051] In specific implementation, step S101 includes: obtaining the clock difference between the steered satellite-borne atomic clock and the space reference clock through an inter-satellite comparison measurement link.

[0052] S102: The clock error state quantity is estimated by using the Kalman filter algorithm with the clock error as input. Specifically, the clock error between the driven satellite-borne atomic clock and the space reference clock is obtained as the input of the Kalman filter algorithm at any time, and the observation equation of the Kalman filter is constructed based on the clock error. The Kalman filter algorithm estimates the system state by minimizing the state estimation error, that is, the clock error state quantity is estimated; in this way, the requirements for measurement accuracy and continuity of measurement values ​​can be reduced, which is suitable for the frequency steering scenario of satellite-borne atomic clocks with large measurement noise and discontinuous steering reference.

[0053] Furthermore, the step S102 specifically includes: performing a one-step prediction of the clock error state quantity with a control quantity by using a Kalman filter algorithm; based on the clock error, updating and correcting the clock error state quantity predicted in the one-step prediction by using a Kalman filter algorithm. The Kalman filter algorithm estimates the system state by minimizing the state estimation error, and mainly includes two steps: prediction and update.

[0054] In the prediction step of the Kalman filter algorithm, the traditional Kalman timekeeping algorithm generally assumes the state equation of the atomic clock to be a linear differential equation, which is used to describe the free-running atomic clock model. However, in the application scenario of atomic clock frequency control, due to the existence of frequency control, the state equation of the Kalman filter algorithm for one-step prediction of the clock error state quantity with control quantity should be:

[0055] x(k+1|k)=φ(τ)x(k)+b(τ)u(k)+w(k);

[0056] Where x is the clock error state vector of the system; k is the discrete time; φ(τ) is the state transfer matrix; τ is the discrete time interval; b(τ) is the propagation term; u(k) is the frequency control value; w(k) is the atomic clock noise, and satisfies w(k)~N(0,Q R );

[0057] The state transfer matrix φ(τ) is:

[0058]

[0059] The propagation term b(τ) is:

[0060]

[0061] The mean square error of the Kalman filter algorithm in one-step prediction of the clock error state quantity with control quantity is:

[0062] P(k+1|k)=φ(τ)P(k)φ T (τ)+Q R .

[0063] Since the onboard atomic clock has a certain frequency drift rate, x in the onboard atomic clock frequency steering algorithm of this embodiment is specifically a three-dimensional state vector of phase, frequency and frequency drift.

[0064] In the update step of the Kalman filter algorithm, the current measurement value is used to correct the above state equation; specifically, the equation for correcting the clock error state quantity predicted in one step based on the clock error is:

[0065] x(k+1)=x(k+1|k)+Kk +1 (z(k+1)-Hx(k+1|k));

[0066] Where z is the measured value of the clock error; H is the measurement matrix; K k+1 is the filter gain;

[0067] The filter gain K k+1 for:

[0068] K k+1 =P(k+1|k)H T (HP(k+1|k)H T +R) -1 ;

[0069] The measured value z is the phase difference between the driven atomic clock and the reference clock, and the measurement matrix H describes the system measurement process. Therefore, the measurement equation of the Kalman filter algorithm is:

[0070] z(k+1)=Hx(k+1)+v(k+1);

[0071] H =

[100] ;

[0072] Wherein, v(k+1) is the measurement noise and satisfies v(k+1)~N(0,R).

[0073] Based on the measurement equation provided in step S102, the clock error state quantity at the next moment can be estimated, and then the process proceeds to step S103. Figure 2 shown.

[0074] S103: According to the clock error state quantity output by the Kalman filter algorithm, the optimal frequency control value is calculated by the LQR control algorithm; the LQR (Linear Quadratic Regulator) control algorithm is an optimal control algorithm based on the state space model; its goal is to design a feedback controller so that the linear system can achieve optimal control under the premise of meeting certain performance indicators. In this step S103, the optimal frequency control value is obtained by optimizing a quadratic cost function based on the clock error state quantity obtained in step S102 and the LQR control algorithm.

[0075] In specific implementation, the optimal frequency control value is calculated by the LQR control algorithm based on the following formula:

[0076] u(k)=-G0x(k);

[0077] Among them, G0 is the gain matrix;

[0078] The gain matrix G0 is:

[0079] G0=(B T K0B+W R ) -1 B T K0φ(τ);

[0080] Wherein, K0 is a linear quadratic regulator; and the linear quadratic regulator is calculated based on the steady-state Ricatti equation:

[0081] K0=φT (τ)K0φ(τ)+W Q -φ T (τ)K0B(B T K0B+W R ) -1 B T K0φ(τ).

[0082] This embodiment adopts the LQR algorithm as a controller design method based on state feedback, which is responsible for designing the controller, obtaining the optimal frequency control value by optimizing a quadratic cost function, and achieving different control speeds by adjusting the relative size relationship of parameters.

[0083] S104: Input the optimal frequency control value to the driven satellite-borne atomic clock to achieve frequency control. Figure 2 The calculated optimal frequency steering value will be input into the driven satellite-borne atomic clock, and the driven satellite-borne atomic clock will implement frequency steering based on the obtained optimal frequency steering value.

[0084] In a specific application example, the atomic clock simulation platform was used to obtain 365 days of clock error simulation data of the space-borne rubidium clock and the space optical clock, with a sampling interval of 300 seconds. The frequency control was implemented, in which the space-borne rubidium clock was used as the controlled atomic clock and the space optical clock was used as the control reference; the phase deviation of the optical clock and the rubidium clock was used as input data, and the frequency control amount of the rubidium clock was calculated using the LQG algorithm, and the frequency control amount of the rubidium clock was deducted to obtain the final control result.

[0085] The accuracy of the clock difference measurement between the driven atomic clock and the reference clock directly determines the accuracy of the measurement value in the Kalman filter algorithm, which in turn affects the calculation of the optimal frequency control value. The influence of phase measurement accuracy on the frequency control result is as follows: Figure 3 As shown in the figure, the phase measurement accuracy is 10ns, 1ns and 0.1ns respectively. It can be seen that the higher the phase measurement accuracy, the better the frequency control effect.

[0086] In summary, the remote discontinuous frequency steering method of the satellite-borne atomic clock described in the present invention obtains the clock difference between the satellite-borne atomic clock being steered and the space reference clock through the inter-satellite comparison measurement link; and based on the clock difference, constructs the observation equation of the Kalman filter, and estimates the system state by minimizing the state estimation error; according to the system state, the LQR control algorithm obtains the optimal frequency steering value by optimizing a quadratic cost function; and inputs the frequency steering value into the satellite-borne atomic clock being steered to achieve frequency steering. In this way, the present invention reduces the requirements for measurement accuracy and continuity of measurement values, and can be applied to the frequency steering scenario of the satellite-borne atomic clock with large measurement noise and discontinuous steering reference; different steering speeds can be achieved by adjusting the relative size relationship of the parameters; the present invention combines the Kalman algorithm and the LQR algorithm, suppresses the system error through state feedback, and minimizes the steady-state deviation and control cost of the system, thereby ensuring the stability and robustness of the system; only the system output needs to be measured, and all state variables do not need to be accurately measured, and the optimal control of the system can be achieved in the presence of state estimation errors.

[0087] Of course, the present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A method for remote non-continuous frequency control of a satellite-borne atomic clock, characterized in that: Includes steps: Obtain the clock difference between the steered satellite-borne atomic clock and the space reference clock; Using the clock error as input, the clock error state quantity is estimated through a Kalman filtering algorithm; Calculate the optimal frequency control value through the LQR control algorithm according to the clock error state quantity output by the Kalman filter algorithm; The optimal frequency steering value is input into the steered satellite-borne atomic clock to achieve frequency steering.

2. The method for remote non-continuous frequency control of a satellite-borne atomic clock according to claim 1, characterized in that: The step of obtaining the clock difference between the steered satellite-borne atomic clock and the space reference clock comprises: The clock difference between the onboard atomic clock of the piloted satellite and the space reference clock is obtained through the inter-satellite comparison measurement link.

3. The method for remote non-continuous frequency control of a satellite-borne atomic clock according to claim 1, characterized in that: The estimating the clock error state quantity by using the clock error as input through the Kalman filtering algorithm includes: The clock error state quantity is predicted with one-step control quantity through Kalman filter algorithm; Based on the clock error, the clock error state quantity of the one-step prediction is updated and corrected using a Kalman filtering algorithm.

4. The method for remote non-continuous frequency control of a satellite-borne atomic clock according to claim 3, characterized in that: The state equation of the Kalman filter algorithm for one-step prediction of the clock error state quantity with control quantity is: x(k+1|k)=φ(τ)x(k)+b(τ)u(k)+w(k); Where x is the clock error state vector of the system; k is the discrete time; φ(τ) is the state transfer matrix; τ is the discrete time interval; b(τ) is the propagation term; u(k) is the frequency control value; w(k) is the atomic clock noise, and satisfies w(k)~N(0,Q R ); The state transfer matrix φ(τ) is: The propagation term b(τ) is: The mean square error of the Kalman filter algorithm in one-step prediction of the clock error state quantity with control quantity is: P(k+1|k)=φ(τ)P(k)φ T (t)+Q R 。 5. The method for remote non-continuous frequency control of a satellite-borne atomic clock according to claim 4, characterized in that: The equation for correcting the clock error state quantity predicted in one step based on the clock error is: x(k+1)=x(k+1|k)+Kk +1 (z(k+1)-Hx(k+1|k)); Wherein, z is the measured value of the clock error; H is the measurement matrix; K k+1 is the filter gain; The filter gain K k+1 for: K k+1 =P(k+1|k)H T (HP(k+1|k)H T +R) -1 ; The measurement equation of the Kalman filter algorithm is: z(k+1)=Hx(k+1)+v(k+1); H＝[1 0 0]； Wherein, v(k+1) is the measurement noise and satisfies v(k+1)~N(0,R).

6. The method for remote non-continuous frequency control of a satellite-borne atomic clock according to claim 5, characterized in that: The optimal frequency control value is calculated by the LQR control algorithm based on the following formula: u(k)=-G0x(k); Among them, G0 is the gain matrix; The gain matrix G0 is: G0=(B T K0B+W R ) -1 B T K0φ(τ); Wherein, K0 is a linear quadratic regulator; and the linear quadratic regulator is calculated based on the steady-state Ricatti equation: K0=φ T (τ)K0φ(τ)+W Q -f T (t)K0B(B T K0B+W R ) -1 B T K0φ(τ).

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