A method and system for cold atom microwave locking of a crystal oscillator

Abstract

The application provides a cold atom microwave clock locking crystal oscillator method and system, the method comprises the following steps: establishing a discrete-time state space model of a crystal oscillator, and defining a state vector; a measurement model is established, a relative frequency deviation output by a cold atom microwave clock is taken as an observation, and an observation matrix is determined; a Kalman filtering algorithm is used to estimate a relative frequency deviation estimation value and a relative frequency drift rate estimation value at a current time; a linear quadratic regulator optimal controller is constructed, a quadratic performance index J containing state variables and control variables is defined, and an optimal feedback gain matrix K is obtained by solving an algebraic Riccati equation; and a control variable is generated according to the state estimation value and the optimal feedback gain matrix, so that the crystal oscillator is locked to the reference frequency of the cold atom microwave clock. In the technical scheme, the state estimation accuracy is improved under the condition that measurement noise exists, and frequency taming control based on a state space model is realized.

Description

Technical Field

[0001] This application relates to the field of atomic frequency standards and frequency control technology, and in particular to a method and system for locking a cold atom microwave clock crystal oscillator. Background Technology

[0002] Cold atom microwave clocks utilize the hyperfine energy level transitions of cooled atoms as a frequency reference. By measuring the deviation between the local oscillator and the hyperfine transition frequency of the atoms, high-stability frequency output is achieved through frequency locking.

[0003] Existing cold atom microwave clock systems typically use a crystal oscillator as the local oscillation source. A microwave frequency synthesizer is used to multiply the output frequency of the crystal oscillator to the microwave frequency value of the cold atom transition. Then, a digital proportional-integral (PI) controller or a proportional-integral-derivative (PID) controller is used to frequency-train the crystal oscillator so that its frequency tracks the atom transition frequency over a long period of time.

[0004] However, existing control methods have the following shortcomings:

[0005] Control parameters are usually tuned based on experience, and the parameter optimization process is complex;

[0006] Atomic clock measurements are affected by detector noise, quantum projection noise, and environmental disturbances.

[0007] Control systems typically use the measured frequency deviation directly for feedback, without fully utilizing system state information;

[0008] The frequency drift and aging information of the crystal oscillator cannot be effectively extracted;

[0009] Traditional control methods struggle to achieve a unified design of state estimation and control processes. Summary of the Invention

[0010] This application provides a method and system for locking a crystal oscillator in a cold atom microwave clock, which can improve the accuracy of state estimation under the presence of measurement noise and realize frequency disciplined control based on a state-space model.

[0011] In a first aspect, a method for locking a crystal oscillator in a cold atom microwave clock is provided, comprising the following steps:

[0012] S1: Establish the discrete-time state-space model of the crystal oscillator and define the state vector. Including relative frequency deviation and relative frequency drift rate And determine the state transition matrix. and control input matrix ;

[0013] S2: Establish a measurement model based on the relative frequency deviation of the cold atom microwave clock output. As an observation, determine the observation matrix. ;

[0014] S3: Using the Kalman filtering algorithm, based on the state-space model and measurement model, recursive calculations are performed to estimate the relative frequency deviation at the current moment in real time. and relative frequency drift rate estimates ;

[0015] S4: Construct the optimal controller for the linear quadratic regulator, define the quadratic performance index J containing state variables and control quantities, and solve the algebraic Riccati equation to obtain the optimal feedback gain matrix K;

[0016] S5: Generate control input based on the state estimate and the optimal feedback gain matrix. The control quantity is output to the digital-to-analog converter, and the crystal oscillator is locked to the reference frequency of the cold atom microwave clock by changing the control voltage of the crystal oscillator.

[0017] In the above technical solution, a discrete-time state-space model of the crystal oscillator is established, and a state vector is defined. Including relative frequency deviation and relative frequency drift rate And determine the state transition matrix. and control input matrix Establish a measurement model based on the relative frequency deviation of the cold atom microwave clock output. As an observation, determine the observation matrix. Using the Kalman filtering algorithm, based on the state-space model and measurement model, recursive calculations are performed to estimate the relative frequency deviation at the current moment in real time. and relative frequency drift rate estimates Construct an optimal linear quadratic regulator controller, define a quadratic performance index J including state variables and control quantities, and solve the algebraic Riccati equation to obtain the optimal feedback gain matrix K; generate the control quantity based on the state estimate and the optimal feedback gain matrix. The control quantity is output to the digital-to-analog converter, and the crystal oscillator is locked to the reference frequency of the cold atom microwave clock by changing the control voltage of the crystal oscillator; the state estimation accuracy is improved under the condition of measurement noise, and frequency disciplined control based on the state space model is realized.

[0018] In one specific implementation scheme, the state vector in step S1 Defined as:

[0019] ;

[0020] in, This represents the relative frequency deviation of the crystal oscillator output frequency from the nominal frequency during the k-th sampling period. It represents the relative frequency drift rate within a unit sampling period.

[0021] In one specific implementation scheme, the discrete state equation in step S1 is:

[0022] ;

[0023] in, The change in the control input applied to the crystal oscillator. The system process noise follows a Gaussian distribution.

[0024] In one specific implementation scheme, the state transition matrix A and the control input matrix B are specifically set as follows:

[0025] ; ;

[0026] Where T is the system sampling period, This is the coefficient between the relative frequency of the crystal oscillator output and the control quantity.

[0027] In one specific implementation scheme, the measurement model expression in step S2 is:

[0028] ;

[0029] in, Measurement noise for cold atom microwave clocks; observation matrix ; The relative frequency deviation is measured by a cold atom microwave clock.

[0030] In one specific implementation scheme, the Kalman filtering recursive process described in step S3 specifically includes:

[0031] State prediction in one step: ;

[0032] Covariance one-step prediction: ;

[0033] Calculate the Kalman gain: ;

[0034] Status Update: ;

[0035] Covariance update: ;

[0036] Thus, the optimal state estimate at the current moment is obtained. .

[0037] In one specific implementation scheme, the quadratic performance index J mentioned in step S4 is defined as:

[0038] ;

[0039] Where Q is the semi-positive definite state weight matrix, used to characterize the system’s attention to the deviation of each state variable from the target value, and to adjust the weight of frequency deviation and drift rate in the performance index; R is the positive definite control weight matrix, used to characterize the cost of control input, and to adjust the trade-off between the control action amplitude and the system response speed.

[0040] In one specific implementation scheme, the optimal feedback gain matrix described in step S4 It is a constant matrix obtained by solving the discrete algebraic Riccati equation, where This is the feedback gain coefficient corresponding to the frequency deviation. This is the feedback gain coefficient corresponding to the frequency drift rate.

[0041] In one specific implementation scheme, the control quantity is generated in step S5. The control quantity is specifically an incremental control algorithm:

[0042] ;

[0043] This incremental control variable is used to eliminate steady-state error and to predict frequency change trends in advance using drift rate information.

[0044] Secondly, a cold atom microwave clock-locked crystal oscillator system is provided, comprising:

[0045] The discrete-time state-space model construction module is used to build a discrete-time state-space model of the crystal oscillator and define the state vector. Including relative frequency deviation and relative frequency drift rate And determine the state transition matrix. and control input matrix ;

[0046] The measurement model building module is used to establish a measurement model based on the relative frequency deviation of the cold atom microwave clock output. As an observation, determine the observation matrix. ;

[0047] The real-time estimation module is used to perform recursive calculations based on the state-space model and the measurement model using the Kalman filtering algorithm to estimate the relative frequency deviation at the current moment in real time. and relative frequency drift rate estimates ;

[0048] The optimal controller construction module is used to construct the optimal controller for a linear quadratic regulator. It defines a quadratic performance index J that includes state variables and control variables, and solves the algebraic Riccati equation to obtain the optimal feedback gain matrix K.

[0049] The control quantity generation module is used to generate control quantities based on the state estimate and the optimal feedback gain matrix. The control quantity is output to the digital-to-analog converter, and the crystal oscillator is locked to the reference frequency of the cold atom microwave clock by changing the control voltage of the crystal oscillator.

[0050] In the above technical solution, a discrete-time state-space model of the crystal oscillator is established, and a state vector is defined. Including relative frequency deviation and relative frequency drift rate And determine the state transition matrix. and control input matrix Establish a measurement model based on the relative frequency deviation of the cold atom microwave clock output. As an observation, determine the observation matrix. Using the Kalman filtering algorithm, based on the state-space model and measurement model, recursive calculations are performed to estimate the relative frequency deviation at the current moment in real time. and relative frequency drift rate estimates Construct an optimal linear quadratic regulator controller, define a quadratic performance index J including state variables and control quantities, and solve the algebraic Riccati equation to obtain the optimal feedback gain matrix K; generate the control quantity based on the state estimate and the optimal feedback gain matrix. The control quantity is output to the digital-to-analog converter, and the crystal oscillator is locked to the reference frequency of the cold atom microwave clock by changing the control voltage of the crystal oscillator; the state estimation accuracy is improved under the condition of measurement noise, and frequency disciplined control based on the state space model is realized. Attached Figure Description

[0051] Figure 1 A flowchart illustrating the cold atom microwave clock crystal locking method provided in this application embodiment;

[0052] Figure 2 This is a structural block diagram of a cold atom microwave clock-locked crystal oscillator system provided in an embodiment of this application. Detailed Implementation

[0053] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. Through these descriptions, the features and advantages of the present application will become clearer and more apparent.

[0054] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0055] Furthermore, the technical features involved in the different embodiments of this application described below can be combined with each other as long as they do not conflict with each other.

[0056] To facilitate understanding of the cold atom microwave clock crystal oscillator locking method and system provided in this application embodiment, its application scenario is first described. The cold atom microwave clock crystal oscillator locking method and system provided in this application embodiment are used to improve state estimation accuracy under conditions of measurement noise and to achieve frequency disciplined control based on a state-space model. The cold atom microwave clock utilizes the hyperfine energy level transitions of cooled atoms as a frequency reference. By measuring the deviation between the local oscillator and the hyperfine transition frequency of the atoms, high-stability frequency output is achieved through frequency locking. Existing cold atom microwave clock systems typically use a crystal oscillator as the local oscillation source, employ a microwave frequency synthesizer to multiply the output frequency of the crystal oscillator to the microwave frequency value of the cold atom transition, and then use a digital proportional-integral (PI) controller or a proportional-integral-derivative (PID) controller to discipline the crystal oscillator's frequency, enabling it to track the atomic transition frequency over a long period. However, existing control methods have the following shortcomings: control parameters usually rely on empirical tuning, and the parameter optimization process is complex; atomic clock measurement results are affected by detection noise, quantum projection noise, and environmental disturbances; control systems usually directly use the measured frequency deviation for feedback, failing to fully utilize system state information; crystal oscillator frequency drift and aging information cannot be effectively extracted; and traditional control methods struggle to achieve unified design of state estimation and control processes. Therefore, this application provides a cold atom microwave clock crystal oscillator locking method and system to improve state estimation accuracy under conditions of measurement noise and achieve frequency disciplined control based on a state-space model. The following detailed description, in conjunction with specific accompanying drawings, illustrates the embodiments.

[0057] exist Figure 1 This application provides a method for locking a crystal oscillator in a cold atom microwave clock, comprising the following steps:

[0058] S1: Establish the discrete-time state-space model of the crystal oscillator and define the state vector. Including relative frequency deviation and relative frequency drift rate And determine the state transition matrix. and control input matrix ;

[0059] S2: Establish a measurement model based on the relative frequency deviation of the cold atom microwave clock output. As an observation, determine the observation matrix. ;

[0060] S3: Using the Kalman filtering algorithm, based on the state-space model and measurement model, recursive calculations are performed to estimate the relative frequency deviation at the current moment in real time. and relative frequency drift rate estimates ;

[0061] S4: Construct the optimal controller for the linear quadratic regulator, define the quadratic performance index J containing state variables and control quantities, and solve the algebraic Riccati equation to obtain the optimal feedback gain matrix K;

[0062] S5: Generate control input based on the state estimate and the optimal feedback gain matrix. The control quantity is output to the digital-to-analog converter, and the crystal oscillator is locked to the reference frequency of the cold atom microwave clock by changing the control voltage of the crystal oscillator.

[0063] In the above technical solution, a discrete-time state-space model of the crystal oscillator is established, and a state vector is defined. Including relative frequency deviation and relative frequency drift rate And determine the state transition matrix. and control input matrix Establish a measurement model based on the relative frequency deviation of the cold atom microwave clock output. As an observation, determine the observation matrix. Using the Kalman filtering algorithm, based on the state-space model and measurement model, recursive calculations are performed to estimate the relative frequency deviation at the current moment in real time. and relative frequency drift rate estimates Construct an optimal linear quadratic regulator controller, define a quadratic performance index J including state variables and control quantities, and solve the algebraic Riccati equation to obtain the optimal feedback gain matrix K; generate the control quantity based on the state estimate and the optimal feedback gain matrix. The control quantity is output to the digital-to-analog converter, and the crystal oscillator is locked to the reference frequency of the cold atom microwave clock by changing the control voltage of the crystal oscillator; the state estimation accuracy is improved under the condition of measurement noise, and frequency disciplined control based on the state space model is realized.

[0064] Specifically, the beneficial effects include:

[0065] A joint state model of frequency deviation and drift rate was established, and frequency state estimation was achieved.

[0066] Kalman filtering is used to reduce the impact of measurement noise on the control system;

[0067] A unified modeling system for state estimation and controller design has been implemented.

[0068] This improves the system's ability to track frequency drift and aging effects;

[0069] A novel implementation method based on a state-space model is provided for frequency discipline of cold atom microwave clocks;

[0070] It is suitable for various cold atom microwave frequency standard systems and high-stability crystal oscillator frequency control scenarios.

[0071] In one specific implementation scheme, the state vector in step S1 Defined as:

[0072] ;

[0073] in, This represents the relative frequency deviation of the crystal oscillator output frequency from the nominal frequency during the k-th sampling period. It represents the relative frequency drift rate within a unit sampling period.

[0074] In one specific implementation scheme, the discrete state equation in step S1 is:

[0075] ;

[0076] in, The change in the control input applied to the crystal oscillator. The system process noise follows a Gaussian distribution.

[0077] In one specific implementation scheme, the state transition matrix A and the control input matrix B are specifically set as follows:

[0078] ; ;

[0079] Where T is the system sampling period, This is the coefficient between the relative frequency of the crystal oscillator output and the control quantity.

[0080] In one specific implementation scheme, the measurement model expression in step S2 is:

[0081] ;

[0082] in, Measurement noise for cold atom microwave clocks; observation matrix ; The relative frequency deviation is measured by a cold atom microwave clock.

[0083] In one specific implementation scheme, the Kalman filtering recursive process described in step S3 specifically includes:

[0084] State prediction in one step: ;

[0085] Covariance one-step prediction: ;

[0086] Calculate the Kalman gain: ;

[0087] Status Update: ;

[0088] Covariance update: ;

[0089] Thus, the optimal state estimate at the current moment is obtained. .

[0090] In one specific implementation scheme, the quadratic performance index J mentioned in step S4 is defined as:

[0091] ;

[0092] Where Q is the semi-positive definite state weight matrix, used to characterize the system’s attention to the deviation of each state variable from the target value, and to adjust the weight of frequency deviation and drift rate in the performance index; R is the positive definite control weight matrix, used to characterize the cost of control input, and to adjust the trade-off between the control action amplitude and the system response speed.

[0093] In one specific implementation scheme, the optimal feedback gain matrix described in step S4 It is a constant matrix obtained by solving the discrete algebraic Riccati equation, where This is the feedback gain coefficient corresponding to the frequency deviation. This is the feedback gain coefficient corresponding to the frequency drift rate.

[0094] In one specific implementation scheme, the control quantity is generated in step S5. The control quantity is specifically an incremental control algorithm:

[0095] ;

[0096] This incremental control variable is used to eliminate steady-state error and to predict frequency change trends in advance using drift rate information.

[0097] In one specific implementation scheme, the cold atom microwave clock crystal oscillator locking method establishes a frequency state-space model of the crystal oscillator, uses the Kalman filtering algorithm to estimate the relative frequency deviation and relative frequency drift rate in real time, and generates an optimal control quantity based on the estimated state to achieve crystal oscillator locking to the reference frequency of the cold atom microwave clock. The method includes the following steps:

[0098] Step 1: Establish the state model of the crystal oscillator.

[0099] The frequency state of the crystal oscillator is represented as:

[0100] ;

[0101] in:

[0102] For the first The relative frequency deviation of each sampling period;

[0103] This represents the relative frequency drift rate.

[0104] Establish discrete state equations:

[0105] ;

[0106] in:

[0107] The change in the control input applied to the crystal oscillator; This refers to system process noise.

[0108] This is the state transition matrix;

[0109] To control the input matrix.

[0110] Step 2: Establish a measurement model.

[0111] The frequency deviation measured by the cold atom microwave clock is used as a system observation:

[0112] ;

[0113] in:

[0114] The relative frequency deviation obtained from measurements using a cold atom microwave clock;

[0115] For measuring noise;

[0116] This is the observation matrix.

[0117] Step 3: Use Kalman filtering for state estimation.

[0118] Recursive state estimation is performed based on the state equation and the measurement equation, including:

[0119] 1. State prediction;

[0120] 2. Covariance prediction;

[0121] 3. Kalman gain calculation;

[0122] 4. Status update;

[0123] 5. Covariance update.

[0124] The estimated values ​​for frequency deviation and frequency drift rate are obtained as follows:

[0125] ;

[0126] This reduces the impact of cold atom microwave clock measurement noise on the control system.

[0127] Step 4: Construct the optimal controller.

[0128] Establish a quadratic performance index based on the state estimation results:

[0129] ;

[0130] Where Q is the semi-positive definite state weight matrix, used to characterize the system’s attention to the deviation of each state variable from the target value, and to adjust the weight of frequency deviation and drift rate in the performance index; R is the positive definite control weight matrix, used to characterize the cost of control input, and to adjust the trade-off between the control action amplitude and the system response speed.

[0131] The optimal feedback gain matrix is ​​obtained by solving the Riccati equation:

[0132] ;

[0133] The control quantity is generated according to the following control law:

[0134] ;

[0135] The control quantity is used to adjust the output of the digital-to-analog converter to change the control voltage of the crystal oscillator and achieve frequency locking.

[0136] Step 5: Output control signal.

[0137] The control quantity is output to the digital-to-analog converter via the digital control system, which generates the crystal oscillator control voltage, adjusts the output frequency of the crystal oscillator, and locks the reference frequency of the cold atom microwave clock.

[0138] Furthermore, the Kalman filter employs an adaptive covariance adjustment mechanism to dynamically adjust the process noise covariance matrix based on the system's operating state. and measurement noise covariance matrix .

[0139] Preferably, the control parameters are dynamically optimized based on the frequency stability evaluation results.

[0140] Preferably, frequency stability is evaluated using Allan variance or overlapping Allan variance.

[0141] In this embodiment, the beneficial effects include:

[0142] A joint state model of frequency deviation and drift rate was established, and frequency state estimation was achieved.

[0143] Kalman filtering is used to reduce the impact of measurement noise on the control system;

[0144] A unified modeling system for state estimation and controller design has been implemented.

[0145] This improves the system's ability to track frequency drift and aging effects.

[0146] In one specific feasible implementation, taking a cold atom fountain clock-locked temperature-controlled crystal oscillator as an example, it includes:

[0147] The cold atom fountain clock periodically measures the relative frequency deviation between the local oscillator and the atomic transition frequency, and sends the measurement results to the digital control system.

[0148] The digital control system establishes a state model of frequency deviation and drift rate, and uses a Kalman filter to estimate the state of the crystal oscillator in real time to obtain the estimated values ​​of relative frequency deviation and relative frequency drift rate.

[0149] The LQG controller is then used to calculate the control input, and the control voltage is output through the digital-to-analog converter to adjust the frequency of the crystal oscillator.

[0150] The system cyclically performs state estimation and control calculations to continuously track the atomic transition frequency of the crystal oscillator, thereby obtaining a stable frequency output.

[0151] Secondly, a cold atom microwave clock-locked crystal oscillator system is provided, comprising:

[0152] The discrete-time state-space model construction module is used to build a discrete-time state-space model of the crystal oscillator and define the state vector. Including relative frequency deviation and relative frequency drift rate And determine the state transition matrix. and control input matrix ;

[0153] The measurement model building module is used to establish a measurement model based on the relative frequency deviation of the cold atom microwave clock output. As an observation, determine the observation matrix. ;

[0154] The real-time estimation module is used to perform recursive calculations based on the state-space model and the measurement model using the Kalman filtering algorithm to estimate the relative frequency deviation at the current moment in real time. and relative frequency drift rate estimates ;

[0155] The optimal controller construction module is used to construct the optimal controller for a linear quadratic regulator. It defines a quadratic performance index J that includes state variables and control variables, and solves the algebraic Riccati equation to obtain the optimal feedback gain matrix K.

[0156] The control quantity generation module is used to generate control quantities based on the state estimate and the optimal feedback gain matrix. The control quantity is output to the digital-to-analog converter, and the crystal oscillator is locked to the reference frequency of the cold atom microwave clock by changing the control voltage of the crystal oscillator.

[0157] In the above technical solution, a discrete-time state-space model of the crystal oscillator is established, and a state vector is defined. Including relative frequency deviation and relative frequency drift rate And determine the state transition matrix. and control input matrix Establish a measurement model based on the relative frequency deviation of the cold atom microwave clock output. As an observation, determine the observation matrix. Using the Kalman filtering algorithm, based on the state-space model and measurement model, recursive calculations are performed to estimate the relative frequency deviation at the current moment in real time. and relative frequency drift rate estimates Construct an optimal linear quadratic regulator controller, define a quadratic performance index J including state variables and control quantities, and solve the algebraic Riccati equation to obtain the optimal feedback gain matrix K; generate the control quantity based on the state estimate and the optimal feedback gain matrix. The control quantity is output to the digital-to-analog converter, and the crystal oscillator is locked to the reference frequency of the cold atom microwave clock by changing the control voltage of the crystal oscillator; the state estimation accuracy is improved under the condition of measurement noise, and frequency disciplined control based on the state space model is realized.

[0158] Those skilled in the art will know that this application can be implemented as a system, method, or computer program product.

[0159] Therefore, this disclosure can be implemented in the following forms: it can be entirely hardware, entirely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software, generally referred to herein as a "circuit," "module," or "system." Furthermore, in some embodiments, this application can also be implemented as a computer program product in one or more computer-readable media, the computer-readable media containing computer-readable program code.

[0160] Any combination of one or more computer-readable media may be used. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in connection with an instruction execution system, apparatus, or device.

[0161] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application. Based on this, various substitutions and improvements can be made to this application, all of which fall within the protection scope of this application.

Claims

1. A method for locking a crystal oscillator in a cold atom microwave clock, characterized in that, Includes the following steps: S1: Establish the discrete-time state-space model of the crystal oscillator and define the state vector. Including relative frequency deviation and relative frequency drift rate And determine the state transition matrix. and control input matrix ; S2: Establish a measurement model based on the relative frequency deviation of the cold atom microwave clock output. As an observation, determine the observation matrix. ; S3: Using the Kalman filtering algorithm, based on the state-space model and measurement model, recursive calculations are performed to estimate the relative frequency deviation at the current moment in real time. and relative frequency drift rate estimates ; S4: Construct the optimal controller for the linear quadratic regulator, define the quadratic performance index J containing state variables and control quantities, and solve the algebraic Riccati equation to obtain the optimal feedback gain matrix K; S5: Generate control input based on the state estimate and the optimal feedback gain matrix. The control quantity is output to the digital-to-analog converter, and the crystal oscillator is locked to the reference frequency of the cold atom microwave clock by changing the control voltage of the crystal oscillator.

2. The method for locking a crystal oscillator in a cold atom microwave clock according to claim 1, characterized in that, The state vector in step S1 Defined as: ； in, This represents the relative frequency deviation of the crystal oscillator output frequency from the nominal frequency during the k-th sampling period. It represents the relative frequency drift rate within a unit sampling period.

3. The method for locking a crystal oscillator in a cold atom microwave clock according to claim 2, characterized in that, The discrete state equation in step S1 is: ； in, The change in the control input applied to the crystal oscillator. The system process noise follows a Gaussian distribution.

4. The method for locking a crystal oscillator in a cold atom microwave clock according to claim 3, characterized in that, The state transition matrix A and the control input matrix B are specifically set as follows: ； ； Where T is the system sampling period, This is the coefficient between the relative frequency of the crystal oscillator output and the control quantity.

5. The method for locking a crystal oscillator in a cold atom microwave clock according to claim 4, characterized in that, The measurement model expression mentioned in step S2 is: ； in, Measurement noise for cold atom microwave clocks; observation matrix ; The relative frequency deviation is measured by a cold atom microwave clock.

6. The method for locking a crystal oscillator in a cold atom microwave clock according to claim 5, characterized in that, The Kalman filtering recursive process described in step S3 specifically includes: State prediction in one step: ; Covariance one-step prediction: ; Calculate the Kalman gain: ; Status Update: ; Covariance update: ; Thus, the optimal state estimate at the current moment is obtained. .

7. The method for locking a crystal oscillator in a cold atom microwave clock according to claim 6, characterized in that, The quadratic performance index J mentioned in step S4 is defined as follows: ； Where Q is the semi-positive definite state weight matrix, used to characterize the system’s attention to the deviation of each state variable from the target value, and to adjust the weight of frequency deviation and drift rate in the performance index; R is the positive definite control weight matrix, used to characterize the cost of control input, and to adjust the trade-off between the control action amplitude and the system response speed.

8. The method for locking a crystal oscillator in a cold atom microwave clock according to claim 7, characterized in that, The optimal feedback gain matrix described in step S4 It is a constant matrix obtained by solving the discrete algebraic Riccati equation, where This is the feedback gain coefficient corresponding to the frequency deviation. This is the feedback gain coefficient corresponding to the frequency drift rate.

9. The method for locking a crystal oscillator in a cold atom microwave clock according to claim 8, characterized in that, In step S5, control variables are generated. The control quantity is specifically an incremental control algorithm: ； This incremental control variable is used to eliminate steady-state error and to predict frequency change trends in advance using drift rate information.

10. A cold atom microwave clock-locked crystal oscillator system, characterized in that, include: The discrete-time state-space model construction module is used to build a discrete-time state-space model of the crystal oscillator and define the state vector. Including relative frequency deviation and relative frequency drift rate And determine the state transition matrix. and control input matrix ; The measurement model building module is used to establish a measurement model based on the relative frequency deviation of the cold atom microwave clock output. As an observation, determine the observation matrix. ; The real-time estimation module is used to perform recursive calculations based on the state-space model and the measurement model using the Kalman filtering algorithm to estimate the relative frequency deviation at the current moment in real time. and relative frequency drift rate estimates ; The optimal controller construction module is used to construct the optimal controller for a linear quadratic regulator. It defines a quadratic performance index J that includes state variables and control variables, and solves the algebraic Riccati equation to obtain the optimal feedback gain matrix K. The control quantity generation module is used to generate control quantities based on the state estimate and the optimal feedback gain matrix. The control quantity is output to the digital-to-analog converter, and the crystal oscillator is locked to the reference frequency of the cold atom microwave clock by changing the control voltage of the crystal oscillator.

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