Dynamic temperature compensation method for ultra-stable crystal oscillator based on thermal inertia model

Abstract

The invention discloses an ultra-stable crystal oscillator dynamic temperature compensation method based on a thermal inertia model, and the method comprises the steps: triggering a sampling logic through a second pulse signal, and collecting the environment temperature and frequency deviation of an ultra-stable crystal oscillator in real time; constructing a third-order static polynomial model containing a plurality of static temperature coefficients to be estimated; taking the output of the third-order static polynomial model as excitation, and constructing a first-order thermal inertia model containing a to-be-estimated thermal time constant; the method comprises the following steps: by taking error minimization between actually measured historical frequency deviation and predicted frequency deviation as a target, combining a third-order static polynomial model and a first-order thermal inertia model, jointly estimating an optimal parameter vector through a nonlinear least square method, and calculating real-time dynamic predicted frequency deviation by utilizing the estimated optimal parameter vector and real-time environment temperature. And subtracting the predicted frequency deviation from the real-time frequency deviation, and outputting a compensated frequency signal. The crystal oscillator frequency drift under the dynamic temperature change can be accurately compensated, and the frequency stability is improved.

Description

Technical Field

[0001] This application belongs to the field of frequency calibration technology for spaceborne ultrastable crystal oscillators, specifically involving a dynamic temperature compensation method for ultrastable crystal oscillators based on a thermal inertia model. Background Technology

[0002] As the core time and frequency reference of spacecraft, the frequency stability of a spaceborne ultra-stable oscillator (USO) directly constrains the overall performance and accuracy of deep space exploration, gravitational wave detection, inter-satellite link synchronization, and satellite navigation systems. In practical applications, while high-quality quartz crystal oscillators can provide superior frequency stability over short timescales, their output frequency is extremely sensitive to changes in ambient temperature during medium- to long-term operation. Although spacecraft typically employ multi-stage thermal control measures, the physical environment temperature of the USO still exhibits complex, unsteady, time-varying characteristics due to variations in solar radiation caused by orbital periods, satellite attitude adjustments, and heat dissipation fluctuations resulting from payload operating mode switching.

[0003] To suppress the impact of temperature on the frequency stability of ultrastable crystal oscillators, existing technologies mainly employ two methods: isothermal control and static compensation. Isothermal control, constrained by the stringent size, weight, and power consumption limitations of spacecraft, often struggles to completely shield against rapid temperature fluctuations from the external environment. Existing software compensation methods are typically based on the quasi-static equilibrium assumption, assuming that the temperature of the resonator inside the crystal oscillator is consistent with the temperature measured by external sensors in real time, and using the static frequency-temperature characteristic curves obtained from ground calibration experiments for correction. However, related experimental studies have shown that because the crystal resonator is usually placed inside a vacuum Dewar flask or a multi-layered thermal insulation structure, there is significant thermal resistance and thermal capacitance between it and the temperature sensor located on the outer shell, resulting in a fixed thermal inertia (TI) in the heat conduction process.

[0004] In dynamic temperature environments, this inherent thermal conduction delay leads to significant thermal hysteresis (TH) during heating and cooling. The root cause is that the actual temperature of the internal resonator and the temperature measured by external sensors cannot maintain real-time thermal equilibrium, resulting in a non-overlapping closed hysteresis loop in the frequency-temperature characteristic curves during heating and cooling cycles. Under this non-equilibrium state, traditional static temperature compensation models fail because they cannot characterize the time-cumulative effect of thermal conduction, making it difficult to accurately eliminate frequency drift caused by dynamic temperature fluctuations. This situation severely restricts the frequency stability of ultrastable crystal oscillators in complex space thermal environments. Therefore, developing a method to effectively correct thermal hysteresis and achieve high-precision dynamic temperature compensation is of significant scientific and engineering value for improving the performance of spacecraft time and frequency references. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this application provides a dynamic temperature compensation method for ultrastable crystal oscillators based on a thermal inertia model. The technical problem to be solved by this application is achieved through the following technical solution: A dynamic temperature compensation method for ultrastable crystal oscillators based on a thermal inertia model includes: S100 samples the ambient temperature and frequency deviation of the ultra-stable crystal oscillator in real time, and uses a second pulse signal to trigger the sampling logic to maintain time axis synchronization, thereby obtaining the real-time ambient temperature and real-time frequency deviation. S200, construct a third-order static polynomial model containing multiple static temperature coefficients to be estimated, to characterize the static response law of the crystal oscillator output frequency as a function of temperature under thermal equilibrium. S300, the output of the third-order static polynomial model is used as the excitation input to construct a first-order thermal inertia model containing the thermal time constant to be estimated; S400 aims to minimize the error between the measured historical frequency deviation and the predicted frequency deviation, and combines the third-order static polynomial model and the first-order thermal inertia model to estimate the optimal parameter vector using the nonlinear least squares method; wherein, the optimal parameter vector includes multiple estimated static temperature coefficients and thermal time constants. S500 uses the estimated optimal parameter vector and the real-time ambient temperature to calculate the real-time dynamic predicted frequency offset, and subtracts the real-time dynamic predicted frequency offset from the real-time frequency deviation to output the compensated frequency signal.

[0006] Beneficial effects: This application discloses a dynamic temperature compensation method for ultra-stable crystal oscillators (USOs) based on a thermal inertia model. The method includes: triggering sampling logic with a second pulse signal to collect the ambient temperature and frequency deviation of the USO in real time; constructing a third-order static polynomial model containing multiple static temperature coefficients to be estimated; using the output of the third-order static polynomial model as excitation to construct a first-order thermal inertia model containing the thermal time constants to be estimated; aiming to minimize the error between the measured historical frequency deviation and the predicted frequency deviation, jointly estimating the optimal parameter vector using the third-order static polynomial model and the first-order thermal inertia model via nonlinear least squares method; calculating the real-time dynamic predicted frequency deviation using the estimated optimal parameter vector and the real-time ambient temperature; subtracting the predicted frequency deviation from the real-time frequency deviation; and outputting the compensated frequency signal. This application combines the physical characteristics of the USO with a dynamic heat conduction mechanism. When the ambient temperature fluctuates rapidly or is in a heating / cooling cycle, the thermal inertia parameters are used to mathematically reconstruct the hysteresis effect, effectively correcting the thermal hysteresis effect of the crystal resonator, eliminating frequency hysteresis loops that cannot be solved by existing static compensation methods, and achieving stable and continuous high-precision frequency output.

[0007] The present application will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0008] Figure 1 This is a flowchart illustrating a dynamic temperature compensation method for an ultrastable crystal oscillator based on a thermal inertia model provided in this application. Figure 2 This is a schematic diagram of the process of a dynamic temperature compensation method for an ultrastable crystal oscillator based on a thermal inertia model provided in this application; Figure 3 This is a time-domain comparison diagram of the frequency deviation before and after compensation provided in this application; Figure 4 This is a diagram showing the effect of thermal hysteresis loop correction before and after compensation provided in this application; Figure 5 This is a comparison chart of Allen's deviation before and after compensation provided in this application. Detailed Implementation

[0009] The present application will be described in further detail below with reference to specific embodiments, but the implementation of the present application is not limited thereto.

[0010] To address the unsteady thermal environment (such as periodic temperature variations caused by payload temperature changes and Earth's shadow entry / exit) faced by spacecraft during orbital operation, this application employs a dynamic temperature compensation method for ultrastable crystal oscillators (USOs) based on a thermal inertia model. The aim is to solve the following problems: First, it addresses the issue that existing compensation models only rely on static frequency-temperature relationships for correction and cannot describe different response paths during heating and cooling processes. Second, it addresses the problem that existing methods are insufficient to compensate for dynamic frequency drift in USO output frequencies under conditions of rapid ambient temperature changes, temperature steps, or periodic thermal cycling. Third, it addresses how to reconstruct and correct the frequency-temperature hysteresis loop caused by thermal inertia by introducing thermal time constants and related model parameters, thereby achieving accurate compensation for dynamic temperature disturbances.

[0011] This application presents a dynamic temperature compensation method for ultra-stable crystal oscillators (USOs) based on a thermal inertia model. This method abandons the existing static equilibrium assumptions and focuses on constructing a dynamic filtering model incorporating a thermal time constant to correct the thermal hysteresis effect of the crystal resonator. It also combines this with a nonlinear optimization algorithm to extract specific temperature drift characteristics from noisy signals. First, a polynomial model is constructed to characterize the basic temperature drift. Then, a thermal inertia recursive filter is introduced to simulate heat conduction delay. The model parameters are identified using a nonlinear least squares method. Finally, the calculated dynamic frequency offset is subtracted from the real-time frequency, achieving high-precision real-time frequency compensation. This method combines the physical characteristics of the USO with the dynamic heat conduction mechanism. When the ambient temperature fluctuates rapidly or is in a heating / cooling cycle, the thermal inertia parameters are used to mathematically reconstruct the hysteresis effect, effectively correcting the thermal hysteresis effect of the crystal resonator and eliminating frequency hysteresis loops that cannot be addressed by existing static compensation methods, achieving stable and continuous high-precision frequency output.

[0012] Combination Figure 1 and Figure 2 This application provides a dynamic temperature compensation method for ultrastable crystal oscillators based on a thermal inertia model, including: S100 samples the ambient temperature and frequency deviation of the ultra-stable crystal oscillator in real time, and uses a second pulse signal to trigger the sampling logic to maintain time axis synchronization, thereby obtaining the real-time ambient temperature and real-time frequency deviation. S200, a third-order static polynomial model containing multiple static temperature coefficients to be estimated is constructed to characterize the static response of the crystal oscillator output frequency as a function of temperature under thermal equilibrium conditions; based on the physical characteristics of the crystal resonator, a third-order static polynomial model containing linear and nonlinear terms is constructed as follows: ; In the formula, express Measured value of frequency deviation at time. These are three static temperature coefficients, representing the linear slope, curvature, and higher-order nonlinear response of the real-time measurement frequency to temperature changes, respectively. for The residual between the measured frequency deviation at time t and the predicted frequency deviation output by the third-order static polynomial model. Indicates the quasi-steady-state time interval. express Temperature deviation at any given time.

[0013] S300, using the output of the third-order static polynomial model as the excitation input, a first-order thermal inertia model containing the thermal time constant to be estimated is constructed; the first-order thermal inertia model is expressed as: ; In the formula, Represents the thermal time constant. express Dynamic temperature frequency deviation at any given time.

[0014] S400 aims to minimize the error between the measured historical frequency deviation and the predicted frequency deviation, and combines the third-order static polynomial model and the first-order thermal inertia model to estimate the optimal parameter vector using the nonlinear least squares method; wherein, the optimal parameter vector includes multiple estimated static temperature coefficients and thermal time constants. In one specific embodiment of this application, S400 includes: S410: Collect historical temperature sequences and measured historical frequency deviation values, and calculate historical temperature deviation sequences based on historical temperature sequences, and then preprocess them to obtain preprocessed historical temperature deviation sequences. This application filters quasi-steady-state sample segments with relatively small rates of temperature change from historical temperature sequences. The criterion can be defined as: over continuous time, if... If the sample at that moment is considered to satisfy the quasi-steady-state condition, then... Indicates the quasi-steady-state time interval. The threshold for the rate of temperature change is defined. Based on this, transient samples, outliers, and missing values ​​after temperature excitation switching are further removed to reduce the impact of thermal inertia hysteresis on static parameter identification.

[0015] S420, based on the measured historical frequency deviation value and the preprocessed historical temperature deviation sequence, combined with the third-order static polynomial model and the first-order thermal inertia model, the initial parameter vector is obtained by solving using the least squares method. In one specific embodiment of this application, S420 includes: S421, Using the third-order static polynomial model, construct the first residual squared integral objective functional for the three static temperature coefficients; Let the reference temperature be Temperature deviation is , The measured frequency deviation at time is The objective functional of the first residual square integral is expressed as: ; In the formula, Indicating targeting The objective functional of the first residual square integral; S422, the preprocessed historical temperature deviation sequence is substituted into the first residual square integral objective functional, and then the initial values ​​of the three static temperature coefficients are obtained by solving the nonlinear optimization algorithm; wherein, the nonlinear optimization algorithm used is the Levenberg-Marquardt algorithm, which guides the search direction by constructing the Jacobian matrix.

[0016] S423, using the three initial values ​​of static temperature coefficients, estimate the initial value of instantaneous temperature frequency deviation; the initial value of instantaneous temperature frequency deviation is expressed as: ; In the formula, This represents the initial value of the instantaneous temperature frequency deviation. This represents the initial values ​​of the three static temperature coefficients; S424, Substitute the initial value of the instantaneous temperature frequency deviation into the first-order thermal inertia model to obtain the dynamic temperature frequency deviation response including the thermal time constant to be estimated; the dynamic temperature frequency deviation response including the thermal time constant to be estimated is expressed as: ; In the formula, express The time contains the thermal time constant to be estimated. The dynamic temperature frequency deviation response; Used to quantify the degree of hysteresis in the temperature response. Indicates the quasi-steady-state time interval The corresponding dynamic response time interval is used to characterize the sample interval where the rate of temperature change exceeds the threshold and the thermal inertia effect cannot be ignored.

[0017] S425, using the dynamic temperature frequency deviation response and the measured historical frequency deviation, construct a second residual squared integral objective functional for the thermal time constant; For each dynamic response time interval Let its starting time be And the initial value of the instantaneous temperature frequency deviation at that starting moment is taken as the initial condition for the first-order thermal inertia equation, that is... In order to obtain The initial value can be denoted as the measured frequency deviation. The model output obtained from the above thermal inertia equation is denoted as... The objective functional of the second residual square integral with respect to the thermal time constant is expressed as: ; In the formula, Indicates the thermal time constant The objective functional of the second residual square integral; S426, Solve the objective functional of the second residual squared integral using the least squares method to obtain the initial value of the thermal time constant; the initial value of the thermal time constant is expressed as: ; In the formula, This represents the initial value of the thermal time constant; S427, using the three initial values ​​of static temperature coefficient and thermal time constant, an initial parameter vector is constructed, which is expressed as: ; In the formula, This indicates transpose.

[0018] This application obtains the aforementioned initial values ​​by utilizing the quasi-steady-state time interval and the dynamic response time interval respectively. That is, the initial parameter vector is used as the initial value for subsequent joint identification, which helps to reduce parameter compensation between the static temperature coefficient and the thermal time constant and improve the stability of joint identification.

[0019] S430, with the goal of minimizing the error between the measured historical frequency deviation and the predicted frequency deviation, the initial parameter vector is substituted into the third-order static polynomial model and the first-order thermal inertia model, and then the optimal parameter vector is estimated by means of nonlinear least squares method.

[0020] In one specific embodiment of this application, S430 includes: S431, using the deviation between the measured historical frequency deviation and the predicted frequency deviation as the residual, construct a joint identification objective functional and set a constraint set; wherein, the joint identification objective functional is expressed as: ; In the formula, The time interval that represents the combined steady-state time interval and dynamic time interval; The constraint set is represented as follows: ; In the formula, ; S432, in each iteration, the prediction objective is to minimize the joint identification target functional. The parameter vector obtained from the previous iteration and the preprocessed historical temperature deviation sequence are substituted into the third-order static polynomial model to obtain the instantaneous temperature frequency deviation obtained in this iteration. The instantaneous temperature frequency deviation after this iteration is substituted into the first-order thermal inertia model to obtain the predicted frequency deviation obtained in this iteration. The predicted frequency deviation obtained in this iteration and the measured historical frequency deviation are substituted into the joint identification target functional to obtain the residual. It is determined whether the residual satisfies the iteration cutoff condition. If not, the next iteration is performed. If yes, the parameter vector input in this iteration is determined as the optimal parameter vector.

[0021] The prediction objective in S432 is expressed as: ; The instantaneous temperature frequency offset obtained in this iteration of S432 is expressed as: ; In the formula, This indicates that the current iteration yielded... Instantaneous temperature frequency deviation at any given moment; The predicted frequency deviation obtained in this iteration of S432 is expressed as follows: ; In the formula, This iteration yielded Predicted frequency deviation at any given time; The optimal parameter vector in S432 is represented as follows: ; In the formula, These represent the three optimal static temperature coefficients. This represents the optimal thermal time constant.

[0022] The joint solution process in this application utilizes all historical samples to simultaneously constrain the static temperature coefficient and thermal time constant, which can effectively reduce the parameter compensation effect and improve the fitting accuracy and compensation accuracy of the model in dynamic temperature scenarios.

[0023] S500 uses the estimated optimal parameter vector and the real-time ambient temperature to calculate the real-time dynamic predicted frequency offset, and subtracts the real-time dynamic predicted frequency offset from the real-time frequency deviation to output the compensated frequency signal.

[0024] In one specific embodiment of this application, S500 includes: S510, calculate the real-time temperature deviation using the real-time ambient temperature and the reference temperature; Obtain the real-time ambient temperature of the USO and the original frequency deviation signal acquired synchronously. Set reference temperature And calculate the temperature deviation. At the same time, the real-time ambient temperature Preprocessing is performed.

[0025] S520, Substitute the optimal parameter vector and the real-time temperature deviation into the third-order static polynomial model and the first-order thermal inertia model to obtain the real-time dynamic predicted frequency deviation. This application substitutes the optimal parameter vector and the real-time temperature deviation into a third-order static polynomial model to obtain the current instantaneous temperature frequency deviation, expressed as: ; In the formula, This is expressed as the current instantaneous temperature frequency deviation; For the current moment Relative to reference temperature Temperature deviation.

[0026] This application introduces a first-order thermal inertia model to account for the frequency deviation of the current instantaneous temperature. Perform dynamic shaping to obtain real-time dynamic predicted frequency offset In discrete implementation, the specific calculation formula is as follows: ; In the formula, To predict frequency offset in real time.

[0027] S530, subtract the real-time dynamic predicted frequency offset from the real-time frequency offset, and output the compensated frequency signal.

[0028] This application subtracts from the real-time frequency deviation. Then the compensated frequency signal is obtained.

[0029] Based on the thermal inertial dynamics model and nonlinear parameter identification algorithm proposed in this application, it can effectively break through the physical boundary of existing static compensation, realize the statistical decoupling of temperature characteristics and background noise by reconstructing the heat conduction hysteresis mechanism, eliminate frequency hysteresis loops under dynamic temperature change environment to the greatest extent, adapt to complex unsteady thermal environment, and meet the stringent requirements of continuous and high-precision frequency stability for missions such as deep space exploration and space gravitational wave detection.

[0030] To verify the effectiveness of the new method, this application constructs a high-fidelity USO thermo-frequency dynamics numerical model suitable for unsteady-state thermal environment tests. The dynamic temperature variation range is set to -10℃ to +45℃ (referencing the typical operating temperature range of intravehicular equipment defined by NASA GEVS aerospace standards and GJB150 military standards) to cover the typical thermal environment inside a low-Earth orbit satellite. In addition, the variable temperature waveform simulates the actual orbital periodic heat exchange process.

[0031] Figure 3 A time-domain comparison of the frequency deviation before and after compensation was plotted. Before using the method of this application, the temperature phase delay caused by thermal inertia had a significant impact (circled line), and the frequency deviation exhibited a hysteretic fluctuation following the temperature, showing a significant periodic characteristic, with the maximum frequency deviation reaching hundreds of ppb. After dynamic compensation using the method of this application, the frequency deviation (crossed line) is close to zero, and the deviation fluctuation is limited to a very small noise floor, proving that the dynamic thermal effect has been effectively removed.

[0032] Figure 4The effects of thermal hysteresis correction before and after compensation are plotted. In the figure, the "circled line" represents the uncompensated data, showing a significant difference in frequency deviation between the heating and cooling processes, forming an almost closed elliptical hysteresis loop. This is the physical root cause of static compensation failure. The "crossed line" represents the frequency data after compensation according to this application. It can be seen that the hysteresis loop is almost eliminated, the frequency deviation no longer changes with temperature, and the cancellation is close to zero. Experiments show that this application successfully established a dynamic compensation mapping relationship between the externally measured temperature and the internal resonant frequency.

[0033] Figure 5 A comparison of Allan Deviation (AD) before and after compensation was plotted. The "circled lines" in the figure represent the uncompensated data, which is affected by temperature drift modulation, and its frequency stability during the integral time... A significant upward trend (exhibiting red noise characteristics) subsequently emerged, leading to a deterioration in medium- to long-term stability. The "crossed line" represents the data after compensation in this application; the curve exhibits continuously decreasing white noise characteristics, indicating that low-frequency noise caused by temperature drift has been effectively suppressed. As can be seen from the figure, especially at millihertz (kiloseconds)... This application significantly improves the frequency stability index, which can meet the requirements of missions such as deep space exploration and space gravitational wave detection for extremely high frequency source stability.

[0034] In summary, by Figures 3 to 5 Simulation results show that without the introduction of a thermal inertia model, the frequency drift will produce a significant hysteresis deviation with the rate of temperature change. However, after compensation by the method of this application, the USO output frequency can resist dynamic temperature disturbances and effectively decouple temperature characteristics from noise, thus achieving stable and high-precision time and frequency services.

[0035] It is worth noting that the terms "first" and "second" in this application are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0036] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of this application and should not be construed as limiting the specific implementation of this application to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of this application, and all such modifications or substitutions should be considered within the scope of protection of this application.

Claims

1. A dynamic temperature compensation method for ultrastable crystal oscillators based on a thermal inertia model, characterized in that, include: S100 samples the ambient temperature and frequency deviation of the ultra-stable crystal oscillator in real time, and uses a second pulse signal to trigger the sampling logic to maintain time axis synchronization, thereby obtaining the real-time ambient temperature and real-time frequency deviation. S200, construct a third-order static polynomial model containing multiple static temperature coefficients to be estimated, to characterize the static response law of the crystal oscillator output frequency as a function of temperature under thermal equilibrium. S300, the output of the third-order static polynomial model is used as the excitation input to construct a first-order thermal inertia model containing the thermal time constant to be estimated; S400 aims to minimize the error between the measured historical frequency deviation and the predicted frequency deviation, and combines the third-order static polynomial model and the first-order thermal inertia model to estimate the optimal parameter vector using the nonlinear least squares method; wherein, the optimal parameter vector includes multiple estimated static temperature coefficients and thermal time constants. S500 uses the estimated optimal parameter vector and the real-time ambient temperature to calculate the real-time dynamic predicted frequency offset, and subtracts the real-time dynamic predicted frequency offset from the real-time frequency deviation to output the compensated frequency signal.

2. The dynamic temperature compensation method for ultrastable crystal oscillators based on a thermal inertia model according to claim 1, characterized in that, The third-order static polynomial model in S200 is represented as follows: ； In the formula, express Measured value of frequency deviation at time. These are three static temperature coefficients, representing the linear slope, curvature, and higher-order nonlinear response of the real-time measurement frequency to temperature changes, respectively. for The residual between the measured frequency deviation at time t and the predicted frequency deviation output by the third-order static polynomial model. Indicates the quasi-steady-state time interval. express Temperature deviation at any given time.

3. The dynamic temperature compensation method for ultrastable crystal oscillators based on a thermal inertia model according to claim 2, characterized in that, The first-order thermal inertia model in S300 is expressed as: ； In the formula, Represents the thermal time constant. express Dynamic temperature frequency deviation at any given time.

4. The dynamic temperature compensation method for ultrastable crystal oscillators based on a thermal inertia model according to claim 3, characterized in that, The S400 includes: S410: Collect historical temperature sequences and measured historical frequency deviation values, and calculate historical temperature deviation sequences based on historical temperature sequences, and then preprocess them to obtain preprocessed historical temperature deviation sequences. S420, based on the measured historical frequency deviation value and the preprocessed historical temperature deviation sequence, combined with the third-order static polynomial model and the first-order thermal inertia model, the initial parameter vector is obtained by solving using the least squares method. S430, with the goal of minimizing the error between the measured historical frequency deviation and the predicted frequency deviation, the initial parameter vector is substituted into the third-order static polynomial model and the first-order thermal inertia model, and then the optimal parameter vector is estimated by means of nonlinear least squares method.

5. The dynamic temperature compensation method for ultrastable crystal oscillators based on a thermal inertia model according to claim 4, characterized in that, The S420 includes: S421, Using the third-order static polynomial model, construct the first residual squared integral objective functional for the three static temperature coefficients; S422, Substitute the preprocessed historical temperature deviation sequence into the first residual square integral objective functional, and then solve for the initial values ​​of the three static temperature coefficients through a nonlinear optimization algorithm. S423, using the three initial values ​​of static temperature coefficients, estimate the initial value of instantaneous temperature frequency deviation; S424, Substitute the initial value of the instantaneous temperature frequency deviation into the first-order thermal inertia model to obtain the dynamic temperature frequency deviation response containing the thermal time constant to be estimated; S425, using the dynamic temperature frequency deviation response and the measured historical frequency deviation, construct a second residual squared integral objective functional for the thermal time constant; S426, the objective functional of the second residual squared integral is solved by the least squares method to obtain the initial value of the thermal time constant; S427. Using the three initial values ​​of static temperature coefficient and thermal time constant, construct an initial parameter vector.

6. The dynamic temperature compensation method for ultrastable crystal oscillators based on a thermal inertia model according to claim 5, characterized in that, The objective functional of the first residual squared integral in S421 is expressed as: ； In the formula, Indicating targeting The objective functional of the first residual square integral; The initial value of the instantaneous temperature frequency deviation in S423 is expressed as: ； In the formula, This represents the initial value of the instantaneous temperature frequency deviation. This represents the initial values ​​of the three static temperature coefficients; The dynamic temperature frequency deviation response in S424, which includes the thermal time constant to be estimated, is expressed as: ； In the formula, express The time contains the thermal time constant to be estimated. The dynamic temperature frequency deviation response; Indicates the quasi-steady-state time interval The corresponding dynamic response time range; The objective functional for the second residual square integral with respect to the thermal time constant in S425 is expressed as follows: ； In the formula, Indicates the thermal time constant The objective functional of the second residual square integral; The initial value of the thermal time constant in S426 is expressed as follows: ； In the formula, This represents the initial value of the thermal time constant; The initial parameter vector in S427 is represented as follows: ； In the formula, This indicates transpose.

7. The method for dynamic temperature compensation of ultrastable crystal oscillators based on a thermal inertia model according to claim 6, characterized in that, The nonlinear optimization algorithm used in S422 is the Levenberg-Marquardt algorithm, which guides the search direction by constructing a Jacobian matrix.

8. The dynamic temperature compensation method for ultrastable crystal oscillators based on a thermal inertia model according to claim 4, characterized in that, The S430 includes: S431, the deviation between the measured historical frequency deviation and the predicted frequency deviation is used as the residual to construct a joint identification objective functional and set a constraint set; S432, in each iteration, the prediction objective is to minimize the joint identification target functional. The parameter vector obtained from the previous iteration and the preprocessed historical temperature deviation sequence are substituted into the third-order static polynomial model to obtain the instantaneous temperature frequency deviation obtained in this iteration. The instantaneous temperature frequency deviation after this iteration is substituted into the first-order thermal inertia model to obtain the predicted frequency deviation obtained in this iteration. The predicted frequency deviation obtained in this iteration and the measured historical frequency deviation are substituted into the joint identification target functional to obtain the residual. It is determined whether the residual satisfies the iteration cutoff condition. If not, the next iteration is performed. If yes, the parameter vector input in this iteration is determined as the optimal parameter vector.

9. The dynamic temperature compensation method for ultrastable crystal oscillators based on a thermal inertia model according to claim 8, characterized in that, The joint target identification functional representation in S431 is as follows: ； In the formula, The time interval that represents the combined steady-state time interval and dynamic time interval; The constraint set described in S431 is represented as follows: ； In the formula, ; The prediction objective described in S432 is expressed as follows: ； The instantaneous temperature frequency offset obtained in this iteration of S432 is expressed as: ； In the formula, This indicates that the current iteration yielded... Instantaneous temperature frequency deviation at any given moment; The predicted frequency deviation obtained in this iteration of S432 is expressed as follows: ； In the formula, This iteration yielded Predicted frequency deviation at any given time; The optimal parameter vector in S432 is represented as follows: ； In the formula, These represent the three optimal static temperature coefficients. This represents the optimal thermal time constant.

10. The method for dynamic temperature compensation of ultrastable crystal oscillators based on a thermal inertia model according to claim 1, characterized in that, The S500 includes: S510, calculate the real-time temperature deviation using the real-time ambient temperature and the reference temperature; S520, Substitute the optimal parameter vector and the real-time temperature deviation into the third-order static polynomial model and the first-order thermal inertia model to obtain the real-time dynamic predicted frequency deviation. S530, subtract the real-time dynamic predicted frequency offset from the real-time frequency offset, and output the compensated frequency signal.

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