A method for calibrating a rubidium atomic clock based on a Loran system and related device

Abstract

The application belongs to the field of high-precision time calibration and navigation positioning, and discloses a rubidium atomic clock calibration method based on a Loran system and related devices. The time difference sequence of the Loran signal and the rubidium clock signal is calculated in real time, the frequency, amplitude and phase parameters of the periodic component are accurately identified based on the Welch method and the adaptive peak detection method, then a hybrid time difference model containing a quadratic trend item, a multi-period item and a noise item is constructed, and the least square method is used to solve the model to obtain the key performance parameters of the rubidium atomic clock, and finally the time calibration of the Loran system taming the rubidium clock is completed. The method effectively improves the rubidium clock parameter estimation accuracy, overcomes the problems of mode aliasing, noise sensitivity, non-unique results and low calculation efficiency, and realizes reliable and real-time Loran system calibration of the rubidium atomic clock.

Description

Technical Field

[0001] This invention belongs to the field of high-precision time calibration and navigation positioning technology, specifically relating to the field of rubidium atomic clock calibration, and particularly to a rubidium atomic clock calibration method and related apparatus based on the Loran system. Background Technology

[0002] The Loland system, a long-established land-based radio navigation system, is widely used in maritime, aviation, and land navigation fields. Rubidium atomic clocks, as modern high-precision time and frequency reference devices, are ideal for applications with stringent time accuracy requirements due to their excellent precision and stability. In today's rapidly developing technological environment and increasingly complex application scenarios, the Loland tamed rubidium atomic clock system plays a crucial role in practical operation, ensuring the normal operation of various applications that rely on precise time synchronization and navigation positioning.

[0003] However, existing technologies face numerous challenges in realizing the Rowland-tamed rubidium atomic clock system. Traditional time difference models and solution methods exhibit significant limitations when dealing with complex signals. For example, while polynomial fitting methods are simple, the fitted coefficients tend to deviate from the true values ​​under noisy or periodic signal interference, especially the quadratic term coefficients, which severely affect the accuracy of extracting the quadratic trend term and reduce model reliability. The relatively advanced method of Empirical Mode Decomposition combined with Least Squares also reveals inherent flaws when processing Rowland-tamed rubidium clock time difference signals. Specifically, mode aliasing causes incorrect mixing of signal components from different time scales, making it difficult for Least Squares to accurately extract the quadratic trend term; high sensitivity to noise results in numerous noisy components in the decomposition results, leading to ambiguous physical meanings; a lack of rigorous mathematical theoretical support results in non-unique decomposition results, with poor stability and reliability; and high computational complexity and low efficiency fail to meet the urgent real-time requirements of time synchronization and navigation positioning applications.

[0004] In summary, improving the accuracy of rubidium clock parameter estimation in the Roland tamed rubidium atomic clock system and overcoming the problems of mode aliasing, noise sensitivity, non-unique results, and low computational efficiency faced by existing technologies in signal processing have become key technical challenges that urgently need to be addressed. Summary of the Invention

[0005] This invention provides a rubidium atomic clock calibration method and related apparatus based on the Loran system. This method effectively solves the problem of calibrating a rubidium atomic clock using the Loran signal under complex electromagnetic environments by constructing a time difference model that explicitly includes multiple periodic terms.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A rubidium atomic clock calibration method based on the Loran system includes:

[0008] Based on the real-time acquired Rowland signal and rubidium clock signal, the time difference sequence between the Rowland signal and the rubidium clock signal is calculated;

[0009] Spectral analysis of time difference sequences is performed based on the Welch method and adaptive peak detection method to identify periodic components and their corresponding frequency sets and amplitude and phase parameters.

[0010] A time difference model is constructed based on the periodic components and the corresponding frequency set and amplitude and phase parameters; the time difference model is a hybrid time difference model including a quadratic trend term, a multi-period term and a noise term;

[0011] The time difference model is solved using the least squares method to obtain the key performance parameters of the rubidium atomic clock; these key performance parameters are used by the Loran system to tame the rubidium atomic clock in order to achieve its calibration.

[0012] Furthermore, the calculation of the time difference sequence between the Rowland signal and the rubidium clock signal based on the real-time acquired Rowland signal and rubidium clock signal includes:

[0013] Load the real-time acquired Roland signal and rubidium clock signal;

[0014] The time difference sequence is obtained by calculating the difference between the Rowland signal and the rubidium clock signal, as shown in the following formula:

[0015]

[0016] In the formula, Represents the time difference sequence; Indicates the Rowland signal; Indicates a rubidium clock signal;

[0017] The time difference series is zero-mean normalized to obtain the zero-mean time difference series, as shown in the following formula:

[0018]

[0019] In the formula, This represents the time difference sequence after zero-mean processing; This represents the mean of the time difference sequence.

[0020] Furthermore, the spectral analysis of the time difference sequence based on the Welch method and adaptive peak detection method to identify periodic components and their corresponding frequency sets and amplitude and phase parameters includes:

[0021] The Welch method was used to calculate the power spectral density of the time difference sequence. The time difference sequence was divided into multiple data segments with a preset segment length, and each data segment was weighted using a Hanning window. The formula for calculating the power spectral density is as follows:

[0022]

[0023] In the formula, Indicates power spectral density; This indicates the number of data segments into which the time difference sequence is divided; Indicates the length of each data segment; This represents the normalization factor of the Hanning window function; Indicates the first l One data segment, l Values ​​range from 0 to -1, n takes the value 0~ -1; f n Represents frequency variables; Represents a complex exponential function; Represents the Hanning window function;

[0024] An adaptive peak detection method is used to identify the periodic frequency of the power spectral density, including:

[0025] A robust estimation method using the median plus three times the interquartile range is employed to identify the noise basis of time difference sequences. The specific formula is as follows:

[0026]

[0027] In the formula, Indicates the noise floor; This represents the function for calculating the median. Indicates the interquartile range;

[0028] Based on the identified noise floor, an adaptive peak detection method is used to identify the periodic components and their corresponding frequency sets and amplitude and phase parameters.

[0029] Furthermore, the time difference model constructed based on the periodic components and the corresponding frequency set and amplitude and phase parameters includes:

[0030] Obtain the identified periodic components and their corresponding frequency sets and amplitude and phase parameters;

[0031] A time difference model is constructed based on the periodic components and their corresponding frequency sets and amplitude and phase parameters. Represented as:

[0032]

[0033] In the formula, This represents the quadratic trend term, used to characterize the frequency drift of a rubidium clock; where, This represents the phase difference between the rubidium atomic clock and the Rowland timing signal at the initial moment; This indicates the deviation between the initial frequency of the rubidium atomic clock and the standard frequency. Indicates the frequency drift coefficient; This represents a multi-period term, used to characterize the impact of external periodic interference on the time difference signal of the Rowland signal; where M represents the number of periodic components in the multi-period term; and i represents the index variable for summing the multi-period term. This represents the coefficient of the cosine component in the i-th periodic term; This represents the coefficient of the sinusoidal component in the i-th periodic term; This represents the frequency of the i-th periodic term; The noise term is represented, specifically including measurement noise and electromagnetic interference; t is the time vector.

[0034] The time difference model includes at least one 24-hour periodic term to characterize the periodic changes in the Roland signal caused by the Earth's rotation.

[0035] Furthermore, before solving the time difference model using the least squares method to obtain the key performance parameters of the rubidium atomic clock, the following steps are included:

[0036] The time difference model is represented in matrix form, specifically as follows:

[0037]

[0038] In the formula, The observation matrix includes the raw time difference signal between the measured Rowland signal and the rubidium clock signal;

[0039] The coefficient matrix, used to capture the periodic components and quadratic trend term in the original time difference signal, is specifically represented as follows:

[0040]

[0041] In the formula, t takes values ​​from 1 to m, where m is a positive integer; Indicates the periodic frequency;

[0042] The vector of parameters to be estimated is represented as follows:

[0043]

[0044] In the formula, These correspond to the phase offset, frequency offset, and frequency drift of a rubidium atomic clock, respectively. The key performance parameters include phase offset, frequency offset, and frequency drift. This represents the amplitude correlation coefficient of the nth periodic term; This represents the phase parameter of the nth periodic term, where n is a positive integer.

[0045] Furthermore, the time vector t is constructed based on a linear interval function; wherein the time vector is from 0 seconds to 86400 seconds, and the sampling interval is 1 second, to cover the complete 24-hour cycle.

[0046] Furthermore, after solving the time difference model using the least squares method to obtain the key performance parameters of the rubidium atomic clock, the process includes:

[0047] Based on the calculated key performance parameters of the rubidium atomic clock, a rubidium atomic clock taming algorithm is used to tame the rubidium atomic clock in order to achieve its calibration.

[0048] A rubidium atomic clock calibration system based on the Loran system includes:

[0049] The data acquisition module is used to calculate the time difference sequence between the Rowland signal and the rubidium clock signal based on the real-time acquired Rowland signal and rubidium clock signal;

[0050] The spectrum analysis module is used to perform spectrum analysis on time difference sequences based on the Welch method and adaptive peak detection method to identify periodic components and the corresponding frequency set and amplitude and phase parameters.

[0051] The model building module is used to construct a time difference model based on the periodic components and the corresponding frequency set and amplitude and phase parameters; the time difference model is a hybrid time difference model including a quadratic trend term, a multi-period term and a noise term;

[0052] The model solving module is used to solve the time difference model using the least squares method to obtain the key performance parameters of the rubidium atomic clock; these key performance parameters are used by the Loran system to tame the rubidium atomic clock in order to achieve the calibration of the rubidium atomic clock.

[0053] A rubidium atomic clock calibration device based on the Loran system includes:

[0054] Memory, used to store computer programs;

[0055] A processor is used to implement the steps of the above-described rubidium atomic clock calibration method based on the Roland system when executing the computer program.

[0056] A computer-readable storage medium storing a computer program, characterized in that the computer program, when executed by a processor, is used to implement the steps of the above-described rubidium atomic clock calibration method based on the Loran system.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] This invention provides a rubidium atomic clock calibration method based on the Loland system. By calculating the time difference sequence between the Loland signal and the rubidium clock signal in real time, spectral analysis based on the Welch method and adaptive peak detection is performed to accurately identify the frequency, amplitude, and phase parameters of the periodic components. A hybrid time difference model including a quadratic trend term, multiple periodic terms, and noise terms is then constructed. The least squares method is used to solve the model to obtain the key performance parameters of the rubidium atomic clock, ultimately completing the time calibration of the rubidium clock tamed by the Loland system. Spectral analysis directly extracts frequency information, avoiding the mode aliasing problem caused by empirical mode decomposition. Adaptive peak detection enhances noise robustness and ensures accurate separation of periodic components. The model structure clearly distinguishes between trend and periodic terms, and the least squares method, supported by optimized parameters, solves efficiently, reducing noise interference and ensuring the uniqueness and stability of the solution. Simultaneously, Welch spectral analysis has low computational complexity, significantly improving processing efficiency. This effectively improves the accuracy of rubidium clock parameter estimation, overcomes problems such as mode aliasing, noise sensitivity, non-unique results, and low computational efficiency, and enables reliable and real-time Roland system calibration of rubidium atomic clocks. Attached Figure Description

[0059] Figure 1 This is a schematic diagram comparing Roland and satellite latency data provided in an embodiment of the present invention;

[0060] Figure 2 This is a full image of obvious periodic terms detected by the Welch method according to an embodiment of the present invention;

[0061] Figure 3 This is a magnified view of a clearly periodic term detected by the Welch method according to an embodiment of the present invention.

[0062] Figure 4 The clock difference between the Roland rubidium atomic clock and standard time provided in this embodiment of the invention;

[0063] Figure 5 This is a comparison chart of the stability of the Roland-trained rubidium atomic clock before and after the invention.

[0064] Figure 6 A flowchart of a rubidium atomic clock calibration method based on the Loran system provided in this embodiment of the invention;

[0065] Figure 7 This is a schematic diagram of a rubidium atomic clock calibration system based on the Loran system, provided as an embodiment of the present invention. Detailed Implementation

[0066] To further understand the content of this invention, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments are merely illustrative and not limiting of the invention.

[0067] To facilitate a better understanding of this technical solution, the technical terms involved in this invention are explained as follows:

[0068] Welch's method is a modern spectral analysis method mainly used for power spectral density estimation. Its core is to achieve smooth and stable estimation of the spectrum through signal segmentation, windowing, and averaging, and effectively reduce variance and spectral leakage errors.

[0069] The Hanning window, also known as the raised cosine window, is a window function widely used in signal processing, primarily to reduce spectral leakage and improve the accuracy of power spectral density estimation.

[0070] As described in the background section, while global navigation satellite systems (GNSS) are widely used in civilian and military fields, their service continuity faces severe challenges, and may even be completely interrupted, under military confrontation, electromagnetic interference, or high-dynamic scenarios. As a typical representative of land-based longwave timing systems, the Loland system, with its superior anti-jamming capabilities and stable signal coverage, has become an important supplement and alternative to GNSS, playing an irreplaceable role, especially in satellite-denied environments. However, the Loland signal is constrained by various complex factors during propagation, resulting in significant time-varying characteristics in its delay characteristics. Specifically: First, multipath effects and ionospheric disturbances: The Loland signal is susceptible to ground reflection, ionospheric disturbances, and changes in atmospheric conditions during propagation, leading to significant time delay fluctuations. Measured data shows that the standard deviation of the Loland signal delay is as high as 64.3812 ns, far exceeding the 11.3402 ns of GNSS signals. This high volatility not only increases the uncertainty of time difference measurement but may also introduce spurious peak interference, seriously affecting the accuracy of signal analysis. Specifically, for example… Figure 1 As shown, the fluctuation amplitude of the Loran signal time delay is significantly greater than that of GNSS (Global Navigation Satellite System) signals, and it exhibits a clear periodic component. This periodic fluctuation not only affects the accuracy of time difference measurement but also poses a severe challenge to the discipline accuracy of rubidium atomic clocks. Secondly, the Earth's rotation Doppler effect: Due to the Earth's rotation, the Loran signal experiences a Doppler shift during propagation, introducing periodic errors into the time delay. For example, the 24-hour periodic diurnal effect and the 12-hour periodic semi-diurnal effect are particularly pronounced in the time difference signal, further exacerbating the signal's complexity. Therefore, to achieve high-precision discipline of rubidium atomic clocks using the Loran signal, effectively handling time difference data interfered with by multiple complex factors has become a core problem urgently needing to be solved in the current field of Loran-disciplined rubidium atomic clock technology. Traditional rubidium clock discipline time difference models suffer from insufficient multi-period interference modeling, limitations in spectral analysis methods, and poor model robustness when processing Loran and rubidium clock time difference data under complex electromagnetic environments, severely restricting the application of the Loran system in the field of high-precision time synchronization.

[0071] To address the aforementioned issues, this embodiment provides a rubidium atomic clock calibration method based on the Loran system. Specifically, this method focuses on the discipline technique of ruthenium atomic clocks based on Loran land-based longwave signals. By constructing a time difference model explicitly containing multiple periodic terms, the method effectively solves the challenge of calibrating rubidium atomic clocks using Loran signals under complex electromagnetic environments, making it particularly suitable for timing backup systems in satellite navigation denied environments.

[0072] For example, such as Figure 6 As shown, this embodiment provides a rubidium atomic clock calibration method based on the Loran system, including:

[0073] Based on the real-time acquired Rowland signal and rubidium clock signal, the time difference sequence between the Rowland signal and the rubidium clock signal is calculated;

[0074] Spectral analysis of time difference sequences is performed based on the Welch method and adaptive peak detection method to identify periodic components and their corresponding frequency sets and amplitude and phase parameters.

[0075] A time difference model is constructed based on the periodic components and the corresponding frequency set and amplitude and phase parameters; the time difference model is a hybrid time difference model including a quadratic trend term, a multi-period term and a noise term;

[0076] The time difference model is solved using the least squares method to obtain the key performance parameters of the rubidium atomic clock; these key performance parameters are used by the Loran system to tame the rubidium atomic clock in order to achieve its calibration.

[0077] The calibration method provided in this embodiment will be further explained below with reference to the accompanying drawings:

[0078] This embodiment provides a rubidium atomic clock calibration method based on the Loren system, the specific steps of which are as follows:

[0079] S1. Acquire the 1PPS (pulse per second) signal from the Roland receiver and the 1PPS (pulse per second) signal from the rubidium clock in real time, and calculate the time difference sequence between them to provide basic data for subsequent analysis. The Roland signal is output by the Roland receiver.

[0080] S2. Based on the Welch method and adaptive peak detection technology, spectral analysis is performed on the time difference sequence to accurately identify the periodic component {Ti} and output the corresponding frequency set and amplitude and phase parameters, providing key information for model construction.

[0081] S3. Construct a time difference model based on periodic components and their corresponding frequency sets and amplitude and phase parameters.

[0082] S4. The time difference model is solved using the least squares method, and the coefficients of the quadratic polynomial and the periodic term parameters are output. Based on the three parameters of phase offset, frequency offset, and frequency drift output by the model, the output phase and frequency of the rubidium clock are adjusted to achieve high-precision discipline of the rubidium clock, ensuring the accuracy and stability of time synchronization.

[0083] Therefore, the calibration method provided in this embodiment has the following specific objectives:

[0084] First, explicit modeling of multiple periodic terms: by introducing interference terms with different periodic components Ti, the periodic fluctuations in the time difference signal are accurately characterized, thereby improving the stability of the time difference signal.

[0085] Second, optimize the spectrum analysis and solution process: adopt advanced spectrum analysis technology to effectively suppress noise interference and improve the detection accuracy of periodic components.

[0086] Third, improve the estimation accuracy of rubidium clock parameters: By using more accurate models and solution methods, improve the estimation accuracy of rubidium clock parameters (such as phase, frequency, and frequency drift), extend the system's fault-free operation time, and meet the requirements of high-precision time synchronization.

[0087] For example, this embodiment provides a rubidium atomic clock calibration method based on the Loran system. The specific discipline process for 24-hour measured data is as follows:

[0088] Step 1: Data Preprocessing: Based on the real-time acquired Rowland signal and rubidium clock signal, the time difference sequence between the Rowland signal and the rubidium clock signal is calculated, including:

[0089] Load the real-time acquired Roland signal and rubidium clock signal;

[0090] The time difference sequence is obtained by calculating the difference between the Loran signal (loranclk) and the rubidium clock signal (rubclk), as shown in the following formula:

[0091]

[0092] In the formula, Represents the time difference sequence; Indicates the Rowland signal; Indicates a rubidium clock signal;

[0093] Zero-mean normalization: The time difference series is normalized to zero to obtain the zero-mean time difference series. The specific formula is as follows:

[0094]

[0095] In the formula, This represents the time difference sequence after zero-mean processing; This represents the mean of the time difference sequence.

[0096] Time vector construction: Construct a time vector t using a linear interval (linspace) function, ranging from 0 seconds to 86400 seconds (24 hours), with a sampling interval of 1 second to ensure coverage of the complete 24-hour period.

[0097] Step 2: Spectrum Analysis and Periodic Detection

[0098] Power spectral density calculation: The Welch method is used to calculate the power spectral density (PSD) of the time difference series. The specific parameter settings are as follows:

[0099] (1) Segment length: 21,600 points (approximately 6 hours); (2) Window function: Hanning window is selected to reduce spectral leakage.

[0100] Significant periodic frequency detection: such as Figure 2 and Figure 3 As shown, the following significant periodic frequencies were detected through spectral analysis:

[0101] (Corresponding to a 24-hour cycle)

[0102] (Corresponding to a 12-hour cycle)

[0103] (Corresponding to an 8-hour cycle)

[0104] In this embodiment, the Welch method is used to calculate the power spectral density of the time difference sequence. The time difference sequence is divided into multiple data segments with a preset segment length, and a Hanning window is used to weight each data segment. The formula for calculating the power spectral density is as follows:

[0105]

[0106] In the formula, Indicates power spectral density; This indicates the number of data segments into which the time difference sequence is divided; Indicates the length of each data segment; This represents the normalization factor of the Hanning window function; Indicates the first l One data segment, l Values ​​range from 0 to -1, n takes the value 0~ -1; f n Represents frequency variables; Represents a complex exponential function; The denot represents the Hanning window function. Compared to the traditional FFT (which is suitable for directly processing complete signals but performs poorly in analyzing non-stationary signals because it cannot reflect the time-varying characteristics of the signal), the Welch method can effectively improve the spectral analysis of non-integer periodic signals.

[0107] An adaptive peak detection method is used to identify the periodic frequency of the power spectral density, including:

[0108] A robust estimation method using the median plus three times the interquartile range is employed to identify the noise basis of time difference sequences. The specific formula is as follows:

[0109]

[0110] In the formula, Indicates the noise floor; This represents the function for calculating the median. Indicates the interquartile range;

[0111] In signals containing impulse noise, this method improves the accuracy of periodic frequency detection from 65% to 92% compared to the traditional mean + 2σ method, significantly enhancing the robustness of noise basis estimation.

[0112] Based on the identified noise floor, an adaptive peak detection method is used to identify the periodic components and their corresponding frequency sets and amplitude and phase parameters.

[0113] Confirmation of the physical significance of periodic components: Based on prior knowledge, it was confirmed that these periodic components are related to physical phenomena such as Earth's rotation and diurnal variation.

[0114] Periodic frequency detection: Identifying significant periodic frequencies using peak detection algorithms. This method combines prior knowledge (such as a known 24-hour cycle) for verification and screening to avoid missing key periodic components. This approach ensures the accuracy and reliability of periodic frequency detection.

[0115] Step 3: Constructing the time difference model:

[0116] A multi-component hybrid model of the Rowland and rubidium clock time difference signal was constructed, namely, a hybrid time difference model containing quadratic polynomials, multi-period terms, and noise, to comprehensively describe the complex characteristics of the Rowland and rubidium clock time difference signal:

[0117]

[0118] In the formula, The term represents the quadratic trend, used to characterize the frequency drift of a rubidium clock; among which, the constant term... Represents the phase difference between the rubidium atomic clock and the Rowland timing signal at the initial moment; coefficient of the first term. This represents the deviation between the initial frequency of the rubidium atomic clock and the standard frequency. This deviation is affected by fluctuations in the internal physical parameters of the rubidium clock and external environmental conditions (such as temperature and pressure); the coefficient of the quadratic term. It represents the frequency drift coefficient (or aging coefficient), which reflects the change in the frequency drift rate of the rubidium clock. Explicitly included periodicity Interference items, such as 24-hour cycles, 12-hour cycles, and other cycles, corresponding to frequencies. These periodic terms are identified from the spectrum using Fourier transform or Welch method, and are used to characterize the impact of external periodic disturbances such as ionospheric diurnal variation and Earth's rotation on the time difference signal of the Rowland signal.

[0119] Where M represents the number of periodic components in the multi-period term; i represents the index variable for the summation of the multi-period term; This represents the coefficient of the cosine component in the i-th periodic term; This represents the coefficient of the sinusoidal component in the i-th periodic term; This represents the frequency of the i-th periodic term; The noise term is represented, specifically including measurement noise and electromagnetic interference. After separating the periodic components, its characteristics are approximately white noise; t is the time vector.

[0120] To simplify the complex time zone model and facilitate subsequent parameter estimation, this embodiment transforms the time zone model into an intuitive matrix form. Specifically, the time zone model can be represented as:

[0121]

[0122] In the formula, The observation matrix includes the raw time difference signal between the measured Rowland signal and the rubidium clock signal;

[0123] The coefficient matrix, used to capture the periodic components and quadratic trend term in the original time difference signal, is specifically represented as follows:

[0124]

[0125] In the formula, t takes values ​​from 1 to m, where m is a positive integer; Indicates the periodic frequency;

[0126] The vector of parameters to be estimated is represented as follows:

[0127]

[0128] In the formula, These correspond to the phase offset, frequency offset, and frequency drift of a rubidium atomic clock, respectively. The key performance parameters include phase offset, frequency offset, and frequency drift. This represents the amplitude correlation coefficient of the nth periodic term; This represents the phase parameter of the nth periodic term, where n is a positive integer.

[0129] The periodic frequency obtained from the above matrix through spectral analysis A framework was constructed to comprehensively describe the characteristics of time difference signals.

[0130] Step 4: Solve the time difference model:

[0131] In this embodiment, the least squares method is used to solve the time difference model. By transforming the matrix equation, we obtain:

[0132]

[0133] Using the above formulas, the matrix equations can be solved using the least squares method to obtain the performance parameters a, b, and c of the rubidium atomic clock, as well as the amplitude and phase of each periodic term, thus completing the model construction and parameter estimation. Finally, based on the solved parameters, a mature rubidium atomic clock taming algorithm can be used to tame the rubidium clock. The results of Roland's rubidium clock taming are as follows... Figure 4 and Figure 5 As shown, Figure 4 The clock difference between the Roland rubidium atomic clock and standard time (UTC) is shown. It can be seen that the standard deviation of the stabilized rubidium clock is 22.4724 ns, and the fluctuation range is within 45 ns. Figure 5 The study demonstrated that the long-term stability of the tamed rubidium clock improved from 2.5205491e-12 to 2.1323594e-13 over 100,000 seconds, which fully demonstrates the positive role played by the Rowland timing signal in taming the rubidium atomic clock.

[0134] Therefore, this embodiment provides a rubidium atomic clock calibration method based on the Loran system, aiming to address multi-periodic interference (such as 24-hour and 12-hour cycles) and complex noise environments present in the Loran signal. By employing the Welch method for spectral analysis, the various periodic terms in the Loran signal can be explicitly modeled and identified. Then, combined with the least squares method, the quadratic polynomial trend term and periodic components in the time difference signal are effectively separated. Experimental results show that, compared to traditional fitting methods, this method can significantly reduce the estimation error of the rubidium clock adjustment caused by fluctuations in the Loran signal itself and noise interference. This calibration method not only provides accurate adjustment estimation for Loran-tamed rubidium clock technology but also provides crucial technical support for satellite navigation backup systems, ensuring the accuracy and reliability of time synchronization.

[0135] like Figure 7As shown, this embodiment also provides a rubidium atomic clock calibration system based on the Loland system, including: a data acquisition module for calculating the time difference sequence between the Loland signal and the rubidium clock signal based on real-time acquired Loland signal and rubidium clock signal; a spectrum analysis module for performing spectrum analysis on the time difference sequence based on the Welch method and adaptive peak detection method to identify periodic components and corresponding frequency sets and amplitude and phase parameters; a model construction module for constructing a time difference model based on the periodic components and corresponding frequency sets and amplitude and phase parameters; the time difference model is a hybrid time difference model including a quadratic trend term, a multi-period term, and a noise term; and a model solving module for solving the time difference model using the least squares method to obtain the key performance parameters of the rubidium atomic clock; the key performance parameters are used by the Loland system to tame the rubidium atomic clock to achieve the calibration of the rubidium atomic clock.

[0136] The present invention also provides a rubidium atomic clock calibration device based on the Loran system, comprising: a memory for storing a computer program; and a processor for executing the computer program to implement the steps of the rubidium atomic clock calibration method based on the Loran system.

[0137] The present invention also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the steps of the rubidium atomic clock calibration method based on the Roland system.

[0138] When the processor executes the computer program, it implements the above-mentioned steps for calibrating the rubidium atomic clock based on the Loran system. For example: based on the real-time acquired Loran signal and rubidium clock signal, the time difference sequence between the Loran signal and the rubidium clock signal is calculated; the time difference sequence is subjected to spectral analysis based on the Welch method and the adaptive peak detection method to identify the periodic components and the corresponding frequency set and amplitude and phase parameters; a time difference model is constructed based on the periodic components and the corresponding frequency set and amplitude and phase parameters; the time difference model is a hybrid time difference model including a quadratic trend term, a multi-period term and a noise term; the time difference model is solved using the least squares method to obtain the key performance parameters of the rubidium atomic clock; the key performance parameters are used by the Loran system to tame the rubidium atomic clock to achieve the calibration of the rubidium atomic clock.

[0139] Exemplarily, the computer program can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules / units can be a series of computer program instruction segments capable of performing preset functions, the instruction segments describing the execution process of the computer program in the Roland-based rubidium atomic clock calibration device. For example, the computer program can be divided into a data acquisition module, a spectrum analysis module, a model building module, and a model solving module. The specific functions of each module are as follows: The data acquisition module is used to calculate the time difference sequence between the Loran signal and the rubidium clock signal based on real-time acquired Loran and rubidium clock signals; the spectrum analysis module is used to perform spectrum analysis on the time difference sequence based on the Welch method and adaptive peak detection method to identify periodic components and their corresponding frequency sets and amplitude and phase parameters; the model building module is used to construct a time difference model based on the periodic components and their corresponding frequency sets and amplitude and phase parameters; the time difference model is a hybrid time difference model including a quadratic trend term, a multi-periodic term, and a noise term; the model solving module is used to solve the time difference model using the least squares method to obtain the key performance parameters of the rubidium atomic clock; these key performance parameters are used by the Loran system to tame the rubidium atomic clock, thereby achieving the calibration of the rubidium atomic clock.

[0140] The rubidium atomic clock calibration device based on the Loland system can be a computing device such as a desktop computer, laptop, handheld computer, or cloud server. The rubidium atomic clock calibration device based on the Loland system may include, but is not limited to, a processor and memory. Those skilled in the art will understand that the above examples of rubidium atomic clock calibration devices based on the Loland system do not constitute a limitation on rubidium atomic clock calibration devices based on the Loland system. It may include more components than described above, or combine certain components, or different components. For example, the rubidium atomic clock calibration device based on the Loland system may also include input / output devices, network access devices, buses, etc.

[0141] The processor referred to can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor, or any conventional processor. This processor is the control center for the rubidium atomic clock calibration based on the Loran system, connecting various parts of the entire rubidium atomic clock calibration equipment via various interfaces and lines.

[0142] The memory can be used to store the computer program and / or modules. The processor implements various functions of the rubidium atomic clock calibration device based on the Roland system by running or executing the computer program and / or modules stored in the memory and calling the data stored in the memory.

[0143] The memory may primarily include a program storage area and a data storage area. The program storage area may store the operating system and at least one application program required for a function (such as sound playback, image playback, etc.). The data storage area may store data created based on the use of the mobile phone (such as audio data, phonebook, etc.). Furthermore, the memory may include high-speed random access memory and non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart media cards (SMC), secure digital cards (SD cards), flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0144] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the rubidium atomic clock calibration method based on the Loran system.

[0145] If the modules / units integrated in the rubidium atomic clock calibration system based on the Loran system are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0146] Based on this understanding, the present invention can implement all or part of the processes in the above-described rubidium atomic clock calibration method based on the Loran system, or it can be accomplished by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the above-described rubidium atomic clock calibration method based on the Loran system. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or a preset intermediate form, etc.

[0147] The computer-readable storage medium may include: any entity or device capable of carrying the computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal, and software distribution medium, etc.

[0148] It should be noted that the content contained in the computer-readable storage medium may be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the computer-readable storage medium does not include electrical carrier signals and telecommunication signals.

[0149] The above embodiments are merely one of the implementation methods for achieving the technical solution of the present invention. The scope of protection claimed by the present invention is not limited to this embodiment, but also includes any variations, substitutions and other implementation methods that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention.

[0150] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the present invention.

Claims

1. A rubidium atomic clock calibration method based on the Loran system, characterized in that, include: Based on the real-time acquired Rowland signal and rubidium clock signal, the time difference sequence between the Rowland signal and the rubidium clock signal is calculated; Spectral analysis of time difference sequences is performed based on the Welch method and adaptive peak detection method to identify periodic components and their corresponding frequency sets and amplitude and phase parameters. A time difference model is constructed based on the periodic components and the corresponding frequency set and amplitude and phase parameters; the time difference model is a hybrid time difference model including a quadratic trend term, a multi-period term and a noise term; The least squares method is used to solve the time difference model to obtain the key performance parameters of the rubidium atomic clock; these key performance parameters are used by the Loran system to tame the rubidium atomic clock and achieve its calibration. The time difference model constructed based on periodic components and their corresponding frequency sets and amplitude and phase parameters includes: Obtain the identified periodic components and their corresponding frequency sets and amplitude and phase parameters; A time difference model is constructed based on the periodic components and their corresponding frequency sets and amplitude and phase parameters. Represented as: In the formula, This represents the quadratic trend term, used to characterize the frequency drift of a rubidium clock; where, This represents the phase difference between the rubidium atomic clock and the Rowland timing signal at the initial moment; This indicates the deviation between the initial frequency of the rubidium atomic clock and the standard frequency. Indicates the frequency drift coefficient; This represents a multi-period term, used to characterize the impact of external periodic interference on the time difference signal of the Rowland signal; where M represents the number of periodic components in the multi-period term; and i represents the index variable for summing the multi-period term. This represents the coefficient of the cosine component in the i-th periodic term; This represents the coefficient of the sinusoidal component in the i-th periodic term; This represents the frequency of the i-th periodic term; The noise term is represented, specifically including measurement noise and electromagnetic interference; t is the time vector. The time difference model includes at least one 24-hour periodic term to characterize the periodic changes in the Roland signal caused by the Earth's rotation.

2. The rubidium atomic clock calibration method based on the Loran system according to claim 1, characterized in that, The calculation of the time difference sequence between the Rowland signal and the rubidium clock signal based on the real-time acquired Rowland signal and rubidium clock signal includes: Load the real-time acquired Roland signal and rubidium clock signal; The time difference sequence is obtained by calculating the difference between the Rowland signal and the rubidium clock signal, as shown in the following formula: In the formula, Represents the time difference sequence; Indicates the Rowland signal; Indicates a rubidium clock signal; The time difference series is zero-mean normalized to obtain the zero-mean time difference series, as shown in the following formula: In the formula, This represents the time difference sequence after zero-mean processing; This represents the mean of the time difference sequence.

3. The rubidium atomic clock calibration method based on the Loran system according to claim 1, characterized in that, The method based on Welch's method and adaptive peak detection performs spectral analysis on the time difference sequence to identify periodic components and their corresponding frequency sets and amplitude and phase parameters, including: The Welch method was used to calculate the power spectral density of the time difference sequence. The time difference sequence was divided into multiple data segments with a preset segment length, and each data segment was weighted using a Hanning window. The formula for calculating the power spectral density is as follows: In the formula, Indicates power spectral density; This indicates the number of data segments into which the time difference sequence is divided; Indicates the length of each data segment; This represents the normalization factor of the Hanning window function; Indicates the first l One data segment, l Values ​​range from 0 to -1, n takes the value 0~ -1; f n Represents frequency variables; Represents a complex exponential function; Represents the Hanning window function; An adaptive peak detection method is used to identify the periodic frequency of the power spectral density, including: A robust estimation method using the median plus three times the interquartile range is employed to identify the noise basis of time difference sequences. The specific formula is as follows: In the formula, Indicates the noise floor; This represents the function for calculating the median. Indicates the interquartile range; Based on the identified noise floor, an adaptive peak detection method is used to identify the periodic components and their corresponding frequency sets and amplitude and phase parameters.

4. The rubidium atomic clock calibration method based on the Loran system according to claim 1, characterized in that, Before using the least squares method to solve the time difference model to obtain the key performance parameters of the rubidium atomic clock, the following steps are included: The time difference model is represented in matrix form, specifically as follows: In the formula, The observation matrix includes the raw time difference signal between the measured Rowland signal and the rubidium clock signal; The coefficient matrix, used to capture the periodic components and quadratic trend term in the original time difference signal, is specifically represented as follows: In the formula, t takes values ​​from 1 to m, where m is a positive integer; Indicates the periodic frequency; The vector of parameters to be estimated is represented as follows: In the formula, These correspond to the phase offset, frequency offset, and frequency drift of a rubidium atomic clock, respectively. The key performance parameters include phase offset, frequency offset, and frequency drift. This represents the amplitude correlation coefficient of the nth periodic term; This represents the phase parameter of the nth periodic term, where n is a positive integer.

5. The rubidium atomic clock calibration method based on the Loran system according to claim 1, characterized in that, The time vector t is constructed based on a linear interval function; wherein the time vector is from 0 seconds to 86400 seconds, and the sampling interval is 1 second to cover the complete 24-hour period.

6. The rubidium atomic clock calibration method based on the Loran system according to claim 1, characterized in that, After solving the time difference model using the least squares method to obtain the key performance parameters of the rubidium atomic clock, the process includes: Based on the calculated key performance parameters of the rubidium atomic clock, a rubidium atomic clock taming algorithm is used to tame the rubidium atomic clock in order to achieve its calibration.

7. A rubidium atomic clock calibration system based on the Loran system, used to implement the rubidium atomic clock calibration method based on the Loran system as described in any one of claims 1-6, characterized in that, include: The data acquisition module is used to calculate the time difference sequence between the Rowland signal and the rubidium clock signal based on the real-time acquired Rowland signal and rubidium clock signal; The spectrum analysis module is used to perform spectrum analysis on time difference sequences based on the Welch method and adaptive peak detection method to identify periodic components and the corresponding frequency set and amplitude and phase parameters. The model building module is used to construct a time difference model based on the periodic components and the corresponding frequency set and amplitude and phase parameters; the time difference model is a hybrid time difference model including a quadratic trend term, a multi-period term and a noise term; The model solving module is used to solve the time difference model using the least squares method to obtain the key performance parameters of the rubidium atomic clock; these key performance parameters are used by the Loran system to tame the rubidium atomic clock in order to achieve the calibration of the rubidium atomic clock.

8. A rubidium atomic clock calibration device based on the Loran system, characterized in that, include: Memory, used to store computer programs; A processor, configured to execute the computer program to implement the steps of the rubidium atomic clock calibration method based on the Loran system as described in any one of claims 1-6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it is used to implement the steps of the rubidium atomic clock calibration method based on the Loran system as described in any one of claims 1-6.

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