A dynamic master clock selection method based on Kalman filtering and Bayesian estimation

Abstract

The invention discloses a dynamic master clock selection method based on Kalman filtering and Bayesian estimation, which is applied to the technical field of master clock selection. The method comprises the following steps: constructing a virtual clock by calculating observation equations of multiple atomic clocks; performing state estimation on multiple atomic clocks using the Kalman filtering method to obtain state estimation values ​​of multiple atomic clocks; the state estimation value of each atomic clock comprises a phase and frequency estimation value of the atomic clock; the phase of each atomic clock is a phase deviation of the atomic clock relative to the virtual clock, and the frequency estimation value is a frequency estimation value of the atomic clock relative to the virtual clock; calculating the short-term frequency stability and long-term frequency drift rate of each atomic clock based on the state estimation value of the atomic clock, and defining a comprehensive performance index of the atomic clock based on the short-term frequency stability and the long-term frequency drift rate; and calculating the posterior probability of each atomic clock based on the comprehensive performance index of each atomic clock and current observation data using the Bayesian estimation method to select a master clock with high flexibility and reliability.

Description

Technical Field

[0001] The invention belongs to the technical field of master clock selection, and in particular relates to a dynamic master clock selection method based on Kalman filtering and Bayesian estimation. Background Art

[0002] Modern timekeeping systems are key infrastructure in many fields such as global communications, navigation, financial transactions, and scientific research. The master clock, as the signal source for the physical realization of the time reference, has an important impact on the reliability, stability, and accuracy of the entire system. The short-term stability of the master clock determines the time jitter level of the timekeeping system, while the long-term stability and accuracy are directly related to the accumulation of time errors. The modern timekeeping system's reliance on the master clock is not only a requirement for its performance, but also a requirement for it as a time reference and the core of the fault-tolerant mechanism. Multi-clock collaboration and reducing reliance on a single master clock are future development trends, which also puts forward new requirements for the master clock selection algorithm.

[0003] The master clock selection method of modern timekeeping systems continues to develop with the increase in system complexity and the demand for time accuracy. In traditional methods, the master clock selection usually adopts static or fixed rules, that is, according to pre-defined indicators such as short-term stability and long-term drift, an atomic clock with the best performance is selected as the master clock, and a backup clock is configured through redundant design. When the master clock has obvious drift, failure, or the accumulated time error exceeds the allowable threshold, the system will switch to the backup master clock. For example, by monitoring the relative frequency deviation between the master clock and other clocks, the master-backup switch is triggered when the deviation exceeds the set range. This method ensures the stability of the system to a certain extent, but the master clock is determined when the system is built, and the dependence on a single master clock is still high, and the fault tolerance is limited. With the rise of the trend of multi-master clock collaboration, more intelligent and dynamic master clock selection methods have become crucial. The existing master clock selection methods based on fixed rules and simple redundancy mechanisms can no longer meet the requirements for fault tolerance, stability and adaptability in highly complex environments. Summary of the invention

[0004] In order to solve the above problems existing in the prior art, the present invention provides a dynamic master clock selection method based on Kalman filtering and Bayesian estimation.

[0005] The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] In a first aspect, the present invention provides a dynamic master clock selection method based on Kalman filtering and Bayesian estimation, the dynamic master clock selection method comprising:

[0007] Construct a virtual clock by calculating the observation equations of multiple atomic clocks;

[0008] Using the Kalman filter method to perform state estimation on the multiple atomic clocks to obtain state estimation values ​​of the multiple atomic clocks; the state estimation value of each atomic clock includes the phase and frequency estimation value of the atomic clock; wherein the phase of each atomic clock is the phase deviation of the atomic clock relative to the virtual clock; the frequency estimation value of each atomic clock is the frequency estimation value of the atomic clock relative to the virtual clock;

[0009] Calculating the short-term frequency stability and long-term frequency drift rate of each atomic clock based on the estimated state value of the atomic clock, and defining the comprehensive performance index of the atomic clock based on the short-term frequency stability and long-term frequency drift rate of the atomic clock;

[0010] The Bayesian estimation method is used to calculate the posterior probability of each atomic clock based on the comprehensive performance indicators of each atomic clock and the current observation data, and the master clock is selected based on the posterior probability of each atomic clock.

[0011] Optionally, a Bayesian estimation method is used to calculate the posterior probability of each atomic clock based on the comprehensive performance indicators of each atomic clock and the current observation data, and the master clock is selected according to the posterior probability of each atomic clock, including:

[0012] Determine the prior probability of each atomic clock according to its comprehensive performance index;

[0013] Obtaining a likelihood function corresponding to each atomic clock according to the observed deviation of each atomic clock and the observed noise covariance corresponding to the atomic clock; wherein the observed deviation of each atomic clock and the observed noise covariance corresponding to the atomic clock are determined according to current observed data of the atomic clock;

[0014] The posterior probability of each atomic clock is calculated using the Bayesian formula based on the likelihood function corresponding to each atomic clock and the prior probability of each atomic clock;

[0015] The atomic clock with the largest posterior probability is used as the master clock.

[0016] Optionally, the posterior probability of each atomic clock is calculated using the Bayesian formula based on the likelihood function corresponding to each atomic clock and the prior probability of each atomic clock, including:

[0017] ;

[0018] in, represents observation data; Indicates An atomic clock is the master clock; Indicates An atomic clock is the master clock; Indicates The posterior probability of an atomic clock; Indicates The likelihood function corresponding to the atomic clock; Indicates The prior probability of an atomic clock; Indicates The likelihood function corresponding to the atomic clock; Indicates The prior probability of an atomic clock; ; ; Represents the total number of atomic clocks.

[0019] Optionally, the comprehensive performance indicators of each atomic clock are defined based on its short-term frequency stability and long-term frequency drift rate, including:

[0020] ;

[0021] in, Indicates Comprehensive performance indicators of atomic clocks; Indicates The short-term frequency stability of an atomic clock; Indicates The long-term frequency drift rate of an atomic clock; represents a first preset weight coefficient; represents a second preset weight coefficient; ; Represents the total number of atomic clocks.

[0022] Optionally, before calculating the short-term frequency stability and long-term frequency drift rate of each atomic clock based on the state estimation value of the atomic clock, the dynamic master clock selection method further includes:

[0023] The multiple atomic clocks are screened according to a preset monitoring threshold of each atomic clock, so as to calculate the short-term frequency stability and the long-term frequency drift rate of each atomic clock after screening based on the state estimation value of the screened atomic clock.

[0024] Optionally, the preset monitoring threshold of each atomic clock is:

[0025] ;

[0026] in, Indicates The preset monitoring threshold of the atomic clock; Indicates Atomic clocks in The first element of the covariance matrix of the predicted state at the moment; Indicates The observation noise covariance corresponding to the atomic clocks.

[0027] In a second aspect, the present invention provides a dynamic master clock selection device based on Kalman filtering and Bayesian estimation, the dynamic master clock selection device comprising:

[0028] A virtual clock construction module, used to construct a virtual clock by calculating the observation equations of multiple atomic clocks;

[0029] A state estimation module, used for performing state estimation on the multiple atomic clocks by using a Kalman filter method to obtain state estimation values ​​of the multiple atomic clocks; the state estimation value of each atomic clock includes a phase and frequency estimation value of the atomic clock; wherein the phase of each atomic clock is a phase deviation of the atomic clock relative to the virtual clock; and the frequency estimation value of each atomic clock is a frequency estimation value of the atomic clock relative to the virtual clock;

[0030] A comprehensive performance index definition module, used for calculating the short-term frequency stability and long-term frequency drift rate of each atomic clock based on the state estimation value of the atomic clock, and defining the comprehensive performance index of the atomic clock based on the short-term frequency stability and long-term frequency drift rate of the atomic clock;

[0031] The master clock selection module is used to calculate the posterior probability of each atomic clock based on the comprehensive performance indicators of each atomic clock and the current observation data using the Bayesian estimation method, and select the master clock according to the posterior probability of each atomic clock.

[0032] Optionally, the master clock selection module is specifically used to:

[0033] The prior probability of each atomic clock is determined according to its comprehensive performance index; the likelihood function corresponding to the atomic clock is obtained according to the observed deviation of each atomic clock and the observed noise covariance corresponding to the atomic clock; wherein the observed deviation of each atomic clock and the observed noise covariance corresponding to the atomic clock are determined according to the current observed data of the atomic clock; the posterior probability of each atomic clock is calculated using the Bayesian formula based on the likelihood function corresponding to each atomic clock and the prior probability of each atomic clock; the atomic clock with the largest posterior probability is used as the master clock.

[0034] Optionally, the master clock selection module calculates the posterior probability of each atomic clock using the Bayesian formula based on the likelihood function corresponding to each atomic clock and the prior probability of each atomic clock, including:

[0035] ;

[0036] in, represents observation data; Indicates An atomic clock is the master clock; Indicates An atomic clock is the master clock; Indicates The posterior probability of an atomic clock; Indicates The likelihood function corresponding to the atomic clock; Indicates The prior probability of an atomic clock; Indicates The likelihood function corresponding to the atomic clock; Indicates The prior probability of an atomic clock; ; ; Represents the total number of atomic clocks.

[0037] Optionally, the comprehensive performance index definition module defines the comprehensive performance index of each atomic clock based on the short-term frequency stability and long-term frequency drift rate of the atomic clock, including:

[0038] ;

[0039] in, Indicates Comprehensive performance indicators of atomic clocks; Indicates The short-term frequency stability of an atomic clock; Indicates The long-term frequency drift rate of an atomic clock; represents a first preset weight coefficient; represents a second preset weight coefficient; ; Represents the total number of atomic clocks.

[0040] Optionally, the dynamic master clock selection device also includes a screening module for screening the multiple atomic clocks according to a preset monitoring threshold of each atomic clock before the comprehensive performance indicator definition module calculates the short-term frequency stability and long-term frequency drift rate of each atomic clock based on the state estimation value of each atomic clock, so as to calculate the short-term frequency stability and long-term frequency drift rate of the atomic clock based on the state estimation value of each atomic clock after screening.

[0041] Optionally, the preset monitoring threshold of each atomic clock is:

[0042] ;

[0043] in, Indicates The preset monitoring threshold of the atomic clock; Indicates Atomic clocks in The first element of the covariance matrix of the predicted state at the moment; Indicates The observation noise covariance corresponding to the atomic clocks.

[0044] The present invention provides a dynamic master clock selection method based on Kalman filtering and Bayesian estimation. The Kalman filtering method is used to estimate the state of the atomic clock. The state estimation value of the atomic clock can be obtained in a recursive manner. The algorithm only needs the relevant data of the previous moment and does not need to store all historical data. It can process data streams in real time and improve prediction efficiency. The virtual clock constructed by the present invention is obtained by calculating the observation equations of multiple atomic clocks, which can make full use of the advantages of multi-clock collaboration and provide a reliable reference for the selection of the master clock. At the same time, the atomic clock performance can be updated in real time through dynamic a posteriori evaluation based on the Bayesian estimation method, and the current optimal master clock can be flexibly selected to ensure the high accuracy and continuity of the time reference under environmental fluctuations or emergencies.

[0045] The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a flow chart of a dynamic master clock selection method based on Kalman filtering and Bayesian estimation provided by an embodiment of the present invention;

[0047] Figure 2 It is a structural schematic diagram of a dynamic master clock selection device based on Kalman filtering and Bayesian estimation provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0048] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0049] In order to solve the problem that the existing master clock selection method based on fixed rules and simple redundancy mechanism is difficult to meet the requirements of fault tolerance, stability and adaptability in a highly complex environment, the embodiment of the present invention provides a dynamic master clock selection method based on Kalman filtering and Bayesian estimation, see Figure 1 , Figure 1 : is a flow chart of a dynamic master clock selection method based on Kalman filtering and Bayesian estimation provided by an embodiment of the present invention, which specifically includes the following steps:

[0050] Step S101, constructing a virtual clock by calculating observation equations of multiple atomic clocks.

[0051] In practical applications, since it is impossible to obtain the true reading of an atomic clock, only the comparison value between atomic clocks can be obtained. Therefore, in an embodiment of the present invention, a virtual clock can be constructed to merge the states of all atomic clocks into a reference benchmark.

[0052] In the embodiment of the present invention, the operation of defining a virtual clock can be obtained by weighted averaging the observation equations of multiple atomic clocks, where The observation equation of an atomic clock is as follows:

[0053] ;

[0054] in, express Moment, The phase deviation of the atomic clock relative to the virtual clock; express Moment, The weight of the atomic clock; express Moment, The phase deviation of the atomic clock relative to the virtual clock; Indicates a time interval; express Moment, The frequency estimate of the atomic clock relative to the virtual clock; ; ; represents the total number of atomic clocks; Indicates Atomic clocks and The observation noise of the relative deviation between atomic clocks is generally phase white noise; express Moment, Atomic clocks and The phase deviation of the atomic clock. In the initial calculation, , Can be obtained by The atomic clock is estimated relative to a priori data of a reference; and Can be obtained by The atomic clock is estimated relative to a priori data of a reference.

[0055] Step S102, using the Kalman filter method to perform state estimation on multiple atomic clocks to obtain state estimation values ​​of multiple atomic clocks; the state estimation value of each atomic clock includes the phase and frequency estimation values ​​of the atomic clock; wherein the phase of each atomic clock is the phase deviation of the atomic clock relative to the virtual clock; the frequency estimation value of each atomic clock is the frequency estimation value of the atomic clock relative to the virtual clock.

[0056] The Kalman filter method is a recursive algorithm that can predict the state and covariance matrix of the atomic clock at the next moment based on the state and covariance matrix of the atomic clock at the previous moment.

[0057] In the embodiment of the present invention, the definition The state equation of an atomic clock is:

[0058] ;

[0059] in, express Moment, The phase deviation of the atomic clock relative to the virtual clock; express Moment, The phase deviation of the atomic clock relative to the virtual clock; express Moment, The frequency deviation of an atomic clock relative to the virtual clock; Indicates The process noise of the phase deviation of an atomic clock is generally manifested as frequency white noise and frequency random walk noise. express Moment, The frequency deviation of an atomic clock relative to the virtual clock; Indicates The process noise of the frequency deviation of an atomic clock is generally manifested as frequency random walk noise.

[0060] and There is a covariance matrix :

[0061] ;

[0062] in, Indicates The frequency white noise intensity coefficient of the atomic clock; Indicates The frequency random walk noise intensity coefficient of the atomic clock. At this time, is the representation of the covariance matrix of the two-state model of the atomic clock.

[0063] In an embodiment of the present invention, and By constructing a priori Short-term frequency stability of an atomic clock That is, the equation system of the Allan variance is obtained:

[0064] ;

[0065] Among them, Allan variance is a method used to analyze the stability of time series data.

[0066] The first The state equation of an atomic clock is expressed in matrix form:

[0067] ;

[0068] in, Indicates The matrix form of the state equation for an atomic clock; superscript symbols Represents the transpose operation of a matrix.

[0069] In the embodiment of the present invention, the Kalman recursive process when the Kalman filter method is used to perform state estimation on multiple atomic clocks to obtain state estimation values ​​of multiple atomic clocks is specifically as follows:

[0070] ;

[0071] in, Indicates based on Predicted The estimated state of the atomic clock at time; represents the state transfer matrix, ; Indicates that the atomic clock is The estimated value of the state at the moment; express The corresponding covariance matrix; express The corresponding covariance matrix; represents the covariance matrix; represents the Kalman gain coefficient; represents the state observation matrix, ; represents the observation noise covariance, ; Indicates The weight of the atomic clock; Indicates that the atomic clock is The estimated value of the state at the moment; Observational data representing the state of an atomic clock; express The corresponding covariance matrix; represents the second-order identity matrix.

[0072] Step S103, calculating the short-term frequency stability and long-term frequency drift rate of each atomic clock based on the state estimation value of the atomic clock, and defining the comprehensive performance index of the atomic clock based on the short-term frequency stability and long-term frequency drift rate of the atomic clock.

[0073] In an embodiment of the present invention, the short-term frequency stability of an atomic clock is obtained according to the frequency change of the atomic clock between two moments. The smaller the frequency change between two moments, the greater the short-term frequency stability of the atomic clock. Conversely, the greater the frequency change between two moments, the smaller the short-term frequency stability of the atomic clock. Short-term frequency stability is often used to measure the ability of an atomic clock to change frequency in a short period of time, which describes the performance of the atomic clock in terms of instantaneous measurement accuracy.

[0074] In the embodiment of the present invention, the long-term frequency drift rate of the atomic clock can be estimated by converting the phase difference data between the atomic clock and the virtual clock into frequency difference data and then performing linear fitting. The long-term frequency drift rate represents the frequency accuracy and stability of the atomic clock over a long period of time.

[0075] In the embodiment of the present invention, when the atomic clock has obvious frequency drift or aging, it can be considered to use the three-state atomic clock state equation for Kalman filter estimation:

[0076] ;

[0077] in, Indicates Process noise of the atomic clock phase; Indicates Process noise of the atomic clock frequency; Indicates The process noise of the atomic clock frequency drift is generally manifested as random running noise, and its intensity coefficient is ; express Moment, Frequency drift of the atomic clock relative to the virtual clock; For the The long-term frequency drift rate of an atomic clock; express Moment, Frequency drift of the atomic clock relative to the virtual clock; Indicates that the atomic clock is The frequency drift value at the moment.

[0078] In an embodiment of the present invention, is a three-dimensional random Gaussian variable The three components of ; The covariance between for:

[0079] ;

[0080] at this time, is the representation of the covariance matrix of the atomic clock three-state model.

[0081] Noise intensity factor Through the Hadamard variance of atomic clocks The equations are established and estimated:

[0082] ;

[0083] In an embodiment of the present invention, in practical applications, the atomic clocks may be grouped, and the virtual clock obtained by two-state estimation may be used as a reference to estimate the drift rates of other atomic clocks, and the virtual clocks may be jointly calculated after the drift rates are eliminated.

[0084] Since the short-term frequency stability and long-term frequency drift rate are important at different time scales, the comprehensive performance index can reflect the overall performance of each atomic clock by weighting them as follows:

[0085] ;

[0086] in, Indicates Comprehensive performance indicators of atomic clocks; Indicates The short-term frequency stability of an atomic clock; Indicates The long-term frequency drift rate of an atomic clock; represents a first preset weight coefficient; represents a second preset weight coefficient; ; Represents the total number of atomic clocks.

[0087] It should be noted that and is the preset weight coefficient of the short-term frequency stability and the long-term frequency drift rate, where , It should be between 0.8 and 1, and it is necessary to ensure that the final selected master clock has excellent short-term stability and a low frequency drift rate.

[0088] In an embodiment of the present invention, the weight of each atomic clock in the next virtual clock calculation can be determined based on the comprehensive performance index of the atomic clock. The comprehensive performance index of multiple atomic clocks is weighted averaged according to the weight to obtain the comprehensive performance index of the virtual clock, which can be used as the performance estimation of the master clock group. The calculation method of the comprehensive performance index of the virtual clock will be explained below to prove that the virtual clock constructed in the embodiment of the present invention can be used as a reference for selecting the master clock.

[0089] In the embodiment of the present invention, the comprehensive performance index of the atomic clock is defined based on the short-term frequency stability and long-term frequency drift rate of each atomic clock. Atomic clocks with better performance in the short and long term can obtain a higher weight, and atomic clocks with poorer performance can obtain a lower weight. The weight of each atomic clock is determined based on the comprehensive performance index of the atomic clock, including:

[0090] ;

[0091] in, Indicates The weight of the atomic clock; Indicates Comprehensive performance indicators of an atomic clock.

[0092] In the embodiment of the present invention, based on the definition of the virtual clock, the comprehensive performance index of the virtual clock can be obtained by weighted averaging the comprehensive performance indexes of multiple atomic clocks according to the weights of multiple atomic clocks. When the performance of the participating atomic clocks is close, the performance of the virtual clock will be better than that of each single clock, so the virtual clock can be used as a reference for the performance evaluation and selection of the master clock.

[0093] Specifically, the comprehensive performance indicators of the multiple atomic clocks are weighted averaged according to the weights of the multiple atomic clocks to obtain the comprehensive performance indicators of the virtual clock, including:

[0094] ;

[0095] in, Express the expectation of comprehensive performance indicators of the virtual clock; Indicates The expectation of the weights of the atomic clocks, Represents the comprehensive performance index of the virtual clock.

[0096] In the embodiment of the present invention, according to the comprehensive performance index of the virtual clock, it can be known that the constructed virtual clock integrates the short-term frequency stability and long-term frequency drift rate of multiple atomic clocks, and fully utilizes the advantages of multi-clock collaboration. Since the comprehensive performance index of the virtual clock can be obtained by weighted averaging the comprehensive performance indexes of multiple atomic clocks according to the weights of multiple atomic clocks, when the performance of the participating atomic clocks is close, the performance of the virtual clock will be better than that of each atomic clock, so the virtual clock constructed in the embodiment of the present invention can be used as a reference for the performance evaluation and selection of the master clock.

[0097] Step S104, using the Bayesian estimation method, the posterior probability of each atomic clock is calculated based on the comprehensive performance indicators of each atomic clock and the current observation data, and the master clock is selected according to the posterior probability of each atomic clock.

[0098] Bayesian estimation is a statistical inference method based on Bayes' theorem, which is used to estimate the probability distribution of unknown parameters. Bayesian estimation combines prior knowledge of atomic clocks, such as historical comprehensive performance indicators, with current observation data, such as clock errors and noise levels, and dynamically updates the performance evaluation of each atomic clock to select the optimal master clock based on the posterior probability of each atomic clock, so as to achieve accurate selection and real-time adjustment of the master clock and ensure timely adaptation when the system changes.

[0099] Specifically, in the Bayesian estimation method, the prior probability can be defined for each atomic clock based on the comprehensive performance indicators of each atomic clock, and then combined with the likelihood function, the posterior probability of each atomic clock can be calculated.

[0100] In an embodiment of the present invention, the state estimation of the atomic clock is performed using the Kalman filter method, and the state estimation value of the atomic clock can be obtained in a recursive manner. The algorithm only needs the relevant data of the previous moment, does not need to store all historical data, can process data streams in real time, and improves prediction efficiency. The virtual clock constructed by the present invention is obtained by calculating the observation equations of multiple atomic clocks, which can make full use of the advantages of multi-clock collaboration and provide a reliable reference for the selection of the master clock. At the same time, the performance of the atomic clock can be updated in real time through dynamic a posteriori evaluation based on the Bayesian estimation method, and the current optimal master clock can be flexibly selected to ensure the high accuracy and continuity of the time reference under environmental fluctuations or emergencies.

[0101] In one implementation, the Bayesian estimation method is used to calculate the posterior probability of each atomic clock based on the comprehensive performance indicators of each atomic clock and the current observation data, and the master clock is selected according to the posterior probability of each atomic clock, including:

[0102] Determine the prior probability of each atomic clock according to its comprehensive performance index;

[0103] Obtaining a likelihood function corresponding to each atomic clock according to the observed deviation of each atomic clock and the observed noise covariance corresponding to the atomic clock; wherein the observed deviation of each atomic clock and the observed noise covariance corresponding to the atomic clock are determined according to current observed data of the atomic clock;

[0104] The posterior probability of each atomic clock is calculated using the Bayesian formula based on the likelihood function corresponding to each atomic clock and the prior probability of each atomic clock;

[0105] The atomic clock with the largest posterior probability is used as the master clock.

[0106] In the embodiment of the present invention, a priori probability is defined for each atomic clock according to the comprehensive performance index of the atomic clock, which is expressed as:

[0107] ;

[0108] in, Indicates The comprehensive performance index is the comprehensive performance index of the atomic clock before the current moment.

[0109] Normalize the prior probabilities of all atomic clocks:

[0110] ;

[0111] In the embodiment of the present invention, the likelihood function corresponding to each atomic clock is obtained according to the observed deviation of each atomic clock and the observed noise covariance corresponding to the atomic clock. The observed deviation of an atomic clock is , Indicates Atomic clocks in The phase difference prediction residual at time Atomic clocks in The forecast residual at time Ideally, it conforms to the normal distribution, so the first The likelihood function corresponding to the atomic clock is:

[0112] ;

[0113] in, Indicates The likelihood function corresponding to the atomic clock; Indicates The observation noise covariance corresponding to the atomic clocks.

[0114] In the embodiment of the present invention, the posterior probability of each atomic clock is calculated using the Bayesian formula based on the likelihood function corresponding to each atomic clock and the prior probability of each atomic clock, including:

[0115] ;

[0116] in, represents observation data; Indicates An atomic clock is the master clock; Indicates An atomic clock is the master clock; Indicates The posterior probability of an atomic clock; Indicates The likelihood function corresponding to the atomic clock; Indicates The prior probability of an atomic clock; Indicates The likelihood function corresponding to the atomic clock; Indicates The prior probability of an atomic clock; ; ; Represents the total number of atomic clocks.

[0117] In the embodiment of the present invention, the atomic clock with the largest posterior probability is preferably the atomic clock with the best performance at the current moment.

[0118] In addition, as the observed data increases, the posterior probability can be recalculated after each filter update, so that the master clock selection can adapt to changes in system performance in real time.

[0119] In one implementation, before calculating the short-term frequency stability and the long-term frequency drift rate of each atomic clock based on the state estimation value of the atomic clock, the dynamic master clock selection method further includes:

[0120] According to a preset monitoring threshold of each atomic clock, multiple atomic clocks are screened to calculate the short-term frequency stability and long-term frequency drift rate of each atomic clock based on the state estimation value of each screened atomic clock.

[0121] In the embodiment of the present invention, in order to further improve the accuracy of the atomic clock frequency estimation during the operation of the timekeeping system, it is possible to use the frequency stability of the atomic clock to dynamically estimate the state noise of the atomic clock in the Kalman recursive process, and to periodically The atomic clock can also be updated using real-time measured data. The value and observation noise value:

[0122] ;

[0123] ;

[0124] in, Indicates The weight of the atomic clock; express Moment Atomic clock value; express Moment Atomic clock value; is the adjustment coefficient, which is between 0.9 and 1.

[0125] Indicates Atomic clocks in The forecast residual at time :

[0126] ;

[0127] Indicates Atomic clocks in The state of the moment; Indicated in The moment prediction Atomic clocks in The state of the moment.

[0128] No. Atomic clocks in The covariance matrix of the phase difference prediction residuals at time for:

[0129] ;

[0130] in, is the statistical number of prediction residuals, that is, the total number of statistical moments.

[0131] In the embodiment of the present invention, the atomic clocks can be screened according to the preset monitoring threshold value to avoid the introduction of abnormal atomic clocks when subsequently defining the comprehensive performance indicators of the virtual clock, thereby avoiding frequent jumps in the system time.

[0132] In the embodiment of the present invention, the The preset detection threshold of an atomic clock is:

[0133] ;

[0134] in, Indicates The preset monitoring threshold of the atomic clock; Indicates Atomic clocks in The first element of the covariance matrix of the predicted state at the moment; Indicates The observation noise covariance corresponding to the atomic clocks.

[0135] like , it is considered that the atomic clock is abnormal. For abnormal atomic clocks, they can be eliminated or their weights can be reduced when constructing virtual clocks.

[0136] The following is a simulation experiment of a dynamic master clock selection method based on Kalman filtering and Bayesian estimation provided by an embodiment of the present invention:

[0137] Assume that there are 3 atomic clocks, and their comprehensive performance indicators are as follows:

[0138] ;

[0139] ;

[0140] ;

[0141] in, It is the comprehensive performance index of atomic clock 1; It is the comprehensive performance index of atomic clock 2; It is the comprehensive performance indicator of atomic clock 3.

[0142] The observation noise covariance values ​​of the three atomic clocks are as follows:

[0143] ;

[0144] ;

[0145] ;

[0146] in, represents the observation noise covariance value of atomic clock 1; represents the observation noise covariance value of atomic clock 2; Represents the observation noise covariance value of atomic clock 3.

[0147] The observed deviations of the three atomic clocks are as follows:

[0148] ;

[0149] ;

[0150] ;

[0151] in, represents the observed bias of atomic clock 1; represents the observed bias of atomic clock 2; Represents the observed deviation of atomic clock 3.

[0152] Then the prior probabilities of the three atomic clocks are as follows:

[0153] ;

[0154] ;

[0155] ;

[0156] in, represents the prior probability of the atomic clock 1; represents the prior probability of atomic clock 2; represents the prior probability of atomic clock 3.

[0157] The likelihood probabilities of the three atomic clocks, that is, the function values ​​of the likelihood functions, are as follows:

[0158] ;

[0159] ;

[0160] ;

[0161] in, represents the likelihood probability of atomic clock 1; represents the likelihood probability of atomic clock 2; represents the likelihood probability of atomic clock 3.

[0162] The posterior probabilities of the three atomic clocks are calculated as follows:

[0163] ;

[0164] ;

[0165] ;

[0166] in, represents the posterior probability of the atomic clock 1; represents the posterior probability of atomic clock 2; represents the posterior probability of atomic clock 3.

[0167] Therefore, atomic clock 2 can be selected as the master clock.

[0168] Based on the same inventive concept, the embodiment of the present invention also provides a dynamic master clock selection device based on Kalman filtering and Bayesian estimation, see Figure 2 , Figure 2 : is a schematic diagram of a dynamic master clock selection device based on Kalman filtering and Bayesian estimation provided by an embodiment of the present invention, the dynamic master clock selection device comprising:

[0169] A virtual clock construction module 201 is used to construct a virtual clock by calculating observation equations of multiple atomic clocks;

[0170] The state estimation module 202 is used to perform state estimation on multiple atomic clocks using the Kalman filter method to obtain state estimation values ​​of multiple atomic clocks; the state estimation value of each atomic clock includes the phase and frequency estimation value of the atomic clock; wherein the phase of each atomic clock is the phase deviation of the atomic clock relative to the virtual clock; the frequency estimation value of each atomic clock is the frequency estimation value of the atomic clock relative to the virtual clock;

[0171] A comprehensive performance index definition module 203, used to calculate the short-term frequency stability and long-term frequency drift rate of each atomic clock based on the state estimation value of the atomic clock, and define the comprehensive performance index of the atomic clock based on the short-term frequency stability and long-term frequency drift rate of the atomic clock;

[0172] The master clock selection module 204 is used to calculate the posterior probability of each atomic clock based on the comprehensive performance indicators of each atomic clock and the current observation data using the Bayesian estimation method, and select the master clock according to the posterior probability of each atomic clock.

[0173] In an embodiment of the present invention, the state of the atomic clock is estimated by using the Kalman filter method, and the state estimation value of the atomic clock can be obtained in a recursive manner. The algorithm only needs the relevant data of the previous moment, does not need to store all historical data, can process data streams in real time, and improves prediction efficiency. The virtual clock constructed in the embodiment of the present invention is obtained by calculating the observation equations of multiple atomic clocks, which can make full use of the advantages of multi-clock collaboration and provide a reliable reference for the selection of the master clock. At the same time, the performance of the atomic clock can be updated in real time through dynamic a posteriori evaluation based on the Bayesian estimation method, and the current optimal master clock can be flexibly selected to ensure the high accuracy and continuity of the time reference under environmental fluctuations or emergencies.

[0174] Optionally, the master clock selection module 204 is specifically configured to:

[0175] The prior probability of each atomic clock is determined according to its comprehensive performance index; the likelihood function corresponding to the atomic clock is obtained according to the observed deviation of each atomic clock and the observed noise covariance corresponding to the atomic clock; wherein the observed deviation of each atomic clock and the observed noise covariance corresponding to the atomic clock are determined according to the current observed data of the atomic clock; the posterior probability of each atomic clock is calculated using the Bayesian formula based on the likelihood function corresponding to each atomic clock and the prior probability of each atomic clock; the atomic clock with the largest posterior probability is used as the master clock.

[0176] Optionally, the master clock selection module 204 calculates the posterior probability of each atomic clock using the Bayesian formula based on the likelihood function corresponding to each atomic clock and the prior probability of each atomic clock, including:

[0177] ;

[0178] in, represents observation data; Indicates An atomic clock is the master clock; Indicates An atomic clock is the master clock; Indicates The posterior probability of an atomic clock; Indicates The likelihood function corresponding to the atomic clock; Indicates The prior probability of an atomic clock; Indicates The likelihood function corresponding to the atomic clock; Indicates The prior probability of an atomic clock; ; ; Represents the total number of atomic clocks.

[0179] Optionally, the comprehensive performance index definition module 203 defines the comprehensive performance index of each atomic clock based on the short-term frequency stability and long-term frequency drift rate of the atomic clock, including:

[0180] ;

[0181] in, Indicates Comprehensive performance indicators of atomic clocks; Indicates The short-term frequency stability of an atomic clock; Indicates The long-term frequency drift rate of an atomic clock; represents a first preset weight coefficient; represents a second preset weight coefficient; ; Represents the total number of atomic clocks.

[0182] Optionally, the dynamic master clock selection device also includes a screening module for screening multiple atomic clocks according to a preset monitoring threshold of each atomic clock before the comprehensive performance indicator definition module 203 calculates the short-term frequency stability and long-term frequency drift rate of each atomic clock based on the state estimation value of each atomic clock, so as to calculate the short-term frequency stability and long-term frequency drift rate of each atomic clock based on the state estimation value of each atomic clock after screening.

[0183] Optionally, the preset monitoring thresholds for each atomic clock include:

[0184] ;

[0185] in, Indicates The preset monitoring threshold of the atomic clock; Indicates Atomic clocks in The first element of the covariance matrix of the predicted state at the moment; Indicates The observation noise covariance corresponding to the atomic clocks.

[0186] It should be noted that the terms "first", "second", etc. are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Instead, they are merely examples of devices and methods consistent with some aspects of the present invention.

[0187] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification.

[0188] Although the present invention is described herein in conjunction with various embodiments, in the process of implementing the claimed invention, those skilled in the art can understand and implement other changes to the disclosed embodiments by viewing the drawings and the disclosed content. In the description of the present invention, the term "comprising" does not exclude other components or steps, "one" or "an" does not exclude multiple situations, and "multiple" means two or more, unless otherwise clearly and specifically limited. In addition, certain measures are recorded in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0189] As for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0190] It should be noted that the device of an embodiment of the present invention is a device that applies the above-mentioned dynamic master clock selection method based on Kalman filtering and Bayesian estimation. All embodiments of the above-mentioned dynamic master clock selection method based on Kalman filtering and Bayesian estimation are applicable to the device and can achieve the same or similar beneficial effects.

[0191] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A dynamic master clock selection method based on Kalman filtering and Bayesian estimation, characterized in that: The dynamic master clock selection method comprises: Construct a virtual clock by calculating the observation equations of multiple atomic clocks; Using the Kalman filter method to perform state estimation on the multiple atomic clocks to obtain state estimation values ​​of the multiple atomic clocks; the state estimation value of each atomic clock includes the phase and frequency estimation value of the atomic clock; wherein the phase of each atomic clock is the phase deviation of the atomic clock relative to the virtual clock; the frequency estimation value of each atomic clock is the frequency estimation value of the atomic clock relative to the virtual clock; Calculating the short-term frequency stability and long-term frequency drift rate of each atomic clock based on the estimated state value of the atomic clock, and defining the comprehensive performance index of the atomic clock based on the short-term frequency stability and long-term frequency drift rate of the atomic clock; Using the Bayesian estimation method, the posterior probability of each atomic clock is calculated based on the comprehensive performance indicators of each atomic clock and the current observation data, and the master clock is selected based on the posterior probability of each atomic clock; In the Kalman recursive process of obtaining state estimation values ​​of multiple atomic clocks by using the Kalman filter method to estimate the state of multiple atomic clocks, the state estimation values ​​of the atomic clocks are dynamically adjusted by dynamically adjusting the covariance matrix of the atomic clocks and the observation noise covariance; Among them, the method of dynamically adjusting the covariance matrix is: ； The way to dynamically adjust the observation noise covariance is: ； in, Indicates The weight of the atomic clock; express Moment Atomic clock value; express Moment Atomic clock value; is the adjustment coefficient; represents the covariance matrix; ; ; represents the total number of atomic clocks; Indicates Atomic clocks and The observation noise of the relative deviations between atomic clocks; Indicates Atomic clocks in The covariance matrix of the phase difference prediction residuals at each moment; represents the observation noise covariance.

2. The dynamic master clock selection method according to claim 1, characterized in that: The Bayesian estimation method is used to calculate the posterior probability of each atomic clock based on the comprehensive performance indicators of each atomic clock and the current observation data, and the master clock is selected based on the posterior probability of each atomic clock, including: Determine the prior probability of each atomic clock according to its comprehensive performance index; Obtaining a likelihood function corresponding to each atomic clock according to the observed deviation of each atomic clock and the observed noise covariance corresponding to the atomic clock; wherein the observed deviation of each atomic clock and the observed noise covariance corresponding to the atomic clock are determined according to current observed data of the atomic clock; The posterior probability of each atomic clock is calculated using the Bayesian formula based on the likelihood function corresponding to each atomic clock and the prior probability of each atomic clock; The atomic clock with the largest posterior probability is used as the master clock.

3. The dynamic master clock selection method according to claim 2, characterized in that: Based on the likelihood function corresponding to each atomic clock and the prior probability of each atomic clock, the posterior probability of each atomic clock is calculated using the Bayesian formula, including: ； in, represents observation data; Indicates An atomic clock is the master clock; Indicates An atomic clock is the master clock; Indicates The posterior probability of an atomic clock; Indicates The likelihood function corresponding to the atomic clock; Indicates The prior probability of an atomic clock; Indicates The likelihood function corresponding to the atomic clock; Indicates The prior probability of an atomic clock; ; ; Represents the total number of atomic clocks.

4. The dynamic master clock selection method according to claim 1, characterized in that: The comprehensive performance indicators of each atomic clock are defined based on its short-term frequency stability and long-term frequency drift rate, including: ； in, Indicates Comprehensive performance indicators of atomic clocks; Indicates The short-term frequency stability of an atomic clock; Indicates The long-term frequency drift rate of an atomic clock; represents a first preset weight coefficient; represents a second preset weight coefficient; ; Represents the total number of atomic clocks.

5. The dynamic master clock selection method according to claim 1, characterized in that: Before calculating the short-term frequency stability and long-term frequency drift rate of each atomic clock based on the state estimation value of the atomic clock, the dynamic master clock selection method further includes: The multiple atomic clocks are screened according to a preset monitoring threshold of each atomic clock, so as to calculate the short-term frequency stability and the long-term frequency drift rate of each atomic clock after screening based on the state estimation value of the screened atomic clock.

6. The method for selecting a dynamic master clock according to claim 5, characterized in that: The preset monitoring threshold for each atomic clock is: ； in, Indicates The preset monitoring threshold of the atomic clock; Indicates Atomic clocks in The first element of the covariance matrix of the predicted state at the moment; Indicates The observation noise covariance corresponding to the atomic clocks.

7. A dynamic master clock selection device based on Kalman filtering and Bayesian estimation, characterized in that: The dynamic master clock selection device comprises: A virtual clock construction module, used to construct a virtual clock by calculating the observation equations of multiple atomic clocks; A state estimation module, used for performing state estimation on the multiple atomic clocks by using a Kalman filter method to obtain state estimation values ​​of the multiple atomic clocks; the state estimation value of each atomic clock includes a phase and frequency estimation value of the atomic clock; wherein the phase of each atomic clock is a phase deviation of the atomic clock relative to the virtual clock; and the frequency estimation value of each atomic clock is a frequency estimation value of the atomic clock relative to the virtual clock; A comprehensive performance index definition module, used for calculating the short-term frequency stability and long-term frequency drift rate of each atomic clock based on the state estimation value of the atomic clock, and defining the comprehensive performance index of the atomic clock based on the short-term frequency stability and long-term frequency drift rate of the atomic clock; The master clock selection module is used to calculate the posterior probability of each atomic clock based on the comprehensive performance indicators of each atomic clock and the current observation data using the Bayesian estimation method, and select the master clock according to the posterior probability of each atomic clock; In the Kalman recursive process of obtaining state estimation values ​​of multiple atomic clocks by using the Kalman filter method to estimate the state of multiple atomic clocks, the state estimation values ​​of the atomic clocks are dynamically adjusted by dynamically adjusting the covariance matrix of the atomic clocks and the observation noise covariance; Among them, the method of dynamically adjusting the covariance matrix is: ； The way to dynamically adjust the observation noise covariance is: ； in, Indicates The weight of the atomic clock; express Moment Atomic clock value; express Moment Atomic clock value; is the adjustment coefficient; represents the covariance matrix; ; ; represents the total number of atomic clocks; Indicates Atomic clocks and The observation noise of the relative deviations between atomic clocks; Indicates Atomic clocks in The covariance matrix of the phase difference prediction residuals at each moment; represents the observation noise covariance.

8. The dynamic master clock selection device according to claim 7, characterized in that: The master clock selection module is specifically used for: The prior probability of each atomic clock is determined according to its comprehensive performance index; the likelihood function corresponding to the atomic clock is obtained according to the observed deviation of each atomic clock and the observed noise covariance corresponding to the atomic clock; wherein the observed deviation of each atomic clock and the observed noise covariance corresponding to the atomic clock are determined according to the current observed data of the atomic clock; the posterior probability of each atomic clock is calculated using the Bayesian formula based on the likelihood function corresponding to each atomic clock and the prior probability of each atomic clock; the atomic clock with the largest posterior probability is used as the master clock.

9. The dynamic master clock selection device according to claim 8, characterized in that: The master clock selection module calculates the posterior probability of each atomic clock using the Bayesian formula based on the likelihood function corresponding to each atomic clock and the prior probability of each atomic clock, including: ； in, represents observation data; Indicates An atomic clock is the master clock; Indicates An atomic clock is the master clock; Indicates The posterior probability of an atomic clock; Indicates The likelihood function corresponding to the atomic clock; Indicates The prior probability of an atomic clock; Indicates The likelihood function corresponding to the atomic clock; Indicates The prior probability of an atomic clock; ; ; Represents the total number of atomic clocks.

10. The dynamic master clock selection device according to claim 7, characterized in that: The comprehensive performance index definition module defines the comprehensive performance index of each atomic clock based on the short-term frequency stability and long-term frequency drift rate of the atomic clock, including: ； in, Indicates Comprehensive performance indicators of atomic clocks; Indicates The short-term frequency stability of an atomic clock; Indicates The long-term frequency drift rate of an atomic clock; represents a first preset weight coefficient; represents a second preset weight coefficient; ; Represents the total number of atomic clocks.

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