Clock error prediction method and device based on variational Bayesian Kalman filtering

Abstract

The invention provides a clock error prediction method and device based on variational Bayesian Kalman filtering. The method comprises the following steps: predicting a state vector and a covariance matrix of a clock error model, and predicting observation noise matrix parameters; the predicted value of the covariance matrix is updated, the predicted value of the state vector is updated, the predicted value of the measurement vector at the previous moment is obtained through calculation according to the predicted value of the state vector of the clock error model, and the predicted value of the cross covariance matrix at the previous moment is obtained through the predicted value of the cross covariance matrix; initializing relevant parameters of the observation noise, and iterating the initialized observation noise for a preset number of times by adopting a predicted value of the measurement vector at the previous moment and a predicted value of the cross covariance matrix at the previous moment; and estimating observation noise and system noise, and carrying out iterative prediction on a measurement vector by adopting an estimated value. According to the invention, the clock error filtering and self-holding performance of the timekeeping system is improved when the timekeeping system is subjected to external interference or even time cheating.

Description

Technical Field

[0001] The embodiments of the present invention relate to the technical field of clock error prediction optimization, and in particular to a clock error prediction method and device based on variational Bayesian Kalman filtering. Background Art

[0002] Clock deviation prediction refers to predicting the clock error of atomic clocks in the future based on historical clock error data. Accurate clock error prediction is the key to achieving real-time, reliable dynamic precision point positioning, accurate satellite autonomous navigation, and high-precision and effective control of atomic clock systems. Satellite clocks are an important part of the navigation system. Their performance and accurate prediction are crucial to ensuring the accuracy of navigation and positioning and achieving autonomous navigation and precise positioning. Therefore, it is necessary to ensure their accuracy, real-time and continuity. Satellite-borne atomic clocks have complex physical properties and are easily interfered by external factors, so it is difficult to capture complex and subtle change patterns; related competitive fields often use deceptive interference to interfere with navigation satellite signals, resulting in time superposition noise, clock deviation and even timestamp jumps in the timekeeping system. Therefore, establishing a high-precision satellite clock error prediction model with anti-deceptive interference has become a challenging task. The relevant technical means use different single models to apply to various precision satellite-borne atomic clocks. The scope of application is limited, and there are certain limitations in the actual satellite clock error prediction. Therefore, developing a clock error prediction method and device based on variational Bayes Kalman filtering can effectively overcome the defects in the above-mentioned related technologies, which has become a technical problem that needs to be solved urgently in the industry. Summary of the invention

[0003] In view of the above problems existing in the prior art, an embodiment of the present invention provides a clock error prediction method and device based on variational Bayesian Kalman filtering.

[0004] In a first aspect, an embodiment of the present invention provides a clock error prediction method based on variational Bayes Kalman filtering, comprising: predicting the state vector and covariance matrix of the clock error model, and predicting the observation noise matrix parameters; updating the predicted value of the covariance matrix, and updating the predicted value of the state vector, calculating the predicted value of the measurement vector at the previous moment according to the predicted value of the state vector of the clock error model, and obtaining the predicted value of the cross-covariance matrix at the previous moment according to the predicted value of the cross-covariance matrix; initializing relevant parameters of the observation noise, using the predicted value of the measurement vector at the previous moment and the predicted value of the cross-covariance matrix at the previous moment, and iterating the initialized observation noise a predetermined number of times; estimating the observation noise and the system noise, obtaining the estimated value of the state vector according to the estimated value of the observation noise and the estimated value of the system noise, and iteratively predicting the measurement vector using the estimated value of the state vector.

[0005] Based on the content of the above method embodiment, the clock error prediction method based on variational Bayes Kalman filtering provided in the embodiment of the present invention, wherein the state vector of the clock error model is predicted, comprises:

[0006] x k|k-1 =Fx k-1|k-1

[0007] Among them, x k|k-1 is the predicted value of the state vector at time k-1; F is the n-order state transfer matrix from time k-1 to time k; x k-1|k-1 is the estimated value of the state vector at time k-1.

[0008] Based on the content of the above method embodiment, the clock error prediction method based on variational Bayes Kalman filtering provided in the embodiment of the present invention, the prediction of the covariance matrix includes:

[0009]

[0010] Among them, P k|k-1 is the prediction error covariance at time k-1; P k-1 is the error covariance at time k-1; T is the matrix transpose symbol; L k-1 is the system noise driving matrix at time k-1; Q k is the k-time process noise covariance matrix; Q k-1 is the k-1 moment process noise covariance matrix; q k is the Gaussian white noise of the process at time k; E is the expectation of the noise covariance of the calculation process.

[0011] Based on the content of the above method embodiment, the clock error prediction method based on variational Bayesian Kalman filtering provided in the embodiment of the present invention, and predicting the observation noise matrix parameters, includes:

[0012] v k|k-1 =ρ(v k-1 -n-1)+n+1

[0013] V k|k-1 =GV k-1 G T

[0014]

[0015] Among them, v k|k-1 is the predicted value of the second observation noise matrix parameter v at time k-1; ρ is the coefficient of variation and is greater than 0 and less than 1; v k-1 is the estimated value of the second observation noise matrix parameter v at time k-1; V k|k-1is the predicted value of the first observation noise matrix parameter V at time k-1; G is the conversion matrix; I is the unit matrix; V k-1 is the estimated value of the first observation noise matrix parameter V at time k-1.

[0016] Based on the content of the above method embodiment, the clock error prediction method based on variational Bayes Kalman filtering provided in the embodiment of the present invention, the predicted value of the covariance matrix is ​​updated, and the predicted value of the state vector is updated, and the predicted value of the measurement vector at the previous moment is calculated according to the predicted value of the state vector of the clock error model, and the predicted value of the cross-covariance matrix is ​​obtained. The predicted value of the cross-covariance matrix at the previous moment includes:

[0017] y k|k-1 =Hx k|k-1

[0018] P xy,k|k-1 =P k|k-1 H T

[0019] Among them, y k|k-1 is the predicted value of the m-order measurement vector at time k-1; H is the m-order observation matrix; P xy,k|k-1 is the predicted value of the cross-covariance matrix at time k-1; P k|k-1 is the predicted value of the error covariance at time k-1.

[0020] Based on the content of the above method embodiment, the clock error prediction method based on variational Bayes Kalman filtering provided in the embodiment of the present invention, the initialization of the relevant parameters of the observation noise includes:

[0021] v k|k =v k|k-1 +1

[0022] V k|k =V k|k-1

[0023] Among them, v k|k V is the predicted value of the second observation noise matrix parameter v at time k; k|k is the predicted value of the first observation noise matrix parameter v at time k.

[0024] Based on the content of the above method embodiment, the clock error prediction method based on variational Bayes Kalman filtering provided in the embodiment of the present invention, wherein the predicted value of the measurement vector at the previous moment and the predicted value of the cross-covariance matrix at the previous moment are used to iterate the initialized observation noise for a predetermined number of times, includes:

[0025]

[0026] Where i is the i-th cycle; ε k is the observation error, is the observation noise, is the observation error covariance matrix, is the Kalman filter gain, is the estimated value of the state vector, is the estimated value of the covariance matrix, is the estimated value of the relevant parameters of the observation noise R, M k-1 and A are the first and second related variables for calculating the system noise Q based on the Sage-Husa algorithm; the related parameter d for the system noise Q updated at time k-1 k-1 =(1-b) / (1-b k ), and 0.95≤b≤0.99, b is the relevant parameter variable; y k is the actual observation value at time k; K is the predicted value of the first observed noise matrix parameter V at time k-1 in the i-th cycle; k is the Kalman filter gain; P k is the error covariance at time k.

[0027] In the second aspect, an embodiment of the present invention provides a clock error prediction device based on variational Bayes Kalman filtering, including: a first main module, used to predict the state vector and covariance matrix of the clock error model, and predict the observation noise matrix parameters; a second main module, used to update the predicted value of the covariance matrix, and update the predicted value of the state vector, calculate the predicted value of the measurement vector at the previous moment according to the predicted value of the state vector of the clock error model, and obtain the predicted value of the cross-covariance matrix at the previous moment according to the predicted value of the cross-covariance matrix; a third main module, used to initialize the relevant parameters of the observation noise, use the predicted value of the measurement vector at the previous moment and the predicted value of the cross-covariance matrix at the previous moment, and iterate the initialized observation noise for a predetermined number of times; a fourth main module, used to estimate the observation noise and the system noise, obtain the estimated value of the state vector according to the estimated value of the observation noise and the estimated value of the system noise, and use the estimated value of the state vector to iteratively predict the measurement vector.

[0028] In a third aspect, an embodiment of the present invention provides an electronic device, including:

[0029] At least one processor, at least one memory and a communication interface; wherein,

[0030] The processor, memory and communication interface communicate with each other;

[0031] The memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the clock error prediction method based on variational Bayes Kalman filtering provided by any one of the various implementations of the first aspect.

[0032] In a fourth aspect, an embodiment of the present invention provides a non-transitory computer-readable storage medium, which stores computer instructions, and the computer instructions enable a computer to execute a clock error prediction method based on variational Bayes Kalman filtering provided by any one of the various implementation methods of the first aspect.

[0033] The clock error prediction method and device based on variational Bayesian Kalman filtering provided in an embodiment of the present invention, by iteratively estimating and correcting the observation noise R and the system noise Q using the inverse Wishart distribution, estimates the covariance of the system state and the observation noise, and applies it to the Kalman filter, thereby improving the adaptability of the Kalman filter clock deviation prediction. The method is applied to the satellite clock error prediction of satellite common view time comparison and PPP precise single point positioning. The clock deviation prediction based on this method can improve the clock error filtering and self-maintaining performance of the timekeeping system under external interference or even time deception, providing a new application method for improving the anti-interference and anti-deception performance of the timekeeping system. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, a brief introduction is given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0035] Figure 1 A schematic flow chart of a clock error prediction method based on variational Bayesian Kalman filtering provided in an embodiment of the present invention;

[0036] Figure 2 A schematic diagram of the structure of a clock error prediction device based on variational Bayesian Kalman filtering provided in an embodiment of the present invention;

[0037] Figure 3 A schematic diagram of the physical structure of an electronic device provided by an embodiment of the present invention;

[0038] Figure 4 A schematic diagram showing the comparison of the root mean square error of the filtering results of the GPS satellite PRN02 using the KF algorithm and the VB-SHKF algorithm provided in an embodiment of the present invention;

[0039] Figure 5This is a schematic diagram showing the comparison of the prediction errors of GPS satellite PRN02 using the KF algorithm and the VB-SHKF algorithm provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical scheme and advantages of the embodiment of the present invention clearer, the technical scheme in the embodiment of the present invention will be clearly and completely described in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present invention. In addition, the technical features in the various embodiments or single embodiments provided by the present invention can be combined with each other arbitrarily to form a feasible technical solution. This combination is not subject to the constraints of the sequence of steps and / or the structural composition mode, but must be based on the ability of ordinary technicians in the field to achieve. When the combination of technical solutions is contradictory or cannot be achieved, it should be considered that the combination of such technical solutions does not exist and is not within the scope of protection required by the present invention. If there are step numbers in the following embodiments, they are only set for the convenience of explanation, and the order between the steps is not limited in any way. The execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0041] In order to enhance the robustness of Kalman filtering, a Gaussian mixture model is used to model non-Gaussian states or noise, replacing the traditional Gaussian distribution. A combination of a variational Bayesian Kalman algorithm and a Sage-Husa adaptive Kalman filter algorithm is proposed and applied in satellite clock error prediction, and simulation experiments are carried out to verify its performance.

[0042] The embodiment of the present invention provides a clock error prediction method based on variational Bayesian Kalman filtering, see Figure 1 The method includes: predicting the state vector and covariance matrix of the clock error model, and predicting the observation noise matrix parameters; updating the predicted value of the covariance matrix, and updating the predicted value of the state vector, calculating the predicted value of the measurement vector at the previous moment according to the predicted value of the state vector of the clock error model, and obtaining the predicted value of the cross-covariance matrix at the previous moment according to the predicted value of the cross-covariance matrix; initializing the relevant parameters of the observation noise, using the predicted value of the measurement vector at the previous moment and the predicted value of the cross-covariance matrix at the previous moment, and iterating the initialized observation noise for a predetermined number of times; estimating the observation noise and the system noise, obtaining the estimated value of the state vector according to the estimated value of the observation noise and the estimated value of the system noise, and iteratively predicting the measurement vector using the estimated value of the state vector.

[0043] Based on the content of the above method embodiment, as an optional embodiment, the clock error prediction method based on variational Bayes Kalman filtering provided in the embodiment of the present invention, wherein the state vector of the clock error model is predicted, comprises:

[0044] x k|k-1 =Fx k-1|k-1 (1)

[0045] Among them, x k|k-1 is the predicted value of the state vector at time k-1; F is the n-order state transfer matrix from time k-1 to time k; x k-1|k-1 is the estimated value of the state vector at time k-1.

[0046] Specifically, the clock error model is shown in formula (2):

[0047]

[0048] Among them, x k is the n-order state vector at time k, q k-1 is the k-1 time process Gaussian white noise, H is the m-order observation matrix, r k To measure Gaussian white noise, L k-1 is the system noise driving matrix.

[0049] Based on the content of the above method embodiment, as an optional embodiment, the clock error prediction method based on variational Bayes Kalman filtering provided in the embodiment of the present invention, wherein the prediction of the covariance matrix includes:

[0050]

[0051] Among them, P k|k-1 is the prediction error covariance at time k-1; P k-1 is the error covariance at time k-1; T is the matrix transpose symbol; L k-1 is the system noise driving matrix at time k-1; Q k is the k-time process noise covariance matrix; Q k-1 is the k-1 moment process noise covariance matrix; q k is the Gaussian white noise of the process at time k; E is the expectation of the noise covariance of the calculation process.

[0052] Based on the content of the above method embodiment, as an optional embodiment, the clock error prediction method based on variational Bayes Kalman filtering provided in the embodiment of the present invention, and predicting the observation noise matrix parameters, includes:

[0053] v k|k-1 =ρ(v k-1 -n-1)+n+1 (5)

[0054] V k|k-1 =GV k-1 G T (6)

[0055]

[0056] Among them, v k|k-1 is the predicted value of the second observation noise matrix parameter v at time k-1; ρ is the coefficient of variation and is greater than 0 and less than 1; v k-1 is the estimated value of the second observation noise matrix parameter v at time k-1; V k|k-1 is the predicted value of the first observation noise matrix parameter V at time k-1; G is the conversion matrix; I is the unit matrix; V k-1 is the estimated value of the first observation noise matrix parameter V at time k-1.

[0057] Based on the content of the above method embodiment, as an optional embodiment, the clock error prediction method based on variational Bayes Kalman filtering provided in the embodiment of the present invention, the predicted value of the covariance matrix is ​​updated, and the predicted value of the state vector is updated, and the predicted value of the measurement vector at the previous moment is calculated according to the predicted value of the state vector of the clock error model, and the predicted value of the cross-covariance matrix is ​​obtained. The predicted value of the cross-covariance matrix at the previous moment includes:

[0058] y k|k-1 =Hx k|k-1 (8)

[0059] P xy,k|k-1 =P k|k-1 H T (9)

[0060] Among them, y k|k-1 is the predicted value of the m-order measurement vector at time k-1; H is the m-order observation matrix; P xy,k|k-1 is the predicted value of the cross-covariance matrix at time k-1; P k|k-1 is the predicted value of the error covariance at time k-1.

[0061] Based on the content of the above method embodiment, as an optional embodiment, the clock error prediction method based on variational Bayes Kalman filtering provided in the embodiment of the present invention, the initialization of the relevant parameters of the observation noise includes:

[0062] v k|k =v k|k-1 +1 (10)

[0063] V k|k =V k|k-1 (11)

[0064] Among them, vk|k V is the predicted value of the second observation noise matrix parameter v at time k; k|k is the predicted value of the first observation noise matrix parameter v at time k.

[0065] Based on the content of the above method embodiment, as an optional embodiment, the clock error prediction method based on variational Bayes Kalman filtering provided in the embodiment of the present invention, wherein the predicted value of the measurement vector at the previous moment and the predicted value of the cross-covariance matrix at the previous moment are used to iterate the initialized observation noise for a predetermined number of times, includes:

[0066]

[0067] Where i is the i-th cycle; ε k is the observation error, is the observation noise, is the observation error covariance matrix, is the Kalman filter gain, is the estimated value of the state vector, is the estimated value of the covariance matrix, is the estimated value of the relevant parameters of the observation noise R, M k-1 and A are the first and second related variables for calculating the system noise Q based on the Sage-Husa algorithm; the related parameter d for the system noise Q updated at time k-1 k-1 =(1-b) / (1-b k ), and 0.95≤b≤0.99, b is the relevant parameter variable; y k is the actual observation value at time k; K is the predicted value of the first observed noise matrix parameter V at time k-1 in the i-th cycle; k is the Kalman filter gain; P k is the error covariance at time k.

[0068] Specifically, the observation noise in equation (12) is After continuous updating and convergence under the iteration of the variational Bayesian Kalman filter algorithm, the system noise Q k Under the iteration of the Sage-Husa filtering method, the convergence is continuously updated, and finally x is achieved. k|k and P k|k Effective estimation. After effective estimation of the state vector, the observation value y can be obtained. k Iterative prediction.

[0069] The clock error prediction method based on variational Bayesian Kalman filtering provided in an embodiment of the present invention improves the adaptability of the Kalman filter clock deviation prediction by iteratively estimating and correcting the observation noise R and the system noise Q using the inverse Wishart distribution, estimating the covariance of the system state and the observation noise, and applying it to the Kalman filter. The method is applied to the satellite clock error prediction of satellite common view time comparison and PPP precise single point positioning. The clock deviation prediction based on this method can improve the clock error filtering and self-maintaining performance of the timekeeping system under external interference or even time deception, providing a new application method for improving the anti-interference and anti-deception performance of the timekeeping system.

[0070] In another embodiment, a combination of a variational Bayes Kalman algorithm and a Sage Husa adaptive Kalman filter algorithm is used to improve the precision of precise ephemeris clock error data filtering and clock error prediction in satellite common view time comparison and PPP precise point positioning clock error prediction. Method First, the satellite clock bias model can be expressed as:

[0071] x(t)=a0+a1t+0.5a2t 2 +ξ(t) (16)

[0072] In formula (16), a0 is the difference between the initial onboard atomic clock and the reference clock; a1 is the frequency difference between the initial onboard atomic clock and the reference clock; a2 is the aging rate of the onboard atomic clock itself, ξ(t) is the noise, and t is the sampling time.

[0073] From equations (2) and (16), we can see that when predicting the clock bias of the onboard atomic clock, the kth sampling state vector x k The superposition is:

[0074] x k =Fx k-1 +L k-1 q k-1 (17)

[0075]

[0076] Among them, x k-1 =[a 0,k-1 ,a 1,k-1 ,a 2,k-1 ] T ,q k-1 is a three-dimensional noise with zero mean and a normal distribution that is uncorrelated.

[0077] The clock error measurement value y of the kth sampling k as follows:

[0078] y k =Hx+r k (19)

[0079] Where H = [1, 0, 0], r k is a one-dimensional white noise with the initial value set to a constant, 0.95≤b≤0.99. The experimental results can be found in Figure 4 and Figure 5 The results show that the satellite clock error filtering performance and prediction performance of the combination of variational Bayesian Kalman filtering and Sage-Husa filtering with VB-SHKF algorithm are improved compared with the traditional Kalman filtering KF algorithm. Figure 4 The root mean square error of the filtering result of GPS satellite PRN02 in is smaller (using this method), Figure 5 The prediction error of GPS satellite PRN02 is closer to zero, which provides a new application method for improving the anti-interference and anti-deception performance of the timekeeping system.

[0080] The implementation basis of each embodiment of the present invention is to implement programmed processing through a device with a processor function. Therefore, in engineering practice, the technical solutions and functions of each embodiment of the present invention can be encapsulated into various modules. Based on this reality, on the basis of the above embodiments, an embodiment of the present invention provides a clock error prediction device based on variational Bayes Kalman filtering, which is used to execute the clock error prediction method based on variational Bayes Kalman filtering in the above method embodiment. Figure 2 The device includes: a first main module, which is used to predict the state vector and covariance matrix of the clock error model, and predict the observation noise matrix parameters; a second main module, which is used to update the predicted value of the covariance matrix, and update the predicted value of the state vector, and calculate the predicted value of the measurement vector at the previous moment according to the predicted value of the state vector of the clock error model, and obtain the predicted value of the cross-covariance matrix at the previous moment according to the predicted value of the cross-covariance matrix; a third main module, which is used to initialize the relevant parameters of the observation noise, and use the predicted value of the measurement vector at the previous moment and the predicted value of the cross-covariance matrix at the previous moment to iterate the initialized observation noise for a predetermined number of times; a fourth main module, which is used to estimate the observation noise and the system noise, and obtain the estimated value of the state vector according to the estimated value of the observation noise and the estimated value of the system noise, and use the estimated value of the state vector to iteratively predict the measurement vector.

[0081] The clock error prediction device based on variational Bayesian Kalman filtering provided by the embodiment of the present invention adopts Figure 2Several modules in the proposed method use the inverse Wishart distribution to iteratively estimate and correct the observation noise R and system noise Q, estimate the covariance of the system state and the observation noise, and apply it to the Kalman filter, thereby improving the adaptive ability of the Kalman filter clock bias prediction. This method is applied to the satellite common view time comparison and PPP precise point positioning satellite clock error prediction. The clock bias prediction based on this method can improve the clock error filtering and self-maintaining performance of the timekeeping system under external interference or even time deception, providing a new application method for improving the anti-interference and anti-deception performance of the timekeeping system.

[0082] It should be noted that the device in the device embodiment provided by the present invention can be used to implement the method in the above method embodiment as well as the method in other method embodiments provided by the present invention. The only difference is that the corresponding functional modules are set, and the principle is basically the same as the principle of the above device embodiment provided by the present invention. As long as the technical personnel in the field refer to the specific technical solutions in other method embodiments on the basis of the above device embodiment, obtain the corresponding technical means and the technical solutions composed of these technical means by combining technical features, the device in the above device embodiment can be improved on the premise of ensuring the practicality of the technical solution, thereby obtaining the corresponding device class embodiment, which is used to implement the methods in other method class embodiments. For example:

[0083] Based on the content of the above device embodiment, as an optional embodiment, the clock error prediction device based on variational Bayes Kalman filtering provided in the embodiment of the present invention further includes: a first submodule, which is used to realize the prediction of the state vector of the clock error model, including:

[0084] x k|k-1 =Fx k-1|k-1

[0085] Among them, x k|k-1 is the predicted value of the state vector at time k-1; F is the n-order state transfer matrix from time k-1 to time k; x k-1|k-1 is the estimated value of the state vector at time k-1.

[0086] Based on the content of the above device embodiment, as an optional embodiment, the clock error prediction device based on variational Bayes Kalman filtering provided in the embodiment of the present invention further includes: a second submodule, which is used to realize the prediction of the covariance matrix, including:

[0087]

[0088]

[0089] Among them, P k|k-1is the prediction error covariance at time k-1; P k-1 is the error covariance at time k-1; T is the matrix transpose symbol; L k-1 is the system noise driving matrix at time k-1; Q k is the k-time process noise covariance matrix; Q k-1 is the k-1 moment process noise covariance matrix; q k is the Gaussian white noise of the process at time k; E is the expectation of the noise covariance of the calculation process.

[0090] Based on the content of the above device embodiment, as an optional embodiment, the clock error prediction device based on variational Bayes Kalman filtering provided in the embodiment of the present invention further includes: a third submodule, which is used to implement and predict the observation noise matrix parameters, including:

[0091] v k|k-1 =ρ(v k-1 -n-1)+n+1

[0092] V k|k-1 =GV k-1 G T

[0093]

[0094] Among them, v k|k-1 is the predicted value of the second observation noise matrix parameter v at time k-1; ρ is the coefficient of variation and is greater than 0 and less than 1; v k-1 is the estimated value of the second observation noise matrix parameter v at time k-1; V k|k-1 is the predicted value of the first observation noise matrix parameter V at time k-1; G is the conversion matrix; I is the unit matrix; V k-1 is the estimated value of the first observation noise matrix parameter V at time k-1.

[0095] Based on the content of the above device embodiment, as an optional embodiment, the clock error prediction device based on variational Bayes Kalman filtering provided in the embodiment of the present invention further includes: a fourth submodule, which is used to implement the updating of the predicted value of the covariance matrix and the predicted value of the state vector, and calculate the predicted value of the measurement vector at the previous moment according to the predicted value of the state vector of the clock error model, and obtain the predicted value of the cross-covariance matrix at the previous moment, including:

[0096] y k|k-1 =Hx k|k-1

[0097] P xy,k|k-1 =P k|k-1 H T

[0098] Among them, y k|k-1 is the predicted value of the m-order measurement vector at time k-1; H is the m-order observation matrix; P xy,k|k-1 is the predicted value of the cross-covariance matrix at time k-1; P k|k-1 is the predicted value of the error covariance at time k-1.

[0099] Based on the content of the above device embodiment, as an optional embodiment, the clock error prediction device based on variational Bayes Kalman filtering provided in the embodiment of the present invention further includes: a fifth submodule, which is used to implement the initialization of the relevant parameters of the observation noise, including:

[0100] v k|k =v k|k-1 +1

[0101] V k|k =V k|k-1

[0102] Among them, v k|k V is the predicted value of the second observation noise matrix parameter v at time k; k|k is the predicted value of the first observation noise matrix parameter v at time k.

[0103] Based on the content of the above device embodiment, as an optional embodiment, the clock error prediction device based on variational Bayes Kalman filtering provided in the embodiment of the present invention further includes: a sixth submodule, which is used to implement the predicted value of the measurement vector at the previous moment and the predicted value of the cross-covariance matrix at the previous moment, and iterate the initialized observation noise for a predetermined number of times, including:

[0104]

[0105]

[0106] Where i is the i-th cycle; ε k is the observation error, is the observation noise, is the observation error covariance matrix, is the Kalman filter gain, is the estimated value of the state vector, is the estimated value of the covariance matrix, is the estimated value of the relevant parameters of the observation noise R, M k-1 and A are the first and second related variables for calculating the system noise Q based on the Sage-Husa algorithm; the related parameter d for the system noise Q updated at time k-1 k-1 =(1-b) / (1-b k ), and 0.95≤b≤0.99, b is the relevant parameter variable; yk is the actual observation value at time k; K is the predicted value of the first observed noise matrix parameter V at time k-1 in the i-th cycle; k is the Kalman filter gain; P k is the error covariance at time k.

[0107] The method of the embodiment of the present invention is implemented by relying on electronic devices, so it is necessary to introduce the relevant electronic devices. Based on this purpose, the embodiment of the present invention provides an electronic device, such as Figure 3 As shown, the electronic device includes: at least one processor, a communication interface, at least one memory, and a communication bus, wherein at least one processor, the communication interface, and at least one memory communicate with each other through the communication bus. At least one processor can call the logic instructions in at least one memory to execute all or part of the steps of the method provided by the aforementioned various method embodiments.

[0108] In addition, the logic instructions in the at least one memory mentioned above can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on this understanding, the technical solution of the present invention can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each method embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0109] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0110] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiment.

[0111] The flowcharts and block diagrams in the accompanying drawings show the possible architecture, functions and operations of the systems, methods and computer program products according to multiple embodiments of the present invention. Based on this understanding, each box in the flowchart or block diagram can represent a module, a program segment or a part of a code, and the module, a program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order from the order marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and sometimes in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or the flowchart, and the combination of the boxes in the block diagram and / or the flowchart can be implemented with a dedicated hardware-based system that performs a specified function or action, or can be implemented with a combination of dedicated hardware and computer instructions.

[0112] It should be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "includes..." do not exclude the existence of other identical elements in the process, method, article or device including the elements. Any "predetermined threshold", "preset threshold" and other similar expressions that do not indicate specific values ​​can be determined by a person of ordinary skill in the art through simple experiments or corresponding debugging.

[0113] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A clock error prediction method based on variational Bayesian Kalman filtering, characterized in that: include: Predict the state vector and covariance matrix of the clock error model, and predict the observation noise matrix parameters; update the predicted value of the covariance matrix, and update the predicted value of the state vector, and calculate the predicted value of the measurement vector at the previous moment based on the predicted value of the state vector of the clock error model, and the predicted value of the cross-covariance matrix at the previous moment; Initialize the relevant parameters of the observation noise, use the predicted value of the measurement vector at the previous moment and the predicted value of the cross-covariance matrix at the previous moment, and iterate the initialized observation noise for a predetermined number of times; The observation noise and the system noise are estimated, and the estimated value of the state vector is obtained according to the estimated value of the observation noise and the estimated value of the system noise. The estimated value of the state vector is used to iteratively predict the measurement vector.

2. The clock error prediction method based on variational Bayesian Kalman filtering according to claim 1, characterized in that: The predicting of the state vector of the clock error model includes: xk|k-1=Fxk-1|k-1 Among them, xk|k-1 is the predicted value of the state vector at time k-1; F is the n-order state transfer matrix from time k-1 to time k; xk-1|k-1 is the estimated value of the state vector at time k-1.

3. The clock error prediction method based on variational Bayesian Kalman filtering according to claim 2 is characterized in that: The predicting of the covariance matrix includes: Where Pk|k-1 is the prediction error covariance at time k-1; Pk-1 is the error covariance at time k-1; T is the matrix transpose symbol; L k-1 is the system noise driving matrix at time k-1; Qk is the process noise covariance matrix at time k; Qk-1 is the process noise covariance matrix at time k-1; qk is the process Gaussian white noise at time k; E is the expectation of the calculated process noise covariance.

4. The clock error prediction method based on variational Bayesian Kalman filtering according to claim 3 is characterized in that: The observation noise matrix parameters are described and predicted, including: vk|k-1= ρ (vk-1-n-1)+n+1 Vk|k-1=GVk-1GT Among them, vk|k-1 is the predicted value of the second observation noise matrix parameter v at time k-1; ρ is the coefficient of variation and is greater than 0 and less than 1; vk-1 is the estimated value of the second observation noise matrix parameter v at time k-1; Vk|k-1 is the predicted value of the first observation noise matrix parameter V at time k-1; G is the transformation matrix; I is the unit matrix; Vk-1 is the estimated value of the first observation noise matrix parameter V at time k-1.

5. The clock error prediction method based on variational Bayesian Kalman filtering according to claim 4 is characterized in that: The predicted value of the covariance matrix is ​​updated, and the predicted value of the state vector is updated. The predicted value of the measurement vector at the previous moment is calculated according to the predicted value of the state vector of the clock error model, and the predicted value of the cross-covariance matrix is ​​obtained. The predicted value of the cross-covariance matrix at the previous moment includes: yk|k-1=Hxk|k-1 Pxy,k|k-1=Pk|k-1HT Among them, yk|k-1 is the predicted value of the m-order measurement vector at time k-1; H is the m-order observation matrix; Pxy,k|k-1 is the predicted value of the cross covariance matrix at time k-1; Pk|k-1 is the predicted value of the error covariance at time k-1.

6. The clock error prediction method based on variational Bayesian Kalman filtering according to claim 5 is characterized in that: The initializing of the relevant parameters of the observation noise includes: vk|k=vk|k-1+1 Vk|k=Vk|k-1 Among them, vk|k is the predicted value of the second observation noise matrix parameter v at time k; Vk|k is the predicted value of the first observation noise matrix parameter v at time k.

7. The clock error prediction method based on variational Bayesian Kalman filtering according to claim 6, characterized in that: The method of using the predicted value of the measurement vector at the previous moment and the predicted value of the cross-covariance matrix at the previous moment to iterate the initialized observation noise for a predetermined number of times includes: Among them, i is the i-th cycle; ε k is the observation error, is the observation noise, Py(yi,+k1|)k-1 is the observation error covariance matrix, is the Kalman filter gain, is the estimated value of the state vector, is the estimated value of the covariance matrix, is the estimated value of the relevant parameter of the observed noise R, Mk-1 and A are the first relevant variable and the second relevant variable for calculating the system noise Q based on the Sage-Husa algorithm; the relevant parameter dk-1=(1-b) / (1-bk) updated by the system noise Q at time k-1, and 0.95≤b≤0.99, b is the relevant parameter variable; yk is the actual observed value at time k; is the predicted value of the first observation noise matrix parameter V at time k-1 in the i-th cycle; Kk is the Kalman filter gain; Pk is the error covariance at time k.

8. A clock error prediction device based on variational Bayesian Kalman filtering, characterized in that: include: The first main module is used to predict the state vector and covariance matrix of the clock error model and predict the observation noise matrix parameters; The second main module is used to update the predicted value of the covariance matrix and the predicted value of the state vector. The predicted value of the measurement vector at the previous moment is calculated based on the predicted value of the state vector of the clock error model, and the predicted value of the cross-covariance matrix is ​​used to obtain the predicted value of the cross-covariance matrix at the previous moment. The third main module is used to initialize the relevant parameters of the observation noise, and the predicted value of the measurement vector at the previous moment and the predicted value of the cross-covariance matrix at the previous moment are used to iterate the initialized observation noise for a predetermined number of times; the fourth main module is used to estimate the observation noise and the system noise, and obtain the estimated value of the state vector according to the estimated value of the observation noise and the estimated value of the system noise, and use the estimated value of the state vector to iteratively predict the measurement vector.

9. An electronic device, characterized in that: include: At least one processor, at least one memory and a communication interface; wherein, The processor, memory and communication interface communicate with each other; The memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the method according to any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium, characterized in that: The non-transitory computer-readable storage medium stores computer instructions, which cause a computer to execute the method of any one of claims 1 to 7.

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