Clock error prediction method and device based on variational bayes kalman filter

Abstract

The application 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 an observation noise matrix parameter; updating the predicted value of the covariance matrix, and updating the predicted value of the state vector, calculating the predicted value of a measurement vector at a previous moment according to the predicted value of the state vector of the clock error model, and obtaining the predicted value of a cross-covariance matrix at the previous moment by crossing the predicted value of the cross-covariance matrix; initializing the related 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 iteratively predicting the initialized observation noise for a predetermined number of times; estimating the observation noise and the system noise, and iteratively predicting the measurement vector using the estimated value. The application improves the clock error filtering and self-maintaining performance of a time-keeping system when the system is disturbed by external interference or even time deception.

Description

TECHNICAL FIELD

[0001] The embodiment of the present application relates to the technical field of clock error prediction optimization, in particular to a clock error prediction method and device based on variational Bayesian Kalman filtering. BACKGROUND

[0002] Clock error prediction refers to predicting the clock error of an atomic clock in a future period according to historical clock error data. Accurate clock error prediction is the key to realizing real-time and reliable dynamic precise point positioning, precise satellite autonomous navigation and high-precision and effective control of an atomic clock system. Satellite clocks are an important part of a navigation system, and their performance and accurate prediction are crucial to ensuring the accuracy of navigation and positioning and realizing autonomous navigation and precise positioning, so it is necessary to ensure their accuracy, real-time performance and continuity. Satellite-borne atomic clocks have complex physical characteristics and are easily disturbed by external factors, so it is difficult to capture complex and subtle change patterns. In related competitive fields, a method of cheating and interfering with navigation satellite signals leads to time superposition noise, clock error deviation and even time stamp jumps in a time keeping system, so it has become a challenging task to establish a high-precision satellite clock error prediction model with anti-cheating interference, and related technical means have limited scope of application of different single models for various precision satellite-borne atomic clocks, and there is certain limitation in actual satellite clock error prediction. Therefore, developing a clock error prediction method and device based on variational Bayesian Kalman filtering can effectively overcome the defects in the related art, and has become a technical problem to be solved in the industry. SUMMARY

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

[0004] In a first aspect, the embodiment of the present application provides a clock error prediction method based on variational Bayesian Kalman filtering, which comprises: predicting a state vector and a covariance matrix of a clock error model, and predicting an observation noise matrix parameter; updating the predicted value of the covariance matrix, and updating the predicted value of the state vector, calculating the predicted value of a measurement vector at a previous time according to the predicted value of the state vector of the clock error model, and obtaining the predicted value of a cross-covariance matrix at the previous time by crossing the predicted value of the cross-covariance matrix; initializing the related parameters of the observation noise, using the predicted value of the measurement vector at the previous time and the predicted value of the cross-covariance matrix at the previous time, and iteratively predicting 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.

[0005] Based on the above method embodiments, the clock error prediction method based on variational Bayesian Kalman filtering provided in this embodiment of the invention includes the following steps for predicting the state vector of the clock error model:

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

[0007] Where, x k|k-1 Let x be the predicted state vector value at time k-1; F is the n-order state transition matrix from time k-1 to time k; k-1|k-1 This is the estimated state vector value at time k-1.

[0008] Based on the above method embodiments, the clock error prediction method based on variational Bayesian Kalman filtering provided in this embodiment of the invention includes the following steps for predicting the covariance matrix:

[0009]

[0010] Among them, P k|k-1 P represents the prediction error covariance at time k-1; k-1 L is the error covariance at time k-1; T is the sign of the matrix transpose; L k-1 Q is the system noise driving matrix at time k-1; k Let Q be the process noise covariance matrix at time k; k-1 Let q be the process noise covariance matrix at time k-1; k Let k be the Gaussian white noise at time k; E is the expected value of the process noise covariance.

[0011] Based on the above method embodiments, the clock error prediction method based on variational Bayesian Kalman filtering provided in this embodiment of the invention, wherein the prediction of 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 The second observation noise matrix parameter v is the predicted value at time k-1; ρ is the variation coefficient, which is greater than 0 and less than 1; v k-1 V represents the estimated value of the second observation noise matrix parameter v at time k-1; k|k-1is the prediction value of the first observation noise matrix parameter V at k-1 moment; G is a conversion matrix; I is a unit matrix; V k-1 is the estimation value of the first observation noise matrix parameter V at k-1 moment.

[0016] On the basis of the above method embodiment content, the clock difference prediction method based on the variational Bayesian Kalman filter provided in the embodiment of the application updates the prediction value of the covariance matrix and updates the prediction value of the state vector, calculates the prediction value of the measurement vector at the previous moment according to the state vector prediction value of the clock difference model, and obtains the prediction value of the cross-covariance matrix at the previous moment according to the prediction value of the cross-covariance matrix, and the method comprises the following steps:

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

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

[0019] wherein y k|k-1 is the prediction value of the m-order measurement vector at k-1 moment; H is an m-order observation matrix; P xy,k|k-1 is the prediction value of the cross-covariance matrix at k-1 moment; P k|k-1 is the prediction value of the error covariance at k-1 moment.

[0020] On the basis of the above method embodiment content, the clock difference prediction method based on the variational Bayesian Kalman filter provided in the embodiment of the application initializes the related parameters of the observation noise, and the method comprises the following steps:

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

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

[0023] wherein v k|k is the prediction value of the second observation noise matrix parameter v at k moment; V k|k is the prediction value of the first observation noise matrix parameter v at k moment.

[0024] On the basis of the above method embodiment content, the clock difference prediction method based on the variational Bayesian Kalman filter provided in the embodiment of the application iterates the initialized observation noise a predetermined number of times by using the prediction value of the measurement vector at the previous moment and the prediction value of the cross-covariance matrix at the previous moment, and the method comprises the following steps:

[0025]

[0026] wherein i is the i-th loop; ε k is an observation error, is an observation noise, is an observation error covariance matrix, is a Kalman filter gain, is a state vector estimate value, is a covariance matrix estimate value, is an estimate value of a correlation parameter of the observation noise R, M k-1 and A are first and second correlation variables for calculating the system noise Q based on the Sage-Husa algorithm; the correlation parameter d k-1 of the system noise Q is updated at the k-1 time k , and 0.95≤b≤0.99, b is a correlation parameter variable; y k is an actual observation value at the k time; is a prediction value of the first observation noise matrix parameter V at the k-1 time in the i-th loop; K k is a Kalman filter gain; P k is an error covariance at the k time.

[0027] In a second aspect, an embodiment of the present application provides a clock error prediction device based on variational Bayesian Kalman filtering, comprising: a first main module configured to predict a state vector and a covariance matrix of a clock error model, and predict an observation noise matrix parameter; a second main module configured to update a prediction value of the covariance matrix, and update a prediction value of the state vector, calculate a prediction value of a measurement vector at a previous time according to the prediction value of the state vector of the clock error model, and cross a prediction value of a covariance matrix to obtain a prediction value of the covariance matrix at the previous time; a third main module configured to initialize a correlation parameter of the observation noise, and iterate the initialized observation noise for a predetermined number of times by using the prediction value of the measurement vector at the previous time and the prediction value of the covariance matrix at the previous time; and a fourth main module configured to estimate the observation noise and a system noise, obtain an estimate value of the state vector according to an estimate value of the observation noise and an estimate value of the system noise, and iteratively predict the measurement vector by using the estimate value of the state vector.

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

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

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

[0031] The memory stores program instructions executable by the processor, and the processor invokes the program instructions to execute the clock difference prediction method based on variational Bayesian Kalman filtering provided in any of the various implementation manners of the first aspect.

[0032] In a fourth aspect, an embodiment of the present application provides a non-transitory computer-readable storage medium storing computer instructions, and the computer instructions cause a computer to execute the clock difference prediction method based on variational Bayesian Kalman filtering provided in any of the various implementation manners of the first aspect.

[0033] The clock difference prediction method and device based on variational Bayesian Kalman filtering provided by the embodiment of the present application estimate the covariance of the system state and the observation noise by using the inverse Wishart distribution iterative estimation and correction of the observation noise R and the system noise Q, and apply it to the Kalman filter, thereby improving the adaptive ability of the Kalman filter clock bias prediction. When the method is applied to satellite common view time comparison and satellite clock error prediction of ppp precise point positioning, the clock bias prediction based on the method can improve the clock system clock difference filtering and self-maintenance performance under external interference or even time fraud, and provides a new application method for improving the anti-interference and anti-fraud performance of the clock system. BRIEF DESCRIPTION OF DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiment or prior art description will be briefly introduced. Obviously, the drawings in the following description are some embodiments of the present application, and those skilled in the art can also obtain other drawings according to these drawings without creative labor.

[0035] Figure 1 The clock difference prediction method based on variational Bayesian Kalman filtering provided by the embodiment of the present application is shown in the flowchart.

[0036] Figure 2 The clock difference prediction device based on variational Bayesian Kalman filtering provided by the embodiment of the present application is shown in the structural diagram.

[0037] Figure 3 The physical structure of the electronic device provided by the embodiment of the present application is shown in the structural diagram.

[0038] Figure 4 The root mean square error comparison effect diagram of the filtering results of KF algorithm and VB-SHKF algorithm GPS satellite PRN02 provided by the embodiment of the present application is shown in the diagram.

[0039] Figure 5The schematic diagram of the comparison effect of the KF algorithm provided by the embodiment of the present application and the VB-SHKF algorithm on the prediction error of GPS satellite PRN02 is shown in the figure. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work belong to the protection scope of the present application. In addition, the technical features in each embodiment or in a single embodiment provided by the present application can be combined with each other at will to form a feasible technical scheme, and such combination is not restricted by the order of steps and / or structure composition mode, but must be based on the implementation by those skilled in the art, when the combination of technical schemes appears contradictory or unimplementable, it should be considered that such combination of technical schemes does not exist, and is not within the protection scope required by the present application. If there are step numbers in the following embodiments, they are set only for the convenience of description and explanation, and the order between the steps is not limited in any way, and the execution order of each step in the embodiments 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 the non-Gaussian state or noise, instead of the traditional Gaussian distribution. A combination algorithm of variational Bayesian Kalman filtering algorithm and Sage-Husa adaptive Kalman filtering algorithm is proposed for application in satellite clock error prediction, and simulation experiments are conducted to verify its performance.

[0042] The clock difference prediction method based on variational Bayesian Kalman filtering provided by the embodiments of the present application comprises the following steps of: Figure 1 predicting the state vector and the covariance matrix of the clock difference model, and predicting the observation noise matrix parameter; 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 difference model, and obtaining the predicted value of the cross-covariance matrix at the previous moment by crossing the predicted value of the cross-covariance matrix; initializing the related 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 iteratively predicting 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 Bayesian Kalman filtering provided in the embodiment of the application, the prediction of the state vector of the clock error model comprises:

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

[0045] wherein x k|k-1 is the state vector prediction value at k-1 moment; F is an n-order state transition matrix from k-1 to k moment; x k-1|k-1 is the state vector estimation value at k-1 moment.

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

[0047]

[0048] wherein x k is an n-order state vector at k moment, q k-1 is a process Gaussian white noise at k-1 moment, H is an m-order observation matrix, r k is a measurement Gaussian white noise, L k-1 is a 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 Bayesian Kalman filtering provided in the embodiment of the application, the prediction of the covariance matrix comprises:

[0050]

[0051] wherein P k|k-1 is a prediction error covariance at k-1 moment; P k-1 is an error covariance at k-1 moment; T is a matrix transpose symbol; L k-1 is a system noise driving matrix at k-1 moment; Q k is a process noise covariance matrix at k moment; Q k-1 is a process noise covariance matrix at k-1 moment; q k is a process Gaussian white noise at k moment; E is an expectation of calculating the process noise covariance.

[0052] Based on the content of the above method embodiment, as an optional embodiment, the clock error prediction method based on variational Bayesian Kalman filtering provided in the embodiment of the application, the prediction of the observation noise matrix parameter comprises:

[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] wherein, v k|k-1 is the predicted value of the second observation noise matrix parameter v at k-1 time; ρ is a change coefficient 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 k-1 time; V k|k-1 is the predicted value of the first observation noise matrix parameter V at k-1 time; G is a conversion matrix; I is a unit matrix; V k-1 is the estimated value of the first observation noise matrix parameter V at k-1 time.

[0057] Based on the content of the above method embodiment, as an optional embodiment, the clock difference prediction method based on variational Bayesian Kalman filtering provided in the embodiment of the application, 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 time is calculated according to the state vector predicted value of the clock difference model, the predicted value of the cross-covariance matrix at the previous time is obtained by crossing the predicted value of the cross-covariance matrix, and the method comprises the following steps.

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

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

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

[0061] Based on the content of the above method embodiment, as an optional embodiment, the clock difference prediction method based on variational Bayesian Kalman filtering provided in the embodiment of the application, the related parameters of the observation noise are initialized, and the method comprises the following steps.

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

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

[0064] wherein, vk|k is the prediction value of the second observation noise matrix parameter v at k moment; V k|k is the prediction value of the first observation noise matrix parameter v at k moment.

[0065] Based on the content of the above method embodiment, as an optional embodiment, the clock difference prediction method based on variational Bayesian Kalman filtering provided in the embodiment of the application adopts the prediction value of the measurement vector at the previous moment and the prediction value of the cross-covariance matrix at the previous moment, iterates the initialized observation noise for a predetermined number of times, and includes:

[0066]

[0067] wherein 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 state vector estimate value, is the covariance matrix estimate value, is the estimate value of the related parameter 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 parameters d k-1 of the system noise Q updated at k-1 moment, k 0.95≤b≤0.99, b is a related parameter variable; y k is the actual observation value at k moment; is the prediction value of the first observation noise matrix parameter V at k-1 moment in the i-th cycle; K k is the Kalman filter gain; P k is the error covariance at k moment.

[0068] Specifically, the observation noise in formula (12) is continuously updated and converges under the iteration of the variational Bayesian Kalman filter algorithm, the system noise Q k is continuously updated and converges under the iteration of the Sage-Husa filter method, and finally x k|k and P k|k are effectively estimated. Through the effective estimation of the state vector, the iteration prediction of the observation value y k can be performed.

[0069] The clock difference prediction method based on the variational Bayesian Kalman filtering provided by the embodiment of the application estimates and corrects the observation noise R and the system noise Q by using the inverse Wishart distribution iterative estimation, estimates the covariance of the system state and the observation noise, and applies the covariance to the Kalman filter, thereby improving the adaptive ability of the Kalman filter clock bias prediction. When the method is applied to satellite common view time comparison and satellite clock error prediction of ppp precise point positioning, the clock bias prediction based on the method can improve the time-keeping system clock difference filtering and self-maintaining performance under external interference or even time fraud, and provides a new application method for improving the anti-interference and anti-fraud performance of the time-keeping system.

[0070] In another embodiment, a combination algorithm of the variational Bayesian Kalman algorithm and the Sage Husa adaptive Kalman filtering algorithm is applied to improve the precise ephemeris clock difference data filtering and clock difference prediction accuracy in satellite common view time comparison and PPP precise point positioning. 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 value of the initial satellite-borne atomic clock and the reference clock, a1 is the frequency difference of the initial satellite-borne atomic clock and the reference clock, a2 is the aging rate of the satellite-borne atomic clock itself, ξ(t) is noise, and t is the sampling time.

[0073] As can be seen from formula (2) and formula (16), when the clock bias of the satellite-borne atomic clock is predicted, the superposition of the kth sampling state vector x k is as follows:

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

[0075]

[0076] Wherein, x k-1 =[a 0,k-1 ,a 1,k-1 ,a 2,k-1 ] T , q k-1 is a three-dimensional noise that conforms to a normal distribution with zero mean and is irrelevant.

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

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

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

[0080] The implementation of the various embodiments of this invention is based on programmed processing through a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of this invention can be encapsulated into various modules. Based on this reality, and building upon the above embodiments, this invention provides a clock bias prediction device based on variational Bayesian Kalman filtering, which is used to execute the clock bias prediction method based on variational Bayesian Kalman filtering in the above method embodiments. See also... Figure 2 The device includes: a first main module for predicting the state vector and covariance matrix of the clock error model, and predicting the parameters of the observation noise matrix; a second main module for updating the predicted values ​​of the covariance matrix and the state vector, calculating the predicted value of the measurement vector at the previous time step based on 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 time step based on the predicted value of the cross-covariance matrix; a third main module for initializing the relevant parameters of the observation noise, iterating the initialized observation noise a predetermined number of times using the predicted values ​​of the measurement vector and the cross-covariance matrix at the previous time step; and a fourth main module for estimating the observation noise and system noise, obtaining the estimated value of the state vector based on the estimated values ​​of the observation noise and system noise, and iteratively predicting the measurement vector using the estimated value of the state vector.

[0081] The clock error prediction device based on variational Bayesian Kalman filtering provided in this embodiment of the invention employs... Figure 2The method is applied to satellite common view time comparison and satellite clock error prediction of precise point positioning (PPP), and clock bias prediction based on the method can improve the filtering and self-maintaining performance of a time-keeping system clock under external interference or time fraud, and provides a new application method for improving the anti-interference and anti-fraud performance of the time-keeping system.

[0082] It should be noted that the device in the device embodiment provided by the application can be used to implement the method in the method embodiment, and can also be used to implement the method in other method embodiments provided by the application, the difference being only that corresponding functional modules are arranged, and the principle is basically the same as that of the above-mentioned device embodiment, as long as the person skilled in the art improves the device in the above-mentioned device embodiment on the basis of the above-mentioned device embodiment, refers to the specific technical solutions in other method embodiments, obtains corresponding technical means by combining technical features, and the technical solutions formed by the technical means, on the premise of ensuring the practicability of the technical solutions, the device in the above-mentioned device embodiment can be improved, so that the corresponding device embodiment is obtained, and the method in other method embodiments is implemented. For example:

[0083] Based on the content of the above device embodiment, as an optional embodiment, the clock difference prediction device based on variational Bayesian Kalman filtering provided in the embodiment of the application further includes: a first sub-module configured to predict a state vector of a clock difference model, including:

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

[0085] wherein x k|k-1 is a state vector prediction value at k-1 time; F is an n-order state transition matrix from k-1 to k time; and x k-1|k-1 is a state vector estimation value at k-1 time.

[0086] Based on the content of the above device embodiment, as an optional embodiment, the clock difference prediction device based on variational Bayesian Kalman filtering provided in the embodiment of the application further includes: a second sub-module configured to predict a covariance matrix, including:

[0087]

[0088]

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

[0090] Based on the content of the above device embodiment, as an optional embodiment, the clock difference prediction device based on variational Bayesian Kalman filtering provided in the embodiment of the application further comprises: a third sub-module configured to implement the prediction of the observation noise matrix parameter, 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] wherein v k|k-1 is the predicted value of the second observation noise matrix parameter v at k-1 time; ρ is a variation coefficient 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 k-1 time; V k|k-1 is the predicted value of the first observation noise matrix parameter V at k-1 time; G is a conversion matrix; I is a unit matrix; V k-1 is the estimated value of the first observation noise matrix parameter V at k-1 time.

[0095] Based on the content of the above device embodiment, as an optional embodiment, the clock difference prediction device based on variational Bayesian Kalman filtering provided in the embodiment of the application further comprises: a fourth sub-module configured to implement the updating of the predicted value of the covariance matrix and the updating of the predicted value of the state vector, and calculate the predicted value of the measurement vector at the previous time according to the state vector predicted value of the clock difference model, and cross the covariance matrix to obtain the predicted value of the cross covariance matrix at the previous time, including:

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

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

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

[0099] Based on the content of the above device embodiment, as an optional embodiment, the clock difference prediction device based on variational Bayesian Kalman filtering provided in the embodiment of the application further comprises a fifth sub-module configured to initialize the related parameters of the observation noise, including:

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

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

[0102] wherein v k|k is the prediction value of the second observation noise matrix parameter v at k time; V k|k is the prediction value of the first observation noise matrix parameter v at k time.

[0103] Based on the content of the above device embodiment, as an optional embodiment, the clock difference prediction device based on variational Bayesian Kalman filtering provided in the embodiment of the application further comprises a sixth sub-module configured to iteratively initialize the observation noise a predetermined number of times by using the prediction value of the measurement vector at the previous time and the prediction value of the cross-covariance matrix at the previous time, including:

[0104]

[0105]

[0106] wherein 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 state vector estimate value, is the covariance matrix estimate value, is the estimate value of the related 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 parameters d k-1 of the system noise Q updated at k-1 time are (1-b) / (1-b k ), and 0.95≤b≤0.99, b is a related parameter variable; yk The actual observed value at time k; K represents the predicted value of the first observation noise matrix parameter V at time k-1 in the i-th iteration; k P is the Kalman filter gain; k Let be the error covariance at time k.

[0107] The method in this embodiment of the invention is implemented using an electronic device; therefore, it is necessary to introduce the relevant electronic device. For this purpose, this embodiment of the invention provides an electronic device, such as... Figure 3 As shown, the electronic device includes at least one processor, a communications interface, at least one memory, and a communications bus, wherein the at least one processor, the communications interface, and the at least one memory communicate with each other via the communications bus. The at least one processor can invoke logical instructions stored in the at least one memory to execute all or part of the steps of the methods provided in the foregoing method embodiments.

[0108] Furthermore, when the logical instructions in at least one of the aforementioned memories can be implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various method embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0109] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0110] Those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary universal hardware platform, and of course can also be implemented by hardware. Based on such an understanding, the above technical solutions essentially or in other words the part of the prior art that makes a contribution can be embodied in the form of a software product, which can be stored in a computer readable storage medium, such as a ROM / RAM, a magnetic disk, an optical disk, and the like, and includes a number of instructions for causing 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 embodiments.

[0111] The flowcharts and block diagrams in the drawings show the possible implementation architectures, functions and operations of the systems, methods and computer program products according to the embodiments of the present application. Based on this understanding, each block in the flowchart or block diagram can represent a module, a program segment or a part of code, which includes one or more executable instructions for implementing the specified logical functions. It should also be noted that in some alternative implementations, the functions noted in the blocks can occur in different orders from that shown in the drawings. For example, two consecutive blocks can actually be executed substantially in parallel, and sometimes in reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, and the combination of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system that performs the specified functions or actions, or can be implemented by a combination of dedicated hardware and computer instructions.

[0112] It should be noted that the terms "comprising", "including", or any other variant thereof are intended to cover non-exclusive inclusions, so that a process, method, article or device that includes a list of elements does not only include those elements, but also includes other elements not explicitly listed, or further includes elements inherent in such a process, method, article or device. Without more limitations, the elements defined by the statement "comprising" do not exclude the presence of other identical elements in the process, method, article or device that includes the elements. Any "predetermined threshold", "preset threshold" or similar expression, if not marked with a specific numerical value, can be determined by a person skilled in the art through simple experiments or corresponding debugging.

[0113] It should be pointed out finally that the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit the same; and although the present application has been described in detail with reference to the foregoing embodiments, it should be appreciated by those skilled in the art that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features thereof can be replaced equivalently; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A clock error prediction method based on variational Bayesian Kalman filtering, characterized in that, include: The state vector and covariance matrix of the clock error model are predicted, and the parameters of the observation noise matrix are also predicted. The predicted values ​​of the covariance matrix and the state vector are updated. The predicted value of the measurement vector at the previous time step is calculated based on the predicted value of the state vector of the clock error model. The predicted value of the cross covariance matrix at the previous time step is obtained based on the predicted value of the cross covariance matrix. The relevant parameters of the observation noise are initialized by using the predicted values ​​of the measurement vector and the cross-covariance matrix at the previous time step, and the initialized observation noise is iterated a predetermined number of times. The observation noise and system noise are estimated, and the estimated value of the state vector is obtained based on the estimated values ​​of the observation noise and system noise. The estimated value of the state vector is then used to iteratively predict the measurement vector. The method involves using the predicted values ​​of the measurement vector and the cross-covariance matrix from the previous time step, and iterating the initialized observation noise a predetermined number of times, including: Where i represents the i-th iteration; ε k For observation error, To observe the noise, The observation error covariance matrix, For Kalman filter gain, This is the estimated value of the state vector. This is the estimated value of the covariance matrix. M is the estimated value of the correlation parameters of the observed noise R. k-1 Let A be the first and second correlation variables for calculating the system noise Q based on the Sage-Husa algorithm; and let d be the correlation parameter d updated by the system noise Q at time k-1. k-1 = (1-b) / (1-b) k ), and 0.95≤b≤0.99, where b is the relevant parameter variable; y k The actual observed value at time k; K represents the predicted value of the first observation noise matrix parameter V at time k-1 in the i-th iteration; k P is the Kalman filter gain; k Let be the error covariance at time k.

2. The clock error prediction method based on variational Bayesian Kalman filtering according to claim 1, characterized in that, The prediction of the state vector of the clock error model includes: x k|k-1 =Fx k-1|k-1 Where, x k|k-1 Let x be the predicted state vector value at time k-1; F is the n-order state transition matrix from time k-1 to time k; k-1|k-1 This is the estimated state vector value at time k-1.

3. The clock error prediction method based on variational Bayesian Kalman filtering according to claim 2, characterized in that, The prediction of the covariance matrix includes: Among them, P k|k-1 P represents the prediction error covariance at time k-1; k-1 L is the error covariance at time k-1; T is the sign of the matrix transpose; L k-1 Q is the system noise driving matrix at time k-1; k Let Q be the process noise covariance matrix at time k; k-1 Let q be the process noise covariance matrix at time k-1; k Let k be the Gaussian white noise at time k; E is the expected value of the process noise covariance.

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

5. The clock error prediction method based on variational Bayesian Kalman filtering according to claim 4, characterized in that, The process of updating the predicted values ​​of the covariance matrix and the state vector, calculating the predicted value of the measurement vector at the previous time step based on the predicted value of the state vector from the clock error model, and obtaining the predicted value of the cross-covariance matrix at the previous time step based on the predicted value of the cross-covariance matrix, includes: and k|k-1 =Hx k|k-1 P xy,k|k-1 =P k|k-1 H T Among them, y k|k-1 P is the predicted value of the m-th order measurement vector at time k-1; H is the m-th order observation matrix; xy,k|k-1 P is the predicted value of the cross covariance matrix at time k-1; k|k-1 This 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, characterized in that, The initialization of the relevant parameters of the observation noise includes: v k|k =v k|k-1 +1 V k|k =V k|k-1 Among them, v k|k V is the predicted value of the second observation noise matrix parameter v at time k; k|k Let v be the predicted value of the first observation noise matrix parameter v at time k.

7. 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 to predict the parameters of the observation noise matrix. The second main module is used to update the predicted values ​​of the covariance matrix and the state vector. It calculates the predicted value of the measurement vector at the previous time step based on the predicted value of the state vector from the clock error model, and obtains the predicted value of the cross-covariance matrix at the previous time step from the predicted value of the cross-covariance matrix. The third main module is used to initialize the relevant parameters of the observation noise. It iterates the initialized observation noise a predetermined number of times using the predicted values ​​of the measurement vector and the cross-covariance matrix at the previous time step. The fourth main module is used to estimate the observation noise and system noise. It obtains the estimated value of the state vector based on the estimated values ​​of the observation noise and system noise, and uses the estimated value of the state vector to iteratively predict the measurement vector. The method involves using the predicted values ​​of the measurement vector and the cross-covariance matrix from the previous time step, and iterating the initialized observation noise a predetermined number of times, including: Where i represents the i-th iteration; εk represents the observation error. To observe the noise, The observation error covariance matrix, For Kalman filter gain, This is the estimated value of the state vector. This is the estimated value of the covariance matrix. M is the estimated value of the correlation parameters of the observed noise R. k-1 Let A be the first and second correlation variables for calculating the system noise Q based on the Sage-Husa algorithm; and let d be the correlation parameter d updated by the system noise Q at time k-1. k-1 = (1-b) / (1-b) k ), and 0.95≤b≤0.99, where b is the relevant parameter variable; y k The actual observed value at time k; K represents the predicted value of the first observation noise matrix parameter V at time k-1 in the i-th iteration; k P is the Kalman filter gain; k Let be the error covariance at time k.

8. 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, which invokes the program instructions to perform the method described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions that cause the computer to perform the method described in any one of claims 1 to 6.

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