CN110850450A - Adaptive estimation method for satellite clock error parameters - Google Patents
Adaptive estimation method for satellite clock error parameters Download PDFInfo
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- CN110850450A CN110850450A CN201911223600.3A CN201911223600A CN110850450A CN 110850450 A CN110850450 A CN 110850450A CN 201911223600 A CN201911223600 A CN 201911223600A CN 110850450 A CN110850450 A CN 110850450A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/13—Receivers
- G01S19/24—Acquisition or tracking or demodulation of signals transmitted by the system
- G01S19/25—Acquisition or tracking or demodulation of signals transmitted by the system involving aiding data received from a cooperating element, e.g. assisted GPS
- G01S19/256—Acquisition or tracking or demodulation of signals transmitted by the system involving aiding data received from a cooperating element, e.g. assisted GPS relating to timing, e.g. time of week, code phase, timing offset
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/13—Receivers
- G01S19/35—Constructional details or hardware or software details of the signal processing chain
- G01S19/37—Hardware or software details of the signal processing chain
Abstract
A self-adaptive estimation method for satellite clock error parameters. According to the technical scheme of the embodiment of the application, whether the actual estimation error information of the clock difference parameter at the second moment and the theoretical estimation error of the clock difference parameter at the second moment meet a convergence criterion or not is judged, and if the actual estimation error information of the clock difference parameter at the second moment and the theoretical estimation error of the clock difference parameter at the second moment meet the convergence criterion, the error covariance matrix value of the clock difference parameter at the second moment is determined through a first mode; and if the actual estimation error information of the clock error parameter at the second moment and the theoretical estimation error of the clock error parameter at the second moment do not meet the convergence criterion, determining the estimation value of the error covariance matrix of the clock error parameter at the first moment through a second mode. The clock difference parameter estimation method and device can be applied to the condition that signals and prior information in a clock difference system are unknown, the defect that a model is sensitive to initial conditions is overcome, dynamic tracking performance of clock difference parameter estimation is improved, and the requirement of a high-precision time synchronization system is met.
Description
Technical Field
The embodiment of the application relates to the field of satellites, in particular to a satellite clock error parameter self-adaptive estimation method.
Background
Along with the increasing development of national defense modernization construction and the increasing progress of scientific technology in China, various industries have more and more requirements on precise time, and the time index reaches microsecond level, nanosecond level or even higher requirements. With the continuous development of satellite positioning systems, it is relatively economical and convenient to acquire high-precision time frequency by synchronizing a local crystal oscillator with a standard time signal, so that it is very important to perform accurate dynamic estimation on clock error data between the standard time signal and the local crystal oscillator. The traditional Kalman filtering needs to be established on the basis that a model is accurate and statistical characteristics of random interference signals are known, but for an actual application system, because of the influence of factors such as environmental change, device aging, system impact and the like, the system generally has the condition that the model is uncertain or the statistical characteristics of noise signals are not completely known, so that the filtering accuracy of clock error data is reduced or even diverged, and a high-precision time synchronization task is difficult to meet.
Disclosure of Invention
In order to solve the above technical problem, an embodiment of the present application provides a method for adaptively estimating a satellite clock error parameter, where the method includes:
establishing a model of clock error parameters, wherein the model of the clock error parameters comprises a state equation of the clock error parameters and a measurement equation of the clock error parameters, and the states of the clock error parameters comprise time difference, frequency difference and frequency drift; the state equation is an equation representing the relationship between the state of the clock difference parameter at the first moment and the state of the clock difference parameter at the second moment; the measurement equation is an equation representing the relationship between the state of the clock difference parameter at the first moment and the measurement value at the first moment; the second moment is a moment after the first moment;
determining a prior state variable estimated value of the clock error parameter at a first moment; the prior state variable estimation value of the first moment represents the state value of the first moment of the clock difference parameter estimated according to the state of the third moment of the clock difference parameter; the third moment is a moment before the first moment;
determining an estimated value of a state variable of the clock error parameter at a second moment according to a prior state variable estimated value of the clock error parameter at a first moment and an actual observed value of the clock error parameter at the first moment;
determining an estimated value of an error covariance matrix of a clock error parameter at a first moment; the estimation value of the error covariance matrix at the first moment represents that the error covariance matrix value at the first moment of the clock error parameter is estimated according to the error covariance matrix value at the third moment of the clock error parameter;
determining an error covariance matrix value of the clock error parameter at a second moment according to an estimated value of the error covariance matrix of the clock error parameter at a first moment;
determining the innovation of the first moment of the clock difference parameter according to the prior state variable estimation value of the first moment of the clock difference parameter and the actual observation value of the first moment of the clock difference parameter; the innovation of the clock difference parameter at the first moment is the difference value of the actual observed value of the clock difference parameter at the first moment and the prior state variable estimated value of the clock difference parameter at the first moment;
setting a weighting coefficient of the clock difference parameter at a first moment; determining an estimated value of an error covariance matrix of the clock error parameter at the first moment according to the weighting coefficient of the clock error parameter at the first moment and the error covariance matrix value of the clock error parameter at the third moment;
determining an updated value of a state variable of the clock error parameter at a second moment according to the prior state variable estimation value of the clock error parameter at a first moment and the innovation of the clock error parameter at the first moment;
determining an updated value of the error covariance matrix of the clock error parameter at the first moment according to the estimated value of the error covariance matrix of the clock error parameter at the first moment and the measurement noise of the clock error parameter at the second moment;
setting a forgetting factor of the clock difference parameter at a second moment; determining a second-moment adaptive noise variance matrix of the clock difference parameter according to a forgetting factor of the clock difference parameter at a second moment;
judging whether the actual estimation error information of the clock error parameter at the second moment and the theoretical estimation error of the clock error parameter at the second moment meet a convergence criterion or not, and determining an error covariance matrix value of the clock error parameter at the second moment based on a judgment result; if the actual estimation error information of the second moment of the clock error parameter and the theoretical estimation error of the second moment of the clock error parameter meet the convergence criterion, directly determining the error covariance matrix value of the second moment of the clock error parameter according to the estimation value of the error covariance matrix of the first moment of the clock error parameter without introducing the weighting coefficient of the first moment of the clock error parameter; and if the actual estimation error information of the clock error parameter at the second moment and the theoretical estimation error of the clock error parameter at the second moment do not meet the convergence criterion, introducing a weighting coefficient of the clock error parameter at the first moment, and determining the estimation value of the error covariance matrix of the clock error parameter at the first moment according to the weighting coefficient of the clock error parameter at the first moment and the error covariance matrix value of the clock error parameter at the third moment.
In an optional embodiment of the present application, the method further comprises:
determining a system noise of a system state equation of a clock difference parameter based on a Hadamard variance of phase data and determining the clock difference parameter based on the Hadamard variance;
based on the system noise of the system state equation of the clock difference parameter, determining an initial value of a covariance matrix of the system noise, an initial value of a covariance matrix of the measurement noise, and an initial value of a covariance matrix of errors of the state vector.
In an optional embodiment of the present application, the determining the clock difference parameter is based on a hadamard variance of the phase data, and the determining the system noise of the system state equation of the clock difference parameter is based on the hadamard variance; the method comprises the following steps:
determining a process noise parameter of the system state equation based on the Hadamard variance, and determining the system noise of the system state equation of the clock error parameter according to the process noise parameter; wherein the process noise parameters include: the variance of white phase modulation noise, the variance of white frequency modulation noise, and the variance of frequency random walk noise.
In an alternative embodiment of the present application, the weighting factor of the first time of the clock error parameter is obtained by automatic calculation, and is used to adjust the estimated value of the error covariance matrix of the first time of the clock error parameter, so as to adjust the gain matrix of the process of determining the updated value of the state variable of the second time.
In an optional embodiment of the present application, a value of the forgetting factor is between 0 and 1.
According to the technical scheme of the embodiment of the application, whether the actual estimation error information of the clock error parameter at the second moment and the theoretical estimation error of the clock error parameter at the second moment meet the convergence criterion or not is judged by establishing a model of the clock error parameter, and the error covariance matrix value of the clock error parameter at the second moment is determined based on the judgment result; if the actual estimation error information of the second moment of the clock error parameter and the theoretical estimation error of the second moment of the clock error parameter meet the convergence criterion, directly determining the error covariance matrix value of the second moment of the clock error parameter according to the estimation value of the error covariance matrix of the first moment of the clock error parameter without introducing the weighting coefficient of the first moment of the clock error parameter; and if the actual estimation error information of the clock error parameter at the second moment and the theoretical estimation error of the clock error parameter at the second moment do not meet the convergence criterion, introducing a weighting coefficient of the clock error parameter at the first moment, and determining the estimation value of the error covariance matrix of the clock error parameter at the first moment according to the weighting coefficient of the clock error parameter at the first moment and the error covariance matrix value of the clock error parameter at the third moment. Therefore, the method can be applied to the condition that signals and prior information in the clock difference system are unknown, the defect that the model is sensitive to initial conditions is overcome, the dynamic tracking performance of clock difference parameter estimation is improved, and the requirement of a high-precision time synchronization system is met.
Drawings
Fig. 1 is a schematic flowchart of a method for adaptively estimating a satellite clock error parameter according to an embodiment of the present disclosure;
FIG. 2 is a flowchart illustrating a recursion of an estimated value of an error covariance matrix at k-th time for determining a clock error parameter using a first mode according to an embodiment of the present disclosure;
fig. 3 is a schematic flowchart of a process of performing clock offset parameter estimation when k is 2 according to an embodiment of the present application;
fig. 4 is a graph showing the results of simulation verification using Matlab software when k is 2.
Detailed Description
So that the manner in which the features and elements of the present embodiments can be understood in detail, a more particular description of the embodiments, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings.
In one embodiment, the smoothed time difference of the clock error data and the estimated values of the current frequency difference and the current frequency drift are obtained by adopting a classical Kalman filtering mode. Kalman filtering is a time-domain filtering method, the method adopts a recursion form, the data storage capacity is small, the result is accurate and reliable, and the method has the advantages that least square and Wiener (Wiener) filtering methods do not have, but Kalman filtering needs to be established on the basis that a model is accurate and the statistical characteristics of random interference signals are known, for an actual application system, because of the influence of factors such as environmental change, device aging, system impact and the like, the condition that the model is uncertain or the statistical characteristics of noise signals are not completely known generally exists in the system, if the conventional Kalman filtering is still adopted for processing, the filtering precision is reduced or even diverged, and the high-precision time synchronization task is difficult to meet.
In another embodiment, the estimated value of the clock error parameter is obtained by means of adaptive kalman filtering. The noise variance matrix of the self-adaptive Kalman filter is self-adaptive, noise parameters do not need to be input in advance, and the noise parameters are automatically updated in the recursion process and are self-adaptively changed along with the change of noise. However, the adaptive kalman filtering method is sensitive to the selection of the initial conditions, and the selection of different initial conditions may cause a large difference in the estimation result of the clock error data.
Based on the problems of the solutions of the two embodiments, various examples of the present application are proposed.
Fig. 1 is a schematic flowchart of a method for adaptively estimating a satellite clock error parameter according to an embodiment of the present application, where as shown in fig. 1, the method includes:
s101: and establishing a model of the clock error parameters, wherein the model of the clock error parameters comprises a state equation of the clock error parameters and a measurement equation of the clock error parameters, and the states of the clock error parameters comprise time difference, frequency difference and frequency drift.
Here, the state equation is an equation representing a relationship between a state at a first time and a state at a second time of the clock difference parameter; the measurement equation is an equation representing the relationship between the state of the clock difference parameter at the first moment and the measurement value at the first moment; the second moment is a moment after the first moment.
In the following equations (1) to (22), time k represents the first time in the embodiment of the present application, time k +1 represents the second time in the embodiment of the present application, and time k-1 represents the third time in the embodiment of the present application.
Taking the model for establishing the 3-dimensional clock error parameter as an example, the state equation of the established model for the clock error parameter is as follows:
wherein: xk+1、XkRespectively representing the system states of the clock error parameter at the k +1 moment and the k moment, and the initial value of the system state of the clock error parameter is set as X1＝[0；0；0](ii) a A represents a state transition matrix; q. q.skA process noise parameter representing a system state equation; τ represents a sampling time interval; x (t), y (t) and z (t) represent the time difference, frequency difference and frequency drift of the clock difference parameter at time t, respectively, and y (t) is the time derivative of x (t), and z (t) is the time derivative of y (t); Δ x, Δ y and Δ z represent random model errors independent of x (t), y (t) and z (t)Zero-mean normal distributions and are not correlated in time.
The measurement equation for establishing the model of the clock error parameter is as follows:
wherein: y iskRepresenting the measured value of the clock error parameter at time k, H representing the observation measurement matrix, rkRepresenting a 1-dimensional measurement noise vector.
Here, the error of the state vector after k measurements is defined as Xk,k-XkDefining the covariance matrix of the errors as:
Pk,k＝E[|Xk,k-Xk|·|Xk,k-Xk|T](3)
wherein, Xk,kState estimation, X, of a clock error parameter representing time kkRepresenting the actual state value of the clock difference parameter at time k.
It should be noted that step 101 is used to establish a model of the clock difference parameter and determine an initial state of the model of the clock difference parameter.
In an optional embodiment of the present application, determining a clock error parameter is based on a hadamard variance of phase data, and determining a system noise of a system state equation of the clock error parameter based on the hadamard variance;
based on the system noise of the system state equation of the clock difference parameter, determining an initial value of a covariance matrix of the system noise, an initial value of a covariance matrix of the measurement noise, and an initial value of a covariance matrix of errors of the state vector.
In an optional embodiment of the present application, the determining the clock difference parameter is based on a hadamard variance of the phase data, and the determining the system noise of the system state equation of the clock difference parameter is based on the hadamard variance; the method comprises the following steps:
determining a process noise parameter of the system state equation based on the Hadamard variance, and determining the system noise of the system state equation of the clock error parameter according to the process noise parameter; wherein the process noise parameters include: the variance of white phase modulation noise, the variance of white frequency modulation noise, and the variance of frequency random walk noise.
Specifically, the expression of the Hadamard variance of the phase data based on the clock difference parameter is as follows:
wherein m represents a smoothing factor, and the value range satisfiesτ represents the time interval of adjacent phase data, xiRepresenting the clock error data, N representing the number of clock error data,
hadamard variance of phase data representing a clock error parameter with a sample interval τ.
Four Hadamard variances were obtained with four sets of clock error data according to equation (4).
In the case of neglecting flicker noise, the Hadamard variance and several kinds of noise affecting the stability of the atomic clock are used for description, and the Hadamard variance of the clock difference parameter and several kinds of noise affecting the stability of the atomic clock satisfy the H-q equation of the formula (5):
wherein, H σ2(τ) Hadamard variance of clock difference parameter representing sampling interval τ, q1Representing the variance of white phase modulation noise (α ═ 2), q2Representing the variance of the white fm noise (α ═ 0), q3Represents the variance of the frequency-frequency random walk noise (α ═ 2), q4Representing measurement noise.
Substituting the four Hadamard variances obtained according to the formula (5) into the formula (2) to obtain a standard quaternion linear equation set, and solving the equation set by using Matlab software to obtain q1～q4。
In an optional embodiment of the present application, based on the system noise of the system state equation of the clock difference parameter, an initial value of a covariance matrix of the system noise, an initial value of a covariance matrix of a measurement noise, and an initial value of a covariance matrix of an error of a state vector are determined.
Specifically, the covariance matrix of the system noise satisfies formula (6):
wherein Q iskA covariance matrix representing the system noise at time k. Q to be determined according to equation (5)1～q3The initial value of the covariance matrix of the system noise can be determined by substitution.
The covariance matrix of the measurement noise satisfies formula (7):
Rk＝E[rkrk T]＝q4(7)
wherein R iskRepresenting the measurement noise at time k. According to q determined according to formula (5)4The initial value of the covariance matrix of the measurement noise can be determined.
Based on a traditional classical method, selecting an initial value of a covariance matrix of errors of a state vector to satisfy formula (8):
wherein, P1The initial value of the covariance matrix representing the error of the state vector. According to q determined according to formula (5)1～q4The initial value of the covariance matrix of the errors of the state vectors can be determined.
S102: determining a prior state variable estimated value of the clock error parameter at a first moment; the prior state variable estimation value of the first moment represents the state value of the first moment of the clock difference parameter estimated according to the state of the third moment of the clock difference parameter; the third moment is a moment before the first moment;
s103: determining an estimated value of a state variable of the clock error parameter at a second moment according to a prior state variable estimated value of the clock error parameter at a first moment and an actual observed value of the clock error parameter at the first moment;
s104: determining an estimated value of an error covariance matrix of a clock error parameter at a first moment; the estimation value of the error covariance matrix at the first moment represents that the error covariance matrix value at the first moment of the clock error parameter is estimated according to the error covariance matrix value at the third moment of the clock error parameter;
specifically, the system noise q is initially disregardedkAnd measuring the noise rkUnder the influence, the estimated values of the prior state variable and the error covariance matrix are respectively as follows:
wherein, Xk,k-1Representing the estimation of a state value at time k, P, from the state at time k-1k,k-1Representing the estimation of the k-time error variance matrix value according to the k-1 time error variance matrix value.
The estimation of the new state quantities depends on the previous estimation and the current measurement:
Xk,k＝Xk,k-1+Kk[Zk-HXk,k-1](10)
wherein Z iskRepresenting the actual observed value at time k; kkRepresenting a gain matrix, and selecting the trace minimum of an error covariance matrix, namely:
where α represents a gain factor, which is an empirical value, α -10 may be set in the model.
Finally, the update value of the error covariance matrix is:
Pk,k＝[I-KkH]Pk,k-1(12)
wherein I is a unit matrix, PkRepresentative errorUpdate values of the covariance matrix.
In steps 103 to 105, the first mode is used to determine the estimated value of the error covariance matrix of the clock error parameter at k th time. The first mode is the classical Kalman filtering mode.
Fig. 2 is a flowchart illustrating a recursion of determining an estimated value of an error covariance matrix of k-th time of a clock error parameter using a first mode according to an embodiment of the present application.
S105: determining an error covariance matrix value of the clock error parameter at a second moment according to an estimated value of the error covariance matrix of the clock error parameter at a first moment;
s106: determining the innovation of the first moment of the clock difference parameter according to the prior state variable estimation value of the first moment of the clock difference parameter and the actual observation value of the first moment of the clock difference parameter; the innovation of the clock difference parameter at the first moment is the difference value of the actual observed value of the clock difference parameter at the first moment and the prior state variable estimated value of the clock difference parameter at the first moment;
specifically, the prior state variable estimation value is as follows:
Xk,k-1＝AXk-1,k-1(13)
innovation (residual) is:
vk＝Zk-HXk,k-1(14)
wherein v iskRepresenting the innovation at time k.
S107: setting a weighting coefficient of the clock difference parameter at a first moment; determining an estimated value of an error covariance matrix of the clock error parameter at the first moment according to the weighting coefficient of the clock error parameter at the first moment and the error covariance matrix value of the clock error parameter at the third moment;
the error covariance matrix estimate is:
Pk,k-1＝SkAPk-1,k-1AT+Qk-1(15)
wherein the adaptive weighting coefficient SkThe calculation method comprises the following steps:
the gain matrix is:
s108: determining an updated value of a state variable of the clock error parameter at a second moment according to the prior state variable estimation value of the clock error parameter at a first moment and the innovation of the clock error parameter at the first moment;
specifically, the updated value of the state variable is:
Xk,k＝Xk,k-1+Kkvk(18)
wherein, Xk,kRepresenting updated values of state variables.
S109: determining an updated value of the error covariance matrix of the clock error parameter at the first moment according to the estimated value of the error covariance matrix of the clock error parameter at the first moment and the measurement noise of the clock error parameter at the second moment;
here, the update values of the error variance matrix are:
Pk,k＝[I-KkH]Pk,k-1[I-KkH]T+KkRk-1Kk T(19)
wherein, Pk,kRepresenting the updated values of the error variance matrix.
S110: setting a forgetting factor of the clock difference parameter at a second moment; determining a second-moment adaptive noise variance matrix of the clock difference parameter according to a forgetting factor of the clock difference parameter at a second moment;
specifically, the adaptive noise variance matrix is:
wherein d isk-1＝(1-b)/(1-bk) And b represents a forgetting factor, and the value of the forgetting factor b is between 0 and 1.
It should be noted that, in steps 106 to 111, the estimated value of the error covariance matrix of k-th of the clock error parameter is determined by using the second mode. The second mode is an adaptive Kalman filtering mode.
S111: and judging whether the actual estimation error information of the second moment of the clock error parameter and the theoretical estimation error of the second moment of the clock error parameter meet a convergence criterion, and determining the error covariance matrix value of the second moment of the clock error parameter based on the judgment result.
If the actual estimation error information of the second moment of the clock error parameter and the theoretical estimation error of the second moment of the clock error parameter meet the convergence criterion, directly determining the error covariance matrix value of the second moment of the clock error parameter according to the estimation value of the error covariance matrix of the first moment of the clock error parameter without introducing the weighting coefficient of the first moment of the clock error parameter; and if the actual estimation error information of the clock error parameter at the second moment and the theoretical estimation error of the clock error parameter at the second moment do not meet the convergence criterion, introducing a weighting coefficient of the clock error parameter at the first moment, and determining the estimation value of the error covariance matrix of the clock error parameter at the first moment according to the weighting coefficient of the clock error parameter at the first moment and the error covariance matrix value of the clock error parameter at the third moment.
Specifically, the filter convergence criterion is as follows:
wherein γ represents a stock system (γ ≧ 1), and tr represents a square matrix trace-finding symbol. The left side of the inequality is the square sum of 'innovation', and the actual estimation error information of the clock error parameter is reflected; the right side of the inequality is related to the trace of covariance of the "innovation" sequence, reflecting the theoretical prediction error information of the clock error parameter.
The final form of the criterion can be expressed as:
when the above formula (22) is satisfied, it indicates that the filter is in the optimal working state, and then the weighting coefficient of the clock difference parameter at the first moment is not introduced, and the error covariance matrix value of the clock difference parameter at the second moment is determined directly according to the estimated value of the error covariance matrix of the clock difference parameter at the first moment, that is, the error covariance matrix value of the clock difference parameter at the second moment is determined by adopting the first mode
When the above equation is not satisfied, it indicates that the actual estimation error of the filter will exceed γ times of the theoretical expected value, and is in a divergent state, and at this time, if the actual estimation error information of the second time of the clock difference parameter and the theoretical estimation error of the second time of the clock difference parameter do not satisfy the convergence criterion, the weighting coefficient of the first time of the clock difference parameter is introduced, and the estimation value of the error covariance matrix of the first time of the clock difference parameter is determined according to the weighting coefficient of the first time of the clock difference parameter and the error covariance matrix value of the third time of the clock difference parameter, that is, the error covariance matrix value of the second time of the clock difference parameter is determined by using the second mode. By automatically calculating a weighting coefficient SkFor adjusting Pk,k-1Of (i) i.e. adjusting the gain matrix KkSo as to better develop the current observed quantity ZkTo suppress filter divergence.
Through the steps, the optimal estimation of the clock difference data can be completed.
Fig. 3 is a schematic flow chart of performing clock offset parameter estimation when k is 2 according to an embodiment of the present application. As shown in fig. 3, when k is 2, a mode for determining the state of the clock difference signal is selected according to whether a convergence criterion is satisfied, when the convergence criterion is satisfied, the optimal estimation of the clock difference data is completed by using a first mode, when the convergence criterion is not satisfied, the optimal estimation of the clock difference data is completed by using a second mode,
fig. 4 is a graph showing the results of simulation verification using Matlab software when k is 2, and the error curve of the clock offset parameter after simulation is shown in fig. 4. As can be seen from fig. 4, the accuracy of the estimation of the clock difference parameter can be improved by using the technical solution of the embodiment of the present application.
According to the technical scheme of the embodiment of the application, whether the actual estimation error information of the clock error parameter at the second moment and the theoretical estimation error of the clock error parameter at the second moment meet the convergence criterion or not is judged, and the error covariance matrix value of the clock error parameter at the second moment is determined based on the judgment result. By adopting two modes to estimate the clock difference parameters, the method can be applied to the condition that signals and prior information in a clock difference system are unknown, can make up the defect that a model is sensitive to initial conditions, improves the dynamic tracking performance of the clock difference parameter estimation, and meets the requirement of a high-precision time synchronization system.
The technical solutions described in the embodiments of the present application can be arbitrarily combined without conflict.
In the several embodiments provided in the present application, it should be understood that the disclosed method may be implemented in other ways.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present application, and shall be covered by the scope of the present application.
Claims (5)
1. A method for adaptive estimation of satellite clock error parameters, the method comprising:
establishing a model of clock error parameters, wherein the model of the clock error parameters comprises a state equation of the clock error parameters and a measurement equation of the clock error parameters, and the states of the clock error parameters comprise time difference, frequency difference and frequency drift; the state equation is an equation representing the relationship between the state of the clock difference parameter at the first moment and the state of the clock difference parameter at the second moment; the measurement equation is an equation representing the relationship between the state of the clock difference parameter at the first moment and the measurement value at the first moment; the second moment is a moment after the first moment;
determining a prior state variable estimated value of the clock error parameter at a first moment; the prior state variable estimation value of the first moment represents the state value of the first moment of the clock difference parameter estimated according to the state of the third moment of the clock difference parameter; the third moment is a moment before the first moment;
determining an estimated value of a state variable of the clock error parameter at a second moment according to a prior state variable estimated value of the clock error parameter at a first moment and an actual observed value of the clock error parameter at the first moment;
determining an estimated value of an error covariance matrix of a clock error parameter at a first moment; the estimation value of the error covariance matrix at the first moment represents that the error covariance matrix value at the first moment of the clock error parameter is estimated according to the error covariance matrix value at the third moment of the clock error parameter;
determining an error covariance matrix value of the clock error parameter at a second moment according to an estimated value of the error covariance matrix of the clock error parameter at a first moment;
determining the innovation of the first moment of the clock difference parameter according to the prior state variable estimation value of the first moment of the clock difference parameter and the actual observation value of the first moment of the clock difference parameter; the innovation of the clock difference parameter at the first moment is the difference value of the actual observed value of the clock difference parameter at the first moment and the prior state variable estimated value of the clock difference parameter at the first moment;
setting a weighting coefficient of the clock difference parameter at a first moment; determining an estimated value of an error covariance matrix of the clock error parameter at the first moment according to the weighting coefficient of the clock error parameter at the first moment and the error covariance matrix value of the clock error parameter at the third moment;
determining an updated value of a state variable of the clock error parameter at a second moment according to the prior state variable estimation value of the clock error parameter at a first moment and the innovation of the clock error parameter at the first moment;
determining an updated value of the error covariance matrix of the clock error parameter at the first moment according to the estimated value of the error covariance matrix of the clock error parameter at the first moment and the measurement noise of the clock error parameter at the second moment;
setting a forgetting factor of the clock difference parameter at a second moment; determining a second-moment adaptive noise variance matrix of the clock difference parameter according to a forgetting factor of the clock difference parameter at a second moment;
judging whether the actual estimation error information of the clock error parameter at the second moment and the theoretical estimation error of the clock error parameter at the second moment meet a convergence criterion or not, and determining an error covariance matrix value of the clock error parameter at the second moment based on a judgment result; if the actual estimation error information of the second moment of the clock error parameter and the theoretical estimation error of the second moment of the clock error parameter meet the convergence criterion, directly determining the error covariance matrix value of the second moment of the clock error parameter according to the estimation value of the error covariance matrix of the first moment of the clock error parameter without introducing the weighting coefficient of the first moment of the clock error parameter; and if the actual estimation error information of the clock error parameter at the second moment and the theoretical estimation error of the clock error parameter at the second moment do not meet the convergence criterion, introducing a weighting coefficient of the clock error parameter at the first moment, and determining the estimation value of the error covariance matrix of the clock error parameter at the first moment according to the weighting coefficient of the clock error parameter at the first moment and the error covariance matrix value of the clock error parameter at the third moment.
2. The method of claim 1, further comprising:
determining a system noise of a system state equation of a clock difference parameter based on a Hadamard variance of phase data and determining the clock difference parameter based on the Hadamard variance;
based on the system noise of the system state equation of the clock difference parameter, determining an initial value of a covariance matrix of the system noise, an initial value of a covariance matrix of the measurement noise, and an initial value of a covariance matrix of errors of the state vector.
3. The method of claim 2, wherein determining the clock difference parameter is based on a hadamard variance of the phase data, and wherein determining the system noise of the system state equation for the clock difference parameter is based on the hadamard variance; the method comprises the following steps:
determining a process noise parameter of the system state equation based on the Hadamard variance, and determining the system noise of the system state equation of the clock error parameter according to the process noise parameter; wherein the process noise parameters include: the variance of white phase modulation noise, the variance of white frequency modulation noise, and the variance of frequency random walk noise.
4. The method of claim 1, wherein the weighting factor for the first instance of the clock difference parameter is automatically calculated for adjusting the estimated value of the error covariance matrix for the first instance of the clock difference parameter, thereby adjusting the gain matrix of the process of determining the updated value of the state variable for the second instance.
5. The method according to any one of claims 1 to 4, wherein the forgetting factor has a value between 0 and 1.
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