阅读说明：本技术 一种用于卫星导航授时型接收机的钟差估算方法 (Clock error estimation method for satellite navigation time service type receiver ) 是由 李志强 于永 于 2019-10-25 设计创作，主要内容包括：本发明公开了一种用于卫星导航授时型接收机的钟差估算方法。该方法包括步骤有拟合多项式、模型简化和矩阵求解,其中在模型简化中,引入切比雪夫模型,由于切比雪夫模型的多项式各项组成的矢量满足标准化正交特性,由此可以简化参数估计及其统计特性分析,并可以提高对系数参数的估值精度,可以实现更加精确的钟差估算和钟差预报。该方法适用于对导航接收机常用温补晶振和恒温晶振的钟差进行精确估算,从而提高授时型接收机在卫星导航信号中断情况下继续提供高精度时间服务的能力。(The invention discloses a clock error estimation method for a satellite navigation time service type receiver. The method comprises the steps of fitting a polynomial, model simplification and matrix solution, wherein a Chebyshev model is introduced in the model simplification, and because vectors formed by various items of the polynomial of the Chebyshev model meet the standardized orthogonal characteristic, the parameter estimation and the statistical characteristic analysis can be simplified, the estimation precision of coefficient parameters can be improved, and more accurate clock error estimation and clock error prediction can be realized. The method is suitable for accurately estimating the clock error of the common temperature compensation crystal oscillator and the constant temperature crystal oscillator of the navigation receiver, so that the capability of the time service type receiver for continuously providing high-precision time service under the condition of satellite navigation signal interruption is improved.)

1. A clock error estimation method for a satellite navigation time service type receiver is characterized by comprising the following steps:

first, fitting a polynomial, at time t₀、t₁、t₂、…、t_N-1The clock error data of (1) correspond to x respectively₀、x₁、x₂、…、x_N-1Then the clock error data fits as:

wherein: a is₀、a₁、a₂、…、a_mFor fitting polynomial coefficients, m is the polynomial degree, e_iFor model error, i ═ 0,1,2, …, N-1;

and secondly, simplifying the model, adopting a second-order polynomial model, and expressing the clock error data as follows:

x_t＝a₀+a₁(t-t₀)+a₂(t-t₀)²+e_i，

wherein the polynomial coefficient a₀、a₁、a₂Also called initial clock error, clock bias and clock drift;

thirdly, matrix solving, further expressed in a matrix form as:

X＝Ha+e，

wherein: x is an N-dimensional observation vector, a is an m-dimensional coefficient vector, e is an N-dimensional error vector, and H is a design matrix which can be expressed as:

and estimating by adopting a least square method, wherein the coefficient vector a to be estimated is as follows:

2. the method of claim 1, wherein a Chebyshev model is introduced in the model reduction, and x (t) is a sampling interval τ₀The clock difference sequence of (1): { x (t)₀),x(t₁),…,x(t_N-1) And t, and t_i＝iτ₀And then:

x(t)＝q₀Φ₀(t)+q₁Φ₁(t)+q₂Φ₂(t)+e(t)，

in the formula:

3. the method of claim 2, wherein in said matrix solving, a vector Φ is defined_i＝[Φ_i(t₀) Φ_i(t₁) … Φ_i(t_N-1)]^TEstablishing a coefficient matrix phi ═ phi₀Φ₁Φ₂) And then:

and recording the N-dimensional observation vector as L and V as the residual vector of model estimation, then:

V＝Φq-L，

in the formula: observation vector L ═ x (t)₀) x(t₁) … x(t_N-1)]^TThe residual vector V ═ e (t)₀) e(t₁) … e(t_N-1)]^T，q＝[q₁q₂q₃]^TPhi is a coefficient matrix for a parameter to be estimated;

if the observation sequences are independent and equal in precision, and the least square method is adopted for estimation, the estimation of the parameter vector q to be estimated is represented as follows:

q＝(Φ^TΦ)^-1Φ^TL。

4. the method of claim 3, wherein the Chebyshev polynomial satisfies the normalized orthogonality property, Φ^TΦ＝I₃，I₃In 3-order unit matrix, the estimated value of the parameter q isCan be expressed as:

q＝Φ^TL。

Technical Field

The invention relates to the field of satellite communication, in particular to a clock error estimation method for a satellite navigation time service type receiver.

Background

The clock error of the satellite navigation time service receiver is precisely estimated and forecasted, the capability of the receiver for continuously providing high-precision time service under the condition of satellite signal interruption or interference can be improved, and the method is a basic requirement for the time service receiver. The conventional clock error estimation method is proposed for the atomic clock error, a temperature compensation crystal oscillator and a constant temperature crystal oscillator are mainly used in a time service type receiver, and the physical mechanisms and corresponding physical characteristics of two types of frequency sources are different, so that the method is not suitable for adopting the completely same clock error estimation method.

Therefore, the clock difference of the common temperature compensation crystal oscillator and the constant temperature crystal oscillator of the navigation receiver needs to be accurately estimated, so that the capability of the time service type receiver for continuously providing high-precision time service under the condition of satellite navigation signal interruption is improved.

Disclosure of Invention

The invention mainly solves the technical problem of providing a clock error estimation method for a satellite navigation time service type receiver, and solves the problem that a clock error estimation method based on a temperature compensation crystal oscillator and a constant temperature crystal oscillator in the time service type receiver in the prior art is lack of a corresponding accurate clock error estimation method.

In order to solve the above technical problems, one technical solution adopted by the present invention is to provide a clock error estimation method for a satellite navigation time service type receiver, including the following steps: first, fitting a polynomial, at time t₀、t₁、t₂、…、t_N-1The clock error data of (1) correspond to x respectively₀、x₁、x₂、…、x_N-1Then the clock error data fits as:

wherein: a is₀、a₁、a₂、…、a_mFor fitting polynomial coefficients, m is the polynomial degree, e_iFor model error, i ═ 0,1,2, …, N-1; and secondly, simplifying the model, adopting a second-order polynomial model, and expressing the clock error data as follows: x is the number of_t＝a₀+a₁(t-t₀)+a₂(t-t₀)²+e_iWherein the polynomial coefficient a₀、a₁、a₂Also called initial clock error, clock bias and clock drift; thirdly, matrix solving, further expressed in a matrix form as: x ═ Ha + e, where: x is an N-dimensional observation vector, a is an m-dimensional coefficient vector, e is an N-dimensional error vector, and H is a design matrix which can be expressed as:

and estimating by adopting a least square method, wherein the coefficient vector a to be estimated is as follows:

in another embodiment of the clock error estimation method for the satellite navigation time service receiver, a Chebyshev model is introduced in the model simplification, and x (t) is set as a sampling interval tau₀The clock difference sequence of (1): { x (t)₀)，x(t₁),…,x(t_N-1) And t, and t_i＝iτ₀And then:

x(t)＝q₀Φ₀(t)+q₁Φ₁(t)+q₂Φ₂(t)+e(t)，

in the formula:

in another embodiment of the clock error estimation method for the satellite navigation time service type receiver, in the matrix solution, a vector phi is defined_i＝[Φ_i(t₀) Φ_i(t₁) … Φ_i(t_N-1)]^TEstablishing a coefficient matrix phi ═ phi₀Φ₁Φ₂) And then:

and recording the N-dimensional observation vector as L and V as the residual vector of model estimation, then:

V＝Φq-L

in the formula: observation vector L ═ x (t)₀) x(t₁) … x(t_N-1)]^TThe residual vector V ═ e (t)₀) e(t₁) … e(t_N-1)]^T，q＝[q₁q₂q₃]^TPhi is a coefficient matrix for a parameter to be estimated;

if the observation sequences are independent and equal in precision, and least square estimation is adopted, the estimation of the parameter vector q to be estimated is represented as follows:

q＝(Φ^TΦ)^-1Φ^TL。

in another embodiment of the clock error estimation method for the satellite navigation time service type receiver, as the terms of the Chebyshev polynomial meet the normalized orthogonal characteristic, namely phi^TΦ＝I₃，I₃For a 3 rd order unit matrix, the estimated value of the parameter q can be expressed as:

q＝Φ^TL。

the invention has the beneficial effects that: the invention discloses a clock error estimation method for a satellite navigation time service type receiver. The method comprises the steps of fitting a polynomial, model simplification and matrix solution, wherein a Chebyshev model is introduced in the model simplification, and because vectors formed by various items of the polynomial of the Chebyshev model meet the standardized orthogonal characteristic, the parameter estimation and the statistical characteristic analysis can be simplified, the estimation precision of coefficient parameters can be improved, and more accurate clock error estimation and clock error prediction can be realized. The method is suitable for accurately estimating the clock error of the common temperature compensation crystal oscillator and the constant temperature crystal oscillator of the navigation receiver, thereby improving the capability of the time service receiver for continuously providing high-precision time service under the condition of satellite navigation signal interruption.

Drawings

FIG. 1 is a flow chart of an embodiment of a clock error estimation method for a satellite navigation time service type receiver according to the invention;

FIG. 2 is a simulation diagram of phase difference prediction accuracy analysis of a temperature compensated crystal oscillator according to another embodiment of the clock difference estimation method for a satellite navigation time service type receiver according to the present invention;

FIG. 3 is a simulation diagram of frequency offset prediction accuracy analysis of a temperature compensated crystal oscillator in another embodiment of the clock offset estimation method for a satellite navigation time service receiver according to the present invention;

FIG. 4 is a simulation diagram of phase difference prediction accuracy analysis of a constant temperature crystal oscillator according to another embodiment of the clock difference estimation method for a satellite navigation time service type receiver of the present invention;

FIG. 5 is a simulation diagram of frequency offset prediction accuracy analysis of a constant temperature crystal oscillator according to another embodiment of the clock offset estimation method for a satellite navigation time service type receiver.

Detailed Description

In order to facilitate an understanding of the invention, the invention is described in more detail below with reference to the accompanying drawings and specific examples. Preferred embodiments of the present invention are shown in the drawings. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.

It is to be noted that, unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.

Fig. 1 shows a flowchart of an embodiment of a clock error estimation method for a satellite navigation time service type receiver according to the invention. In fig. 1, the following steps are included:

in a first step S101, a polynomial is fitted at a time t₀、t₁、t₂、…、t_N-1The clock error data of (1) correspond to x respectively₀、x₁、x₂、…、x_N-1Then the clock error data fits as:

wherein: a is₀、a₁、a₂、…、a_mFor fitting polynomial coefficients, m is the polynomial degree, e_iFor model error, i ═ 0,1,2, …, N-1;

step S102, simplifying the model, adopting a second-order polynomial model, and expressing the clock error data as:

x_t＝a₀+a₁(t-t₀)+a₂(t-t₀)²+e_iwherein the polynomial coefficient a₀、a₁、a₂Also called initial clock error, clock bias and clock drift;

step S103, matrix solution, which is further expressed in a matrix form as follows:

x ═ Ha + e, where: x is an N-dimensional observation vector, a is an m-dimensional coefficient vector, e is an N-dimensional error vector, and H is a design matrix which can be expressed as:

and adopting least square estimation, wherein the coefficient vector a to be estimated is as follows:

preferably, in the model simplification S102, a chebyshev model is introduced, and x (t) is a sampling interval τ₀The clock difference sequence of (1): { x (t)₀),x(t₁),…,x(t_N-1) And t, and t_i＝iτ₀And then:

x(t)＝q₀Φ₀(t)+q₁Φ₁(t)+q₂Φ₂(t)+e(t)，

in the formula:

preferably, in the matrix solving S103, a vector Φ is defined_i＝[Φ_i(t₀) Φ_i(t₁) … Φ_i(t_N-1)]^TEstablishing a coefficient matrix phi ═ phi₀Φ₁Φ₂) And then:

and recording the N-dimensional observation vector as L and V as the residual vector of model estimation, then:

V＝Φq-L，

in the formula: observation vector L ═ x (t)₀) x(t₁) … x(t_N-1)]^TThe residual vector V ═ e (t)₀) e(t₁) … e(t_N-1)]^T，q＝[q₁q₂q₃]^TPhi is a coefficient matrix for a parameter to be estimated; if the observation sequences are independent and equal in precision, and least square estimation is adopted, the estimation of the parameter vector q to be estimated is represented as follows:

q＝(Φ^TΦ)^-1Φ^TL。

further preferably, since the chebyshev polynomial terms satisfy the normalized orthogonality property, i.e., Φ^TΦ＝I₃，I₃For a 3 rd order unit matrix, the estimated value of the parameter q can be expressed as:

q＝Φ^TL。

furthermore, the residual error results after the chebyshev model introduced in step S102 of the present application is used to fit the clock error and the frequency difference of the temperature compensated crystal oscillator and the constant temperature crystal oscillator are respectively given. And (3) carrying out polynomial fitting by using 3600 measurement data in 1 hour in the simulation to obtain coefficient parameters of the model, and then predicting the clock error by using the parameters.

If the data measurement error is zero, the simulation result shows that the short-term fitting and clock error and frequency error forecasting results of the Chebyshev model are better, and the forecasting precision of the model is reduced along with the prolonging of the forecasting time.

As shown in fig. 2 and 3, the predicted residual error of the phase data of the temperature-compensated crystal oscillator in a short period (within 1 hour) is 10^-7Magnitude, residual error of frequency data at 10^-9Magnitude, long-term (after 1 hour) prediction residual of phase data increases with increasing prediction time, and residual error of frequency data is 10^-8Magnitude, with a longest prediction time of 2261 second.

As shown in FIGS. 4 and 5, for a constant temperature crystal oscillator, the phase data of the short term (within 1 hour) is obtainedPredicted residual error is 10^-9Magnitude, residual error of frequency data at 10^-11Magnitude, long-term (after 1 hour) prediction residual of phase data increases with increasing prediction time, and residual error of frequency data is 10^-10On the order of magnitude, a prediction error of not more than 1 microsecond is required for the navigation receiver, and the maximum prediction time is 13122 seconds.

Therefore, the invention discloses a clock error estimation method for a satellite navigation time service type receiver. The method comprises the steps of fitting a polynomial, model simplification and matrix solution, wherein a Chebyshev model is introduced in the model simplification, and because vectors formed by various items of the polynomial of the Chebyshev model meet the standardized orthogonal characteristic, the parameter estimation and the statistical characteristic analysis can be simplified, the estimation precision of coefficient parameters can be improved, and more accurate clock error estimation and clock error prediction can be realized. The invention mainly aims at the clock error modeling problem of a satellite navigation time service receiver, and the receiver can utilize a clock model to switch into a high-precision time keeping mode by accurately modeling and forecasting the clock error of a local clock when a satellite signal is interrupted or interfered, so as to continuously provide high-precision time and frequency services for a user. The method is suitable for accurately estimating the clock error of the common temperature compensation crystal oscillator and the constant temperature crystal oscillator of the navigation receiver, thereby improving the capability of the time service receiver for continuously providing high-precision time service under the condition of satellite navigation signal interruption.

The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all equivalent structural changes made by using the contents of the present specification and the drawings, or applied directly or indirectly to other related technical fields, are included in the scope of the present invention.