Method for correcting BeiDou and crystal oscillator second clocks based on differential observation and regression equation model

Abstract

The present invention discloses a method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation models. First, a differential observation model is established between a public end and other users to reduce the random drift error of the Beidou second clock. Then, a quadratic regression equation model is established for the deviation between the crystal oscillator second clock and the Beidou second clock. The current estimated value of the regression coefficient of the regression equation model is calculated in real time, and the correction value of the crystal oscillator second clock is calculated based on the estimated value. The present invention uses a differential observation model to eliminate the influence of receiver error factors on satellite signals during transmission, thereby reducing the random drift error of the Beidou second clock and correcting the Beidou second clock. Using the corrected Beidou second clock signal as a parameter will improve the fitting accuracy of the quadratic regression equation model for the deviation between the crystal oscillator second clock and the Beidou second clock, thereby improving the accuracy of the time signal.

Description

Technical Field

[0001] The present invention relates to the field of satellite timing technology, and in particular to a method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation models. Background Art

[0002] As society becomes increasingly information-based, high-precision timing is becoming increasingly widespread and ubiquitous. While BeiDou timing technology currently meets most needs in work and life, in areas such as power system fault location, fourth- and fifth-generation mobile communications, and spacecraft flight control, where time accuracy requirements reach microseconds or even nanoseconds, improving timing accuracy has garnered widespread attention.

[0003] The currently used satellite timing method has the following defects:

[0004] 1) Since satellite signals are affected by satellite clock errors, ionospheric errors, tropospheric errors, receiver errors, and too few tracking satellites during transmission, random jitter will occur, making it difficult to guarantee signal accuracy and stability.

[0005] 2) Due to the influence of factors such as aging and temperature, the output signal of the ground crystal oscillator will contain cumulative errors, resulting in frequency offset;

[0006] In order to improve the accuracy and stability of satellite clocks, some scholars have proposed using the Kalman filter algorithm to overcome the jitter and measurement noise of Beidou satellite second signals. However, this method does not consider the influence of crystal oscillator frequency drift, and the real-time performance of this method is not high, so its application is subject to certain limitations. Summary of the Invention

[0007] In view of the technical problems existing in the prior art, the present invention provides a high-precision synchronous clock generation method with simple implementation, high precision and good real-time performance.

[0008] A method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model, comprising the following steps:

[0009] Step 1: Select a reference user as the common end and establish a differential observation model between the common end and other users to reduce the random drift error of the Beidou second clock, thereby continuously correcting the Beidou second clock.

[0010] Step 2: Establish a quadratic regression equation model of the deviation between the crystal oscillator second clock and the Beidou second clock, and generate a first corrected crystal oscillator second clock signal based on the frequency of the crystal oscillator signal.

[0011] Step 3: Compare the phases of the corrected crystal oscillator second clock with the corrected Beidou second clock to obtain the current deviation, which includes the random drift error of the Beidou second clock and the cumulative error of the crystal oscillator second clock. The current estimated value of the regression coefficient of the regression equation model is calculated in real time based on the current deviation. Based on the current estimated value of the regression coefficient, the estimated cumulative error between the crystal oscillator second clock and the international standard time is calculated, and then the compensation value for the next correction of the crystal oscillator second clock is calculated. The compensation value is then added to the frequency of the crystal oscillator signal to obtain the comparison value of the next correction of the crystal oscillator second clock. The crystal oscillator signal is then counted. When the count value equals the comparison value, the signal is output as the correction crystal oscillator second clock, and step 3 is repeated, thereby continuously correcting the crystal oscillator second clock.

[0012] The method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model, wherein step 1 of reducing the random drift error of the Beidou second clock comprises the following steps:

[0013] A reference user is selected as the common end for measuring the relative clock deviation of the Beidou second clock. The same satellite is synchronously observed by satellite receivers at the locations of the reference user and the user who needs to reduce random errors to measure the relative deviation of the two users' receiver clocks.

[0014] L1=ρ1+Cdt-CdT1+Trop-Ion+ξ1

[0015] L2=ρ2+Cdt-CdT2+Trop-Ion+ξ2

[0016] Where L is the known phase observation of the satellite by the user's receiver, ρ is the known geometric distance from the satellite to the receiver, dt is the satellite clock error, dT is the receiver clock error, Trop and Ion are the tropospheric and ionospheric delays, respectively, ξ is the additional noise in the observation, and C is the speed of light in vacuum. The subscript 1 or 2 indicates the user number.

[0017] The difference between the observation values, that is, the differential observation model, is: ΔL = Δρ - CΔdT + Δξ′

[0018] Where Δρ = ρ1 - ρ2, ΔdT = dT1 - dT2. Δξ′ = ξ1 - ξ2, which can be ignored in the calculation.

[0019] Substituting the user's position coordinates, the relative receiver clock difference between the two user clocks is obtained as:

[0020]

[0021] The local time of the base user station receiver is used as the base time. The receiver clock error is the difference between the local time of the receiver and the base time. Then ΔT p =0, where ΔT p 、 are the reference user receiver clock error and the user receiver clock error, ΔdT PP1 is the clock difference between the reference user and the user's relative receiver.

[0022] Thus, the user receiver clock error is calculated That is, it can eliminate the receiver clock error in the Beidou second clock random drift error ε, which is composed of the receiver clock error, accidental error and satellite clock error, thereby reducing the Beidou second clock random drift error ε.

[0023] In the method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model, the reference user is selected from the geographical locations of all users whose random errors in Beidou timing need to be reduced, and the user geographically closest to the center within the selected range is selected as the reference user.

[0024] In the method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model, in step 2, a quadratic regression equation model is established by the following steps:

[0025] Based on the deviation ε between the Beidou second clock and the international standard time UCT, and ε follows a normal distribution:

[0026] ε~N(0,σ 2 )

[0027] Where σ represents the standard deviation and N is the symbol for normal distribution.

[0028] Then the deviation between the xth second clock output by the Beidou second clock and the international standard time is μ′(x)=ε x

[0029] Therefore, the international standard time y′ corresponding to the xth second clock output by the Beidou second clock is x for

[0030] y′ x =x-ε x ,x=1,2,...,n

[0031] Let the initial deviation between the zeroth second clock and the UTC be a in the crystal oscillator second clock sequence. The initial deviation between the zeroth second clock cycle and the UTC second cycle is R. The drift of each second interval is d. Then the deviation between the xth second clock cycle and the UTC second cycle is ΔT x for:

[0032] ΔT x =R+dx

[0033] The deviation μ″(x) between the xth second clock output by the crystal oscillator second clock and the international standard time is:

[0034]

[0035] remember

[0036] Then the time error μ″(x) of the x-th crystal oscillator second clock is recorded as:

[0037] μ″(x)=a+bx+cx 2

[0038] Then the crystal oscillator second clock outputs the international standard time y" corresponding to the xth second clock x for:

[0039] y″ x =x+a+bx+cx 2 ,x=1,2,...,n

[0040] The quadratic regression analysis model y of the deviation between the crystal oscillator second clock and the Beidou second clock is obtained x for:

[0041] y x =y″ x -y′ x =a+bx+cx 2 +ε x ,x=1,2...,n。

[0042] The method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model, in the step 2, the first corrected crystal oscillator second clock signal is generated based on the frequency of the crystal oscillator signal, and the crystal oscillator signal is counted by a counter. When the counting result of the counter is equal to the frequency value of the crystal oscillator signal, the frequency dividing circuit outputs a high-level signal as the first corrected crystal oscillator second clock signal.

[0043] The method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model, wherein in step 3, the phase of the corrected crystal oscillator second clock is compared with the Beidou second clock to obtain the current deviation including the random drift error of the Beidou second clock and the accumulated error of the crystal oscillator second clock, includes the following process:

[0044] Compare the phase difference between the Beidou second clock signal and the current corrected crystal second clock signal to determine the order of appearance of the two signals, so as to determine the positive or negative value of the random drift error. Apply a high-frequency oscillation counting pulse signal to the counter, and use the counter to count the number of counting pulses in the time interval between the two signals to obtain the absolute value used to reflect the random drift error value, thereby obtaining the random drift error value φ. x .

[0045] Then calculate the current deviation Y between the Beidou second clock and the crystal oscillator second clock x for:

[0046]

[0047] where c i is the compensation value of the crystal oscillator error. x When c i Take 0.

[0048] The method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model, wherein in step 3, obtaining the current estimated value of the regression coefficient of the regression equation model in real time according to the current deviation, includes the following process:

[0049] The coefficients a, b, and c in the quadratic regression analysis model are estimated by least squares.

[0050] Since the independent variable x of the quadratic regression model is the deviation Y between the Beidou second clock and the crystal oscillator second clock x The time series X of the constructed sequence Y is:

[0051] 1, 2, 3, 4,...,x,...,n

[0052] And the independent variable x is an equally spaced value. Use orthogonal polynomial analysis to select a set of orthogonal polynomials:

[0053]

[0054] in for:

[0055]

[0056] Then the regression equation becomes:

[0057]

[0058] The estimated values of coefficients b0, b1, and b2 are:

[0059]

[0060]

[0061]

[0062] where Y x Obtained from the deviation between the Beidou second clock and the crystal oscillator second clock, x=1, 2, 3, ..., n.

[0063] Calculate the estimated value Finishing

[0064] Right now

[0065] Then with formula y x =y″ x -y′ x =a+bx+cx 2 +ε x After comparison, the estimated values of the quadratic regression coefficients (a, b, c) are obtained. in

[0066] The method for correcting Beidou and the crystal oscillator second clock based on differential observation and regression equation model, wherein in step 3, the estimated cumulative error between the crystal oscillator second clock and the universal time is calculated based on the current estimated value of the regression coefficient, and then the compensation value for the next correction of the crystal oscillator second clock is calculated, and then the compensation value is added to the frequency of the crystal oscillator signal to obtain the comparison value for the next correction of the crystal oscillator second clock, includes the following process:

[0067] According to the estimated value of the regression coefficient of the regression equation model and Get the estimated value of the cumulative error between the next (n+1) crystal oscillator second clock and the international standard time

[0068]

[0069] The (n+1)th compensation value is calculated based on the cumulative error estimate:

[0070]

[0071] In order to make the compensation value an integer, Round off to the nearest integer and record as: Where R is the rounding symbol, the compensation value of the (n+1)th crystal oscillator second clock is:

[0072]

[0073] Then the comparison value S of (n+1) times n+1 For S n+1 =f0+c n+1 .

[0074] The method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model, in step three, counting the crystal oscillator signal, and when the count value is equal to the comparison value, outputting the signal as the correction crystal oscillator second clock is as follows:

[0075] The crystal oscillator signal is counted by the counter. When the count result of the counter is equal to the current comparison value, the frequency divider circuit outputs a high level signal. When the frequency divider circuit outputs a high level signal, the counter count value is cleared to restart the counting.

[0076] Compared with the prior art, the advantages of the present invention are:

[0077] 1. A differential observation model is used to eliminate the effects of receiver errors on satellite signals during transmission, thereby reducing the random drift error of the Beidou second clock and correcting the Beidou second clock. Using the corrected Beidou second clock signal as a parameter improves the fitting accuracy of the quadratic regression equation model for the deviation between the crystal oscillator second clock and the Beidou second clock, thereby improving the accuracy of the time signal.

[0078] 2. The present invention can perform online compensation for time errors and improve the accuracy of the output clock. The larger the number of samples for parameter estimation, the higher the fitting accuracy of the quadratic regression equation model of the deviation between the crystal oscillator second clock and the Beidou second clock, and the higher the accuracy of the output clock. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 This is a flow chart for correcting the generation of a crystal oscillator second clock signal according to the present invention;

[0080] Figure 2 Schematic diagram of the inter-station single difference measurement of the present invention. DETAILED DESCRIPTION

[0081] See also Figure 1 The method provided in this embodiment for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model includes the following steps:

[0082] Step 1: First, select a reference user as the common end. The reference user in this embodiment is based on the geographical location of all users who need to reduce the random error of the Beidou second clock as the selection range, and within this selection range, the user who is geographically closest to the center of the selection range is used as the reference user. The reference user is then used as the common end for measuring the relative clock deviation of Beidou timing, that is, other users within the selection range use the reference user as the reference for correcting the Beidou second clock, and at the locations of the reference user and the user who needs to reduce the random error, the same satellite is synchronously observed by satellite receivers to measure the relative deviation of the two users' receiver clocks. Then:

[0083] L1=ρ1+Cdt-CdT1+Trop-Ion+ξ1

[0084] L2=ρ2+Cdt-CdT2+Trop-Ion+ξ2

[0085] Where L is the known phase observation of the satellite by the user's receiver, ρ is the known geometric distance from the satellite to the receiver, dt is the satellite clock error, dT is the receiver clock error, Trop and Ion are the tropospheric and ionospheric delays, respectively, ξ is the observed noise, and C is the speed of light in vacuum. The subscripts 1 or 2 indicate the user number, for example, 1 represents the reference user serving as the public end, and 2 represents the user for which random error reduction is required.

[0086] Then the difference in observation values between two users, that is, the differential observation model, is: ΔL = Δρ - CΔdT + Δξ′

[0087] Where Δρ = ρ1 - ρ2, ΔdT = dT1 - dT2, and Δξ′ = ξ1 - ξ2. In the actual application of this embodiment, the geographical distance between the reference user and other users requiring correction does not exceed several hundred kilometers. Therefore, the values of Trop, Ion, and ξ are approximate and can be ignored.

[0088] Then, the user position coordinates are substituted into the differential observation model to obtain the relative receiver clock difference between the two user clocks:

[0089]

[0090] Then, the local time of the base user station receiver is used as the base time, and the receiver clock error is the difference between the local time of the receiver and the base time, so ΔT p =0, where ΔT p 、 are the reference user receiver clock error and the user receiver clock error, ΔdT PP1 is the clock difference between the reference user and the user's relative receiver.

[0091] Thus, the user receiver clock error is calculated This eliminates the receiver clock error from the BeiDou second clock's random drift error ε, which is composed of the receiver clock error, random errors, and satellite clock errors. This reduces the BeiDou second clock's random drift error ε. Since L and ρ change with satellite position, ΔdT is continuously calculated based on these changes, allowing for continuous correction of the BeiDou second clock.

[0092] Step 2: Establish a quadratic regression equation model for the deviation between the crystal oscillator second clock and the Beidou second clock. Since there is a deviation ε between the Beidou second clock and the international standard time UCT, and ε follows a normal distribution:

[0093] ε~N(0,σ 2 )

[0094] Where σ represents the standard deviation and N is the symbol for normal distribution.

[0095] Then we can know that the deviation between the xth second clock output by the Beidou second clock and the international standard time is μ′(x)=ε x , so the xth second clock output by the Beidou second clock corresponds to the international standard time y′ x for

[0096] y′ x =x-ε x ,x=1,2,...,n

[0097] Let the initial deviation between the zeroth second clock and the UTC be a in the crystal oscillator second clock sequence. The initial deviation between the zeroth second clock cycle and the UTC second cycle is R. The drift of each second interval is d. Then the deviation between the xth second clock cycle and the UTC second cycle is ΔT x for:

[0098] ΔT x =R+dx

[0099] Then the deviation μ″(x) between the xth second clock output by the crystal oscillator second clock and the international standard time is:

[0100]

[0101] Here we introduce two intermediate variables b and c to simplify the expression.

[0102] Then the time error μ″(x) of the x-th crystal oscillator second clock is converted to:

[0103] μ″(x)=a+bx+cx 2

[0104] Then the crystal oscillator second clock outputs the international standard time y" corresponding to the xth second clock x for:

[0105] y″ x =x+a+bx+cx 2 ,x=1,2,...,n

[0106] The quadratic regression analysis model y of the deviation between the crystal oscillator second clock and the Beidou second clock is obtained x for:

[0107] y x =y″ x -y′ x =a+bx+cx 2 +ε x ,x=1,2...,n。

[0108] Next, a first corrected crystal oscillator second clock signal is generated based on the frequency of the crystal oscillator signal. In this embodiment, the crystal oscillator signal is counted by a counter. When the count result of the counter is equal to the frequency value of the crystal oscillator signal, a high-level signal is output by the frequency dividing circuit as the first corrected crystal oscillator second clock signal.

[0109] Step 3: Compare the phases of the corrected crystal oscillator second clock and the corrected Beidou second clock. This phase comparison is performed to determine the order of appearance of the two signals through the phase difference, thereby determining the positive or negative value of the random drift error. Then, a high-frequency oscillating counting pulse signal is applied to the counter. The counter counts the number of counting pulses in the time interval between the two signals to obtain the absolute value reflecting the random drift error value, thereby obtaining the random drift error value φ. x Next, calculate the current deviation Y between the Beidou second clock and the crystal oscillator second clock. x for:

[0110]

[0111] where c i is the compensation value of the crystal oscillator error. Here, when Y is calculated for the first time x When the compensation value of crystal oscillator error is c i Take 0, that is, directly use the random drift error value φ x As Y x Starting from the second calculation, add the calculated compensation value c i to Y x in the calculation process.

[0112] Then according to the estimated value of the regression coefficient of the regression equation model and Get the estimated value of the cumulative error between the next (n+1) crystal oscillator second clock and the international standard time

[0113]

[0114] The (n+1)th compensation value is calculated based on the cumulative error estimate:

[0115]

[0116] In order to make the compensation value an integer, Round off to the nearest integer and record as: Where R is the rounding symbol, the compensation value of the (n+1)th crystal oscillator second clock is:

[0117]

[0118] Then the comparison value S of (n+1) timesn+1 For S n+1 =f0+c n+1 .

[0119] Next, the counter counts the crystal oscillator signal. When the counter's count equals the current comparison value, the frequency divider circuit outputs a high-level signal. When the frequency divider circuit outputs a high-level signal, the counter value is reset to zero and the count is restarted. Step 3 is repeated, continuously correcting the crystal oscillator's second clock.

Claims

1. A method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model, characterized in that: The following steps are involved: Step 1: Select a reference user as the common end and establish a differential observation model between the common end and other users to reduce the random drift error of the Beidou second clock, thereby continuously correcting the Beidou second clock; Step 2: Establish a quadratic regression equation model of the deviation between the crystal oscillator second clock and the Beidou second clock, and generate a first corrected crystal oscillator second clock signal based on the frequency of the crystal oscillator signal; Step 3: First, compare the phase of the corrected crystal oscillator second clock with the corrected Beidou second clock to obtain the current deviation including the random drift error of the Beidou second clock and the accumulated error of the crystal oscillator second clock: Including the following process, Compare the phase difference between the Beidou second clock signal and the current corrected crystal second clock signal to determine the order of appearance of the two signals, so as to determine the positive or negative value of the random drift error. Apply a high-frequency oscillation counting pulse signal to the counter, and use the counter to count the number of counting pulses in the time interval between the two signals to obtain the absolute value used to reflect the random drift error value, thereby obtaining the random drift error value φ. x ; Then calculate the current deviation Y x for: where c i is the compensation value of the crystal oscillator error. x When c i Take 0; Then, the current estimated value of the regression coefficient of the regression equation model is calculated in real time according to the current deviation; Then, based on the current estimated value of the regression coefficient, the estimated cumulative error between the crystal oscillator second clock and the universal standard time is calculated, and then the compensation value for the next correction of the crystal oscillator second clock is calculated; Then add the compensation value to the frequency of the crystal oscillator signal to obtain the comparison value for the next correction of the crystal oscillator second clock. Next, count the crystal oscillator signal. When the count value is equal to the comparison value, output it as a signal for correcting the crystal oscillator second clock, and re-execute step three, thereby continuously correcting the crystal oscillator second clock.

2. The method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model according to claim 1, characterized in that: In step 1, reducing the random drift error of the Beidou second clock includes the following steps: A reference user is selected as the common end for measuring the relative clock bias of the Beidou second clock. At the locations of the reference user and the user whose random error needs to be reduced, satellite receivers are used to synchronously observe the same satellite to measure the relative bias of the two user receiver clocks. L1=ρ1+Cdt-CdT1+Trop-Ion+ξ1 L2=ρ2+Cdt-CdT2+Trop-Ion+ξ2 Where L is the known phase observation value of the satellite by the user's receiver, ρ is the known geometric distance from the satellite to the receiver; dt is the satellite clock error; dT is the receiver clock error; Trop and Ion are the tropospheric delay and ionospheric delay respectively; ξ is the other noise of the observation value; C is the speed of light in vacuum; the subscript number 1 or 2 indicates the user number; The difference between the observation values, that is, the differential observation model, is: ΔL = Δρ - CΔdT + Δξ′ Among them, Δρ=ρ1-ρ2, ΔdT=dT1-dT2; Δξ′=ξ1-ξ2, which are ignored in the calculation; Substituting the user's position coordinates, the relative receiver clock difference between the two user clocks is obtained as: The local time of the base user station receiver is used as the base time. The receiver clock error is the difference between the local time of the receiver and the base time. Then ΔT p =0, where ΔT p 、 are the reference user receiver clock error and the user receiver clock error, ΔdT PP1 is the clock difference between the reference user and the user's relative receiver; Thus the user receiver clock error is calculated That is, it can eliminate the receiver clock error in the Beidou second clock random drift error ε, which is composed of the receiver clock error, accidental error and satellite clock error, thereby reducing the Beidou second clock random drift error ε.

3. The method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model according to claim 2, characterized in that: The benchmark user is selected based on the geographical location of all users who need to reduce the random error of Beidou timing, and the user geographically closest to the center within the selected range is selected as the benchmark user.

4. The method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model according to claim 1, characterized in that: In the step 2, the quadratic regression equation model is established by the following steps: Based on the deviation ε between the Beidou second clock and the international standard time UCT, and ε follows a normal distribution: ε~N(0,σ 2 ) Where σ represents the standard deviation and N is the symbol for normal distribution; Then the deviation between the xth second clock output by the Beidou second clock and the international standard time is μ′(x)=ε x Therefore, the international standard time y′ corresponding to the xth second clock output by the Beidou second clock is x for y′ x =x-ε x ,x=1.2,...,n In addition, the initial deviation between the zeroth second clock and the international standard time in the crystal oscillator second clock sequence is a; the initial deviation between the zeroth second clock cycle and the international standard time second cycle is R; the drift of each second time interval is d; then the deviation between the xth second clock cycle and the international standard time second cycle ΔT x for: ΔT x =R+dx The deviation μ″(x) between the xth second clock output by the crystal oscillator second clock and the international standard time is: remember Then the time error μ″(x) of the x-th crystal oscillator second clock is recorded as: μ″(x)=a+bx+cx 2 The crystal oscillator second clock outputs the international standard time y corresponding to the xth second clock x "for: y″ x =x+a+bx+cx 2 ,x=1,2,...,n The quadratic regression analysis model y of the deviation between the crystal oscillator second clock and the Beidou second clock is obtained x for: and x =y″ x -and' x =a+bx+cx 2 +ε x ,x=1,2...,n。 5. The method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model according to claim 4, characterized in that: In the step 2, the first corrected crystal oscillator second clock signal is generated based on the frequency of the crystal oscillator signal. The crystal oscillator signal is counted by a counter. When the counting result of the counter is equal to the frequency value of the crystal oscillator signal, the frequency dividing circuit outputs a high-level signal as the first corrected crystal oscillator second clock signal.

6. The method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model according to claim 5, characterized in that: In step 3, obtaining the current estimated value of the regression coefficient of the regression equation model in real time based on the current deviation includes the following process: The coefficients a, b, and c in the quadratic regression analysis model are estimated by least squares. Since the independent variable x of the quadratic regression model is the deviation Y between the Beidou second clock and the crystal oscillator second clock x The time series X of the constructed sequence Y is: 1, 2, 3, 4,...,x,...,n And the independent variable x is an equally spaced value. Use orthogonal polynomial analysis to select a set of orthogonal polynomials: in for: Then the regression equation becomes: The estimated values of coefficients b0, b1, and b2 are: where Y x Obtained from the deviation between the Beidou second clock and the crystal oscillator second clock, x = 1, 2, 3, ..., n; Calculate the estimated value Finishing Right now Then with formula y x =y x ″-y x ′=a+bx+cx 2 +ε x After comparison, the estimated values of the quadratic regression coefficients (a, b, c) are obtained. in 7. The method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model according to claim 6, characterized in that: In the above step 3, the estimated cumulative error between the crystal oscillator second clock and the international standard time is calculated based on the current estimated value of the regression coefficient, and then the compensation value for the next correction of the crystal oscillator second clock is calculated. Then, the compensation value is added to the frequency of the crystal oscillator signal to obtain the comparison value for the next correction of the crystal oscillator second clock. The following processes are included: According to the estimated value of the regression coefficient of the regression equation model and Get the estimated value of the cumulative error between the next (n+1) crystal oscillator second clock and the international standard time The (n+1)th compensation value is calculated based on the cumulative error estimate: In order to make the compensation value an integer, Round off to the nearest integer and record as: Where R is the rounding symbol, the compensation value of the (n+1)th crystal oscillator second clock is: Then the comparison value S of (n+1) times n+1 For S n+1 =f0+c n+1 .

8. The method for correcting Beidou and crystal oscillator second clocks based on differential observation and regression equation model according to claim 7, characterized in that: In step 3, the crystal oscillator signal is counted, and when the count value is equal to the comparison value, the process of outputting the signal as the correction crystal oscillator second clock is as follows: The crystal oscillator signal is counted by the counter. When the counting result of the counter is equal to the current comparison value, a high-level signal is output by the frequency dividing circuit. When the frequency dividing circuit outputs a high-level signal, the counter count value is cleared to restart counting.

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