Inter-station time synchronization method for short-time low-signal-to-noise-ratio GPS common-view clock difference data

Abstract

The invention discloses an inter-station time synchronization method for short-time low-signal-to-noise-ratio GPS common-view clock error data, and the method comprises the steps: firstly carrying out the linear interpolation and expansion of an REFGPS through an SRGPS, and solving a clock error estimation error caused by a small number of fitting points when the observation time is short; then, linear weighted least square fitting is carried out on the expanded REFGPS by using DSG, and the problems of large fluctuation of measurement data and poor clock difference estimation precision are further solved. When the number of GPS clock error data points is small and the fluctuation of the data quality is large, the robustness and the precision of the clock error estimation result of the method provided by the invention are remarkably improved.

Description

Technical Field

[0001] The invention belongs to the technical field of aerospace measurement and control, and in particular relates to an inter-station time synchronization method for short-term low signal-to-noise ratio GPS common view clock difference data. Background Art

[0002] The premise of deep space station networking is to achieve high-precision time and frequency synchronization. At present, most of my country's deep space stations use GPS common view technology to achieve high-precision time synchronization between stations. GPS common view technology was proposed by the National Institute of Standards and Technology (NIST) in the early 1990s. It achieves time and frequency synchronization between atomic clocks in any two places on the earth by simultaneously receiving time signals from the same GPS satellite for time and frequency comparison. GPS common view method is currently one of the most cost-effective methods for long-distance clock difference comparison, and the transmission uncertainty can reach nanoseconds. Therefore, it is used by many international time comparison institutions as one of the means of time synchronization between stations.

[0003] Table 1 GGTTS standard data format

[0004]

[0005]

[0006] In order to standardize GPS common view technology, the International Consultative Committee on Time and Frequency (CCTF) presided over the development of the GPS common view technology standard data format (GGTTS GPSData Format), which contains clock error measurement data parameters as shown in Table 1. Existing inter-station time synchronization methods based on GPS common view often only achieve inter-station time synchronization by fitting REFGPS. This type of method has the problem of poor clock error estimation accuracy when the observation time is short and the measurement data quality fluctuates greatly. Summary of the invention

[0007] The purpose of the present invention is to provide an inter-station time synchronization method for short-term low signal-to-noise ratio GPS common view clock error data, which solves the problem of poor clock error estimation accuracy in existing methods when the observation time is short and the measurement data quality fluctuates greatly.

[0008] The technical solution adopted by the present invention is: a method for inter-station time synchronization for short-term low signal-to-noise ratio GPS common view clock difference data, comprising the following steps:

[0009] Step 1: Read the common view data of the two deep space stations respectively according to the GGTTS data format and perform preprocessing;

[0010] Step 2: Find the data time when the two deep space stations simultaneously observe the same navigation satellite, and use the slope SRGPS to interpolate and expand the REFGPS at the corresponding time;

[0011] Step 3: Subtract the interpolated and expanded REFGPS of the two deep space stations to obtain the clock difference of the two deep space stations, and calculate the variance of the clock difference between the two deep space stations according to the variance of the corresponding time of the two deep space stations;

[0012] Step 4: Use the variance of the inter-station clock error to eliminate outliers in the clock errors of the two deep space stations;

[0013] Step 5: Based on the clock differences of the two deep space stations after outliers are eliminated, the optimal estimates of the clock differences and clock drift are obtained using the weighted least squares criterion;

[0014] Step 6: Obtain the clock difference at the specified time by linear extrapolation.

[0015] The present invention is also characterized in that:

[0016] The preprocessing in step 1 is to perform tropospheric and ionospheric delay corrections and remove data with elevation angles below 15°.

[0017] The interpolation expansion process in step 2 is:

[0018]

[0019] In the formula, and are the GPS clock error data after interpolation and expansion of the two deep space stations A and B, t k,l t k The interpolation time series corresponding to the moment data, after interpolation, the continuous tracking data is expanded from the previous 1 point to L+1 points every 780 seconds.

[0020] In step 3, the clock difference y(t k,l ), expressed as:

[0021]

[0022] In step 3, the variance σ of the inter-station clock error is calculated by the following formula (5): 2 (y(t k,l )):

[0023]

[0024] Step 4 is as follows: Based on the 3σ point-cutting principle, the variance σ of the inter-station clock difference is used 2 (y(t k,l )) for the clock difference y(t k,l ) to eliminate 3σ outliers.

[0025] The 3σ point elimination principle is to convert the clock difference y(t k,l ) was used for linear fitting, and data points with fitting residuals greater than 3 times σ were removed as outliers.

[0026] Step 5 specifically includes the following steps:

[0027] Step 5.1: Use the linear model to remove the outliers and calculate the clock difference y(t k,l ) for modeling:

[0028] y(t k,l )=at k,l +b+n k,l (4)

[0029] In the formula, a is the linear clock drift, b is t k,l = clock difference at 0, n k,l is the observation error;

[0030] Step 5.2: Write equation (4) in matrix form:

[0031] y=Hx+n (6)

[0032] Where:

[0033] y=[y1,…,y k , …, y K ] T (7)

[0034] y k =[y(t k,0 ),…,y(t k,l ),…,y(t k,L )] (8)

[0035]

[0036] t k =[t k,0 ,…,t k,l ,…,t k,L ] (10)

[0037] 1 1×K(L+1) is a 1×K(L+1)-dimensional all-one matrix, x=[a,b] T is the vector to be estimated consisting of clock error and clock drift, and n is the vector consisting of observation errors. The optimal estimate of clock error and clock drift is obtained by weighted least squares method:

[0038]

[0039] In the formula, Q y= Cov(n), which is the covariance matrix of the inter-station clock observation error, and is based on σ 2 (y(t k,l )) is a diagonal matrix with diagonal elements.

[0040] The beneficial effects of the present invention are as follows: the inter-station time synchronization method for short-term low signal-to-noise ratio GPS common view clock difference data of the present invention first uses SRGPS to perform linear interpolation and expansion on REFGPS to solve the clock difference estimation error caused by the small number of fitting points when the observation time is short; then, DSG is used to perform linear weighted least squares fitting on the expanded REFGPS to further solve the problem of poor clock difference estimation accuracy due to large fluctuations in measurement data. When the number of GPS clock difference data points is small and its data quality fluctuates greatly, the robustness and accuracy of the clock difference estimation results of the method provided by the present invention are significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flow chart of the inter-station time synchronization method for short-term low signal-to-noise ratio GPS common view clock difference data of the present invention. DETAILED DESCRIPTION

[0042] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0043] Example 1

[0044] The present invention provides an inter-station time synchronization method for short-term low signal-to-noise ratio GPS common view clock error data, which fully exploits the slope (SRGPS) and root mean square error (DSG) information contained in the GGTTS standard data format, and solves the problem of poor clock error estimation accuracy in existing methods when the observation time is short and the measurement data quality fluctuates greatly.

[0045] Example 2

[0046] The present invention provides an inter-station time synchronization method for short-term low signal-to-noise ratio GPS common view clock difference data. Firstly, SRGPS is used to perform linear interpolation and expansion on REFGPS to solve the clock difference estimation error caused by the small number of fitting points when the observation time is short; then, DSG is used to perform linear weighted least squares fitting on the expanded REFGPS, thereby achieving the purpose of solving the problem of poor clock difference estimation accuracy due to large fluctuations in measurement data, and effectively improving the time synchronization accuracy when short-term observations and clock difference data have poor quality.

[0047] Example 3

[0048] The present invention provides an inter-station time synchronization method for short-term low signal-to-noise ratio GPS common view clock difference data. Based on Example 2, the specific method of linearly interpolating and expanding REFGPS using SRGPS is as follows:

[0049] Taking into account REFGPS A (t k ) and REFGPS B (t k ) is the midpoint value of the linear fit of 780 seconds of continuous tracking data, using only REFGPS A (t k ) and REFGPS B (t k ) cannot represent the full picture of the data, so the slope information SRGPS is first used A (t k ) and SRGPS B (t k ) to perform linear interpolation. The specific interpolation process is as follows:

[0050]

[0051] In the formula, and are the GPS clock error data after interpolation and expansion of the two deep space stations A and B, t k,l t k The interpolation time series corresponding to the moment data, after interpolation, the continuous tracking data is expanded from the previous 1 point to L+1 points every 780 seconds.

[0052] Example 4

[0053] The present invention provides a method for inter-station time synchronization for short-term low signal-to-noise ratio GPS common view clock difference data. Based on Example 2, the specific method of using DSG to perform linear weighted least squares fitting on the expanded REFGPS is as follows:

[0054] When the observation time is short, a linear model can be used to model the clock difference data between two stations:

[0055] y(t k,l )=at k,l +b+n k,l (4)

[0056] In the formula, y(t k,l ) indicates that two deep space stations A and B are at t k,l The station clock difference at the time is In physical terms, a is the linear clock drift, b is t k,l = clock difference at 0, n k,l is y(t k,l ) observation error. Because stations A and B receive and process GPS signals independently, REFGPS A (t k ) and REFGPS B (tk ) are independent, so we can calculate y(t k,l ) is:

[0057]

[0058] Then we write formula (4) into matrix form:

[0059] y=Hx+n (6)

[0060] Where:

[0061] y=[y1,…,y k , …, y K ] T (7)

[0062] y k =[y(t k,0 ),…,y(t k,l ),…,y(t k,L )] (8)

[0063]

[0064] t k =[t k,0 ,…,t k,l ,…,t k,L ] (10)

[0065] 1 1×K(L+1) is a 1×K(L+1)-dimensional all-one matrix, x=[a,b] T is the vector to be estimated consisting of clock error and clock drift, and n is the vector consisting of observation errors. Based on the weighted least squares estimation, the optimal estimate of clock error and clock drift can be obtained as:

[0066]

[0067] In the formula, Q y = Cov(n), is the covariance matrix of the inter-station clock observation error, and is the square root of 2 (y(t k,l )) is a diagonal matrix with diagonal elements.

[0068] Example 5

[0069] The present invention provides a method for inter-station time synchronization for short-term low signal-to-noise ratio GPS common view clock difference data, such as Figure 1 As shown, the specific steps include:

[0070] Step 1: Read the common view data of the two deep space stations respectively according to the GGTTS data format, perform tropospheric and ionospheric delay corrections, and remove data with elevation angles below 15°;

[0071] Step 2: Find the data time when the two deep space stations simultaneously observe the same navigation satellite, and use the slope SRGPS to interpolate and expand the REFGPS at the corresponding time. The interpolation and expansion process is:

[0072]

[0073]

[0074] In the formula, and are the GPS clock error data after interpolation and expansion of the two deep space stations A and B, t k,l t k The interpolation time series corresponding to the moment data, after interpolation, the continuous tracking data is expanded from the previous 1 point to L+1 points every 780 seconds;

[0075] Step 3: Subtract the interpolated and expanded REFGPS of the two deep space stations to obtain the clock difference of the two deep space stations The variance of the clock error between the two deep space stations is calculated based on the variance of the corresponding time between the two deep space stations. 2 (y(t k,l )):

[0076]

[0077] Step 4: Substitute the clock difference y(t k,l ) to perform linear fitting, and remove data points with fitting residuals greater than 3 times σ as outliers;

[0078] Step 5: Obtain the optimal estimate of the clock error and clock drift based on the clock errors of the two deep space stations after outliers are eliminated using the weighted least squares criterion; specifically, the following steps are included:

[0079] Step 5.1: Use the linear model to remove the outliers and calculate the clock difference y(t k,l ) for modeling:

[0080] y(t k,l )=at k,l +b+n k,l (4)

[0081] In the formula, a is the linear clock drift, b is t k,l = clock difference at 0, n k,l is the observation error;

[0082] Step 5.2: Write equation (4) in matrix form:

[0083] y=Hx+n (6)

[0084] Where:

[0085] y=[y1,…,y k , …, y K ] T (7)

[0086] y k =[y(t k,0 ),…,y(t k,l ),…,y(t k,L )] (8)

[0087]

[0088] t k =[t k,0 ,…,t k,l ,…,t k,L ] (10)

[0089] 1 1×K(L+1) is a 1×K(L+1)-dimensional all-one matrix, x=[a,b] T is the vector to be estimated consisting of clock error and clock drift, and n is the vector consisting of observation errors. The optimal estimate of clock error and clock drift is obtained by weighted least squares method:

[0090]

[0091] In the formula, Q y = Cov(n), which is the covariance matrix of the inter-station clock observation error, and is based on σ 2 (y(t k,l )) is a diagonal matrix with diagonal elements;

[0092] Step 6: Obtain the clock difference at the specified time by linear extrapolation.

[0093] Example 6

[0094] The actual GGTTS data generated by the common-view receivers of the two deep space stations are used. The position coordinates of the two stations in the ground-fixed system are (-2872638, 3331395, 4603413) and (1150059, 4870668, 3943036), and the data arc is from 0:00 on November 5, 2020 to 12:00 on November 6, 2020, Beijing time.

[0095] 1) Read the common view data of the two stations respectively according to the GGTTS data format, make tropospheric and ionospheric delay corrections, and remove abnormal data such as data with elevation angles below 15° to obtain standard data;

[0096] 2) Find the data time when the two stations simultaneously observe the same navigation satellite, and use the slope SRGPS to interpolate and expand the REFGPS at the corresponding time;

[0097] 3) Subtract the interpolated and expanded REFGPS of the two stations to obtain the clock difference between the two stations, and calculate the variance of the clock difference between the two stations according to the variance of the corresponding time of the two stations as σ 2 =DSG A 2 +DSG B 2 ;

[0098] 4) Perform a preliminary linear fit on the clock difference data between the two stations, and remove data points with fitting residuals greater than 3 times σ as outliers;

[0099] 5) Based on the inter-station clock error data after outliers are removed, the weighted least squares criterion is used to obtain the optimal estimate of clock error and clock drift;

[0100] 6) Obtain the clock error at the specified time by linear extrapolation.

Claims

1. A method for inter-station time synchronization based on short-term low signal-to-noise ratio GPS common view clock difference data, characterized in that: The following steps are involved: Step 1: Read the common view data of the two deep space stations respectively according to the GGTTS data format and perform preprocessing; Step 2: Find the data time when the two deep space stations simultaneously observe the same navigation satellite, and use the slope SRGPS to interpolate and expand the REFGPS at the corresponding time; Step 3: Subtract the interpolated and expanded REFGPS of the two deep space stations to obtain the clock difference of the two deep space stations, and calculate the variance of the clock difference between the two deep space stations according to the variance of the corresponding time of the two deep space stations; Step 4: Use the variance of the inter-station clock error to eliminate outliers in the clock errors of the two deep space stations; Step 5: Based on the clock differences of the two deep space stations after outliers are eliminated, the optimal estimates of the clock differences and clock drift are obtained using the weighted least squares criterion; Step 6: Obtain the clock difference at the specified time by linear extrapolation.

2. The inter-station time synchronization method for short-term low signal-to-noise ratio GPS common view clock difference data as claimed in claim 1, characterized in that: The preprocessing in step 1 is to perform tropospheric and ionospheric delay corrections and remove data with elevation angles lower than 15°.

3. The inter-station time synchronization method for short-term low signal-to-noise ratio GPS common view clock difference data as claimed in claim 1, characterized in that: The interpolation expansion process in step 2 is: In the formula, and are the GPS clock error data after interpolation and expansion of the two deep space stations A and B, t k,l t k The interpolation time series corresponding to the moment data, after interpolation, the continuous tracking data is expanded from the previous 1 point to L+1 points every 780 seconds.

4. The inter-station time synchronization method for short-term low signal-to-noise ratio GPS common view clock difference data as claimed in claim 3, characterized in that: In step 3, the clock difference y(t k,l ), expressed as:

5. The inter-station time synchronization method for short-term low signal-to-noise ratio GPS common view clock difference data as claimed in claim 4, characterized in that: In step 3, the variance σ of the inter-station clock error is calculated by the following formula (5): 2 (y(t k,l )):

6. The inter-station time synchronization method for short-term low signal-to-noise ratio GPS common view clock difference data as claimed in claim 5, characterized in that: The step 4 is specifically as follows: based on the 3σ point elimination principle, the variance σ of the clock difference between stations is used 2 (y(t k,l )) for the clock difference y(t k,l ) to eliminate 3σ outliers.

7. The inter-station time synchronization method for short-term low signal-to-noise ratio GPS common view clock difference data as claimed in claim 6, characterized in that: The 3σ point elimination principle is to convert the clock difference y(t k,l ) was used for linear fitting, and data points with fitting residuals greater than 3 times σ were removed as outliers.

8. The inter-station time synchronization method for short-term low signal-to-noise ratio GPS common view clock difference data as claimed in claim 6, characterized in that: The step 5 specifically comprises the following steps: Step 5.1: Use the linear model to remove the outliers and calculate the clock difference y(t k,l ) for modeling: y(t k,l )=at k,l +b+n k,l (4) In the formula, a is the linear clock drift, b is t k,l = clock difference at 0, n k,l is the observation error; Step 5.2: Write equation (4) in matrix form: y=Hx+n (6) Where: y=[y1,…,y k ,…,y K ] T (7) and k =[y(t k,0 ),…,and(t k,l ),…,and(t k,L )] (8) t k =[t k,0 ,…,t k,l ,…,t k,L ] (10) 1 1×K(L+1) is a 1×K(L+1)-dimensional all-one matrix, x=[a,b] T is the vector to be estimated consisting of clock error and clock drift, and n is the vector consisting of observation errors. The optimal estimate of clock error and clock drift is obtained by weighted least squares method: In the formula, Q y = Cov(n), which is the covariance matrix of the inter-station clock observation error, and is based on σ 2 (y(t k,l )) is a diagonal matrix with diagonal elements.

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