Satellite two-way and gps different time frequency transfer link fusion method

Abstract

A satellite bidirectional and GPS different time frequency transmission link fusion method, data preprocessing, obtaining link data set W and link data set G; respectively establishing state model and measurement model of link data set W and link data set G; using wavelet decomposition method to scale decomposition of state model and measurement model of link data set W and link data set G, link data set W and link data set G are decomposed to the same resolution, obtaining state model and measurement model of link data set W and link data set G on low resolution; Kalman filtering fusion is carried out on link data set W and link data set G at the same resolution; the Kalman filtering fusion result is obtained by using wavelet decomposition coefficient reconstruction method to obtain the original data fusion result; judge the reduction and stability of the fused link noise.

Description

Technical Field

[0001] This invention relates to the field of time and frequency data processing technology, specifically to a method for fusing different time and frequency transmission links of satellite two-way and GPS. Background Technology

[0002] The Bureau of International Des Poidset Measures (BIPM) calculates atomic time using a weighted algorithm across more than 420 atomic clocks in over 80 timekeeping laboratories in various countries. This requires an accurate time transfer link connecting these atomic clocks. Two-way satellite time-frequency transfer (TWSTFT) and GPS Precise Point Positioning (GPSPPP) time transfer are the two main technologies currently used for Coordinated Universal Time (UTC) generation. Major timekeeping laboratories operate both technologies simultaneously. TWSTFT is a two-way method used for UTC generation since 1999, where two ground stations transmit time signals via a geostationary satellite. TWSTFT offers advantages in high accuracy and long-term stability for time transfer. However, it has low resolution and is susceptible to diurnal effects, which are a major source of error in TWSTFT links. GPS PPP is a one-way method that uses precise satellite orbit and clock differences generated by the International GNSS (Global Navigation Satellite System) to obtain the difference between the local clock and the International GNSS Service System (IGS) time. GPSPPP offers advantages in high short-term stability and high resolution. Therefore, the integration of TWSTFT and GPS PPP is an ideal solution for effectively improving the quality of the UTC time link.

[0003] With the construction of various GNSS systems, UTC time transfer networks have become increasingly redundant. Simultaneously, the development of high-precision time and frequency standards, such as optical clocks and fountain clocks, places increasingly higher demands on the accuracy of long-distance time links. How to fully utilize redundant links to improve the accuracy and stability of time transfer has always been a key research focus. Current research mainly includes weighted averaging of TWSTFT and GPS PPP data; fusing TWSTFT and GPS PPP data based on the Vondrak-Cepeck fusion smoothing algorithm; and using TWSTFT data as an additional observation equation for GPS common-view least squares. These research results primarily focus on data fusion at a single scale. However, in practice, comparison data from different time transfer link systems have different resolutions, and the noise characteristics of different time transfer links vary, typically exhibiting different types of noise in different frequency bands. It is necessary to simultaneously reduce the influence of multiple types of noise to improve the accuracy and stability of the fused comparison results. Therefore, it is necessary to solve multi-resolution fusion techniques while reducing the influence of different types of noise in different frequency bands, so as to better utilize the complementary information of data at different resolutions and achieve better fusion results. Therefore, a fusion method for different time and frequency transfer links of TWSTFT and GPS PPP needs to be proposed. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a method for fusing satellite two-way and GPS time-frequency transmission links with good time-frequency transmission performance, high accuracy and high stability.

[0005] The technical solution adopted to solve the above-mentioned technical problems is: a method for fusing satellite two-way and GPS different time frequency transmission links, including the following steps:

[0006] Step 1. Data Preprocessing

[0007] Every 30 minutes, the satellite two-way time-frequency transfer link data TWSTFT is sampled to obtain the link dataset W. At the same time, every 5 minutes, the GPS precise point positioning link data GPS PPP is sampled to obtain the link dataset G. The data in the link dataset W and the link dataset G are converted into nanoseconds respectively, and then the data integrity and outlier checks are performed.

[0008] Step 2. Establish the state model and measurement model for link dataset W and link dataset G respectively.

[0009] The state model of the link dataset W is:

[0010]

[0011]

[0012]

[0013] In the formula, Let a be the phase deviation of the data at time k in the link dataset W, where k is the time of data calculation and a is a constant. The frequency deviation of the data at time k in the link dataset W. Let T be the noise vector at time k in the state model of the link dataset W, and let T be the transpose sign.

[0014] The measurement model for the link dataset W is:

[0015]

[0016]

[0017] In the formula, For the measurement model of the link dataset W at time k, The observation error at time k is the measurement model of the link dataset W;

[0018] The state model of the link dataset G is as follows:

[0019]

[0020]

[0021]

[0022] In the formula, Let b be the phase deviation of the data at time k in the link dataset G, where b is a constant. The frequency deviation of the data at time k in the link dataset G. Let T be the noise vector at time k in the state model of the link dataset G, and let T be the transpose.

[0023] The measurement model for the link dataset G is as follows:

[0024]

[0025]

[0026] In the formula, For the measurement model of the link dataset G at time k, The observation error at time k in the measurement model of the link dataset G;

[0027] Step 3. Use wavelet decomposition to scale the state model and measurement model of the link dataset W and the state model and measurement model of the link dataset G, decompose the link dataset W and the link dataset G to the same resolution, and obtain the state model and measurement model of the link dataset W and the link dataset G at low resolution.

[0028] Step 4. At the same resolution, perform Kalman filtering fusion on the link dataset W and the link dataset G according to the following formula.

[0029]

[0030]

[0031]

[0032]

[0033]

[0034]

[0035] In the formula, For the one-step prediction result at time k, Φ k,k-1 Let k be the state transition matrix. This is the fusion result at time k-1. For the fusion result at time k, P k / k-1 Let P be the one-step prediction covariance matrix at time k. k-1 Let Q be the error covariance matrix at time k-1. k-1 Let k be the model noise covariance matrix at time k-1. The Kalman filter gain matrix of the link dataset W. For the observations of the measurement model of the link dataset W, Let G be the Kalman filter gain matrix of the link dataset G. For the observations of the measurement model of dataset G, P k Let be the error covariance matrix at time k. Let W be the covariance matrix of the link dataset W. Let I be the covariance matrix of the link dataset G, and let I be the identity matrix.

[0036] Step 5. Use the wavelet decomposition coefficient reconstruction method to reconstruct the Kalman filter fusion result obtained in Step 4 to obtain the fusion result of the original data, namely the fusion result of the original TWSTFT link and GPS PPP link data;

[0037] The wavelet decomposition coefficient reconstruction method is as follows:

[0038]

[0039] In the formula, X j (m) represents the m-th scaling coefficient, j represents the scale, m represents the order of the scaling coefficients, R represents a positive integer, t represents the order of the wavelet coefficients, h() represents the first filter, g() represents the second filter, and Y j-1 (t) represents the t-th wavelet coefficient;

[0040] Step 6. Obtain the gain of the fused TWSTFT link and GPS PPP link according to the following formula, which is used to determine the reduction of link noise after fusion;

[0041] Q=(σ a -σ b ) / σ a

[0042] In the formula, σ a It is the standard deviation of the original TWSTFT link and GPS PPP link data, σ b is the standard deviation of the fused data, where a is a constant and b is a constant;

[0043] Step 7. Obtain the Allan variance of the fused TWSTFT link and GPS PPP link according to the following formula, which is used to determine the stability of the fused link;

[0044]

[0045] p2 = M + 1 - 2n

[0046] In the formula, Let x be the Allan variance, y be a constant, and x be the variance. k+2n Let x be the clock difference at time k+2n. k+n Let x be the clock difference at time k+n. k Let k be the clock difference at time k, M be the number of measurements, n be the sampling period, and τ0 be the basic sampling interval.

[0047] As a preferred technical solution, the wavelet decomposition method in step 3 is the Daubechies 2 wavelet decomposition method.

[0048] As a preferred technical solution, the data integrity verification method is as follows: based on the data comparison date, subtract the previous item from the later item to determine whether there is a jump. If there is a jump, the data is missing; otherwise, there is no missing data. For the missing data, the nearest neighbor difference method or linear interpolation method is used to supplement it.

[0049] The outlier detection method is as follows: the Wright criterion is used for detection, and the nearest neighbor difference method is used for interpolation and replacement.

[0050] The beneficial effects of this invention are as follows:

[0051] Based on the characteristics of different link datasets, this invention combines wavelet transform decomposition algorithm to decompose link data with different sampling rates to the same scale for fusion processing, thereby improving the reliability of time and frequency transmission compared to using data from only a single link.

[0052] When fusing different link datasets, this invention utilizes Kalman filtering to fuse data at the wavelet decomposition scale. The algorithm based on this invention simultaneously reduces the impact of multiple types of noise in the link data, thereby improving the short-term and long-term stability of the link data.

[0053] Finally, by analyzing the gain of the fused results relative to the link data, it was concluded that the fused link reduced the diurnal effect of link dataset W and the error of link dataset G. Compared to single link data, it improved the accuracy of time and frequency transmission. Attached Figure Description

[0054] Figure 1 This is a flowchart illustrating the present invention.

[0055] Figure 2 This is a diagram illustrating the organization of the wavelet three-scale decomposition of the link dataset W and the link dataset G in this invention.

[0056] Figure 3 This is a flowchart of the data fusion process between link datasets W and G based on Kalman filtering.

[0057] Figure 4 This is a comparison chart of the fusion results with TWSTFT and GPS PPP.

[0058] Figure 5 This is a comparison chart of the Allan bias of the fusion result with the Allan bias of TWSTFT and GPS PPP. Detailed Implementation

[0059] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, but the present invention is not limited to the following embodiments.

[0060] exist Figure 1 , 2 In section 3, the fusion method for satellite two-way and GPS different time-frequency transmission links in this embodiment is characterized by including the following steps:

[0061] Step 1. Data Preprocessing

[0062] Every 30 minutes, the satellite two-way time-frequency transfer link data TWSTFT is sampled to obtain the link dataset W. At the same time, every 5 minutes, the GPS precise point positioning link data GPS PPP is sampled to obtain the link dataset G. The data in the link dataset W and the link dataset G are converted into nanoseconds respectively, and then the data integrity and outlier checks are performed.

[0063] The data integrity verification method is as follows: based on the data comparison date, subtract the previous item from the next item to determine whether there is a jump. If there is a jump, the data is missing; otherwise, there is no missing data. For missing data, the nearest neighbor difference method or linear interpolation method is used to supplement it.

[0064] The outlier detection method employs the Wright criterion and uses nearest neighbor difference interpolation for replacement. Specifically, the link data is first fitted to obtain fitted values. Using the residual between the measured and fitted values ​​as the base value, the variance is calculated, and a standard value is obtained. If the outlier value is within t... j Moment, Satisfaction Form | X i (t j )-S i (t j )|>3σ,X i (t j ) for t j The measured value at time S i (t j ) for t j The fitted value at time t, where σ is the standard value, then X i (t j The detected outliers are then replaced by interpolation of the fitted values.

[0065] Step 2. Establish the state model and measurement model for link dataset W and link dataset G respectively.

[0066] The state model of the link dataset W is:

[0067]

[0068]

[0069]

[0070] In the formula, Let a be the phase deviation of the data at time k in the link dataset W, where k is the time of data calculation and a is a constant. The frequency deviation of the data at time k in the link dataset W. Let T be the noise vector at time k in the state model of the link dataset W, and let T be the transpose sign.

[0071] The measurement model for the link dataset W is:

[0072]

[0073]

[0074] In the formula, For the measurement model of the link dataset W at time k, The observation error at time k is the measurement model of the link dataset W;

[0075] The state model of the link dataset G is as follows:

[0076]

[0077]

[0078]

[0079] In the formula, Let b be the phase deviation of the data at time k in the link dataset G, where b is a constant. The frequency deviation of the data at time k in the link dataset G. Let T be the noise vector at time k in the state model of the link dataset G, and let T be the transpose.

[0080] The measurement model for the link dataset G is as follows:

[0081]

[0082]

[0083] In the formula, For the measurement model of the link dataset G at time k, The observation error at time k in the measurement model of the link dataset G;

[0084] Step 3. Use the Daubechies 2 wavelet decomposition method to scale the state model and measurement model of the link dataset W and the state model and measurement model of the link dataset G, decompose the link dataset W and the link dataset G to the same resolution, and obtain the state model and measurement model of the link dataset W and the state model and measurement model of the link dataset G at low resolution.

[0085] Step 4. At the same resolution, perform Kalman filtering fusion on the link dataset W and the link dataset G according to the following formula.

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] In the formula, For the one-step prediction result at time k, Φ k,k-1 Let k be the state transition matrix. This is the fusion result at time k-1. For the fusion result at time k, P k / k-1 Let P be the one-step prediction covariance matrix at time k. k-1 Let Q be the error covariance matrix at time k-1. k-1 Let k be the model noise covariance matrix at time k-1. The Kalman filter gain matrix of the link dataset W. For the observations of the measurement model of the link dataset W, Let G be the Kalman filter gain matrix of the link dataset G. For the observations of the measurement model of dataset G, P k Let be the error covariance matrix at time k. Let W be the covariance matrix of the link dataset W. Let I be the covariance matrix of the link dataset G, and let I be the identity matrix.

[0093] Step 5. Use the wavelet decomposition coefficient reconstruction method to reconstruct the Kalman filter fusion result obtained in Step 4 to obtain the fusion result of the original data, namely the fusion result of the original TWSTFT link and GPS PPP link data;

[0094] The wavelet decomposition coefficient reconstruction method is as follows:

[0095]

[0096] In the formula, X j (m) represents the m-th scaling coefficient, j represents the scale, m represents the order of the scaling coefficients, R represents a positive integer, t represents the order of the wavelet coefficients, h() represents the first filter, g() represents the second filter, and Y j-1 (t) represents the t-th wavelet coefficient;

[0097] Step 6. Obtain the gain of the fused TWSTFT link and GPS PPP link according to the following formula, which is used to determine the reduction of link noise after fusion;

[0098] Q=(σ a -σ b ) / σ a

[0099] In the formula, σ a It is the standard deviation of the original TWSTFT link and GPS PPP link data, σ b is the standard deviation of the fused data, where a is a constant and b is a constant;

[0100] Step 7. Obtain the Allan variance of the fused TWSTFT link and GPS PPP link according to the following formula, which is used to determine the stability of the fused link. The result is as follows: Figure 5 ;

[0101]

[0102] p2 = M + 1 - 2n

[0103] In the formula, Let x be the Allan variance, y be a constant, and x be the variance. k+2n Let x be the clock difference at time k+2n. k+n Let x be the clock difference at time k+n. k Let k be the clock difference at time k, M be the number of measurements, n be the sampling period, and τ0 be the basic sampling interval.

[0104] This invention utilizes Kalman filtering to fuse data at the wavelet decomposition scale when fusing different link datasets. This simultaneously reduces the impact of multiple types of noise in the link data, improving both short-term and long-term stability. Finally, the gain of the fused link data relative to the total link data shows that the fused link reduces the diurnal variation of link dataset W and the error of link dataset G. Figure 4 and Figure 5 Compared to single-link data, it improves the accuracy of time and frequency transmission.

Claims

1. A method for fusing satellite two-way and GPS transmission links at different time frequencies, characterized in that, Includes the following steps: Step 1. Data Preprocessing Every 30 minutes, the satellite two-way time-frequency transfer link data TWSTFT is sampled to obtain the link dataset W. At the same time, every 5 minutes, the GPS precise point positioning link data GPS PPP is sampled to obtain the link dataset G. The data in the link dataset W and the link dataset G are converted into nanoseconds respectively, and then the data integrity and outlier checks are performed. Step 2. Establish the state model and measurement model for link dataset W and link dataset G respectively. The state model of link dataset W is as follows: In the formula, Let a be the phase deviation of the data at time k in the link dataset W, where k is the time of data calculation and a is a constant. The frequency deviation of the data at time k in the link dataset W. Let T be the noise vector at time k in the state model of the link dataset W, and let T be the transpose sign. The measurement model for the link dataset W is as follows: In the formula, For the measurement model of the link dataset W at time k, The observation error at time k is the measurement model of the link dataset W; The state model of the link dataset G is as follows: In the formula, Let b be the phase deviation of the data at time k in the link dataset G, where b is a constant. The frequency deviation of the data at time k in the link dataset G. Let T be the noise vector at time k in the state model of the link dataset G, and let T be the transpose. The measurement model for the link dataset G is as follows: In the formula, For the measurement model of the link dataset G at time k, The observation error at time k in the measurement model of the link dataset G; Step 3. Use wavelet decomposition to scale the state model and measurement model of the link dataset W and the state model and measurement model of the link dataset G, decompose the link dataset W and the link dataset G to the same resolution, and obtain the state model and measurement model of the link dataset W and the link dataset G at low resolution. Step 4. At the same resolution, perform Kalman filtering fusion on the link dataset W and the link dataset G according to the following formula. In the formula, For the one-step prediction result at time k, Φ k,k-1 Let k be the state transition matrix. This is the fusion result at time k-1. For the fusion result at time k, P kk-1 Let P be the one-step prediction covariance matrix at time k. k-1 Let Q be the error covariance matrix at time k-1. k-1 Let k be the model noise covariance matrix at time k-1. The Kalman filter gain matrix of the link dataset W. For the observations of the measurement model of the link dataset W, Let G be the Kalman filter gain matrix of the link dataset G. For the observations of the measurement model of dataset G, P k Let be the error covariance matrix at time k. Let W be the covariance matrix of the link dataset. Let I be the covariance matrix of the link dataset G, and let I be the identity matrix. Step 5. Use the wavelet decomposition coefficient reconstruction method to reconstruct the Kalman filter fusion result obtained in Step 4 to obtain the fusion result of the original data, namely the fusion result of the original TWSTFT link and GPS PPP link data; The wavelet decomposition coefficient reconstruction method is as follows: In the formula, X j (m) represents the m-th scaling coefficient, j represents the scale, m represents the order of the scaling coefficients, R represents a positive integer, t represents the order of the wavelet coefficients, h() represents the first filter, g() represents the second filter, and Y j-1 (t) represents the t-th wavelet coefficient; Step 6. Obtain the gain of the fused TWSTFT link and GPS PPP link according to the following formula, which is used to determine the reduction of link noise after fusion; Q=(σ a -s b )s a In the formula, σ a It is the standard deviation of the original TWSTFT link and GPS PPP link data, σ b is the standard deviation of the fused data, where a is a constant and b is a constant; Step 7. Obtain the Allan variance of the fused TWSTFT link and GPS PPP link according to the following formula, which is used to determine the stability of the fused link; p2 = M + 1 - 2n In the formula, Let x be the Allan variance, y be a constant, and x be the variance. k+2n Let x be the clock difference at time k+2n. k+n Let x be the clock difference at time k+n. k Let k be the clock difference at time k, M be the number of measurements, n be the sampling period, and τ0 be the basic sampling interval.

2. The method for fusing satellite two-way and GPS time-frequency transmission links according to claim 1, characterized in that, The wavelet decomposition method in step 3 is the Daubechies 2 wavelet decomposition method.

3. The method for fusing satellite two-way and GPS time-frequency transmission links according to claim 1, characterized in that, The data integrity verification method is as follows: based on the data comparison date, subtract the previous item from the next item to determine whether there is a jump. If there is a jump, the data is missing; otherwise, there is no missing data. For missing data, the nearest neighbor difference method or linear interpolation method is used to supplement it. The outlier detection method is as follows: the Wright criterion is used for detection, and the nearest neighbor difference method is used for interpolation and replacement.

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