阅读说明：本技术 一种星地精密时间同步及载波相位周跳探测方法 (Satellite-ground precise time synchronization and carrier phase cycle slip detection method ) 是由 白燕 韩子彬 高帅和 郭燕铭 邹德财 卢晓春 张首刚 于 2021-08-27 设计创作，主要内容包括：本发明提供了一种星地精密时间同步及载波相位周跳探测方法,采用单上行和双下行三条微波链路的组合方式实现地面站和低轨航天器间的载波相位测量和伪距测量；然后进行周跳探测,包括三频组合周跳探测和MW组合周跳探测；将三频组合周跳探测和MW组合周跳探测确定的周跳历元组合整理,确实数据中所有的周跳历元；根据联立三组线性无关的检验量方程,对周跳进行解算,在相位观测值中修复周跳；基于载波相位测量实现双向时间同步,最后求钟差拟合残差的RMS值,以RMS值评估其双向时间同步性能,实现了高精度星地双向时间同步。(The invention provides a satellite-ground precise time synchronization and carrier phase cycle slip detection method, which adopts a combination mode of a single uplink microwave link and a double downlink microwave link to realize carrier phase measurement and pseudo-range measurement between a ground station and a low-orbit spacecraft; then, cycle slip detection is carried out, wherein the cycle slip detection comprises three-frequency combined cycle slip detection and MW combined cycle slip detection; combining and sorting the cycle slip epochs determined by the three-frequency combined cycle slip detection and the MW combined cycle slip detection to ensure all the cycle slip epochs in the data; resolving cycle slip according to three sets of simultaneous linearly independent inspection quantity equations, and repairing the cycle slip in the phase observation value; and realizing bidirectional time synchronization based on carrier phase measurement, finally solving the RMS value of the clock error fitting residual error, and evaluating the bidirectional time synchronization performance of the clock error fitting residual error by the RMS value, thereby realizing high-precision satellite-ground bidirectional time synchronization.)

1. A satellite-ground precise time synchronization and carrier phase cycle slip detection method is characterized by comprising the following steps:

1) the low-orbit spacecraft and the ground station respectively transmit microwave signals with different frequencies to each other, the carrier phase measurement and the pseudo-range measurement between the ground station and the low-orbit spacecraft are realized by adopting a combination mode of a single uplink microwave link and a double downlink microwave link, and a single uplink f is obtained_GSCarrier phase observation, pseudo-range observation and dual downlink f_SG1And f_SG2The carrier phase observed value and the pseudo-range observed value;

2) performing cycle slip detection, including three-frequency combined cycle slip detection and MW combined cycle slip detection;

during three-frequency combined cycle slip detection, subtracting a double downlink code pseudo-range, a carrier phase pseudo-range and a corresponding uplink pseudo-range to obtain a differenced combined observation equation, subtracting the phase pseudo-range to obtain a combined observed quantity only retaining ionosphere errors, whole-cycle ambiguity and residual errors, and differencing combined observed quantity epochs to obtain a corresponding detected quantity

Wherein, λ is the carrier wavelength, N is the integer ambiguity, and Δ is the ionospheric error residual error and integer ambiguity caused by epoch difference,for a carrier phase observation value, SG1, SG2 and GS subscripts respectively represent a downlink double-frequency and uplink single-frequency corresponding microwave link, and t represents an epoch;

if the inspection quantity is larger than the set threshold value, the cycle slip is considered to occur from the epoch t to the epoch t +1, otherwise, the cycle slip is not occurred;

when MW combined cycle slip detection is carried out, a MW combined observation equation is established

In the formula, λ_WFor a known wide-lane wavelength, N_WIs the width lane ambiguity, epsilon_WObserving noise for the combination;

thereby obtaining the width lane ambiguity

Deducing the mean value of the widelane ambiguity from the first epoch to the t-th epoch through a recursion formula<N_W>_tSum variance

Wherein N is_W(t) widelane ambiguity for the t-th epoch; if satisfy | N_W(t)-<N_W>_t-1|≥4σ_tAnd | N_W(t+1)-N_W(t) if the (t) | is less than or equal to 1, the t epoch is considered to have cycle slip, otherwise, the cycle slip does not occur;

if at least one epoch in the three-frequency combined cycle slip detection and the MW combined cycle slip detection has cycle slip, entering the step 3), and otherwise, entering the step 6);

3) combining and sorting the cycle slip epochs determined by the three-frequency combined cycle slip detection and the MW combined cycle slip detection to ensure all the cycle slip epochs in the data;

4) resolving cycle slip according to three simultaneous linearly independent check quantity equations to obtain the following matrix equation:

Q＝AX

whereinIn order for the test quantity to be known,in the form of a matrix of coefficients,according to the least square method X ═ A^TA)^-1A^TQ, solving a cycle skip value floating solution on a corresponding frequency point;

5) bringing the cycle slip floating point solution of each epoch of each frequency point obtained in the step 4) into a cycle slip occurrence epoch in the phase observed value and all phase observed values subsequent to the epoch, and repairing the cycle slip in the phase observed value;

6) bidirectional time synchronization is realized based on carrier phase measurement, and bidirectional satellite-ground clock difference is obtained through sorting

Wherein rho is the geometric distance between the satellite and the ground station, Delta d is the distance reduction correction quantity between the satellite and the ground,andis the prior orbit coordinate, t, of the ground station and the low orbit spacecraft under the ECI coordinate system₀、Respectively calculating the regression time, the spacecraft signal emission time and the ground station signal emission time according to the regression time t₀Calculating the launching time of the spacecraft and the ground station, and obtaining the prior orbit of the launching time of the spacecraft and the ground station by utilizing a 9-order Lagrange interpolation algorithmThe road coordinate is used for obtaining the required correction according to a correction formula;

7) and 6) according to the bidirectional satellite-ground clock difference obtained in the step 6), after n-order least square fitting processing, subtracting the clock difference solution value and the fitting value to obtain a clock difference fitting residual error, and finally solving the RMS value of the clock difference fitting residual error to evaluate the bidirectional time synchronization performance of the clock difference fitting residual error by the RMS value.

2. The method according to claim 1, wherein the checking quantity Δ N in step 2) is₁And Δ N₂The error in 3 times of is the set threshold.

3. The method according to claim 1, wherein step 7) is performed by using a 2-order least square fit to obtain a hydrogen clock or a rubidium clock.

Technical Field

The invention belongs to a time-frequency technology and a space technology, and is mainly suitable for realizing precise time synchronization between a spacecraft and the ground in a high dynamic environment.

Background

The commonly used long-distance time frequency transmission methods mainly include a two-way time difference measurement and time synchronization method, a one-way time synchronization method, a reverse positioning method and a laser ranging method. These methods are characterized in that the two-way time difference measurement and the time synchronization method can realize higher time synchronization precision. In the 'satellite-ground bidirectional time synchronization method under an inter-satellite link system' of Luhongchun et al, the satellite-ground bidirectional time synchronization precision under the inter-satellite link system is analyzed, and the fitting precision of 1-week, 1-day and 1-hour clock errors can reach 3.42ns, 0.30ns and 0.15ns respectively. However, as the precision of the space-time frequency reference is higher and higher, a space-time frequency transmission technology and time synchronization precision matched with the transmission precision are required to be used as application supports, neither the current pseudo-code-based time-frequency transmission method nor the current pseudo-code-based time-frequency synchronization method can meet the application of the high-precision time-frequency reference, and guo yanming et al provides a three-frequency-mode high-precision satellite-ground time comparison system based on the pseudo-code in the patent 'a three-frequency-mode high-precision satellite-ground time comparison system and method', but the pseudo-code-based time comparison cannot meet the requirement of measurement precision.

The traditional carrier phase cycle slip detection and repair method mainly comprises single-frequency downlink data, double-frequency downlink data and triple-frequency downlink data, wherein the cycle slip real-time detection and repair of a Beidou triple-frequency carrier observed value is realized by using pseudo-range phase combination and non-geometric phase combination in the 'cycle slip real-time detection and repair of a Beidou triple-frequency carrier observed value' of Yao-Yifei et al, and the improvement of the pseudo-range phase combination quantity detection and repair cycle slip algorithm is realized by Zhang et al in the 'improvement of the pseudo-range/phase combination quantity detection and repair cycle slip algorithm'. The conventional cycle slip detection and repair method is only suitable for downlink data, uplink data are not preprocessed in a single-uplink and double-downlink three-frequency mode, the single-frequency processing precision is relatively low in the conventional cycle slip detection and repair method, and the conventional cycle slip detection and repair method is insensitive to small cycle slip detection.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides a bidirectional precise time synchronization and carrier phase cycle slip detection and repair method based on carrier phase measurement, and the requirement of measurement precision is met.

The technical scheme adopted by the invention for solving the technical problem comprises the following steps:

1) the low-orbit spacecraft and the ground station respectively transmit microwave signals with different frequencies to each other, the carrier phase measurement and the pseudo-range measurement between the ground station and the low-orbit spacecraft are realized by adopting a combination mode of a single uplink microwave link and a double downlink microwave link, and a single uplink f is obtained_GSCarrier phase observation, pseudo-range observation and dual downlink f_SG1And f_SG2The carrier phase observed value and the pseudo-range observed value;

2) performing cycle slip detection, including three-frequency combined cycle slip detection and MW combined cycle slip detection;

during three-frequency combined cycle slip detection, subtracting a double downlink code pseudo-range, a carrier phase pseudo-range and a corresponding uplink pseudo-range to obtain a differenced combined observation equation, subtracting the phase pseudo-range to obtain a combined observed quantity only retaining ionosphere errors, whole-cycle ambiguity and residual errors, and differencing combined observed quantity epochs to obtain a corresponding detected quantity

Wherein, λ is the carrier wavelength, N is the integer ambiguity, and Δ is the ionospheric error residual error and integer ambiguity caused by epoch difference,for a carrier phase observation value, SG1, SG2 and GS subscripts respectively represent a downlink double-frequency and uplink single-frequency corresponding microwave link, and t represents an epoch;

if the inspection quantity is larger than the set threshold value, the cycle slip is considered to occur from the epoch t to the epoch t +1, otherwise, the cycle slip is not occurred;

when MW combined cycle slip detection is carried out, a MW combined observation equation is established

In the formula, λ_WFor a known wide-lane wavelength, N_WIs the width lane ambiguity, epsilon_WObserving noise for the combination;

thereby obtaining the width lane ambiguity

Deducing the mean value of the widelane ambiguity from the first epoch to the t-th epoch through a recursion formula<N_W>_tSum variance

Wherein N is_W(t) widelane ambiguity for the t-th epoch; if it satisfies|N_W(t)-<N_W>_t-1|≥4σ_tAnd | N_W(t+1)-N_W(t) if the (t) | is less than or equal to 1, the t epoch is considered to have cycle slip, otherwise, the cycle slip does not occur;

if at least one epoch in the three-frequency combined cycle slip detection and the MW combined cycle slip detection has cycle slip, entering the step 3), and otherwise, entering the step 6);

3) combining and sorting the cycle slip epochs determined by the three-frequency combined cycle slip detection and the MW combined cycle slip detection to ensure all the cycle slip epochs in the data;

4) resolving cycle slip according to three simultaneous linearly independent check quantity equations to obtain the following matrix equation:

Q＝AX

whereinIn order for the test quantity to be known,in the form of a matrix of coefficients,according to the least square method X ═ A^TA)^-1A^TQ, solving a cycle skip value floating solution on a corresponding frequency point;

5) bringing the cycle slip floating point solution of each epoch of each frequency point obtained in the step 4) into a cycle slip occurrence epoch in the phase observed value and all phase observed values subsequent to the epoch, and repairing the cycle slip in the phase observed value;

6) bidirectional time synchronization is realized based on carrier phase measurement, and bidirectional satellite-ground clock difference is obtained through sorting

Wherein rho is the geometric distance between the satellite and the ground station, Delta d is the distance reduction correction quantity between the satellite and the ground,andis the prior orbit coordinate, t, of the ground station and the low orbit spacecraft under the ECI coordinate system₀、Respectively calculating the regression time, the spacecraft signal emission time and the ground station signal emission time according to the regression time t₀Calculating the launching moments of the spacecraft and the ground station, obtaining the prior orbit coordinates of the launching moments of the spacecraft and the ground station by utilizing a 9-order Lagrange interpolation algorithm, and finally obtaining the required correction according to a correction formula;

7) and 6) according to the bidirectional satellite-ground clock difference obtained in the step 6), after n-order least square fitting processing, subtracting the clock difference solution value and the fitting value to obtain a clock difference fitting residual error, and finally solving the RMS value of the clock difference fitting residual error to evaluate the bidirectional time synchronization performance of the clock difference fitting residual error by the RMS value.

In the step 2), the check quantity delta N is used₁And Δ N₂The error in 3 times of is the set threshold.

And 7) fitting a hydrogen clock or a rubidium clock by using 2-order least squares.

The invention has the beneficial effects that:

1) the invention adopts the carrier phase measurement with higher measurement precision to realize high-precision bidirectional time synchronization, the measurement precision of the carrier phase decimal part is superior to 1 percent of the wavelength, and the measurement precision of the carrier phase is far higher than that of the pseudo code measurement. The invention adopts a new three-frequency mode, simultaneously transmits carrier phase ranging data through the low-orbit spacecraft and the ground station, realizes data transmission between satellites and the ground, and obtains high-precision satellite-ground bidirectional time synchronization through data preprocessing and resolving.

2) The invention provides a cycle slip detection and repair method suitable for a three-frequency mode aiming at a single-uplink and double-downlink three-frequency system, integrates carrier phase data of three links, avoids the problems of incomplete cycle slip detection, low detection precision and the like of separate processing, realizes the comprehensive detection of the cycle slip of the three links, ensures that the cycle slip on the three links can be detected, and improves the sensitivity of small cycle slip detection, wherein the delta N is theoretically obtained by a three-frequency combination method₁The detected quantity can detect cycle slip (delta N) of more than 0.311 cycles₂The cycle slip of more than 0.215 cycle can be detected by the inspection quantity, two detection equations in the three-frequency combination make up for each other, the cycle slip of an uplink and a downlink three-frequency microwave link can be detected in the embodiment, and the cycle slip repair precision of mm level is realized, so that the time synchronization precision of ps level is guaranteed.

3) The invention adopts the combination of the MW combination and the three-frequency combination, compensates the detection of insensitive cycle slip pairs in the three-frequency combination through MW combination detection, theoretically realizes cycle slip detection for more than 0.0774 weeks in a three-frequency mode of the MW combination, combines the MW combination detection equation with the three-frequency combination detection equation, realizes the solution of unique solution of cycle slip on three links according to the cycle slip solution equation, and avoids the condition of multiple solutions.

4) The invention utilizes the prior orbits of the low-orbit spacecraft and the ground station to calculate the distance regression correction quantity, regresses the bidirectional phase pseudo-range to the same moment, and realizes bidirectional time synchronization at the same moment. And after the clock difference is solved, subtracting the measured value by adopting n-order least square fitting to obtain a fitting residual error of the clock difference, and finally realizing the performance evaluation of the bidirectional time synchronization through a root mean square.

5) The double-line time synchronization precision after cycle slip detection and restoration can reach ps level.

Drawings

FIG. 1 is a schematic diagram of a tri-frequency microwave link;

FIG. 2 is a flow chart of a two-way time synchronization performance evaluation;

FIG. 3 is a flow chart of the overall scheme of the present invention;

FIG. 4 is a three-frequency combination Δ N₁A schematic diagram of a detection sequence;

FIG. 5 is a three-frequency combination Δ N₂A schematic diagram of a detection sequence;

FIG. 6 is a schematic diagram of a MW combined detection sequence;

fig. 7 is a schematic diagram of a two-way time synchronization performance analysis.

Detailed Description

The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.

Aiming at a complex satellite-ground environment, because the flight dynamics of a low-orbit spacecraft is high, the transmission frequency of a time-frequency transmission link is high, the carrier Doppler effect is large, the carrier phase measurement is easy to generate gross error and cycle slip, in order to obtain a carrier phase observation value with high reliability and high accuracy, data preprocessing is required, namely cycle slip detection and repair in a carrier phase, the traditional cycle slip detection and repair method aims at single-frequency downlink data, double-frequency downlink data and triple-frequency downlink data, and effective detection and repair are not carried out on uplink data.

The technical points of the invention include:

1. bidirectional precise time synchronization based on carrier phase measurement

As shown in FIG. 1, the satellite-to-ground transmission link has three microwave links, a single uplink and a dual downlink, where the uplink f_GSAnd downlink f_SG1Together performing high precision bi-directional time synchronization, downlink f_SG1And downlink f_SG2Implementing atmospheric corrections and combining uplinks f_GSAnd the detection and repair of carrier phase cycle slip are realized.

According to such a signal system, without considering multipath effects, its two-way pseudorange observation equation may be expressed as:

P_SG1＝ρ_SG+c·Δδ_SG+I_SG1+T_SG1+R_SG1+G_SG1+ε_SG1 (1)

P_SG2＝ρ_SG+c·Δδ_SG+I_SG2+T_SG2+R_SG2+G_SG2+ε_SG2 (2)

P_GS＝ρ_GS+c·Δδ_GS+I_GS+T_GS+R_GS+G_GS+ε_GS (3)

in the formula, SG1, SG2 and GS subscripts respectively represent downlink dual-band and uplink single-band corresponding microwave links, P is a code pseudo-range observed value, ρ is a geometric distance between a satellite and a ground station, Δ δ is a clock error between the satellite and the ground, c is a light speed, I is an ionosphere error, T is a troposphere error, R is an error caused by relativity, G is a gravity time delay error, and epsilon is observation noise.

Likewise, without accounting for multipath effects, the two-way carrier phase measurement observation equation can be expressed as:

wherein the content of the first and second substances,for the carrier phase observation, λ is the carrier wavelength, N is the integer ambiguity, and the other symbols are consistent with the above expression. In order to realize high-precision time frequency transmission, the advantage of high carrier phase measurement precision is utilized, and error cancellation in a two-way time difference measurement method is fused to obtain high-precision satellite-ground time synchronization. Similar to the two-way measurement of pseudo-code, the carrier-based observation equation is written out according to the carrier phaseEquation for measuring the two-way time difference of the phase, and the uplink f_GSAnd downlink f_SG1Differencing the corresponding phase pseudorange values

The relation of the clock difference between the star and the earth is delta_GS＝-Δδ_SGTherefore, the arrangement can obtain the clock difference between the star and the ground

Where Δ includes ionospheric delay, tropospheric delay, relativistic effect delay, and gravitational delay due to path asymmetry, these errors must be considered in the overall two-way moveout measurement, and are not related to cycle slip repair performance evaluation, and are not described in detail here. In the process of transmitting signals in space, due to transmission delay and high-speed movement of satellites, satellite positions at different moments are contained in satellite-to-ground bidirectional pseudo-range measured values, so that time-space information contained in bidirectional phase pseudo-ranges needs to be reduced to the same moment, and most errors can be eliminated by subtracting the bidirectional phase pseudo-ranges at the same moment. Equation (8) can be modified as:

in the formula, Δ d is the distance reduced correction amount between the star and the ground, and the corresponding distance reduced correction amount can be obtained by the formulas (10) and (11), whereinAndis the prior orbit coordinate, t, of the ground station and the low orbit spacecraft under the ECI coordinate system₀、Respectively calculating the regression time, the spacecraft signal emission time and the ground station signal emission time according to the regression time t₀And calculating the launching time of the spacecraft and the ground station, obtaining the prior orbit coordinates of the launching time of the spacecraft and the ground station by utilizing a 9-order Lagrange interpolation algorithm, and finally obtaining the required correction according to a correction formula.

Under the condition of not considering other errors, the inter-satellite-ground clock error can be obtained after the preprocessing of phase observation data and the reduction of the distance between the satellites and the ground.

After the satellite-ground clock difference is solved, the RMS value of the fitting residual error of the satellite-ground clock difference is further solved to evaluate the satellite-ground bidirectional time synchronism, the bidirectional clock difference is solved according to the bidirectional time difference measurement, after n-order least square fitting processing, the fitting order is taken as different values according to different clock characteristics, the clock difference solution value and the fitting value are subjected to difference to obtain the clock difference fitting residual error, and finally the RMS value of the clock difference fitting residual error is solved, wherein the specific method is shown in FIG. 2.

2. Three-frequency combination for realizing cycle slip detection

Because the satellite local time and the ground station local time are different, even if the receiving time in the uplink observation file and the receiving time in the downlink observation file are the same, the geometric distance and the clock error are not completely the same, so the analysis can not be carried out by the traditional cycle slip detection and repair method, in order to fuse the uplink data and the downlink data, firstly, the double downlink code pseudo-range, the carrier phase pseudo-range and the corresponding uplink pseudo-range are subtracted, and the differenced combined observation equation is obtained:

wherein the symbols correspond to those indicated above, wherein₁、Δε₂、Δε₃And Δ ε₄To observe the noise residual. In the differenced combined observation equation, except for a separation layer error and a whole-cycle ambiguity between a pseudo range and a phase, other items are kept consistent, namely at the same clock face time t, the downlink geometric distance of the satellite and the ground geometric distance of the uplink, the clock error between the satellite and the ground and the errors are correspondingly equal, and the phase is subtracted from the pseudo range to obtain a combined observation quantity only keeping the whole-cycle ambiguity and a residual error:

in the formulaAndrepresenting the difference in observed noise residuals. The three-frequency combination eliminates the geometrical distance between the satellite and the ground, the clock error between the satellite and the ground, the troposphere error and other errors, only reserves the ionosphere error, the ambiguity and the observation noise, and is very suitable for detecting the cycle slip. The difference between the epochs of the formulas (16) and (17) can obtain the corresponding check quantity formula:

after the difference between epochs is found, the combined sequence without cycle slip will fluctuate around "0", and after cycle slip occurs, mutation will occur. Under the condition of no cycle slip, the quantity influencing the fluctuation of the inspection quantity only has observation noise, and the phase observation noise generally corresponds to 0.01 cycle of the frequency point, namely corresponds toThe pseudo range observation noise is one percent of the length of a code element of the ranging code, and for the simulation system, the pseudo range measurement error is 0.0005mExamining the quantity Δ N according to the law of error propagation₁And Δ N₂Can be expressed as:

and taking the error in the 3-time as a detection threshold value, namely the detection | delta N | > 0.003, generating cycle slip from the epoch t to the epoch t +1, and otherwise, generating no cycle slip. The inspection volume threshold is divided by the amount that the corresponding wavelength can be converted into a unit of a cycle, so that the delta N can be obtained theoretically by the three-frequency combination method₁The detected quantity can detect cycle slip (delta N) of more than 0.311 cycles₂The test quantity can detect cycle slip of more than 0.215 weeks. Further, as can be seen from equations (18) and (19), when the cycle slip ratio and the frequency ratio are the same, the cycle slip cannot be detected, and the method is not suitable for detecting the cycle slipThe method is failed. For the situation, additional combinations are needed to make up for the insensitive cycle slip detection of the method, and three unknowns of two testing quantity equations cannot solve the cycle slip, so that the detection of the insensitive cycle slip can be complemented by selecting and combining the MW combination, and the cycle slip can be solved simultaneously.

MW Combined cycle slip detection

The MW combination method eliminates the influence of the inter-satellite-ground geometric distance, the inter-satellite-ground clock error and the atmospheric error by reducing the narrow lane pseudo-range through the wide lane phase, effectively utilizes the double downlink observation data, and solves the cycle slip through the parallel vertical three-frequency combination. From the pseudo-range phase observation equation above, the MW combined observation equation can be expressed as:

in the formula (f)_SG1And f_SG2For dual downlink microwave link frequencies, λ_WIs a wide lane wavelength, N_WIs the width lane ambiguity, epsilon_WThe noise is observed for the combination. The widelane ambiguity can thus be obtained as:

error factors such as geometric distance between the satellite and the ground, clock error between the satellite and the ground, atmospheric error and the like are eliminated through the combined widelane ambiguity, only the influence of observation noise is left on the premise of not considering multipath effect, and the measurement noise is correspondingly reduced through the combined widelane with longer wavelength. The Blewitt deduces the wide lane ambiguity mean value from the first epoch to the t epoch through a recursion formula<N_W>_tSum varianceThe recurrence formula is as follows:

wherein N is_W(t) is the widelane ambiguity for the t-th epoch,<N_W>_tis the average value of the width lane ambiguities of the first t epochs,is the variance of the first t epochs. Judging whether cycle slip exists or not through inter-epoch widelane ambiguity difference, and if yes, judging whether cycle slip exists or not_W(t)-<N_W>_t-1|≥4σ_tAnd | N_W(t+1)-N_WAnd (t) is less than or equal to 1, the t epoch is considered to have cycle slip. Calculating the mean error of MW combination according to the observed errors of the phase and the pseudo rangeWith the error of 3 times as the detection threshold, the threshold value of +/-0.0774, namely | Delta N, can be obtained_WIf < 0.0774, no cycle slip occurs from epoch t to epoch t +1, otherwise, cycle slip occurs between epochs.

4. Cycle slip resolution and repair

Insensitive cycle slip pairs exist in the three-frequency combination and the MW combination, the two methods are complementary to each other, the preset cycle slip pairs can be detected, the epoch where the combined cycle slip is located is determined, and the cycle slip is solved according to three groups of simultaneous linearly independent inspection quantity equations to obtain the following matrix equation:

Q＝AX (26)

in the formula (I), the compound is shown in the specification,a is coefficient matrixUsing least square method X ═ A^TA)^-1A^TQ can obtain the cycle slip value floating solution on the corresponding frequency point and repair the solution in the phase observed value.

As shown in fig. 3, the present invention comprises the steps of:

1) transmitting microwave signals with different frequencies from the low-orbit spacecraft to the ground station and from the ground station to the low-orbit spacecraft, realizing carrier phase measurement and pseudo range measurement between the ground station and the low-orbit spacecraft by adopting a combination mode of a single uplink microwave link and a double downlink microwave link, and obtaining a single uplink f_GSCarrier phase observation, pseudo-range observation and dual downlink f_SG1And f_SG2The carrier phase observed value and the pseudo-range observed value;

2) performing cycle slip detection, including three-frequency combined cycle slip detection and MW combined cycle slip detection;

during three-frequency combined cycle slip detection, subtracting a double downlink code pseudo-range, a carrier phase pseudo-range and a corresponding uplink pseudo-range to obtain a differenced combined observation equation, subtracting the phase pseudo-range to obtain a combined observed quantity only retaining ionosphere errors, whole-cycle ambiguity and residual errors, and differencing combined observed quantity epochs to obtain a corresponding detected quantity

Wherein, λ is the carrier wavelength, N is the integer ambiguity, and Δ is the ionospheric error residual error and integer ambiguity caused by epoch difference,for a carrier phase observation value, SG1, SG2 and GS subscripts respectively represent a downlink double-frequency and uplink single-frequency corresponding microwave link, and t represents an epoch;

by the check quantity Δ N₁And Δ N₂The error in the 3 times is a check quantity threshold value, namely the check quantity is larger than the threshold value, the cycle slip from the epoch t to the epoch t +1 is considered to occur, otherwise, the cycle slip does not occur;

when MW combined cycle slip detection is carried out, a MW combined observation equation is established

In the formula, λ_WFor a known wide-lane wavelength, N_WIs the width lane ambiguity, epsilon_WObserving noise for the combination;

thereby obtaining the width lane ambiguity

Deducing the mean value of the widelane ambiguity from the first epoch to the t-th epoch through a recursion formula<N_W>_tSum variance

Wherein N is_W(t) widelane ambiguity for the t-th epoch; if satisfy | N_W(t)-<N_W>_t-1|≥4σ_tAnd | N_W(t+1)-N_W(t) if the (t) | is less than or equal to 1, the t epoch is considered to have cycle slip, otherwise, the cycle slip does not occur;

if at least one epoch in the three-frequency combined cycle slip detection and the MW combined cycle slip detection has cycle slip, entering the step 3), and otherwise, entering the step 6);

3) the cycle slip epochs determined by the three-frequency combination cycle slip detection and the MW combination cycle slip detection are combined and sorted, all the cycle slip epochs in the data are determined, wherein insensitive cycle slip pairs exist in the three-frequency combination and the MW combination, one combination can not detect the cycle slip but the other combination can detect the cycle slip, and the cycle slip epochs detected by the two combinations are integrated to determine all the cycle slip epochs in the data;

4) resolving cycle slip according to three simultaneous linearly independent check quantity equations to obtain the following matrix equation:

Q＝AX

whereinIn order for the test quantity to be known,in the form of a matrix of coefficients,according to the least square method X ═ A^TA)^-1A^TQ, solving a cycle skip value floating solution on a corresponding frequency point;

5) bringing the cycle slip floating point solution of each epoch of each frequency point obtained in the step 4) into a cycle slip occurrence epoch in the phase observed value and all phase observed values subsequent to the epoch, and repairing the cycle slip in the phase observed value;

6) bidirectional time synchronization is realized based on carrier phase measurement, and bidirectional satellite-ground clock difference is obtained through sorting

Wherein rho is the geometric distance between the satellite and the ground station, Delta d is the distance reduction correction quantity between the satellite and the ground,andis the prior orbit coordinate, t, of the ground station and the low orbit spacecraft under the ECI coordinate system₀、Respectively calculating the regression time, the spacecraft signal emission time and the ground station signal emission time according to the regression time t₀Calculating the launching moments of the spacecraft and the ground station, obtaining the prior orbit coordinates of the launching moments of the spacecraft and the ground station by utilizing a 9-order Lagrange interpolation algorithm, and finally obtaining the required correction according to a correction formula;

7) according to the bidirectional satellite-ground clock difference obtained in the step 6), after n-order least square fitting processing, the fitting order is taken as different values according to different atomic clock characteristics, a well-known hydrogen clock rubidium clock can use 2-order least square fitting, the difference between the clock difference solution value and the fitting value is obtained to obtain a clock difference fitting residual error, finally, the RMS value of the clock difference fitting residual error is calculated, and the bidirectional time synchronization performance of the clock difference fitting residual error is evaluated according to the RMS value.

In the embodiment of the present invention, assuming that one of the two parties realizing precise time synchronization is a low-orbit spacecraft a and the other party is a ground station B, the time synchronization between the low-orbit spacecraft and the ground station is taken as an example for description, and the specific steps of the two parties realizing high-precision time synchronization based on carrier phases are as follows:

1) generating and obtaining pseudo range observation data and carrier phase observation data between the low-orbit spacecraft A and the ground station B according to the atmosphere and other related models, wherein a (1,1, -1) cycle slip pair exists at a 30 th epoch in the carrier phase observation data; there is a (2,2,0) cycle slip pair at epoch 60; there is a (-1,0,1) cycle slip pair at epoch 90; there are (2, -3,2), (4,5, -5) and (-7,2,7) cycle slip pairs at the 150 th epoch, the 151 th epoch, and the 152 th epoch; the presence of (3, -4,3), (-6,6,9) and (4,9, -4) cycle slip pairs at the 200 th epoch, the 201 th epoch and the 202 nd epoch; there is a (10,10,10) cycle slip pair at epoch 250, where the cycle slip pair format is (f)_GS,f_SG1,f_SG2)。

2) Detecting cycle slip in the carrier phase observation data according to a three-frequency combination method and a MW combination method, and judging whether a cycle occurs according to fluctuation of the inspection quantity to obtain fluctuation curves of the three inspection quantities shown in figures 4,5 and 6;

3) determining a cycle slip occurrence epoch according to the inspection quantity mutation, solving the floating point solution of the cycle slip occurrence epoch by the algorithm in the invention content 4, and restoring the carrier phase observation data by the solved cycle slip floating point solution;

4) according to a clock error resolving formula, firstly, processing repaired phase observation data by utilizing a Lagrange interpolation algorithm, reducing satellite-ground bidirectional phase pseudo range data to the same moment, and resolving the bidirectional clock error of the low-orbit spacecraft A and the ground station B through bidirectional time difference measurement;

5) and subtracting the satellite-ground clock difference solution value and the fitting value by using a performance evaluation method to obtain a fitting residual error, and solving the RMS value of the fitting residual error to evaluate the bidirectional time synchronization performance. The performance of the satellite-ground bidirectional time synchronization between the low-orbit spacecraft a and the ground station B is shown in fig. 7, and the clock error fitting residual RMS between the low-orbit spacecraft a and the ground station B is 0.2256 ps.

As can be seen from fig. 4,5, and 6, the carrier phase cycle slip detection and restoration method provided by the present invention can effectively detect cycle slips on three links and realize restoration, and as can be seen from fig. 7, under the condition of only considering cycle slip restoration residual and spatial distance correction, a time synchronization result with higher precision can be achieved, and the bidirectional time synchronization precision can reach 0.2256 ps.