CN117706902A - Clock stability evaluation method, device and medium - Google Patents

Abstract

The invention discloses a clock stability evaluation method, a device and a medium, wherein the method comprises the following steps: taking the crystal oscillator to be detected as an internal clock of a first receiver, and acquiring observation data by capturing tracking satellite signals, wherein the observation data reflects the clock characteristics of the crystal oscillator to be detected; the second receiver is externally connected with a time-frequency reference source as a local clock to obtain observation data; performing time transfer calculation on the observation data and the broadcast ephemeris of the first receiver and the second receiver to obtain receiver clock error; and processing the clock error of the receiver through the deviation, and evaluating and analyzing the stability of the frequency of the crystal oscillator to be tested. The invention can be realized by data processing statistical analysis only by using a differential precision time transfer technology, and does not need high-precision time frequency detection analysis equipment; and combining the differential precise time transmission technology with the corrected Allan deviation to obtain the time reference stability of the atomic clock/crystal oscillator clock to be detected.

Description

Clock stability evaluation method, device and medium

Technical field

The invention belongs to the technical field of high-precision time-frequency transmission of Global Navigation Satellite System (GNSS), and more specifically, relates to a clock stability evaluation method, device and medium.

Background technique

Atomic clocks and crystal oscillator clocks are widely used in many fields such as communications, navigation, and time synchronization due to their high-precision characteristics. The frequency stability of atomic clocks and crystal oscillator clocks is an important indicator for evaluating their applicable scenarios, which depends on whether the frequency of the signals they generate remains stable under various environmental conditions. With the continuous advancement of technology, some high-precision time-frequency application scenarios have put forward more stringent requirements for performance indicators such as the frequency stability of crystal oscillator clocks.

The Global Navigation Satellite System (GNSS) is a satellite-based radio positioning system, which mainly includes the American Global Positioning System (GPS), China's Beidou (BDS), Russia's GLONASS (GLONASS), and Europe's The four major systems of Galileo. In the field of timing service, the use of GNSS receivers for timing service has the characteristics of high accuracy, low cost and stability. Timing receivers will be more and more widely used in the field of timing service. When the GNSS timing receiver is used in high-precision time-frequency applications, the clock frequency stability needs to be analyzed. The purpose is to use the clock taming model to accurately control the crystal oscillator. In addition, in order to more accurately simulate and predict the state of the crystal oscillator clock when the satellite navigation signal is interrupted, it is necessary to accurately understand the frequency stability and other characteristics of the crystal oscillator clock.

The GNSS timing receiver performs one-way timing, and its accuracy depends on the accuracy of the satellite ephemeris product. For pseudorange single-point positioning technology, the accuracy of the receiver clock error calculated using broadcast ephemeris is approximately 20 nanoseconds. Combined with the precision single-point positioning technology of carrier phase observation, the accuracy of the receiver clock error calculated by using precise satellite orbit and clock error is about 0.2 nanoseconds. In high-precision data processing, carrier phase differential observation not only eliminates errors such as ephemeris residuals and atmospheric residuals, but also restores the integer characteristics of double-difference integer ambiguities, allowing rapid implementation of hundreds of picosecond-level time-frequency services. . Using carrier phase difference time transmission, the receiver receives the observation information of the reference station from the network side, avoiding the shortcomings of relying on precise satellite orbit and clock offset products.

Contents of the invention

The present invention is provided to solve the above-mentioned problems existing in the prior art. Therefore, a clock stability evaluation method, device and medium are needed to further improve the evaluation accuracy of the stability of atomic clocks and crystal oscillator clocks. The present invention provides a clock stability evaluation method based on differential precision time transfer, which will be The measured crystal oscillator OCXO serves as the internal clock of GNSS receiver A, and then observation data is obtained by capturing and tracking satellite signals. The observation data reflects the clock characteristics of the crystal oscillator OCXO to be measured. On the other hand, GNSS receiver B connects an external time-frequency reference source as a local clock to obtain observation data. Then the observation data and broadcast ephemeris of the two receivers are used for DPT time transfer calculation to obtain the receiver clock difference. The clock difference result reflects the difference in the representation time of the crystal oscillator under test relative to the time-frequency reference source. Finally, the frequency stability measurement of the crystal oscillator under test is analyzed through Allan deviation evaluation.

Compared with pseudo-range single-point positioning technology and precision single-point positioning technology combined with carrier phase observation for time transfer to evaluate clock stability, this invention further improves the evaluation of clock stability by fixing the single-difference carrier phase ambiguity between stations. accuracy, making the results more referential.

According to a first aspect of the present invention, a clock stability evaluation method is provided, which method includes:

Use the crystal oscillator to be tested as the internal clock of the first receiver, and obtain observation data by capturing and tracking satellite signals. The observation data reflects the clock characteristics of the crystal oscillator to be tested;

Use the external time-frequency reference source of the second receiver as the local clock to obtain observation data;

The observation data and broadcast ephemeris of the first receiver and the second receiver are subjected to DPT time transfer calculation to obtain the receiver clock difference. The receiver clock difference reflects the characterization time of the crystal oscillator to be measured relative to the time frequency. Differences in reference sources;

The receiver clock error is processed through the deviation, and the frequency stability of the crystal oscillator under test is evaluated and analyzed.

Further, both the first receiver and the second receiver are GNSS receivers.

Further, the time-frequency reference source is UTC(k) or a high-precision atomic clock.

Further, the observation data and broadcast ephemeris of the first receiver and the second receiver are subjected to DPT time transfer calculation to obtain the receiver clock error, which includes:

The single-difference pseudorange and carrier phase observations for any frequency f are as shown in Equation (1):

in Represents the receiver clock difference between the time-frequency reference station and the user station, c is the speed of light, and calculates the floating-point single-difference carrier phase ambiguity of the reference satellite i in equation (1) based on pseudorange and carrier phase observations/> And obtain the carrier phase single difference ambiguity of other visible stars j through equation (2)/>

Combined with the single difference ambiguity in equation (2) and the single-difference carrier phase observation equation to determine the inter-station receiver clock difference as shown in Equation (3):

Determine the single-difference pseudorange and carrier phase dual-frequency IF combined observations as shown in Equation (4):

Through the difference between the ionosphere-free combined double-differenced pseudorange observation and the carrier phase observation, the ionospheric-free combined double-difference floating-point ambiguity is obtained:

Using the floating-point single-difference carrier phase ambiguity of reference satellite i in equation (5) And obtain the single difference carrier phase ambiguity of other visible stars j through equation (6)/>

According to single difference ambiguity and the single-difference carrier phase observation equation to determine the inter-station receiver clock difference as shown in Equation (7):

Further, performing DPT time transfer calculation on the observation data and broadcast ephemeris of the first receiver and the second receiver to obtain the receiver clock error, which also includes:

Through the single-frequency solution of equation (3) or the dual-frequency IF combined solution of equation (7), the inter-station time difference results of each visible satellite are obtained.

Further, performing DPT time transfer calculation on the observation data and broadcast ephemeris of the first receiver and the second receiver to obtain the receiver clock error, which also includes:

While setting the satellite cutoff altitude angle, W _j =θ _j /90° weighting method is used to obtain the time transfer result as shown in Equation (8):

Among them, T _f represents the time-frequency transmission result of the differential single-frequency carrier phase, and T _IF represents the time-frequency transmission result of the differential dual-frequency IF combined carrier phase.

Furthermore, the receiver clock error is processed based on the corrected Allen deviation, and the frequency stability of the crystal oscillator under test is evaluated and analyzed:

According to the second technical solution of the present invention, a clock stability evaluation device is provided, and the device includes:

The first observation module is configured to use the crystal oscillator to be tested as the internal clock of the first receiver, and obtain observation data by capturing and tracking satellite signals, and the observation data reflects the clock characteristics of the crystal oscillator to be tested;

The second observation module is configured to use the external time-frequency reference source of the second receiver as the local clock to obtain observation data;

The receiver clock difference calculation module is configured to perform DPT time transfer calculation on the observation data and broadcast ephemeris of the first receiver and the second receiver to obtain the receiver clock difference. The receiver clock difference is Reflects the difference in the characterization time of the crystal oscillator under test relative to the time-frequency reference source;

The stability evaluation module is configured to process the receiver clock error through deviation and evaluate and analyze the frequency stability of the crystal oscillator to be tested.

Further, the receiver clock difference calculation module is further configured to:

The single-difference pseudorange and carrier phase observations for any frequency f are as shown in Equation (1):

in Represents the receiver clock difference between the time-frequency reference station and the user station, and c is the speed of light;

Calculate the floating-point single-difference carrier phase ambiguity of reference satellite i in equation (1) based on pseudorange and carrier phase observations. And obtain the carrier phase single difference ambiguity of other visible stars j through equation (2)/>

Combined with the single difference ambiguity in equation (2) and the single-difference carrier phase observation equation to determine the inter-station receiver clock difference as shown in Equation (3):

Determine the single-difference pseudorange and carrier phase dual-frequency IF combined observations as shown in Equation (4):

Through the difference between the ionosphere-free combined double-differenced pseudorange observation and the carrier phase observation, the ionospheric-free combined double-difference floating-point ambiguity is obtained:

Using the floating-point single-difference carrier phase ambiguity of reference satellite i in equation (5) And obtain the single difference carrier phase ambiguity of other visible stars j through equation (6)/>

According to single difference ambiguity and the single-difference carrier phase observation equation to determine the inter-station receiver clock difference as shown in Equation (7):

According to the third technical solution of the present invention, a readable storage medium is provided. The readable storage medium stores one or more programs. The one or more programs can be executed by one or more processors to implement method as described above.

The present invention has at least the following beneficial effects:

(1) The present invention has good usability: it realizes hundreds of picosecond-level time transmission through the single difference between carrier phase stations, and can further evaluate the frequency stability performance of crystal oscillator clocks and atomic clocks;

(2) Real-time: This invention can accurately estimate the real-time inter-station clock difference in the receiver, and can evaluate the frequency stability results of the clock in real time;

(3) Strong scalability: The present invention can meet high-precision frequency stability evaluation in static and dynamic scenarios; it can also be used for frequency stability evaluation of remote clocks when real-time precision satellite orbits are introduced.

Description of the drawings

Figure 1 shows an overall flow chart of a clock stability evaluation method according to an embodiment of the present invention;

Figure 2 shows a structural diagram of a clock stability evaluation device according to an embodiment of the present invention.

Detailed ways

In order to enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be described in detail below with reference to the drawings and specific implementation modes. The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and specific examples, but this is not intended to limit the present invention. If the various steps described in this article are not necessarily related to each other, the order in which they are described as an example in this article should not be regarded as a limitation. Those skilled in the art will know that the order can be adjusted as long as As long as the logic between them is not destroyed and the entire process cannot be realized.

Figure 1 shows an overall flow chart of a clock stability evaluation method according to an embodiment of the present invention. As shown in Figure 1, an embodiment of the present invention provides a clock stability evaluation method, which includes steps 1 to 5. , the details are as follows:

step 1:

Use the crystal oscillator OCXO to be tested as the internal clock of GNSS receiver A, and then obtain observation data by capturing and tracking satellite signals. The observation data reflects the clock characteristics of the crystal oscillator OCXO to be tested. Note that the crystal oscillator OCXO is in a clock free oscillation state at this time.

Step 2:

GNSS receiver B connects an external time-frequency reference source as a local clock to obtain observation data. The time-frequency reference source can choose UTC(k) or a high-precision atomic clock.

Step 3: Differential Precision Time Transfer Method

Inter-station single difference solution is performed for pseudorange and carrier phase observations. The single-difference pseudorange and carrier phase observations for any frequency f are shown in Equation (1).

in Indicates the receiver clock difference between the time-frequency reference station and the user station.

After fixing the double-difference carrier phase ambiguity through RTK technology, pseudorange and carrier phase observations are used to calculate the floating-point single-difference carrier phase ambiguity of the reference satellite i in equation (1) And obtain the carrier phase single difference ambiguity of other visible stars j through equation (2)/>

In order to obtain the precise time difference between the two stations, combined with the single difference ambiguity in equation (2) and the single-difference carrier phase observation equation, the inter-station receiver clock difference is shown in Equation (3).

For short baselines of a few kilometers, errors such as single-difference ephemeris error residuals, single-difference tropospheric delay residuals, and single-difference ionospheric delay residuals are ignored. As the length of the baseline increases, the error caused by the ionospheric delay is one of the main errors that affects the accuracy of time transmission. The ranging error caused by the ionosphere can reach meter-level or even hundred-meter-level errors. If the ionosphere in the observation is not correct, Delay in making corrections will have a huge impact on the accuracy and reliability of satellite navigation time delivery results. For longer distance baselines, this paper uses a dual-frequency ionosphere-free combination to eliminate the delay effect of the first-order ionospheric term. The single-difference pseudorange and carrier phase dual-frequency IF combined observations are shown in Equation (4).

By making a difference between the ionosphere-free combined double-difference pseudorange observation and the carrier phase observation, the ionosphere-free combined double-difference floating-point ambiguity is obtained.

Further, using the floating-point single-difference carrier phase ambiguity of the reference satellite i in equation (5) And obtain the single difference carrier phase ambiguity of other visible stars j through equation (6)/>

The single difference ambiguity combined with the above formula And the single-difference carrier phase observation equation, the inter-station receiver clock difference is shown in Equation (7).

Through the single-frequency solution of equation (3) or the dual-frequency IF combined solution of equation (7), the inter-station time difference results of each visible satellite can be obtained. For the inter-station time difference solution of multiple satellites, how to reasonably determine the weight is the key to improving the accuracy of single-difference carrier phase time-frequency transmission. While setting the satellite cut-off altitude angle, the single-difference carrier phase time-frequency transmission result is determined based on the satellite altitude angle weighting method. Here, W _j =θ _j /90° weighting method is used to obtain the time transfer result as shown in the following formula.

Among them, T _f represents the time-frequency transmission result of the differential single-frequency carrier phase, and T _IF represents the time-frequency transmission result of the differential dual-frequency IF combined carrier phase.

Step 4: Use the observation data and broadcast ephemeris of the two receivers to perform DPT time transfer calculation through step 3 to obtain the receiver clock difference. The clock difference result reflects the difference in the characterization time of the crystal oscillator under test relative to the time-frequency reference source. .

Step 5: Process the receiver clock error through the corrected Allan deviation, and evaluate and analyze the measurement of the frequency stability of the crystal oscillator to be tested.

The following embodiments of the present invention will be combined with specific calculation examples to further illustrate the feasibility and progress of the present invention.

The National Atomic Time Scale UTC (NIM) of the China Institute of Metrology is selected as the frequency reference source, and the frequency stability of the crystal OCXO clock is evaluated and analyzed using the DPT method. The specific experimental plan is as follows:

(1) Obtain the time transfer result of the crystal oscillator OCXO clock relative to UTC (NIM) through carrier phase differential precision time transfer; (2) Obtain the second pulse result of the crystal oscillator OCXO clock relative to UTC (NIM) output through the time interval counter, and Convert to frequency error.

The results obtained by the two solutions are analyzed through the corrected Allan deviation, and the evaluation results of the frequency stability of the crystal OCXO clock during free oscillation are obtained.

An embodiment of the present invention provides a clock stability evaluation device. As shown in Figure 2, the device 200 includes:

The first observation module 201 is configured to use the crystal oscillator to be tested as the internal clock of the first receiver, and obtain observation data by capturing and tracking satellite signals. The observation data reflects the clock characteristics of the crystal oscillator to be tested;

The second observation module 202 is configured to connect the second receiver to an external time-frequency reference source as the local clock to obtain observation data;

The receiver clock difference calculation module 203 is configured to perform DPT time transfer calculation on the observation data and broadcast ephemeris of the first receiver and the second receiver to obtain the receiver clock difference. The difference reflects the difference in the characterization time of the crystal oscillator under test relative to the time-frequency reference source;

The stability evaluation module 204 is configured to process the receiver clock error through the deviation, and evaluate and analyze the frequency stability of the crystal oscillator to be tested.

In some embodiments, the first receiver and the second receiver are both GNSS receivers.

In some embodiments, the time-frequency reference source is UTC(k) or a high-precision atomic clock.

In some embodiments, the receiver clock difference calculation module is further configured to:

The single-difference pseudorange and carrier phase observations for any frequency f are as shown in Equation (1):

in Represents the receiver clock difference between the time-frequency reference station and the user station;

Calculate the floating-point single-difference carrier phase ambiguity of reference satellite i in equation (1) based on pseudorange and carrier phase observations. And obtain the carrier phase single difference ambiguity of other visible stars j through equation (2)/>

Combined with the single difference ambiguity in equation (2) and the single-difference carrier phase observation equation to determine the inter-station receiver clock difference as shown in Equation (3):

Determine the single-difference pseudorange and carrier phase dual-frequency IF combined observations as shown in Equation (4):

Through the difference between the ionosphere-free combined double-differenced pseudorange observation and the carrier phase observation, the ionospheric-free combined double-difference floating-point ambiguity is obtained:

Using the floating-point single-difference carrier phase ambiguity of reference satellite i in equation (5) And obtain the single difference carrier phase ambiguity of other visible stars j through equation (6)/>

According to single difference ambiguity and the single-difference carrier phase observation equation to determine the inter-station receiver clock difference as shown in Equation (7):

In some embodiments, the receiver clock difference calculation module is further configured to:

Through the single-frequency solution of equation (3) or the dual-frequency IF combined solution of equation (7), the inter-station time difference results of each visible satellite are obtained.

In some embodiments, the receiver clock difference calculation module is further configured to:

While setting the satellite cutoff altitude angle, W _j =θ _j /90° weighting method is used to obtain the time transfer result as shown in Equation (8):

Among them, T _f represents the time-frequency transmission result of the differential single-frequency carrier phase, and T _IF represents the time-frequency transmission result of the differential dual-frequency IF combined carrier phase.

In some embodiments, the stability evaluation module is further configured to process the receiver clock error through the corrected Allen deviation to evaluate and analyze the frequency stability of the crystal oscillator under test:

It should be noted that the device described in this embodiment and the previously described method belong to the same technical idea and can achieve the same technical effect, and will not be described again here.

Embodiments of the present invention provide a readable storage medium that stores one or more programs, and the one or more programs can be executed by one or more processors to implement the above embodiments. method described.

The above description is intended to be illustrative rather than restrictive. For example, the above examples (or one or more versions thereof) may be used in combination with each other. For example, other embodiments may be used by those of ordinary skill in the art upon reading the above description. Additionally, in the above detailed description, various features may be grouped together to simplify the invention. This should not be construed as an intention that an unclaimed feature of the invention is essential to any claim. Rather, inventive subject matter may lie in less than all features of a particular inventive embodiment. Thus, the following claims are hereby incorporated into the Detailed Description as examples or embodiments, with each claim standing on its own as a separate embodiment, and with it being contemplated that these embodiments may be combined with one another in various combinations or permutations. The scope of the invention should be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.

Claims (10)

1. A method of clock stability assessment, the method comprising:

taking the crystal oscillator to be detected as an internal clock of a first receiver, and acquiring observation data by capturing tracking satellite signals, wherein the observation data reflects the clock characteristics of the crystal oscillator to be detected;

the second receiver is externally connected with a time-frequency reference source as a local clock to obtain observation data;

performing DPT time transfer calculation on the observation data and the broadcast ephemeris of the first receiver and the second receiver to obtain receiver clock differences, wherein the receiver clock differences reflect the difference of the characterization time of the crystal oscillator to be detected relative to a time-frequency reference source;

and processing the clock error of the receiver through the deviation, and evaluating and analyzing the stability of the frequency of the crystal oscillator to be tested.

2. The method of claim 1, wherein the first receiver and the second receiver are both GNSS receivers.

3. The method of claim 1, wherein the time-frequency reference source is UTC (k) or a high precision atomic clock.

4. The method of claim 1, wherein performing a DPT time transfer solution on the observed data and the broadcast ephemeris of the first receiver and the second receiver to obtain a receiver clock difference, comprising:

the single difference pseudorange and carrier phase observations for any frequency f are shown in equation (1):

wherein the method comprises the steps ofRepresenting the receiver clock difference between the time-frequency reference station and the subscriber station, c is the speed of light,/->For single difference pseudorange observations between stations, +.>For tropospheric delay single difference residual value, < >>For ionospheric delay single difference residual value, +.>Measurement noise for inter-station single difference pseudorange observations, < >>Lambda is the single difference carrier phase observation between stations _f Wavelength of frequency f，/>Floating-point single-difference carrier-phase ambiguity for reference satellite i,>measuring noise which is a single-difference carrier phase observation value between stations;

calculating floating single-difference carrier-phase ambiguity for reference satellite i in (1) from pseudorange and carrier-phase observationsAnd obtaining carrier phase single difference ambiguity +.>

Wherein the method comprises the steps ofThe double-difference carrier phase integer ambiguity of the satellite j relative to the reference satellite i is directly obtained through double-difference observation of the existing RTK technology;

single difference ambiguity in combined (2)And a single-difference carrier phase observation equation, wherein the clock difference of the receiver between stations is determined as shown in a formula (3):

wherein,is the single difference geometry distance between stations from the satellite to the receiver;

the determination of the single-difference pseudo-range and carrier-phase dual-frequency IF combined observations is shown in equation (4):

wherein,ionosphere-free combined observations for single-difference pseudoranges between stations,>for single-difference carrier phase ionosphere-free combined observations between stations,>for single difference ionosphere free combined geometry distance from satellite to receiver +.>For ionosphere-free combined receiver clock difference of time-frequency reference station and subscriber station, +.>For troposphere delay single difference no ionosphere combined residual value, +.>Measurement noise, lambda, without ionosphere combination for single-difference pseudorange observations between stations _IF For ionosphere-free combined wavelengths,floating single difference ionosphere-free combined carrier phase ambiguity for reference satellite i, +.>Measurement noise without ionosphere combination for inter-station single difference carrier phase observations, c=λ _f ·f；

Obtaining double-difference floating ambiguity of the ionosphere-free combination by making a difference between the ionosphere-free combination double-difference pseudo-range observation and the carrier phase observation:

floating single-difference carrier-phase ambiguity using reference satellite i in (5)And obtaining single-difference carrier phase ambiguity +.f. for other visible star j through (6)>

According to single difference ambiguityAnd a single-difference carrier phase observation equation, wherein the clock difference of the receiver between stations is determined as shown in a formula (7):

5. the method of claim 4, wherein DPT time transfer resolving the observations and broadcast ephemeris of the first receiver and the second receiver to obtain a receiver clock bias, further comprising:

and obtaining the inter-station time difference result of each visible satellite through single-frequency solution of the formula (3) or double-frequency IF combination solution of the formula (7).

6. The method of claim 5, wherein DPT time transfer resolving the observations and broadcast ephemeris of the first receiver and the second receiver to obtain a receiver clock bias, further comprising:

at the same time of setting satellite cut-off altitude angle, adopting W _j ＝θ _j The time transfer result obtained by the/90 degree weighting method is shown as a formula (8):

wherein T is _f Representing the differential single-frequency carrier phase time-frequency transfer result, T _IF Representing the differential dual-band IF combined carrier phase time-frequency transfer result, W _j Represents W _j ＝θ _j Weight of the 90 degree weighting method, θ _j Representing the satellite cut-off altitude.

7. The method according to claim 1, wherein the receiver clock correction is processed based on the corrected alembic bias, and the crystal oscillator frequency stability to be measured is evaluated and analyzed.

8. A clock stability assessment method apparatus, the apparatus comprising:

the first observation module is configured to take the crystal oscillator to be detected as an internal clock of the first receiver, acquire observation data by capturing tracking satellite signals, and the observation data reflect the clock characteristics of the crystal oscillator to be detected;

the second observation module is configured to take a time-frequency reference source externally connected with the second receiver as a local clock to obtain observation data;

the receiver clock difference calculation module is configured to carry out DPT time transfer calculation on the observation data and the broadcast ephemeris of the first receiver and the second receiver to obtain receiver clock differences, and the receiver clock differences reflect the difference of the characterization time of the crystal oscillator to be detected relative to a time-frequency reference source;

and the stability evaluation module is configured to process the clock error of the receiver through deviation, evaluate and analyze the stability of the crystal oscillator frequency to be tested.

9. The apparatus of claim 8, wherein the receiver clock difference calculation module is further configured to:

the single difference pseudorange and carrier phase observations for any frequency f are shown in equation (1):

wherein the method comprises the steps ofThe clock difference of the receiver of the time-frequency reference station and the user station is represented, and c is the speed of light;

calculating floating single-difference carrier-phase ambiguity for reference satellite i in (1) from pseudorange and carrier-phase observationsAnd obtaining carrier phase single difference ambiguity +.>

Single difference ambiguity in combined (2)And a single-difference carrier phase observation equation, wherein the clock difference of the receiver between stations is determined as shown in a formula (3):

the determination of the single-difference pseudo-range and carrier-phase dual-frequency IF combined observations is shown in equation (4):

obtaining double-difference floating ambiguity of the ionosphere-free combination by making a difference between the ionosphere-free combination double-difference pseudo-range observation and the carrier phase observation:

floating single-difference carrier-phase ambiguity using reference satellite i in (5)And obtaining single-difference carrier phase ambiguity +.f. for other visible star j through (6)>

According to single difference ambiguityAnd a single-difference carrier phase observation equation, wherein the clock difference of the receiver between stations is determined as shown in a formula (7):

10. a readable storage medium storing one or more programs executable by one or more processors to implement the method of any of claims 1-7.