CN114755910B - Real-time UTC (k) time comparison method based on relative hardware delay calibration - Google Patents
Real-time UTC (k) time comparison method based on relative hardware delay calibration Download PDFInfo
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- G04—HOROLOGY
- G04R—RADIO-CONTROLLED TIME-PIECES
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- G04R20/02—Setting the time according to the time information carried or implied by the radio signal the radio signal being sent by a satellite, e.g. GPS
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- G04R—RADIO-CONTROLLED TIME-PIECES
- G04R20/00—Setting the time according to the time information carried or implied by the radio signal
- G04R20/02—Setting the time according to the time information carried or implied by the radio signal the radio signal being sent by a satellite, e.g. GPS
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Abstract
The invention discloses a real-time UTC (k) comparison method based on relative hardware delay calibration, which is characterized in that clock difference data of two receivers accessed to the same time frequency source are calculated, relative hardware delay deviation caused by the two receivers and a cable is obtained, the clock difference of the two receivers at two stations is obtained through real-time PPP processing on the basis of a WPT time service platform in different time laboratories for the two calibrated receivers, relative hardware delay is deducted, and then a real-time UTC (k) time comparison result is obtained, the influence of the hardware delay on the UTC (k) time comparison based on a PPP method is eliminated, the availability of a system is greatly improved under the condition of ensuring real-time, and the real-time UTC (k) comparison method has wide application prospect in time synchronization and high-precision positioning.
Description
Technical Field
The invention belongs to the technical field of satellite navigation, and particularly relates to a real-time UTC (k) time comparison method based on relative hardware delay calibration.
Background
The time belongs to one of seven basic physical quantities, and has very important significance in the fields of daily life, scientific research, engineering construction and the like. To ensure consistency of Time references, the Bureau International des potentials et measures (BIPM) integrates the local Time (UTC (k)) maintained in real Time by more than 80 Time laboratories around the world, and finally generates a Coordinated Universal Time (UTC). Therefore, accurate UTC (k) time alignment is a prerequisite for maintaining UTC.
The traditional high-precision time transfer methods including optical fiber time transfer, satellite two-way time transfer and the like have the defects of high cost, need of relay nodes and the like. In recent years, a low-cost and high-precision Global Navigation Satellite System (GNSS) time transfer method has become a research hotspot in the time-frequency field. In 1980, allan and Weiss proposed Common View (CV) time transfer based on GPS pseudo-range observation, and successfully applied to time alignment of BIPM time link. However, the co-view method has a disadvantage that the time transfer performance is limited by the baseline distance. With the continuous improvement of timeliness and precision of International GNSS Service (IGS) products, the All-In-View (AV) becomes a time transfer means with better performance than the common View method. In 2006, 9, the international commission on counseling Frequency (coustic Committee on Time and Frequency, CCTF) proposed to replace the common-view Time transfer in UTC Time alignment links by the full-view Time transfer at the 17 th CCTF conference. In view of the advantage of the high-precision carrier phase observed value, the conference also provides a study of comparison in a time link based on a Precision Point Positioning (PPP) time transfer method. As a performance-optimized GNSS time transfer method, PPP time transfer accuracy relies on accurate error correction, especially satellite clock and orbit error terms. When IGS post-production precision products are used, the PPP time transfer accuracy (STD) can reach 0.1ns. Currently, about 60% of GNSS time-frequency links employ PPP time transfer methods. In addition, in order to meet the requirement of sub-nanosecond real-time transmission, a big dipper Wide-area precision time service (WPT) prototype system is established by Beijing aerospace university based on a tracking station network of a China regional station and a global IGS station, and can provide high-precision real-time differential correction, so that the sub-nanosecond real-time service is realized.
In the time alignment of UTC (k), the effect of the time alignment on the hardware delay error in the link also needs to be considered. The hardware delay error is stable in a short time, and does not affect the STD value of the time transfer result, but generates systematic deviation. The national time service center also researches a method for calibrating a time service receiver by using a simulator, provides a receiver absolute calibration method based on a clock driving mode, indicates that the time service receivers with different architectures are different in calibration method, and respectively calibrates two receivers of different types, namely Novatel and Septensrio, wherein single-frequency calibration uncertainty is better than 1.5ns, and double-frequency calibration uncertainty is better than 4.5ns. The United States Naval Research Laboratory (NRL) proposes an absolute delay calibration method using a GPS simulator, which first performs time synchronization on the simulator and a receiver in a common clock manner, and then solves for the receiver hardware delay by resolving the clock difference between the observed quantity output by the simulator and the observed quantity output by the receiver, where the calibration uncertainty is 1.1ns for a single frequency point. The international bureau of measurement proposes a difference calibration method, which carries out clock-sharing antenna operation on a receiver to be calibrated and a calibrated receiver, and then compares observed values to calculate the difference of hardware delay of the two receivers, thereby obtaining the hardware delay of the receiver to be calibrated.
So far, the absolute hardware delay of the receiver is still one of the difficulties in time-frequency application, and especially for PPP time transfer, the uncertainty of hardware delay of 1ns restricts the practical application performance of sub-nanosecond time transfer. In the PPP time comparison, the time comparison result is obtained by making single difference through the clock difference of the receiver of the station. Thus, it is the relative hardware delay component between test stations that affects the PPP time delivery results. In order to solve the problem, the invention provides a real-time UTC (k) time comparison method based on relative hardware delay calibration in the WPT technical background. The method can eliminate the influence of hardware delay on PPP time comparison, and further improve the application performance of PPP time transmission in UTC (k) time comparison.
Disclosure of Invention
Because the existing absolute hardware delay calibration precision is only ns magnitude, the uncertainty of the existing absolute hardware delay calibration limits the real-time application of a sub-nanosecond time transfer technology, especially the time comparison of UTC (k). In order to further improve the application performance of the PPP time transfer technology in the UTC (k) time transfer, the invention provides a real-time UTC (k) time comparison method based on relative hardware delay calibration in the WPT technical background. The specific technical scheme of the invention is as follows:
a real-time UTC (k) time alignment method based on relative hardware delay calibration, comprising the steps of:
s1: acquiring a local Clock of the receiver r according to a PPP algorithm by adopting observation data and a post ephemeris r Product benchmark Clockref with clock difference after the fact post Of the difference, i.e. receiver clock difference dt r Comprises the following steps:
dt r ＝Clock r -Clockref post (1)
s2: due to delays in the receiver, antenna and cable hardware, the receiver r local Clock is compared to the standard time UTC (k) generated and maintained by the time laboratory with code k r There is a hardware delay variation delta r I.e. by
Clock r ＝UTC(k)+δ r (2)
Carrying out the formula (1) to obtain:
dt r ＝UTC(k)+δ r -Clockref post (3)
s3: two receivers r 1 And r 2 Accessing the same time frequency source of the time laboratory with the code number k, and obtaining the clock difference dt of the two receivers based on PPP resolving r1 And dt r2 Respectively as follows:
wherein, delta r1 And delta r2 Are respectively receivers r 1 And r 2 Compared to the hardware delay skew of UTC (k);
difference between them
dt r1 -dt r2 ＝UTC(k)+δ r1 -Clockref post -(UTC(k)+δ r2 -Clockref post )
＝δ r1 -δ r2
(5)
Equation (5) is the relative difference between the hardware delay deviations caused by the two receivers, the antenna and the cable;
s4: respectively arranging two receivers, antennas and cables which are subjected to hardware delay calibration in the steps S1-S3 in a time laboratory k 1 And time laboratory k 2 And a receiver r 1 Access time laboratory k 1 Of a time frequency source, receiver r 2 Access time laboratory k 2 A time frequency source of (a); the GNSS real-time observation data stream with the additional standard time information is pushed to a time monitoring server by a TCP/IP communication protocol;
s5: the time monitoring server carries out real-time PPP processing according to the GNSS observation information and the real-time difference correction number returned by the receiverObtaining the receiver clock difference dt under the corresponding clock difference reference utc(k) ，dt utc(k) Characterized by UTC (k) and WPT service platform reference time base T ref Also includes the time delay deviation delta caused by the time ratio to the hardware part in the link k I.e. dt utc(k) Comprises the following steps:
dt utc(k) ＝UTC(k)-T ref +δ r (6)
thus, for respectively located time laboratories k 1 And time laboratory k 2 Of a receiver r 1 And a receiver r 2 The receiver clock difference is respectively:
wherein UTC (k) 1 ) And UTC (k) 2 ) Respectively, by time laboratory k 1 Time laboratory k 2 The generated and maintained standard time;
the clock difference of the two receivers is used as a difference, and the reference time T can be eliminated ref And preserving the relative delay deviation delta between the two receiver chains k1 -δ k2 I.e. by
dt utc(k1) -dt utc(k2) ＝UTC(k 1 )-UTC(k 2 )+δ k1 -δ k2 (8)
UTC(k 1 )-UTC(k 2 )＝(dt utc(k1) -dt utc(k2) )-(δ k1 -δ k2 ) (9)
Based on this, UTC (k) with hardware delay calibration taken into account is realized 1 ) And UTC (k) 2 ) Comparing in real time.
Further, in step S5, the time monitoring server decodes the wide area difference product broadcast by the WPT service platform according to the predetermined format to obtain the real-time difference correction number
Wherein it is present>
Respectively are orbit difference correction numbers of the satellite in three directions; />
The clock error correction number of the satellite;
s5-1: number of track difference corrections
Corresponding to the star-solid coordinate system, the correction vector [ dx dy dz ] needs to be converted into the correction vector under the earth-solid system] T ：
In the formula (I), the compound is shown in the specification,
is a coordinate transformation matrix in which>
Is a unit column vector of the satellite in the radial direction device for selecting or keeping>
Is a unit column vector of the satellite in the direction of the velocity, <' >>
The unit column vectors, which are the directions perpendicular to both the velocity direction and the coordinate direction, of the satellite are respectively expressed as:
in the formula (I), the compound is shown in the specification,
is a coordinate vector of the satellite under the star-fixed system>
The velocity vectors of the satellites are determined by broadcast ephemeris, and x represents the inner product of the vectors;
s5-2: according to the broadcast ephemeris, the coordinates of each satellite in the earth-fixed system at the corresponding moment are calculated
Wherein X n ，Y n ，Z n ，/>
Coordinates and clock differences of the nth satellite in three directions under the earth-fixed system are respectively; and then, recovering the precise satellite orbit and clock error information according to the reduced difference correction number in the formula (10) to obtain the coordinates and clock errors of each corrected satellite: />
Wherein, X s ，Y s ，Z s ，dt s Respectively are coordinates and clock errors of the satellite in three directions under the earth fixed system after real-time differential correction;
s5-3: substituting the recovered clock error information of the precise satellite into a GNSS observation equation based on the ionosphere-free combination to perform real-time PPP algorithm processing:
wherein P is a non-ionosphere combined pseudo range observed value,
for the ionospheric-free combined phase observation, ρ is the geometric distance from the satellite to the receiver, the corrected satellite coordinates and the coordinates X, Y, Z of the receiver in three directions under the earth-fixed system are determined by equation (12), and expressed as ^ H>
c is the speed of light, dt s For the satellite clock difference, dt, obtained by equation (12) utc(k) For the receiver clock error, T is the tropospheric delay, λ is the carrier wavelength, N is the integer ambiguity, ε P And
representing observed noise, multipath effects and other unmodeled errors in the pseudorange observations and the phase observations, respectively;
therefore, when PPP calculation is carried out, the unknown parameters to be estimated are the position parameters X, Y and Z of the receiver, the clock error of the receiver, the troposphere delay T and the ambiguity parameter N; wherein, the receiver clock error can be used as white noise to estimate; the tropospheric delay is composed of a dry delay determined by a model and a wet delay estimated as a parameter of the random walk noise characteristics.
The invention has the beneficial effects that:
1. the invention has good usability: the influence of hardware delay on PPP time transfer is considered, a differential phase relative hardware delay calibration method is provided, and the influence of hardware delay on UTC (k) time comparison based on the PPP method is eliminated.
2. The invention has good real-time property: based on the WPT service platform, the receiver carries out real-time receiver state estimation and can reflect the comparison result of UTC (k) in a laboratory in real time.
3. The invention has good flexibility: the method is not only suitable for the multi-navigation system PPP time transfer application of two time frequency terminals, but also can select one receiver hardware delay as a reference in a station testing network, thereby realizing the unified calibration of a plurality of time frequency terminals relative to the hardware delay.
Drawings
In order to illustrate embodiments of the invention or solutions in the prior art more clearly, the drawings that are needed in the embodiments will be briefly described below, so that the features and advantages of the invention will be more clearly understood by referring to the drawings that are schematic and should not be understood as limiting the invention in any way, and other drawings may be obtained by those skilled in the art without inventive effort. Wherein:
FIG. 1 is a flow chart of relative hardware delay calibration between receivers;
fig. 2 is a flow chart of real-time UTC (k) comparison by a receiver after hardware delay calibration.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention, taken in conjunction with the accompanying drawings and detailed description, is set forth below. It should be noted that the embodiments of the present invention and features of the embodiments may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced otherwise than as specifically described herein and, therefore, the scope of the present invention is not limited by the specific embodiments disclosed below.
As shown in fig. 1, the real-time UTC (k) comparison method based on relative hardware delay calibration according to the present invention includes accessing a receiver to be calibrated and a cable to a same time frequency source for subsequent PPP resolution, obtaining relative hardware delay, then respectively installing the calibrated receivers in different time laboratories, obtaining real-time differential corrections through a WPT time service platform, obtaining clock differences of two stations of receivers through real-time PPP processing in combination with GNSS observation values, and further deducting the relative hardware delay calibration, thereby obtaining a real-time UTC (k) time comparison result, eliminating the influence of hardware delay on the UTC (k) time comparison based on the PPP method, and greatly improving the accuracy of the real-time UTC (k) time comparison.
Concretely, a real-time UTC (k) time comparison method based on relative hardware delay calibration comprises the following steps:
s1: acquiring a local Clock of the receiver r according to a PPP algorithm by adopting observation data and a post ephemeris r Product benchmark Clockref with clock difference after the fact post Of the difference, i.e. receiver clock difference dt r Comprises the following steps:
dt r ＝Clock r -Clockref post (1)
s2: due to delays in the receiver, antenna and cable hardware, the receiver r local Clock is compared to the standard time UTC (k) generated and maintained by the time laboratory with the code k r There is a hardware delay variation delta r I.e. by
Clock r ＝UTC(k)+δ r (2)
Carrying out the formula (1) to obtain:
dt r ＝UTC(k)+δ r -Clockref post (3)
s3: two receivers r 1 And r 2 Accessing the same time frequency source of the time laboratory with the code number k, and obtaining the clock difference dt of the two receivers based on PPP resolving r1 And dt r2 Respectively as follows:
wherein, delta r1 And delta r2 Are respectively receivers r 1 And r 2 Time information of (a) compared to the hardware delay skew of UTC (k);
the two are made a difference
dt r1 -dt r2 ＝UTC(k)+δ r1 -Clockref post -(UTC(k)+δ r2 -Clockref post )
＝δ r1 -δ r2
(5)
Equation (5) is the relative difference between the hardware delay deviations caused by the two receivers, the antenna and the cable;
s4: respectively arranging two receivers, antennas and cables which are subjected to hardware delay calibration in the steps S1-S3 in a time laboratory k 1 And time laboratory k 2 And a receiver r 1 Access time laboratory k 1 Of a time-frequency source, receiver r 2 Access time experimentChamber k 2 A time frequency source of (a); the GNSS real-time observation data stream with the additional standard time information is pushed to a time monitoring server by a TCP/IP communication protocol;
s5: the time monitoring server carries out real-time PPP processing according to the GNSS observation information and the real-time difference correction number returned by the receiver to obtain the receiver clock error dt under the corresponding clock error reference utc(k) ，dt utc(k) Characterized by UTC (k) and WPT service platform reference time base T ref Also includes the time delay deviation delta caused by the time ratio to the hardware part in the link k I.e. dt utc(k) Comprises the following steps:
dt utc(k) ＝UTC(k)-T ref +δ r (6)
thus, for respectively located time labs k 1 And time laboratory k 2 Of a receiver r 1 And a receiver r 2 The receiver clock difference is respectively:
wherein UTC (k) 1 ) And UTC (k) 2 ) Respectively, by time laboratory k 1 Time laboratory k 2 The generated and maintained standard time;
the clock difference of the two receivers is used as a difference, and the reference time T can be eliminated ref And preserving the relative delay deviation delta between the two receiver chains k1 -δ k2 I.e. by
dt utc(k1) -dt utc(k2) ＝UTC(k 1 )-UTC(k 2 )+δ k1 -δ k2 (8)
UTC(k 1 )-UTC(k 2 )＝(dt utc(k1) -dt utc(k2) )-(δ k1 -δ k2 ) (9)
Based on this, UTC (k) with hardware delay calibration taken into account is realized 1 ) And UTC (k) 2 ) Comparing in real time.
In some embodiments, in step S5, the time monitoring server followsDecoding the wide-area differential product broadcasted by the WPT service platform in a set format to obtain a real-time differential correction number
Wherein it is present>
Respectively are orbit difference correction numbers of the satellite in three directions; />
The clock error correction number of the satellite;
s5-1: number of track difference corrections
Corresponding to the star-solid coordinate system, the correction vector [ dx dy dz ] needs to be converted into the correction vector under the earth-solid system] T ：
In the formula (I), the compound is shown in the specification,
is a coordinate transformation matrix in which>
Is a unit column vector of the satellite in the radial direction device for selecting or keeping>
Is a unit column vector of the satellite in the direction of the velocity, <' >>
The unit column vectors, which are the directions perpendicular to both the velocity direction and the coordinate direction, of the satellite are respectively expressed as:
in the formula (I), the compound is shown in the specification,
is a coordinate vector of the satellite under the star-fixed system>
The velocity vectors of the satellites are determined by broadcast ephemeris, and x represents the inner product of the vectors;
s5-2: according to the broadcast ephemeris, the coordinates of each satellite in the earth-fixed system at the corresponding moment are calculated
Wherein, X n ，Y n ，Z n ，/>
Coordinates and clock errors of the nth satellite in three directions under the earth-fixed system are respectively; and then, recovering the precise satellite orbit and clock error information according to the reduced difference correction number in the formula (10) to obtain the coordinates and clock errors of each corrected satellite:
wherein, X s ，Y s ，Z s ，dt s Respectively the coordinates and clock errors of the satellite in three directions under the earth fixed system after the real-time differential correction;
s5-3: substituting the recovered clock error information of the precise satellite into a GNSS observation equation based on the ionosphere-free combination to perform real-time PPP algorithm processing:
wherein P is a non-ionosphere combined pseudo range observed value,
for the ionospheric-free combined phase observation, ρ is the geometric distance from the satellite to the receiver, the corrected satellite coordinates and the coordinates X, Y, Z of the receiver in three directions under the earth-fixed system are determined by equation (12), and expressed as ^ H>
c is the speed of light, dt s For the satellite clock difference, dt, obtained by equation (12) utc(k) For the receiver clock error, T is the tropospheric delay, λ is the carrier wavelength, N is the integer ambiguity, ε P And
representing observed noise, multipath effects and other unmodeled errors in the pseudorange observations and the phase observations, respectively;
therefore, when PPP calculation is carried out, the unknown parameters to be estimated are the position parameters X, Y and Z of the receiver, the clock error of the receiver, the troposphere delay T and the ambiguity parameter N; wherein, the receiver clock error can be used as white noise to estimate; the tropospheric delay is composed of a dry delay determined by a model and a wet delay estimated as a parameter of the random walk noise characteristics.
For the convenience of understanding the above technical aspects of the present invention, the following detailed description will be given of the above technical aspects of the present invention by way of specific examples.
Example 1
Selecting a time-keeping laboratory externally connected with an atomic clock, accessing two receivers to the same time frequency source, and obtaining clock differences dt of the two receivers through post PPP processing k1 And dt k2 . The local clock in the receiver clock difference contains the hardware delay deviation delta generated by the existence of the hardware delay of the receiver and the cable k1 And delta k2 Difference dt between clock differences of the two receivers k1 -dt k2 I.e., the relative hardware delays introduced by the two receivers and the cable.
The two receivers are respectively arranged in time laboratories A and B externally connected with an atomic clock, and the time laboratories are provided with a WPT time service platformThe receiver clock differences under the corresponding clock difference references of A and B are estimated in real time, and at the moment, the difference dt between the two receiver clock differences utc(k1) -dt utc(k2) The difference of the two external UTC (k) times and the sum of the relative hardware delays caused by the two receivers and the cable are determined, and therefore the relative hardware delays are deducted, and the real-time UTC (k) time comparison result between the two stations is obtained.
In summary, the present invention provides a method for comparing time between real-time UTCs (k) based on calibration of relative hardware delay, which can relatively calibrate the hardware delay in the time link and reflect the difference of standard time in the time keeping laboratory in real time, aiming at the problem that the time comparison between the conventional real-time UTCs (k) does not take into account the hardware delay deviation caused by the receiver and the cable. The availability of the system is greatly improved under the condition of ensuring the accuracy, and meanwhile, the real-time UTC (k) comparison result of the two measuring stations can be accurately and truly reflected, so that the method has wide application prospect in time synchronization and high-accuracy positioning.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (2)
1. A real-time UTC (k) time comparison method based on relative hardware delay calibration is characterized by comprising the following steps:
s1: acquiring a local Clock of the receiver r according to a PPP algorithm by adopting observation data and a post ephemeris r Standard Clockref of product with clock error after the fact post Difference of (d), i.e. receiver clock difference dt r Comprises the following steps:
dt r ＝Clock r -Clockref post (1)
s2: due to delays in the receiver, antenna and cable hardware, the receiver r local Clock is compared to the standard time UTC (k) generated and maintained by the time laboratory with code k r There is a hardware delay variation delta r I.e. by
Clock r ＝UTC(k)+δ r (2)
Substituting formula (1) to obtain:
dt r ＝UTC(k)+δ r -Clockref post (3)
s3: two receivers r 1 And r 2 Accessing the same time frequency source of the time laboratory with the code number k, and obtaining the clock difference dt of the two receivers based on PPP resolving r1 And dt r2 Respectively as follows:
wherein, delta r1 And delta r2 Are respectively receivers r 1 And r 2 Time information of (a) compared to the hardware delay skew of UTC (k);
the two are made a difference
dt r1 -dt r2 ＝UTC(k)+δ r1 -Clockref post -(UTC(k)+δ r2 -Clockref post )＝δ r1 -δ r2
(5)
Equation (5) is the relative difference between the hardware delay deviations caused by the two receivers, the antenna and the cable;
s4: respectively arranging two receivers, antennas and cables which are subjected to hardware delay calibration in the steps S1-S3 in a time laboratory k 1 And time laboratory k 2 And a receiver r 1 Access time laboratory k 1 Of a time-frequency source, receiver r 2 Access time laboratory k 2 A time frequency source of (a); the GNSS real-time observation data stream added with the standard time information is pushed to a time monitoring server by a TCP/IP communication protocol;
s5: the time monitoring server carries out real-time PPP processing according to the GNSS observation information and the real-time difference correction number returned by the receiver to obtain the receiver clock under the corresponding clock error referenceDifference dt utc(k) ，dt utc(k) Characterized by UTC (k) and WPT service platform reference time base T ref Also includes the time delay deviation delta caused by the time ratio to the hardware part in the link r I.e. dt utc(k) Comprises the following steps:
dt utc(k) ＝UTC(k)-T ref +δ r (6)
for respectively located time labs k 1 And time laboratory k 2 Of a receiver r 1 And a receiver r 2 The receiver clock differences are respectively:
wherein UTC (k) 1 ) And UTC (k) 2 ) Respectively, by time laboratory k 1 Time laboratory k 2 The generated and maintained standard time;
the difference between the two receiver clocks can eliminate the reference time T ref And preserving the relative delay deviation delta between the two receiver chains r1 -δ r2 I.e. by
dt utc(k1) -dt utc(k2) ＝UTC(k 1 )-UTC(k 2 )+δ ri -δ r2 (8)
UTC(k 1 )-UTC(k 2 )＝(dt utc(k1) -dt utc(k2) )-(δ r1 -δ r2 ) (9)
Based on this, UTC (k) with hardware delay calibration taken into account is realized 1 ) And UTC (k) 2 ) Comparing in real time.
2. The method according to claim 1, wherein in step S5, the time monitoring server decodes the wide area difference product broadcast by the WPT service platform according to a predetermined format to obtain the real-time difference correction number
Wherein it is present>
Respectively are orbit difference correction numbers of the satellite in three directions; />
The clock error correction number of the satellite;
s5-1: number of track difference corrections
Corresponding to the star-solid coordinate system, the correction vector [ dx dy dz ] needs to be converted into the correction vector under the earth-solid system] T ：
In the formula (I), the compound is shown in the specification,
is a coordinate transformation matrix in which>
Is a unit column vector of the satellite in the radial direction device for selecting or keeping>
Is a unit column vector of the satellite in the direction of the velocity, <' >>
The unit column vectors, which are the directions perpendicular to both the velocity direction and the coordinate direction, of the satellite are respectively expressed as:
in the formula (I), the compound is shown in the specification,
is a coordinate vector of the satellite under the star-fixed system>
The velocity vectors of the satellites are determined by broadcast ephemeris, and x represents the inner product of the vectors;
s5-2: according to the broadcast ephemeris, the coordinates of each satellite in the earth-fixed system at the corresponding moment are calculated
Wherein, X n ，Y n ，Z n ，/>
Coordinates and clock differences of the nth satellite in three directions under the earth-fixed system are respectively; and then, recovering the precise satellite orbit and clock error information according to the reduced difference correction number in the formula (10) to obtain the coordinates and clock errors of each corrected satellite:
wherein, X s ，Y s ，Z s ，dt s Respectively are coordinates and clock errors of the satellite in three directions under the earth fixed system after real-time differential correction;
s5-3: substituting the recovered clock error information of the precise satellite into a GNSS observation equation based on the ionosphere-free combination to perform real-time PPP algorithm processing:
wherein P is a non-ionosphere combined pseudo range observed value,
for the ionospheric-free combined phase observation, ρ is the geometric distance from the satellite to the receiver, the corrected satellite coordinates and the coordinates X, Y, Z of the receiver in three directions under the earth-fixed system are determined by equation (12), and expressed as ^ H>
c is the speed of light, dt s For the satellite clock difference, dt, obtained by equation (12) utc(k) For the receiver clock error, T is the tropospheric delay, λ is the carrier wavelength, N is the integer ambiguity, ε P And &>
Representing observed noise, multipath effects and other unmodeled errors in the pseudorange observations and the phase observations, respectively;
when PPP calculation is carried out, the unknown parameters to be estimated are position parameters X, Y and Z of a receiver, clock error of the receiver, troposphere delay T and integer ambiguity N; wherein, the receiver clock error can be used as white noise to estimate; the tropospheric delay is composed of a dry delay determined by a model and a wet delay estimated as a parameter of the random walk noise characteristics.
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