CN115201870B - Multi-frequency multi-mode GNSS non-difference non-combination time transfer method with priori constraints - Google Patents
Multi-frequency multi-mode GNSS non-difference non-combination time transfer method with priori constraints Download PDFInfo
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Abstract
The invention discloses a multi-frequency multi-mode GNSS non-difference non-combination time transfer method with priori constraint, which utilizes reference station network phase observation data to calculate satellite clock frequency deviation based on multi-frequency data; based on multi-frequency multi-system observation information, constructing a GNSS non-differential non-combination time transfer function model of full rank considering IFCB influence through parameter recombination; constructing a random model based on the spectral density; based on the constructed GNSS non-difference non-combination time transfer function model and random model of full rank considering IFCB influence, carrying out parameter estimation by adopting Kalman filtering to obtain receiver clock difference information of a corresponding station; the clock difference information of the receivers of two stations is subjected to time comparison, so that the clock information of the other station is obtained through the clock information of one station and the time comparison information. The invention can improve the reliability and the precision of time transmission.
Description
Technical Field
The invention relates to the field of high-precision positioning, in particular to a multi-frequency multi-mode GNSS non-difference non-combination time transfer method with priori constraints.
Background
With the continuous development of navigation systems, the current global observation frequency of each large navigation system is expanded from double frequency to three frequency or even multiple frequency, which brings new thought and opportunity for multi-frequency multi-mode GNSS data fusion; the multi-frequency multi-mode GNSS data can provide more visible satellites, more abundant frequencies and signals and more robust geometric observation structures, and further improve the service performance and reliability of the GNSS, but is currently under exploration and research.
Disclosure of Invention
The invention mainly aims to provide a multi-frequency multi-mode GNSS non-difference non-combination time transfer method with priori constraints, which improves the reliability and precision of time transfer.
In order to achieve the above purpose, the technical scheme provided by the invention is as follows: the multi-frequency multi-mode GNSS non-difference non-combination time transfer method with priori constraints comprises the following steps:
s1, calculating IFCB based on multi-frequency data by using reference station network phase observation data;
s2, based on multi-frequency multi-system observation information, constructing a GNSS non-difference non-combination time transfer function model of full rank considering IFCB influence through parameter recombination;
s3, constructing a random model based on the spectral density:
3.1, according to IGS station clock information, station clock stability of different stations is obtained;
3.2, fitting based on the corresponding relation between the stability and the noise coefficient to obtain a corresponding noise coefficient;
3.3, obtaining stability of a time transfer corresponding sampling interval according to a noise coefficient, and then obtaining corresponding process noise based on a corresponding relation between process noise spectral densities;
3.4, adopting a plurality of measuring stations to be provided with high-precision atomic clocks, and determining process noise according to a spectrum density average value obtained by Zhong Qun corresponding to clock difference information of the stations;
s4, performing parameter estimation by adopting Kalman filtering based on a constructed GNSS non-difference non-combination time transfer function model and a random model of full rank considering the influence of IFCB (Inter Frequency Clock bias, inter-satellite clock frequency deviation), so as to obtain receiver clock difference information of a corresponding station;
s5, repeating the step S4 to obtain receiver clock difference information of the other station, and comparing the time of the receiver clock differences of the two stations, so that the clock information of the other station is obtained through the clock information and the time comparison information of one station.
According to the method, the S1 specifically comprises the following steps:
1.1, obtaining IFCB information of a corresponding station through double-frequency two-by-two combination difference and inter-epoch difference of a single station;
1.2, calculating IFCB information of a plurality of stations in an observation network formed by a certain number of observation stations based on a height angle weighting mode to obtain inter-epoch variation of IFCB of each satellite single epoch; selecting an initial epoch, and obtaining IFCB information of a single station and a single epoch through accumulation;
and 1.3, based on the IFCB relation between the double-frequency IF combination and the non-combination, obtaining an IFCB correction value corresponding to the f-th frequency point.
According to the method, the method 1.1 specifically comprises the following steps:
satellite clock error based on L1/L2 IF combination
Wherein dt is S B, satellite clock difference not influenced by hardware delay vi Is the time-varying part of the phase delay of the ith (i=1, 2) frequency point satellite, d i For the time-invariant part of the hardware delay of the satellite pseudo-range of the ith frequency point, c is the vacuum light speed, and the satellite clock difference is similarly obtained based on the L1/L3 IF combination, wherein alpha is 1i ＝(f 1 2 )/(f 1 2 -f i 2 )，β 1i ＝-(f i 2 )/(f 1 2 -f i 2 )，b vi Is the time-varying part of the phase delay of the ith (i=1, 3) frequency point satellite, d i Is a time-invariant part of the hardware delay of the satellite pseudo-range of the ith frequency point, so the expression of IFCB is +.>
In b diff For the corresponding initial phase ambiguity difference, diff (L 1 ,L 2 ,L 3 )＝L if,12 -L if,13 I.e. the difference value of the two-by-two combination of the double-frequency observation values, d diff B is the time-invariant receiver phase and satellite phase hardware delay difference diff And d diff By inter-epoch differentiation
Eliminate (I)>
For the inter-epoch variation of IFCB for site r, diff (L 1 ,L 2 ,L 3 )＝L if,12 -L if,13 ，L if,12 And L if,13 For the combined observation value of the double-frequency pairwise ionosphere, k is epoch identification, namely IFCB information of a corresponding station can be obtained through double-frequency pairwise combination difference of a single station and inter-epoch difference
According to the method, in the above 1.2, the calendar of each satellite unit epoch IFCBInter-element variation
r is the number of stations, n is the maximum number of stations, < >>
For the corresponding weight value associated with the altitude angle +.>
Corresponding to the height angle value.
According to the method, the full-rank GNSS non-difference non-combination time transfer function model considering the IFCB effect is as follows:
in->
And->
Observations of pseudo-range and phase after correction of station star-distance and satellite clock-difference, respectively,/>
The three-dimensional position vector is linearized, T is a system identifier type, S is a satellite number, and r is a corresponding receiver number; f is frequency number, f=1, 2, 3..c is vacuum light speed, +.>
Receiver clock error for absorbing pseudorange bias, +.>
Is a coefficient of ionospheric bias delay, +.>
A bias ionospheric delay of 1 st frequency bin,/->
For tropospheric delay, ++>
ISB as projection function T For intersystem deviation>
To absorb the pseudo-range bias and phase ambiguity of the phase bias, it absorbs the receiver-side and satellite-side phase hardware delays, thus having floating solution characteristics, corresponding to IFB information +_multi-band multimode>
And IFCB information->
Is->
Wherein (1)>
λ f For the wavelength corresponding to frequency f +.>
For receiver-side pseudorange bias,/->
Corresponding to L 1 /L 2 And L 1 /L f IFCB information therebetween.
According to the above method, in the GNSS non-differential non-combination time transfer function model of full rank considering IFCB influence, if the corresponding system is a non-reference system, adding the corresponding ISB parameter ISB T The method comprises the steps of carrying out a first treatment on the surface of the The 3 rd frequency point of the pseudo range starts to add IFB parameters
According to the method, 3.1 specifically comprises the following steps: extracting Zhong Zhongcha sequences of an external hydrogen atom station in an IGS network solution clock error product, and adopting Hadamard variance analysis to analyze the stability of different smooth times;
the 3.2 is specifically as follows: according to the corresponding relation expression between the noise coefficient and the Hadamard variance
Fitting to obtain a corresponding noise coefficient; wherein->
Stability result, q, obtained for Hadamard variance corresponding to hydrogen clock 0 For phase modulation of white noise coefficient, q 1 For frequency modulation white noise coefficient, q 2 For frequency modulation random walk noise figure, q 3 For the frequency modulation random running noise coefficient, τ is the corresponding smoothing time;
in 3.3, the corresponding relation between the process noise spectral densities is
Wherein->
C is the vacuum light velocity for the determined process noise;
according to the method, S4 combines the receiver clock difference estimated value of the last epoch in the process of solving based on Kalman filtering parameters, and obtains the current receiver clock difference one-step predicted value and the variance thereof through one-step prediction
Is a one-step predictor of the state vector at time k, and (2)>
A state vector at time k-1; phi k,k-1 For state transition matrix>
For one-step prediction error variance matrix,/a matrix of prediction errors>
The variance of the state vector at time k-1; the receiver clock error prior constraint of the added process noise is that the variance of the one-step prediction variance corresponding to the corresponding receiver clock error after the process noise information is added is +.>
And then introducing the filtered signal into a filtering process for parameter solving.
A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized by: the processor executes the computer program to realize the steps of the multi-frequency multi-mode GNSS non-difference non-combination time transfer method with the prior constraint.
A computer-readable storage medium having stored thereon a computer program, characterized by: the computer program when executed by the processor realizes the steps of the multi-frequency multi-mode GNSS non-difference non-combination time transfer method with the prior constraint.
The invention has the beneficial effects that: based on a non-combined PPP model, a multi-GNSS system is processed in a combined mode, the multi-GNSS system is expanded to a time transfer model compatible with double frequencies, three frequencies and multiple frequencies, the time-varying characteristics of phase deviations of different frequency points are considered, satellite clock inter-frequency deviation correction is added to the function model, the multi-frequency time transfer function model is effectively refined, and therefore the reliability of time transfer is improved; meanwhile, the stability and the strong correlation characteristics between epochs of the high-performance atomic clock are fully considered, process noise is added to the receiver clock error parameters in the time transfer model, a random model is optimized, and the time transfer precision can be effectively guaranteed.
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The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a flow chart of a method of an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
As shown in fig. 1, the present invention provides a multi-frequency multi-mode GNSS non-differential non-combination time transfer method with a priori constraints, comprising the steps of:
s1, calculating IFCB based on multi-frequency data by using the reference station network phase observation data.
Research shows that the inconsistency among the GNSS observation signals causes significant IFCB to exist among satellite clock differences obtained by solving by adopting different observation combinations, and the difference has time-varying characteristics; in dual differential relative positioning, the effect of the bias can be effectively solved, however, the effect of IFCB needs to be fully considered in non-differential three-frequency or even multi-frequency GNSS phase observation value equation.
The following describes the solving process of IFCB in a single system:
1.1, obtaining IFCB information of a corresponding station through double-frequency two-by-two combination difference and inter-epoch difference of a single station.
Taking three-frequency IFCB solution as an example, corresponding IFCB information can be obtained according to the difference between the clock differences of two groups of ionosphere-free (IF) satellites of L1/L2 and L1/L3. Satellite clock error based on L1/L2 IF combination
Wherein dt is S B, satellite clock difference not influenced by hardware delay vi (i=1, 2) is the time-varying part of the phase delay of the satellite at the ith frequency point, d i For the time-invariant part of the hardware delay of the satellite pseudo-range of the ith frequency point, c is the vacuum light speed, and is based on the L1/L3 IF combinationThe resulting satellite clock difference is expressed as
Wherein alpha is 1i ＝(f 1 2 )/(f 1 2 -f i 2 )，β 1i ＝-(f i 2 )/(f 1 2 -f i 2 )，b vi (i=1, 3) is the time-varying part of the phase delay of the satellite at the ith frequency point, d i Is a time-invariant part of hardware delay of the satellite pseudo-range of the ith frequency point, so the IFCB expression is
In->
For the corresponding initial phase ambiguity difference, diff (L 1 ,L 2 ,L 3 )＝L if,12 -L if,13 I.e. the difference of the two-by-two combinations of the double frequency observations,/, is->
For time-invariant receiver phase and satellite phase hardware delay differences, +.>
And->
By inter-epoch differentiation
Elimination, diff (L 1 ,L 2 ,L 3 )＝L if,12 -L if,13 ，L if,12 And L if,13 And k is epoch identification, which is a dual-frequency pairwise ionosphere combined observation value. And then, according to the IFCB information of the corresponding site unit epoch obtained by accumulating the initial epochs, the IFCB information of the corresponding initial epoch can be forcedly set to 0, and the deviation can be absorbed by the phase ambiguity parameter of the floating point without influencing PPP time transfer.
1.2, calculating IFCB information of a plurality of stations in an observation network formed by a certain number of observation stations based on a height angle weighting mode to obtain inter-epoch variation of IFCB of each satellite single epoch; and selecting an initial epoch, and obtaining IFCB information of the single station and the single epoch through accumulation.
IFCB of the kth epoch, the nth station can be expressed as
Corresponding single station single epoch IFCB variation
k is the corresponding epoch number.
The single station IFCB epoch to epoch variable is obtained by 1.1
Then, the inter-epoch differential IFCB values of a plurality of stations in an observation network formed by a certain number of observation stations which are uniformly distributed worldwide are calculated based on a high-angle weighting mode to obtain the inter-epoch variation of the single-epoch IFCB of each satellite>
r is the number of stations, n is the maximum number of stations, < >>
For the corresponding weight value associated with the altitude angle +.>
Corresponding to the height angle value. Then the initial epoch can be selected by accumulating +.>
Obtaining single epoch IFCB information of a station r, wherein k is a corresponding epoch number, and k is 0 The initial epoch is numbered.
And 1.3, obtaining an IFCB correction value corresponding to the f frequency point based on an IFCB relation between a double-frequency IF (Ionosphere Free) combination and a non-combination.
Based on the 1 st and 2 nd frequency points and the 1 st and f frequency points, the three frequencies are used as references to obtain corresponding ionosphere combination IFCB information delta if，1f IFCB information of each frequency point can be according to the corresponding relation delta uc,f ＝-δ if,1f /β 1f Obtained.
S2, based on multi-frequency multi-system observation information, constructing a GNSS non-differential non-combination time transfer function model of full rank considering IFCB influence through parameter recombination.
The non-differential non-combination PPP time transfer model directly builds an observation equation from the original observation values on each frequency, the observation values are mutually independent, correlation cannot be generated due to combination of the observation values, the implementation is more convenient, the accurate establishment of a random model is facilitated, and meanwhile, the observation equation is built based on the original observation values of all frequency points, so that noise of the observation values cannot be amplified. Therefore, the non-differential non-combination PPP can effectively make up the defect of the traditional ionosphere combination model, can be better suitable for the development of the current multi-frequency multi-mode satellite navigation system, and greatly promotes the application of PPP technology in time transfer.
The non-differential non-combined precision single point positioning (Precise Point Positioning, PPP) time transfer model is:
wherein (1)>
And
observations of pseudo-range and phase, respectively, +.>
For station core geometry distance, T denotes system type, S denotes satellite number, r denotes corresponding receiver number, f is frequency number (f=1, 2, 3.)C is the vacuum light speed,/->
And dt (dt) T,S Receiver clock difference and satellite clock difference, respectively, < ->
Z is the tropospheric projection function r For tropospheric delay, ++>
Is a coefficient of ionospheric bias delay, +.>
For carrier phase wavelength corresponding to frequency f +.>
For the first frequency point, ionospheric delay, +.>
And
for frequency dependent receiver pseudorange hardware delay and satellite pseudorange hardware delay, for carrier phase ambiguity, which absorbs receiver side and satellite side phase hardware delay, +.>
Is the sum of pseudo-range observation noise and other unmodeled errors, +.>
Is the sum of carrier phase observation noise and other unmodeled errors.
In the non-differential non-combined observation equation, the satellite clock difference is considered
Absorbing time-invariant part d of pseudo-range hardware delay in L1/L2 1 And d 2 Ionosphere combination effect, and time-varying part of phase hardware delay +.>
And->
The ionospheric combination influence can be expressed as +.>
dt s To absorb satellite clock difference without hardware delay, receiver clock difference absorbs pseudo-range hardware delay b at receiver end r,1 And b r,2 The ionospheric combination of (2) can be expressed as +.>
Taking into consideration the time-varying characteristic of the 3 rd frequency point phase hardware delay, the corresponding IFCB information delta needs to be added into the phase observation value uc,3 Making corrections, the corresponding observation equation can be expressed as:
in the observation equation, the rank deficiency problem caused by the correlation of multiple types of parameters exists, so that parameter recombination is needed; meanwhile, the 3 rd frequency point has difference with the 1 st and 2 nd frequency points due to the difference of the absorbed pseudo-range deviation, so that inter-frequency deviation (inter frequency bias, IFB) is correspondingly added in pseudo-range observation values of the 3 rd frequency point to correct, corresponding ionosphere delay absorbs pseudo-range deviation information of a receiver end and a satellite end on the 1 st and 2 nd frequency points, phase ambiguity absorbs time-invariant information of phase hardware delay, and therefore corresponding phase ambiguity information remains unchanged in a continuous arc section without cycle slip, and an observation equation after parameter recombination can be expressed as follows:
wherein the combination isThe back ionosphere
Inter-frequency offset IFB r Phase ambiguity of each frequency bin>
IFCB correction information->
Pseudo-range deviation correction ζ f And phase deviation correction information eta f The corresponding parameter expression forms are as follows:
for the pseudo-range observation value, the time-varying characteristic of the corresponding inter-frequency deviation is smaller than the pseudo-range observation noise, so that the time-varying characteristic can be ignored, DCB information in the corresponding phase observation value needs to be corrected, and an observation equation after the correction of the external DCB product and MGEX satellite clock difference can be expressed as follows:
taking into account that
Exist between non-combined IFCB and L1/L3 combined IFCB
The corresponding relation of the (3) can be obtained based on the IFCB information of the L1/L3, and then the carrier phase observation value on the L3 is corrected; based on this, the relation between the ionosphere combinations of other frequency points and the non-combination IFCBs can be constructed, i.e.>
Wherein delta if,1f Can be based on L1/L2,according to L1/L2 and L1/L f The determination is made based on the procedure in S1.
The corresponding three-frequency multi-mode GNSS time transfer function model may be expressed as:
according to the characteristics of the non-combined model, the three frequencies can be expanded to multiple frequencies, and the expression of the multiple frequency model is as follows:
in the middle of
And->
The observed values of the pseudo range and the phase after the correction of the satellite distance and the satellite clock error are respectively,
the three-dimensional position vector is linearized, T is a system identifier type, S is a satellite number, and r is a corresponding receiver number; f is frequency number, f=1, 2, 3..c is vacuum light speed, +.>
Receiver clock error for absorbing pseudorange bias, +.>
Is a coefficient of ionospheric bias delay, +.>
A bias ionospheric delay of 1 st frequency bin,/->
For tropospheric delay, ++>
ISB as projection function T For intersystem deviation>
To absorb the pseudo-range bias and phase ambiguity of the phase bias, it absorbs the receiver-side and satellite-side phase hardware delays, thus having floating solution characteristics, corresponding to IFB information +_multi-band multimode>
And IFCB information
Is->
Wherein->
λ f For the wavelength corresponding to the frequency f,
for receiver-side pseudorange bias,/->
Corresponding to L 1 /L 2 And L 1 /L f IFCB information therebetween.
IFB corresponding to multiple frequency and multiple modes is
In the multi-frequency multi-system combined function model, when the corresponding system is a non-reference system, the corresponding ISB parameter ISB is added T The method comprises the steps of carrying out a first treatment on the surface of the The f (f=3, 4.) th frequency point of the pseudo range adds IFB parameter +.>
S3, constructing a random model based on the spectral density:
in conventional PPP and clock error calculation, the clock error of the receiver is generally used as white noise to carry out parameter estimation on an epoch-by-epoch basis, and constraint information that the clock error parameter of the receiver can change more stably between adjacent epochs is not fully explored; the method fully considers the characteristic of stable change among the epochs of the hydrogen atomic clock, determines the relation between the noise coefficient and the stability according to the stability of the atomic clock, acquires the process noise of the time transfer corresponding to the sampling interval, introduces a random model of parameter estimation, and updates the variance of the clock error parameter of the receiver.
Firstly, extracting a sequence of an external hydrogen atom station Zhong Zhongcha in an IGS network solution clock error product, and considering the frequency drift characteristic of a hydrogen clock, determining the stability of different smoothing times by adopting a Hadamard variance which can effectively solve the influence of frequency drift; then according to the noise (phase modulation white noise q 0 Frequency modulation white noise q 1 fM random walk noise q 2 And frequency modulated random running noise q 3 ) And fitting a corresponding relation expression between the coefficient and the Hadamard variance to obtain a corresponding noise coefficient, and determining the process noise of the corresponding sampling rate according to the sampling interval and the noise coefficient through a formula.
3.1, according to IGS station clock information, station clock stability of different stations is obtained; extracting Zhong Zhongcha sequences of an external hydrogen atom station from the IGS net solution clock error product, and adopting Hadamard analysis of variance to analyze the stability of different smooth times.
3.2, fitting based on the corresponding relation between the stability and the noise coefficient to obtain a corresponding noise coefficient; the 3.2 is specifically as follows: according to the corresponding relation expression between the noise coefficient and the Hadamard variance
Fitting to obtain a corresponding noise coefficient; wherein->
Stability result, q, obtained for Hadamard variance corresponding to hydrogen clock 0 For phase modulation of white noise coefficient, q 1 For adjustingWhite noise figure, q 2 For frequency modulation random walk noise figure, q 3 For a fm random running noise figure, τ is the smoothing time.
3.3, obtaining stability of a time transfer corresponding sampling interval according to a noise coefficient, and then obtaining corresponding process noise based on a corresponding relation between process noise spectral densities; wherein the corresponding relation between the process noise spectrum densities is
Wherein->
For determined process noise, c is the vacuum light velocity.
And 3.4, adopting a plurality of measuring stations to be equipped with high-precision atomic clocks, and determining process noise according to a spectrum density average value obtained by corresponding to the clock difference information of the Zhong Qun stations.
And S4, performing parameter estimation by adopting Kalman filtering based on the constructed GNSS non-differential non-combination time transfer function model and the random model of full rank considering IFCB influence, and obtaining receiver clock error information of a corresponding station. In the process of solving based on Kalman filtering parameters, combining the receiver clock error estimated value of the last epoch, obtaining the current receiver clock error one-step predicted value and variance thereof through one-step prediction
Is a one-step predictor of the state vector at time k, and (2)>
A state vector at time k-1; phi k,k-1 For state transition matrix>
For one-step prediction error variance matrix,/a matrix of prediction errors>
The variance of the state vector at time k-1; the receiver clock error prior constraint of the added process noise is that the variance after the one-step prediction variance corresponding to the corresponding receiver clock error is added with the process noise information can be expressed as +.>
And then introducing the filtered signal into a filtering process for parameter solving.
S5, repeating the step S4 to obtain receiver clock difference information of the other station, and comparing the time of the receiver clock differences of the two stations, so that the clock information of the other station is obtained through the clock information and the time comparison information of one station.
The invention fully utilizes GNSS observation information of multiple frequency and multiple systems, takes time-varying characteristics of phase deviation among all frequency points and characteristics of stable change and high correlation among epochs corresponding to a high-performance atomic clock into consideration, and constructs a strict and steady non-difference non-combination time transfer algorithm.
According to the method, modeling is carried out by adopting multi-frequency multi-mode GNSS observation data, the influence of time-varying characteristics of phase deviation corresponding to each frequency point on satellite clock bias is considered, and corresponding inter-frequency clock bias (Inter Frequency Bias, IFCB) is added at a third frequency point for correction; meanwhile, the high performance atomic clock is adopted in time transfer, the high performance of the atomic clock provides guarantee for stable change among satellite clock difference epochs, and corresponding prior information constraint is added to the receiver clock difference in a time transfer model. The multi-frequency multi-mode observation data are fully utilized to construct the full rank flexible, the multi-frequency multi-mode GNSS non-differential non-combination carrier phase time transfer model is compatible, and the reliability of time transfer is improved; the accuracy of the time transfer is improved by taking into account the correction of the satellite clock inter-frequency deviation and optimizing the stochastic model.
The invention also provides a computer device comprising a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the steps of the multi-frequency multi-mode GNSS non-differential non-combination time transfer method with the prior constraint are realized when the processor executes the computer program.
The present invention also provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the multi-frequency multi-mode GNSS non-differential non-combination time transfer method described above with a priori constraints.
It will be understood that modifications and variations will be apparent to those skilled in the art from the foregoing description, and it is intended that all such modifications and variations be included within the scope of the following claims.
Claims (8)
1. The multi-frequency multi-mode GNSS non-difference non-combination time transfer method with priori constraints is characterized by comprising the following steps of:
s1, calculating IFCB based on multi-frequency data by using reference station network phase observation data;
s2, based on multi-frequency multi-mode observation information, constructing a full-rank GNSS non-difference non-combination time transfer function model considering IFCB influence through parameter recombination; the full-rank GNSS non-difference non-combination time transfer function model considering the IFCB effect is as follows:
in->
And->
Observations of pseudo-range and phase after correction of station star-distance and satellite clock-difference, respectively,/>
The three-dimensional position vector is linearized, T is a system identifier type, S is a satellite number, and r is a corresponding receiver number; f is the frequency number, f=1, 2, 3..c is the vacuum light speed,
to absorb the falseReceiver clock difference from offset, +.>
Is a coefficient of ionospheric bias delay, +.>
Delay of the ionosphere for 1 st frequency point, Z r For tropospheric delay, ++>
ISB as projection function T For intersystem deviation>
To absorb the pseudo-range bias and phase ambiguity of the phase bias, it absorbs the receiver-side and satellite-side phase hardware delays, thus having floating solution characteristics, corresponding to IFB information +_multi-band multimode>
And IFCB information->
Is->
Wherein->
λ f For the wavelength corresponding to frequency f +.>
For receiver-side pseudorange bias,/->
Corresponding to L 1 /L 2 And L 1 /L f IFCB information between；
S3, constructing a random model based on the spectral density:
3.1, according to IGS station clock information, station clock stability of different stations is obtained;
3.2, fitting based on the corresponding relation between the stability and the noise coefficient to obtain a corresponding noise coefficient;
3.3, obtaining stability of a time transfer corresponding sampling interval according to a noise coefficient, and then obtaining corresponding process noise based on a corresponding relation between process noise spectral densities; the correspondence between the process noise spectral densities is
Wherein->
C is the vacuum light velocity for the determined process noise;
3.4, adopting a plurality of measuring stations to be provided with high-precision atomic clocks, and determining process noise according to a spectrum density average value obtained by Zhong Qun corresponding to clock difference information of the stations;
s4, performing parameter estimation by adopting Kalman filtering based on a constructed full-rank GNSS non-difference non-combination time transfer function model and a random model which take IFCB influence into consideration, so as to obtain receiver clock difference information of a corresponding station; in the process of solving based on Kalman filtering parameters, S4 combines the receiver clock error estimated value of the last epoch to obtain the current receiver clock error one-step predicted value and variance thereof through one-step prediction
Is a one-step predictor of the state vector at time k, and (2)>
A state vector at time k-1; phi k,k-1 Is a state transition matrix; />
For one-step prediction error variance matrix,/a matrix of prediction errors>
The variance of the state vector at time k-1; the receiver clock error prior constraint of the additive process noise is that the one-step prediction variance corresponding to the corresponding receiver clock error is +.>
Adding process noise information->
After correction of variance, i.e
Then introducing the filter into a filtering process to carry out parameter solving;
s5, repeating the step S4 to obtain receiver clock difference information of the other station, and comparing the time of the receiver clock differences of the two stations, so that the clock information of the other station is obtained through the clock information and the time comparison information of one station.
2. The multi-frequency multi-mode GNSS non-differential non-combination time transfer method with a priori constraints according to claim 1, wherein S1 specifically is:
1.1, obtaining IFCB information of a corresponding station through double-frequency two-by-two combination difference and inter-epoch difference of a single station;
1.2, calculating IFCB information of a plurality of stations based on a height angle weighting mode to obtain inter-epoch variation of each satellite single epoch IFCB; the stations are positioned in an observation network consisting of a certain number of observation stations; selecting initial epochs, and obtaining IFCB information of each epoch of a single station through accumulation;
and 1.3, obtaining an IFCB correction value corresponding to the f frequency point based on an IFCB relation between a double-frequency Ionosphere Free (IF) combination and a non-combination.
3. The multi-frequency multi-mode GNSS non-differential non-combination time transfer method with a priori constraints according to claim 2, wherein 1.1 is specifically:
based on L 1 /L 2 Satellite clock error obtained by IF combination
Wherein dt is S B, satellite clock difference not influenced by hardware delay vi Is the time-varying part of the phase delay of the ith (i=1, 2) frequency point satellite, d i Is the time-invariant part of the hardware delay of the satellite pseudo-range of the ith frequency point, c is the vacuum light speed, and is based on L 1 /L 3 The satellite clock difference obtained by IF combination is expressed as +.>
Wherein alpha is 1i ＝(f 1 2 )/(f 1 2 -f i 2 )，β 1i ＝-(f i 2 )/(f 1 2 -f i 2 )，b vi Is the time-varying part of the phase delay of the ith (i=1, 3) frequency point satellite, d i Is a time-invariant part of the hardware delay of the satellite pseudo-range of the ith frequency point, so the expression of IFCB +.>
Represented as
In b diff For the corresponding initial phase ambiguity difference, diff (L 1 ,L 2 ,L 3 )＝L if,12 -L if,13 I.e. the difference value of the two-by-two combination of the double-frequency observation values, d diff B is the time-invariant receiver phase and satellite phase hardware delay difference diff And d diff By inter-epoch differentiation
Eliminate (I)>
For the inter-epoch variation of IFCB for site r, diff (L 1 ,L 2 ,L 3 )＝L if,12 -L if,13 ，L if,12 And L if,13 For the combined observation value of the double-frequency pairwise ionosphere, k is epoch identification, namely IFCB information of the corresponding station is obtained through double-frequency pairwise combination difference of the single station and the epoch difference
4. The multi-frequency, multi-mode, GNSS non-differential, non-combination time transfer method with a priori constraints of claim 3, wherein in 1.2, the inter-epoch variation of each satellite single epoch IFCB
r is the number of stations, n is the maximum number of stations, < >>
For the corresponding weight value associated with the altitude angle +.>
Corresponding to the height angle value.
5. The method for multi-frequency, multi-mode, GNSS non-differential, non-combination time transfer with a priori constraints of claim 1, wherein in the full-rank GNSS non-differential, non-combination time transfer function model taking IFCB effects into account, if the corresponding system is a non-reference system, adding the corresponding ISB parameter ISB T The method comprises the steps of carrying out a first treatment on the surface of the The 3 rd frequency point of the pseudo range starts to add IFB parameters
6. The multi-frequency multi-mode GNSS non-differential non-combination time transfer method with a priori constraints according to claim 1, wherein 3.1 is specifically: extracting Zhong Zhongcha sequences of an external hydrogen atom station in an IGS network solution clock error product, and adopting Hadamard variance analysis to analyze the stability of different smooth times;
the 3.2 is specifically as follows: according to the corresponding relation expression between the noise coefficient and the Hadamard variance
Fitting to obtain a corresponding noise coefficient; wherein->
Stability result, q, obtained for Hadamard variance corresponding to hydrogen clock 0 For phase modulation of white noise coefficient, q 1 For frequency modulation white noise coefficient, q 2 For frequency modulation random walk noise figure, q 3 For a fm random running noise figure, τ is the corresponding smoothing time.
7. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized by: the processor, when executing the computer program, implements the steps of the multi-frequency multi-mode GNSS non-differential non-combination time transfer method with a priori constraints of any of the above claims 1 to 6.
8. A computer-readable storage medium having stored thereon a computer program, characterized by: the computer program, when executed by a processor, implements the steps of the multi-frequency multi-mode GNSS non-differential non-combination time transfer method of any of the preceding claims 1 to 6 with a priori constraints.
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