CN104459737A - Satellite positioning method based on real-time beacon differential - Google Patents

Abstract

The invention discloses a satellite positioning method based on real-time beacon differential. According to the satellite positioning method based on the real-time beacon differential, in order to solve the problem that ionized layer delay can not be eliminated when a conventional single-frequency beacon positioning method is adopted, the idea that an ionized layer pseudo range eliminating observation value is formed at the base station end by mean of a double-frequency pseudo range observation value is provided; meanwhile, smoothing is conducted on the ionized layer pseudo range eliminating observation value with amplified noise by means of an epoch carrier phase observation value low in noise, a corrected pseudo range value and the rate of change of the corrected pseudo range value along with time are generated according to the known distance between the station and a satellite, coding and sending conducted by means of single-frequency differential data in the prior art are replaced, and the effect of achieving double-frequency positioning by means of the original single-frequency sending technology is achieved. On the user side, a differential correction signal is demodulated through a receiver and is combined with the ionized layer pseudo range eliminating observation value which is received and processed by a user station and is subjected to smoothing for positioning and calculating. By the adoption of the satellite positioning method based on the real-time beacon differential, when the distance between the user station and a differential beacon station reaches 300 km, the planar positioning accuracy can be improved to about 0.15 m from the original 0.65 m.

Description

A kind of satellite positioning method based on beacon real time differential

Technical field

The present invention relates to GLONASS (Global Navigation Satellite System) (GNSS) satellite positioning method, particularly based on the satellite positioning method of beacon difference.

Background technology

Along with the development of waterway construction cause, as waterway construction and maintenance first march---navigation channel mapping operations also more and more shows its importance.Be no matter build in waterway engineering previous work, design, construction so that later evaluation each stage, or in channel maintenance, all based on the surveying and mapping result of navigation channel.Navigation channel mapping is produced as navigation channel, the important step of maintenance management, and its main contents covering scope is extensive, and involved technology, ladder of management are also more, with whole marine traffic engineering measure in close relations.Its main contents comprise land-based area topographical surveying, underwater survey, tidal observation and water lev el control, hydrologic observation and construction location survey etc.From by and large, the development experience of Yangtze River waterway optical measurement stage, photoelectric measurement stage, digitized measurement three phases, continue to advance fast by the direction measured along informationization.In the first stage, the main instrument adopted is transit, spirit-leveling instrument and sextant.In the photoelectric measurement stage, along with the development of instrument of surveying and mapping equipment, measurement means there occurs corresponding change, progressively develops into electromagnetic distance measuring instrument, laser range finder and total powerstation by optical instrument before.But no matter be optical measurement or photoelectric measurement, all need manually more participation, automaticity is low, affect greatly by extraneous factor, cause operating efficiency low, the navigation channel mapping demand day by day expanded cannot be met.

In the digitized measurement stage, mainly have benefited from the development of satellite positioning tech and the renewal of bathymetric survey sonar, GNSS technology is widely used at navigation channel survey field, and it can realize three-dimensional adjustment under unified coordinate frame, sets up the water course survey Controling network of high benchmark.The Changjiang River Trunk Line GPSC level set up as started in 2002, GPSD level Controling network are exactly a typical example.Also significantly improve the quality evaluation level of training works simultaneously, reliable technological means is provided to the maintenance of hydraulic facility and quality monitoring.Within 2012, rise, global position system-BDS (Big Dipper) system of China's independent development capability also completes region networking, starts to provide the service such as time service, location to the Asian-Pacific area.The use of BDS system has increased considerably the quantity of satellites in view, for navigator fix brings stronger reliability.In addition, China autonomous BDS systematic difference is advanced also to seem particularly important.

Beacon difference based on GPS is navigation channel mapping means conventional at present, and the ultimate principle of its location uses pseudo range difference technology.Current Radio Beacon transmits by standard station the impact of baud rate and beacon equipment cost, many employings are based on single-frequency positioning technology, in the region (as reaching 300km) that distance standard station is far away, by the impact of the atmosphere errors such as tropospheric delay, ionosphere delay, can there is obvious systematic bias in positioning result; And being subject to the impact of number of satellite, satellite distribution and observation noise randomness, its stability is not high, fluctuating error scope comparatively large (about ± 2m).

Summary of the invention

Goal of the invention: for above-mentioned prior art, proposes a kind of satellite positioning method based on beacon real time differential, can solve long distance beacon at present and be subject to the problem of ionosphere delayed impact and positioning result instability in locating.

Technical scheme: a kind of satellite positioning method based on beacon real time differential, first utilizes the Pseudo-range Observations composition of dual-frequency receiver without ionosphere Pseudo-range Observations in base station end; Then, to adopt between epoch carrier phase observation data to described without the smoothing process of ionosphere Pseudo-range Observations, obtain level and smooth without ionosphere pseudorange value; Again by described smoothly generate without ionosphere pseudorange corrected value and rate over time thereof without ionosphere pseudorange value in conjunction with known station star distance, described without ionosphere pseudorange corrected value and rate is encoded and launched by transmitter after modulating over time; At subscriber station end, first receive described transmitter and send signal and the differential correcting data generating current epoch after demodulating differential correcting signal; Then utilize described differential correcting data to subscriber station obtain level and smooth without ionosphere Pseudo-range Observations differential correcting, after generating differential correcting without ionosphere Pseudo-range Observations; End user station utilize described differential correcting after position without ionosphere Pseudo-range Observations and resolve.

As preferred version of the present invention, described a kind of satellite positioning method based on beacon real time differential comprises following concrete steps:

1), base station utilizes the Pseudo-range Observations composition of dual-frequency receiver without ionosphere Pseudo-range Observations, shown in (1.1):

$P_{\mathrm{IF}}=\frac{{f_1}^2\·P_1-f_2^2\·P_2}{{f_1}^2-f_2^2}---\left(1.1\right)$

In formula, f ₁and f ₂be respectively the signal frequency of GNSS Dual-frequency Observations; P ₁for signal frequency f ₁on Pseudo-range Observations, P ₂for signal frequency f ₂on Pseudo-range Observations, P _iFfor without ionosphere Pseudo-range Observations;

2), base station utilizes double frequency carrier observations to form without ionosphere carrier observations, shown in (1.2); Utilize the characteristic of the change of geometry item and pseudorange equivalence between carrier wave epoch, to 1) in gained described without ionosphere Pseudo-range Observations P _iFsmoothing process, shown in (1.3):

$\stackrel{\‾}{P_{\mathrm{IF}}}\left(t_i\right)=\frac{1}{i}{P}_{\mathrm{IF}}\left(t_i\right)+\frac{i-1}{i}[\stackrel{\‾}{P_{\mathrm{IF}}}\left(t_{i-1}\right)+\mathrm{\δ}{\mathrm{\φ}}_{\mathrm{IF}}(t_{i-1},t_i)]---\left(1.3\right)$

In formula (1.2)-(1.3), c is the light velocity; for frequency f ₁on carrier phase observation data, for frequency f ₂on carrier phase observation data; φ _iFindicate without ionosphere carrier observations; with be illustrated respectively in t _iand t _i-1moment after smoothing processing without ionosphere Pseudo-range Observations, P _iF(t _i) represent at t _imoment without ionosphere Pseudo-range Observations, i represents level and smooth number of times; δ φ _iF(t _i-1, t _i) represent between epoch without ionosphere carrier observations changing value;

3) base station by described after smoothing processing without ionosphere Pseudo-range Observations in conjunction with known station star distance ρ, generate without ionosphere pseudorange corrected value and without ionosphere pseudorange corrected value rate of change, shown in (1.4) and formula (1.5):

$\mathrm{\Δ}{P}_{\mathrm{IF}}\left(t_i\right)=\stackrel{\‾}{P_{\mathrm{IF}}}\left(t_i\right)-\mathrm{\ρ}-T-c\·\mathrm{\Δt}---\left(1.4\right)$

$\mathrm{\Δ}{\stackrel{\·}{P}}_{\mathrm{IF}}\left(t_i\right)=\mathrm{\Δ}{P}_{\mathrm{IF}}\left(t_i\right)-\mathrm{\Δ}{P}_{\mathrm{IF}}\left(t_{i-1}\right)---\left(1.5\right)$

In formula (1.4)-(1.5), Δ P _iF(t _i) be t _imoment without ionosphere pseudorange corrected value, for t _imoment without ionosphere pseudorange corrected value rate of change; ρ is the station star distance calculated according to satellite position and base station location; T is tropospheric delay; Δ t and Δ t ^kbe respectively the satellite clock (calculating according to broadcast ephemeris) of reference receiver clock correction (being obtained by pseudorange One-Point Location) and a kth satellite;

To described without ionosphere pseudorange corrected value with encode without ionosphere pseudorange corrected value rate of change and send through transmitter after modulating, realize the effect reaching double frequency location with original single-frequency transmission technology;

4), receiver user receives after described transmitter sends signal and demodulates differential correcting signal, and described differential correcting signal comprises difference pseudorange corrected value and pseudorange corrected value rate of change; The differential correcting data Δ P of current epoch is generated according to described differential correcting signal _iF(t _j), shown in (1.6):

$\mathrm{\Δ}{P}_{\mathrm{IF}}\left(t_j\right)=\mathrm{\Δ}{P}_{\mathrm{IF}}\left(t_i\right)+\mathrm{\Δ}{\stackrel{\·}{P}}_{\mathrm{IF}}\left(t_i\right)\·(t_j-t_i)---\left(1.6\right)$

With step 1) to step 2) in base station generate described smoothly without ionosphere Pseudo-range Observations method, subscriber station also utilize Dual Frequency Observation data genaration level and smooth without ionosphere Pseudo-range Observations

Differential correcting data Δ P described in utilization _iF(t _j) to level and smooth without ionosphere Pseudo-range Observations differential correcting described in subscriber station, after generating differential correcting without ionosphere Pseudo-range Observations such as formula (1.7):

$\widetilde{P_{\mathrm{IF}}}\left(t_j\right)=\stackrel{\‾}{P_{\mathrm{IF}}}{\left(t_j\right)}_U+\mathrm{\Δ}{P}_{\mathrm{IF}}\left(t_j\right)---\left(1.7\right)$

5), subscriber station utilize differential correcting after without ionosphere Pseudo-range Observations position and resolve, resolve equation such as formula (1.8):

$V=B\·\hat{X}-L,P---\left(1.8\right)$

In formula, V is residual matrix; B is design matrix; for solve for parameter; L is observing matrix; P is observed reading weight matrix; Wherein:

In formula (1.9), v _iand e _i(i=1,2 ..., n) represent the residual sum elevation of satellite of the corresponding observation equation of i-th satellite respectively; Dx, dy, dz are respectively the coordinate correction value on lower three directions of rectangular coordinate system in space; (X ₀, Y ₀, Z ₀) be subscriber station initial coordinate; ρ _0i, and T _ifor the tropospheric delay value correcting acquisition without ionosphere Pseudo-range Observations and troposphere empirical model after the first initial station star distance of respectively i-th satellite, differential correcting.

Beneficial effect: a kind of satellite positioning method based on beacon real time differential that the present invention proposes, base station utilizes double frequency Pseudo-range Observations to carry out iono-free combination thus eliminates the impact of ionosphere delay error, thus overcomes the principal element of impact long distance beacon Differential positioning precision; Simultaneously for the problem that pseudorange observation noise is larger, propose to utilize without ionosphere carrier phase observation data smoothing pseudo range, thus weaken the impact of pseudorange noise.At subscriber station, electric eliminating absciss layer peace of carrying out Pseudo-range Observations the same as base station is slided and is processed; The pseudo range difference signal (comprising pseudorange corrected value and pseudorange corrected value rate of change) of real-time reception, the transmission of decoding base station simultaneously, the Pseudo-range Observations offseted after ionosphere and smoothing processing is revised, eliminate or weaken the impact of the factor such as satellite clock, troposphere, thus improve positioning precision.Use the beacon Differential positioning method that this patent proposes, subscriber station is when reaching about 300km apart from difference beacon station, and its plane positioning precision can be promoted to about 0.15m by original about 0.65m.

Accompanying drawing explanation

Fig. 1 is based on the instantaneous location algorithm process flow diagram of the Big Dipper three frequency range lane combinational network RTK user side;

Fig. 2 conventional single-frequency pseudo range difference Pattern localization plane error distribution plan;

Fig. 3 double frequency pseudorange is without ionospheric combination difference (unsmooth process) Pattern localization plane error distribution plan;

Fig. 4 double frequency pseudorange is without ionospheric combination difference (smoothing processing) Pattern localization plane error distribution plan.

Embodiment

Below in conjunction with accompanying drawing, the present invention is further described.

As shown in the figure, a kind of satellite positioning method based on beacon real time differential, first utilizes the Pseudo-range Observations composition of dual-frequency receiver without ionosphere Pseudo-range Observations in base station end; Then, to adopt between epoch carrier phase observation data to described without the smoothing process of ionosphere Pseudo-range Observations, obtain level and smooth without ionosphere pseudorange value; Again by described smoothly generate without ionosphere pseudorange corrected value and rate over time thereof without ionosphere pseudorange value in conjunction with known station star distance, described without ionosphere pseudorange corrected value and rate is encoded and launched by transmitter after modulating over time; At subscriber station end, first receive described transmitter and send signal and the differential correcting data generating current epoch after demodulating differential correcting signal; Then utilize described differential correcting data to subscriber station obtain level and smooth without ionosphere Pseudo-range Observations differential correcting, after generating differential correcting without ionosphere Pseudo-range Observations; End user station utilize described differential correcting after position without ionosphere Pseudo-range Observations and resolve.Concrete steps are as follows:

1), base station utilizes the Pseudo-range Observations composition of dual-frequency receiver without ionosphere Pseudo-range Observations, shown in (1.1):

$P_{\mathrm{IF}}=\frac{{f_1}^2\·P_1-f_2^2\·P_2}{{f_1}^2-f_2^2}---\left(1.1\right)$

In formula, f ₁and f ₂be respectively the signal frequency of GNSS Dual-frequency Observations; P ₁for signal frequency f ₁on Pseudo-range Observations, P ₂for signal frequency f ₂on Pseudo-range Observations, P _iFfor without ionosphere Pseudo-range Observations;

2), base station utilize double frequency carrier observations form relative pseudorange have low noise figure without ionosphere carrier observations, shown in (1.2); Utilize the characteristic of the change of geometry item and pseudorange equivalence between carrier wave epoch, to 1) in gained described without ionosphere Pseudo-range Observations P _iFsmoothing process, to reduce the noise disappeared without ionosphere Pseudo-range Observations, shown in (1.3), the Pseudo-range Observations precision after level and smooth is such as formula (1.4):

$\stackrel{\‾}{P_{\mathrm{IF}}}\left(t_i\right)=\frac{1}{i}{P}_{\mathrm{IF}}\left(t_i\right)+\frac{i-1}{i}[\stackrel{\‾}{P_{\mathrm{IF}}}\left(t_{i-1}\right)+\mathrm{\δ}{\mathrm{\φ}}_{\mathrm{IF}}(t_{i-1},t_i)]---\left(1.3\right)$

${\mathrm{\σ}}_{\stackrel{\‾}{P_{\mathrm{IF}}}\left(t_i\right)}=\sqrt{i\·{\left(\frac{1}{i}\right)}^2{\mathrm{\σ}}_{P_{\mathrm{IF}}}^2+[{\left(\frac{i-1}{i}\right)}^2+(i-1)\frac{1}{i^2}]{\mathrm{\σ}}_{{\mathrm{\φ}}_{\mathrm{IF}}}^2}=\sqrt{\frac{1}{i}{\mathrm{\σ}}_{P_{\mathrm{IF}}}^2+\frac{i-1}{i}{\mathrm{\σ}}_{{\mathrm{\φ}}_{\mathrm{IF}}}^2}---\left(1.4\right)$

In formula (1.2)-(1.4), c is the light velocity; for frequency f ₁on carrier phase observation data, for frequency f ₂on carrier phase observation data; φ _iFindicate without ionosphere carrier observations; with be illustrated respectively in t _iand t _i-1moment after smoothing processing without ionosphere Pseudo-range Observations, P _iF(t _i) represent at t _imoment without ionosphere Pseudo-range Observations, i represents level and smooth number of times; δ φ _iF(t _i-1, t _i) represent between epoch without ionosphere carrier observations changing value; represent the Pseudo-range Observations precision smoothly; indicate without ionosphere Pseudo-range Observations P _iFprecision, indicate without ionosphere carrier observations φ _iFprecision;

3) base station by described after smoothing processing without ionosphere Pseudo-range Observations in conjunction with known station star distance ρ, generate without ionosphere pseudorange corrected value and without ionosphere pseudorange corrected value rate of change, shown in (1.5) and formula (1.6):

$\mathrm{\Δ}{P}_{\mathrm{IF}}\left(t_i\right)=\stackrel{\‾}{P_{\mathrm{IF}}}\left(t_i\right)-\mathrm{\ρ}-T-c\·\mathrm{\Δt}---\left(1.5\right)$

$\mathrm{\Δ}{\stackrel{\·}{P}}_{\mathrm{IF}}\left(t_i\right)=\mathrm{\Δ}{P}_{\mathrm{IF}}\left(t_i\right)-\mathrm{\Δ}{P}_{\mathrm{IF}}\left(t_{i-1}\right)---\left(1.6\right)$

In formula (1.5)-(1.6), Δ P _iF(t _i) be t _imoment without ionosphere pseudorange corrected value, for t _imoment without ionosphere pseudorange corrected value rate of change; ρ is the station star distance calculated according to satellite position and base station location; T is tropospheric delay, is calculated by troposphere empirical model; Δ t and Δ t ^kbe respectively the satellite clock (calculating according to broadcast ephemeris) of reference receiver clock correction (being obtained by pseudorange One-Point Location) and a kth satellite;

To described without ionosphere pseudorange corrected value with encode without ionosphere pseudorange corrected value rate of change and send through transmitter after modulating, realize the effect reaching double frequency location with original single-frequency transmission technology.

4), receiver user receives after described transmitter sends signal and demodulates differential correcting signal, and described differential correcting signal comprises difference pseudorange corrected value and pseudorange corrected value rate of change; The differential correcting data Δ P of current epoch is generated according to described differential correcting signal _iF(t _j), shown in (1.7):

$\mathrm{\Δ}{P}_{\mathrm{IF}}\left(t_j\right)=\mathrm{\Δ}{P}_{\mathrm{IF}}\left(t_i\right)+\mathrm{\Δ}{\stackrel{\·}{P}}_{\mathrm{IF}}\left(t_i\right)\·(t_j-t_i)---\left(1.7\right)$

With step 1) to step 2) in base station generate described smoothly without ionosphere Pseudo-range Observations method, subscriber station also utilize Dual Frequency Observation data genaration level and smooth without ionosphere Pseudo-range Observations

Differential correcting data Δ P described in utilization _iF(t _j) to level and smooth without ionosphere Pseudo-range Observations differential correcting described in subscriber station, after generating differential correcting without ionosphere Pseudo-range Observations such as formula (1.8):

$\widetilde{P_{\mathrm{IF}}}\left(t_j\right)=\stackrel{\‾}{P_{\mathrm{IF}}}{\left(t_j\right)}_U+\mathrm{\Δ}{P}_{\mathrm{IF}}\left(t_j\right)---\left(1.8\right)$

5), subscriber station utilize differential correcting after without ionosphere Pseudo-range Observations position and resolve, resolve equation such as formula (1.9):

$V=B\·\hat{X}-L,P---\left(1.9\right)$

In formula, V is residual matrix; B is design matrix; for solve for parameter; L is observing matrix; P is observed reading weight matrix; Wherein:

In formula (1.10), v _iand e _i(i=1,2 ..., n) represent the residual sum elevation of satellite of the corresponding observation equation of i-th satellite respectively; Dx, dy, dz are respectively the coordinate correction value on lower three directions of rectangular coordinate system in space; (X ₀, Y ₀, Z ₀) be subscriber station initial coordinate; ρ _0i, and T _ifor the tropospheric delay value correcting acquisition without ionosphere Pseudo-range Observations and troposphere empirical model after the first initial station star distance of respectively i-th satellite, differential correcting.

Adopt the CORS baseline experimental data of 24 hours of a 300.05km to verify, data sampling is spaced apart 15s, and two base stations are all equipped with Tian Bao (TRIMBLE) NETRS series of reception machine, and base station coordinates is accurate known to reference benchmark.Adopt wherein one be beacon station base station, another for subscriber station carry out ex post simulation beacon difference test resolve.Adopt three kinds and resolve pattern: (1) conventional single-frequency pseudo range difference pattern; (2) double frequency pseudorange is without ionospheric combination difference (unsmooth process); (3) double frequency pseudorange is without ionospheric combination difference (smoothing processing).Wherein pattern (3) is the method that this patent proposes.Under Three models, subscriber station plane positioning result respectively as shown in figs 2-4.

As can be seen from Figure 1, when using forestland (1) positions and resolves, north and south (N) and thing (E) deflection error be distributed in substantially ± 2m within, within single day, medial error statistics is respectively 0.562m and 0.317m, and the total positioning error of plane is 0.645m (see table 1).But simultaneously as can be seen from figure mono-, there is obvious direction asymmetry in positioning error, especially the North and South direction shown in figure mono-, and the distribution of error in southern side is obviously more than north side.This is mainly caused by ionosphere error effect comparatively large (cannot form iono-free combination) by single-frequency observed reading.

As can be seen from Figure 2, when using forestland (2) positions and resolves, due to the impact using double frequency pseudorange iono-free combination to eliminate ionosphere delay, it is obviously better that single-frequency situation symmetry is compared in error distribution, and the randomness that observation noise causes is stronger.But because iono-free combination is exaggerated the noise of Pseudo-range Observations, the scope of its error distribution obviously becomes (namely fluctuating error scope is larger) greatly, within single day, medial error statistics is respectively 1.177m and 0.815m, and the total positioning error of plane is 1.432m (see table 1).By the impact of pseudorange observation noise, positioning precision is generally lower than pattern (1).

Pattern (1) is obvious by ionosphere delayed impact, pattern (2) is not subject to ionosphere delayed impact but is subject to Pseudo-range Observations noise effect larger, based on this, pattern (3) i.e. this patent institute extracting method account for the impact of ionosphere delay and Pseudo-range Observations noise simultaneously, and the distribution of plane positioning error as shown in Figure 4.Use as can be seen from Figure 4 this patent institute's extracting method north and south (N) and thing (E) deflection error be substantially distributed in ± 0.6m within, single day medial error is added up and is respectively 0.117m and 0.094m, and the total positioning error of plane is 0.150m, in table 1.Can see that exit pattern (3) method had both efficiently solved the impact of ionosphere delay, also weaken the impact of observed reading noise, positioning precision is greatly improved.

Table 1 Three models lower plane positioning precision is added up

Can find out according to above experiment, use the satellite positioning method based on beacon real time differential that the present invention proposes, iono-free combination is carried out by utilizing double frequency Pseudo-range Observations, eliminate the impact of ionosphere delay error, thus overcome the principal element of impact long distance beacon Differential positioning precision; Utilize without ionosphere carrier phase observation data smoothing pseudo range simultaneously, significantly weaken the impact of pseudorange observation noise.Subscriber station is when reaching about 300km apart from difference beacon station, and its plane positioning precision is promoted to about 0.15m by original about 0.65m.

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the premise without departing from the principles of the invention; can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (2)

1. based on a satellite positioning method for beacon real time differential, it is characterized in that, first utilize the Pseudo-range Observations composition of dual-frequency receiver without ionosphere Pseudo-range Observations in base station end; Then, to adopt between epoch carrier phase observation data to described without the smoothing process of ionosphere Pseudo-range Observations, obtain level and smooth without ionosphere pseudorange value; Again by described smoothly generate without ionosphere pseudorange corrected value and rate over time thereof without ionosphere pseudorange value in conjunction with known station star distance, described without ionosphere pseudorange corrected value and rate is encoded and launched by transmitter after modulating over time; At subscriber station end, first receive described transmitter and send signal and the differential correcting data generating current epoch after demodulating differential correcting signal; Then utilize described differential correcting data to subscriber station obtain level and smooth without ionosphere Pseudo-range Observations differential correcting, after generating differential correcting without ionosphere Pseudo-range Observations; End user station utilize described differential correcting after position without ionosphere Pseudo-range Observations and resolve.

2. a kind of satellite positioning method based on beacon real time differential according to claim 1, is characterized in that, comprise following concrete steps:

1), base station utilizes the Pseudo-range Observations composition of dual-frequency receiver without ionosphere Pseudo-range Observations, shown in (1.1):

$P_{\mathrm{IF}}=\frac{{f_1}^2\·P_1-f_2^2\·P_2}{{f_1}^2-f_2^2}---\left(1.1\right)$

In formula, f ₁and f ₂be respectively the signal frequency of GNSS Dual-frequency Observations; P ₁for signal frequency f ₁on Pseudo-range Observations, P ₂for signal frequency f ₂on Pseudo-range Observations, P _iFfor without ionosphere Pseudo-range Observations;

2), base station utilizes double frequency carrier observations to form without ionosphere carrier observations, shown in (1.2); Utilize the characteristic of the change of geometry item and pseudorange equivalence between carrier wave epoch, to 1) in gained described without ionosphere Pseudo-range Observations P _iFsmoothing process, shown in (1.3):

$\stackrel{\‾}{P_{\mathrm{IF}}}\left(t_i\right)=\frac{1}{i}{P}_{\mathrm{IF}}\left(t_i\right)+\frac{i-1}{i}[\stackrel{\‾}{P_{\mathrm{IF}}}\left(t_{i-1}\right)+{\mathrm{\δ\φ}}_{\mathrm{IF}}(t_{i-1},t_i)]---\left(1.3\right)$

In formula (1.2)-(1.3), c is the light velocity; for frequency f ₁on carrier phase observation data, for frequency f ₂on carrier phase observation data; φ _iFindicate without ionosphere carrier observations; with be illustrated respectively in t _iand t _i-1moment after smoothing processing without ionosphere Pseudo-range Observations, P _iF(t _i) represent at t _imoment without ionosphere Pseudo-range Observations, i represents level and smooth number of times; δ φ _iF(t _i-1, t _i) represent between epoch without ionosphere carrier observations changing value;

3) base station by described after smoothing processing without ionosphere Pseudo-range Observations in conjunction with known station star distance ρ, generate without ionosphere pseudorange corrected value and without ionosphere pseudorange corrected value rate of change, shown in (1.4) and formula (1.5):

${\mathrm{\ΔP}}_{\mathrm{IF}}\left(t_i\right)=\stackrel{\‾}{P_{\mathrm{IF}}}\left(t_i\right)-\mathrm{\ρ}-T-c\·\mathrm{\Δt}+c\·{\mathrm{\Δt}}^k---\left(1.4\right)$

${\mathrm{\Δ}\stackrel{\·}{P}}_{\mathrm{IF}}\left(t_i\right)={\mathrm{\ΔP}}_{\mathrm{IF}}\left(t_i\right)-{\mathrm{\ΔP}}_{\mathrm{IF}}\left(t_{i-1}\right)---\left(1.5\right)$

In formula (1.4)-(1.5), Δ P _iF(t _i) be t _imoment without ionosphere pseudorange corrected value, for t _imoment without ionosphere pseudorange corrected value rate of change; ρ is the station star distance calculated according to satellite position and base station location; T is tropospheric delay; Δ t and Δ t ^kbe respectively the satellite clock (calculating according to broadcast ephemeris) of reference receiver clock correction (being obtained by pseudorange One-Point Location) and a kth satellite;

To described without ionosphere pseudorange corrected value with encode without ionosphere pseudorange corrected value rate of change and send through transmitter after modulating, realize the effect reaching double frequency location with original single-frequency transmission technology;

4), receiver user receives after described transmitter sends signal and demodulates differential correcting signal, and described differential correcting signal comprises difference pseudorange corrected value and pseudorange corrected value rate of change; The differential correcting data △ P of current epoch is generated according to described differential correcting signal _iF(t _j), shown in (1.6):

${\mathrm{\ΔP}}_{\mathrm{IF}}\left(t_j\right)={\mathrm{\ΔP}}_{\mathrm{IF}}\left(t_i\right)+{\mathrm{\Δ}\stackrel{\·}{P}}_{\mathrm{IF}}\left(t_i\right)\·(t_j-t_i)---\left(1.6\right)$

With step 1) to step 2) in base station generate described smoothly without ionosphere Pseudo-range Observations method, subscriber station also utilize Dual Frequency Observation data genaration level and smooth without ionosphere Pseudo-range Observations

Differential correcting data △ P described in utilization _iF(t _j) to level and smooth without ionosphere Pseudo-range Observations differential correcting described in subscriber station, after generating differential correcting without ionosphere Pseudo-range Observations such as formula (1.7):

$\widetilde{P_{\mathrm{IF}}}\left(t_j\right)=\stackrel{\‾}{P_{\mathrm{IF}}}{\left(t_j\right)}_U+{\mathrm{\ΔP}}_{\mathrm{IF}}\left(t_j\right)---\left(1.7\right)$

5), subscriber station utilize differential correcting after without ionosphere Pseudo-range Observations position and resolve, resolve equation such as formula (1.8):

$V=B\·\hat{X}-L,P---\left(1.8\right)$

In formula, V is residual matrix; B is design matrix; for solve for parameter; L is observing matrix; P is observed reading weight matrix; Wherein:

$B=\left[\begin{array}{cccc}\frac{X^1-X_0}{{\mathrm{\ρ}}_{01}}& \frac{Y^1-Y_0}{{\mathrm{\ρ}}_{01}}& \frac{Z^1-Z_0}{{\mathrm{\ρ}}_{01}}& 1\\ \frac{X^2-X_0}{{\mathrm{\ρ}}_{02}}& \frac{Y^2-Y_0}{{\mathrm{\ρ}}_{02}}& \frac{Z^2-Z_0}{{\mathrm{\ρ}}_{02}}& 1\\ \·& \·& \·& \\ \·& \·& \·& 1\\ \·& \·& \·& \\ \frac{X^n-X_0}{{\mathrm{\ρ}}_{0n}}& \frac{Y^n-Y_0}{{\mathrm{\ρ}}_{0n}}& \frac{Z^n-Z_0}{{\mathrm{\ρ}}_{0n}}& 1\end{array}\right],L=\left[\begin{array}{c}\widetilde{P_{\mathrm{IF}}}{\left(t_j\right)}_1-T_1-{\mathrm{\ρ}}_{01}\\ \widetilde{P_{\mathrm{IF}}}{\left(t_j\right)}_2-T_2-{\mathrm{\ρ}}_{02}\\ \·\\ \·\\ \·\\ \widetilde{P_{\mathrm{IF}}}{\left(t_j\right)}_n-T_n-{\mathrm{\ρ}}_{0n}\end{array}\right]---\left(\mathrm{1.9.2}\right)$

In formula (1.9), v _iand e _i(i=1,2 ..., n) represent the residual sum elevation of satellite of the corresponding observation equation of i-th satellite respectively; Dx, dy, dz are respectively the coordinate correction value on lower three directions of rectangular coordinate system in space; (X ₀, Y ₀, Z ₀) be subscriber station initial coordinate; and T _ifor the tropospheric delay value correcting acquisition without ionosphere Pseudo-range Observations and troposphere empirical model after the first initial station star distance of respectively i-th satellite, differential correcting.