CN104635249A - Quick fixing method for precise point positioning (PPP) ambiguity considering FCBs (Fractional Carrier Bias) - Google Patents

Abstract

The invention discloses a quick fixing method for precise point positioning ambiguity (PPP) considering FCBs (Fractional Carrier Bias). Due to the influence from hardware phase delay bias and initial phase bias of a receiver and a satellite end, the undifferenced ambiguity for the PPP has no integer characteristic. According to the method, part of observation stations is used as a base station; at the base station, a fractional part is separated from real number ambiguity by adopting a non-difference method and is distributed to a mobile station; at the mobile station, ambiguity is fixed as an integer by means of the fractional part, so that a fixed solution for the PPP is obtained.

Description

A kind of quick fixing means of Static Precise Point Positioning blur level taking FCBs into account

Technical field

The present invention relates to blur level fixing means in a kind of satellite precise One-Point Location.

Background technology

The information such as the Precise Orbit that precise single-point positioning technology utilizes IGS (or other mechanisms) to provide and precise clock correction calculate satellite orbit and clock correction, and by perfect physics correction model, the every error in location is corrected, carry out the absolute fix at single station, thus obtain high-precision positioning result.The development of precise single-point positioning technology went through for more than ten years, became the study hotspot of international navigator fix gradually, and achieved large quantities of abundant investigation and application achievement.This technology can be up to the standard the precision of direction grade, elevation direction centimetre-sized, but convergence time still needs more than 30min, and the precision in E direction also has much room for improvement.Precise single-point positioning technology development simultaneously rapidly, Chinese scholars to how improving precision, shorten convergence time and have also been made a lot of research.

The initial phase deviation of satellite and receiver and hardware delay deviation are referred to as the non-calibration delay of phase place, i.e. UPD by Blewitt scholar.He thinks, the fractional phase part deviation FCBs in UPD have impact on the non-integer characteristic of blur level.Two poor technology can this part error of cancellation receiver and satellite end, obtains integer ambiguity.But different from two poor technology, precise single-point positioning technology adopts un-differenced observation, UPD does not eliminate by two difference, and in solution process, this part delay can be absorbed by blur level, causes the non-integer characteristic of blur level.

Within 2008, professor Ge Maorong uses single poor location technology, and from non-poor real number blur level, isolate Liao Kuan Xiang Hezhai lane FCBs, result shows to change in time, and wide lane FCBs value is highly stable, substantially thinks a definite value; Narrow lane FCBs fluctuates comparatively large, and the narrow lane FCBs that every 15min resolves is also more stable, and this conclusion is particularly crucial for the realization of static solution.2006, Calais pointed out that precise single-point positioning technology coordinate repeatability does not in the directione have two difference net solution pattern high.2006, Rizos pointed out the raising fixedly being realized precision by blur level, was one of the novelty problem in GNSS investigation and application Future Ten year.

How being separated from real number blur level by the fraction part FCBs that receiver and satellite end hardware delay deviation and initial phase deviation cause, is the main bugbear realizing static solution.The phase estimation value that singly poor technology obtains is relative value, needs singly poor between survey station solving, and considers to adopt non-difference method to estimate FCBs, and realizes static solution.

Summary of the invention

Goal of the invention: for above-mentioned prior art, a kind of non-poor blur level fixing means of Static Precise Point Positioning taking FCBs into account is proposed, with non-difference method, the fraction part FCBs that receiver and satellite end hardware delay deviation and initial phase deviation cause can be separated from real number blur level, retightening blur level is integer, positioning calculation is done with integer ambiguity, effective raising positioning precision, shortens convergence time.

Technical scheme: a kind of quick fixing means of Static Precise Point Positioning blur level taking FCBs into account, comprises the following steps:

Step (1): choose CORS base station portion survey station as base station, adopts MW combination to carry out parameter estimation to the wide lane ambiguity of non-difference, and by average method smoothes blur level many epoch, obtains stable wide lane real number blur level; Then be benchmark by introducing survey station FCBs, adopt least-squares estimation, solve the wide lane FCBs of receiver, satellite end, further wide lane ambiguity is fixed as integer, concrete steps are:

Step (11), for base station i, adopts MW combined method, in conjunction with carrier phase frequency f ₁, f ₂on pseudorange and carrier phase observation data, form pseudorange, carrier phase observation data equation respectively, as shown in formula (1) formula (2):

$P_w=\frac{f_1{P}_1+f_2{P}_2}{f_1+f_2}={\mathrm{\ρ}}_0+c(\mathrm{dt}-\mathrm{ds})+{\mathrm{\ρ}}_{\mathrm{ion}}+{\mathrm{\ρ}}_{\mathrm{trop}}+{\mathrm{\ϵ}}_{P,s}---\left(1\right)$

${\mathrm{\Φ}}_w=\frac{f_1{\mathrm{\Φ}}_1-f_2{\mathrm{\Φ}}_2}{f_1-f_2}={\mathrm{\ρ}}_0+c(\mathrm{dt}-\mathrm{ds})+{\mathrm{\ρ}}_{\mathrm{ion}}+{\mathrm{\ρ}}_{\mathrm{trop}}+{\mathrm{\λ}}_w{B}_w+{\mathrm{\ϵ}}_{\mathrm{\Φ},s}---\left(2\right)$

In formula, P _wand Φ _wbe respectively pseudorange wide lane combined value and carrier phase wide lane combined value; f ₁and f ₂be respectively L ₁and L ₂carrier phase frequency; P ₁and P ₂be respectively L ₁and L ₂the Pseudo-range Observations of frequency range; Φ ₁and Φ ₂be respectively L ₁and L ₂the carrier phase observation data of frequency range; ρ ₀for the distance between survey station and satellite; C is the light velocity; Dt is receiver clock-offsets; Ds is satellite clock correction; ρ _ionfor ionospheric delay values; ρ _tropfor tropospheric delay error; ε _{p, s}for other errors of pseudorange observation; λ _wfor wide lane wavelength; B _wfor wide lane real number blur level; ε _{Φ, s}for other errors of carrier phase observation;

Described formula (1) and formula (2) are subtracted each other, obtains wide lane real number blur level B _w:

${\stackrel{\·}{B}}_w=\frac{{\mathrm{\Φ}}_w-P_w}{{\mathrm{\λ}}_w}---\left(3\right)$

Step (12), the method adopting many epoch average is to described wide lane real number blur level B _wsmoothing process, obtains level and smooth Hou Kuan lane real number blur level B _w;

Step (13), by described wide lane real number blur level B _wbe divided into three parts, as shown in formula (4):

B _w＝N _w+f _w，r-f _w ^s(4)

In formula, N _wfor by rounding the wide lane integer ambiguity obtained; f _{w, r}for the wide lane FCBs of receiver end; f _w ^sfor the wide lane FCBs of satellite end;

According to step (11) to step (12), obtain the wide lane real number blur level of n base station, and write as matrix form according to formula (4), as shown in formula (5):

$\left[\begin{array}{c}{B}_{w1}\\ B_{w2}\\ .\\ .\\ .\\ B_{\mathrm{wn}}\end{array}\right]=\left[\begin{array}{c}{N}_{w1}\\ N_{w2}\\ .\\ .\\ .\\ N_{\mathrm{wn}}\end{array}\right]+\left[\begin{array}{cc}{R}_{w1}& S_{w1}\\ R_{w2}& S_{w2}\\ .& .\\ .& .\\ .& .\\ R_{\mathrm{wn}}& S_{\mathrm{wn}}\end{array}\right]\left[\begin{array}{c}{f}^{\mathrm{wr}}\\ f^{\mathrm{ws}}\end{array}\right]---\left(5\right)$

In formula, B _wifor the wide lane real number ambiguity vector of base station i, comprise the value of 32 satellites; N _wifor base station i rounds the wide lane integer ambiguity obtained, comprise the value of 32 satellites equally; R _withe matrix of coefficients of the wide lane FCBs of the receiver end for base station i, it is 1 entirely that i-th corresponding base station matrix one arranges, and the corresponding columns of all the other base stations is 0; S _withe matrix of coefficients of the wide lane FCBs of the satellite end for base station i, i-th corresponding satellite place of base station is-1, and all the other satellites are 0; f ^wrfor receiver end wide lane FCBs matrix, comprise n base station; f ^wsfor satellite end wide lane FCBs matrix, comprise 32 satellites;

The FCBs arranging a base station is a benchmark, estimates, obtain each base station f by least square method to unknown number in formula (5) _{w, r}value and 32 satellites value;

Step (14), is averaged, using the value of mean value as the wide lane FCBs of satellite end the wide lane FCBs value of the whole day resolved satellite all epoch every;

Step (15), is brought into described wide lane real number blur level B by the satellite end FCBs that the survey station receiver end FCBs obtained according to described step (13) and step (14) obtain _w, by wide lane real number blur level B _wbe fixed into integer;

Step (2): according to the accurate coordinates that CORS base station is known, using position as constraint condition, adopt non-difference without ionospheric combination PPP model, carry out parameter estimation to without ionosphere blur level, obtain non-difference without ionospheric combination real number blur level, concrete steps are:

Set up non-difference without ionospheric combination Static Precise Point Positioning model, its observation equation is as shown in formula (6):

$\begin{array}{c}{P}_{\mathrm{IF}}=\frac{f_1^2}{f_1^2-f_2^2}{P}_1-\frac{f_2^2}{f_1^2-f_2^2}{P}_2={\mathrm{\ρ}}_0+c(\mathrm{dt}-\mathrm{ds})+{\mathrm{\ρ}}_{\mathrm{trop}}+\mathrm{dm}+{\mathrm{\ϵ}}_P\\ L_{\mathrm{IF}}=\frac{f_1^2}{f_1^2-f_2^2}{L}_1-\frac{f_2^2}{f_1^2-f_2^2}{L}_2={\mathrm{\ρ}}_0+c(\mathrm{dt}-\mathrm{ds})+{\mathrm{\ρ}}_{\mathrm{trop}}+\mathrm{\λ}{B}_{\mathrm{IF}}+\mathrm{\δm}+{\mathrm{\ϵ}}_L\end{array}---\left(6\right)$

In formula, P _iFfor the pseudorange value without ionospheric combination; L _iFfor the carrier phase value without ionospheric combination; Dm is the multipath effect of combined pseudorange observed reading; ε _pfor combined pseudorange observation noise; B _iFfor non-difference is without ionosphere real number blur level; δ m is the multipath effect of combinatorial phase observed reading; ε _lfor combinatorial phase observation noise; Described non-difference is solved without ionosphere real number blur level B by kalman filter method _iF;

Step (3): the non-difference that the wide lane ambiguity of integer described step (1) obtained and step (2) obtain combines without ionosphere real number blur level and obtains Fei Chazhai lane real number blur level, then be benchmark by introducing survey station, adopt the narrow lane FCBs of least-squares estimation receiver, satellite end, concrete steps are:

Step (31), by described wide lane integer ambiguity N _wwith non-difference without ionosphere real number blur level B _iFaccording to formula (7) combination, obtain narrow lane real number blur level

${\stackrel{\·}{B}}_n=\frac{f_1+f_2}{f_1}{B}_{\mathrm{IF}}-\frac{f_2}{f_1-f_2}{N}_w---\left(7\right)$

In formula, B _iFfor without ionosphere real number blur level; N _wfor the fixing wide lane ambiguity of integer;

Step (32), to described narrow lane real number blur level smoothing, obtain metastable narrow lane real number blur level B _n;

By the described narrow lane real number blur level B after smoothing processing _nbe divided into three parts:

B _n＝N _n+f _n，r-f _n ^s(8)

In formula, N _nfor narrow lane integer ambiguity; f _{n, r}for the narrow lane FCBs of receiver end; f _n ^sfor the narrow lane FCBs of satellite end;

Step (33), according to step (31) to step (32), obtains the narrow lane real number blur level of n base station, and is write as matrix form according to formula (8), as shown in formula (9):

$\left[\begin{array}{c}{B}_{n1}\\ B_{n2}\\ .\\ .\\ .\\ B_{\mathrm{nn}}\end{array}\right]=\left[\begin{array}{c}{N}_{n1}\\ N_{n2}\\ .\\ .\\ .\\ N_{\mathrm{nn}}\end{array}\right]+\left[\begin{array}{cc}{R}_{n1}& S_{n1}\\ R_{n2}& S_{n2}\\ .& .\\ .& .\\ .& .\\ R_{\mathrm{nn}}& S_{\mathrm{nn}}\end{array}\right]\left[\begin{array}{c}{f}^{\mathrm{nr}}\\ f^{\mathrm{ns}}\end{array}\right]---\left(9\right)$

In formula, B _nifor the Fei Chazhai lane real number ambiguity vector of base station i, comprise the value of 32 satellites; N _nifor base station i is by rounding the wide lane integer ambiguity obtained to wide lane real number blur level, comprise the value of 32 satellites equally; R _nithe matrix of coefficients of the narrow lane FCBs of the receiver end for base station i, it is 1 entirely that i-th corresponding base station matrix one arranges, and the corresponding columns of all the other base stations is 0; S _nisatellite end for base station i narrow lane FCBs matrix of coefficients, i-th corresponding satellite place of base station is-1, and all the other satellites are 0; f ^nrfor receiver end narrow lane FCBs matrix, comprise n survey station; f ^nsfor narrow lane satellite end FCBs matrix, comprise 32 satellites;

Step (34), carries out staging treating to the narrow lane ambiguity of whole day, every 10min average computation one Ge Zhai lane value, then adopts least square method to the narrow lane ambiguity of every 10min, estimates the f of each base station according to formula (9) _{n, r}the f of value and 32 satellites _n ^svalue;

Step (4): the wide lane f of every satellite that non-for least square difference method is resolved _w ^swith narrow lane f _n ^sbroadcast to rover station, the wide lane ambiguity N of rover station _winteger is fixed as, the narrow lane ambiguity N of rover station by rounding _nbe fixed as integer by LAMBDA algorithm, then both are reassembled into without ionosphere blur level according to formula (10), are called that non-difference is without ionosphere blur level static solution.

$N_{\mathrm{IF}}=\frac{f_1{f}_2}{{f_1}^2-{f_2}^2}{N}_w+\frac{f_1}{f_1+f_2}{N}_n---\left(10\right)$

Beneficial effect: due to the impact of receiver and satellite end hardware delay deviation and initial phase deviation, the non-poor blur level of Static Precise Point Positioning is made not have integer characteristic, this method selected part survey station is as base station, non-difference method is adopted fraction part to be separated from real number blur level at base station, fraction part is broadcast to rover station, it is integer that rover station fixes self blur level by decimal, thus realizes PPP static solution.Compared to prior art, have the following advantages:

(1) the present invention calculates and all adopts non-difference method without ionosphere, Kuan Xiang, narrow lane ambiguity, does not need difference algorithm, succinctly efficiently.(2) the present invention adopts non-difference method to estimate the FCBs value in wide lane, narrow lane, the accuracy of guarantee value and stability.(3) the present invention is by the estimation of FCBs, and can fix non-difference preferably without ionosphere blur level, fixing blur level back substitution, can realize high precision, fast Static Precise Point Positioning.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the non-poor blur level fixing means of Static Precise Point Positioning taking FCBs into account;

Fig. 2 is example Chongqing CORS data survey station distribution plan;

Tu3Shi Kuan lane satellite end FCBs estimates result;

Satellite end FCBs estimation in Tu4Shi Kuan lane is compared with total epoch correct epoch;

Tu5Shi Zhai lane satellite end FCBs value;

Fig. 6 is that the wide lane ambiguity of rover station is fixed into power;

Fig. 7 is that the narrow lane ambiguity of rover station is fixed into power;

Fig. 8 is traditional floating-point solution static immobilization result;

Fig. 9 is static solution static immobilization result;

Figure 10 is that floating-point solution compares with static solution locating effect.

Embodiment

Below in conjunction with accompanying drawing the present invention done and further explain.

Static Precise Point Positioning observation equation is as follows, is made up of pseudorange and carrier phase two parts:

P _s＝ρ ₀+c(dt-ds)+ρ _ion+ρ _trop+ε _P，s

(1)

Φ _s＝ρ ₀+c(dt-ds)-ρ _ion+ρ _trop+c(δ _r+δ _s)+λN _s+λ(φ _r(t ⁰)-φ _s(t ⁰))+ε _Φ，s

In formula, P _sand Φ _sbe respectively pseudorange and carrier phase value; ρ ₀for the distance between survey station and satellite; Dt is receiver clock-offsets; Ds is satellite clock correction; ρ _ionfor ionospheric delay values; ρ _tropfor tropospheric delay error; ε _{p, s}for other errors of pseudorange observation; δ _rand δ _sbe respectively receiver end and satellite end phase deviation; λ is carrier phase wavelength; N _sfor ambiguity of carrier phase; φ _r(t ⁰) and φ _s(t ⁰) be respectively receiver and satellite end initial phase; ε _{Φ, s}for other errors of carrier phase observation.

As can be seen from the formula of carrier phase, the phase deviation of receiver and satellite end and initial phase are difficult to separate, and these two errors are referred to as non-calibration hardware delay distortion (UPD, Uncalibrated Phase Delays).UPD is added in blur level item by usual carrier phase formula, as formula (2), and B here _sbe no longer integer ambiguity, but real number form.

Φ _s＝ρ ₀+c(dt-ds)-ρ _ion+ρ _trop+λB _s+ε _Φ，s(2)

Non-difference does not have integer characteristic without ionospheric combination blur level, and the UPD primarily of receiver and satellite end causes, if it can be separated, blur level can be retightened as integer.In order to reach this purpose, consider that leniently lane, narrow lane ambiguity extract decimal, realize the fixing of integer ambiguity.

Take the quick fixing means of Static Precise Point Positioning blur level of FCBs into account, comprise the following steps:

Step (1): choose CORS base station portion survey station as base station, adopts MW combination to carry out parameter estimation to the wide lane ambiguity of non-difference, and by average method smoothes blur level many epoch, obtains stable wide lane real number blur level; Then be benchmark by introducing survey station FCBs, adopt least-squares estimation, solve the wide lane FCBs of receiver, satellite end, further wide lane ambiguity is fixed as integer, concrete steps are:

Step (11), for base station i, adopts MW combined method, in conjunction with carrier phase frequency f ₁, f ₂on pseudorange and carrier phase observation data, form pseudorange, carrier phase observation data equation respectively, as shown in formula (3) formula (4):

$P_w=\frac{f_1{P}_1+f_2{P}_2}{f_1+f_2}={\mathrm{\ρ}}_0+c(\mathrm{dt}-\mathrm{ds})+{\mathrm{\ρ}}_{\mathrm{ion}}+{\mathrm{\ρ}}_{\mathrm{trop}}+{\mathrm{\ϵ}}_{P,s}---\left(3\right)$

${\mathrm{\Φ}}_w=\frac{f_1{\mathrm{\Φ}}_1-f_2{\mathrm{\Φ}}_2}{f_1-f_2}={\mathrm{\ρ}}_0+c(\mathrm{dt}-\mathrm{ds})+{\mathrm{\ρ}}_{\mathrm{ion}}+{\mathrm{\ρ}}_{\mathrm{trop}}+{\mathrm{\λ}}_w{B}_w+{\mathrm{\ϵ}}_{\mathrm{\Φ},s}---\left(4\right)$

In formula, P _wand Φ _wbe respectively pseudorange wide lane combined value and carrier phase wide lane combined value; f ₁and f ₂be respectively L ₁and L ₂carrier phase frequency; P ₁and P ₂be respectively L ₁and L ₂the Pseudo-range Observations of frequency range; Φ ₁and Φ ₂be respectively L ₁and L ₂the carrier phase observation data of frequency range; ρ ₀for the distance between survey station and satellite; C is the light velocity; Dt is receiver clock-offsets; Ds is satellite clock correction; ρ _ionfor ionospheric delay values; ρ _tropfor tropospheric delay error; ε _{p, s}for other errors of pseudorange observation; λ _wfor wide lane wavelength, b _wfor wide lane real number blur level; ε _{Φ, s}for other errors of carrier phase observation;

Formula (3) and formula (4) are subtracted each other, obtains wide lane real number blur level

${\stackrel{\·}{B}}_w=\frac{{\mathrm{\Φ}}_w-P_w}{{\mathrm{\λ}}_w}---\left(5\right)$

Step (12), the method adopting many epoch average is to wide lane real number blur level smoothing process, obtains level and smooth Hou Kuan lane real number blur level B _w, shown in (6):

$B_w=\frac{<{\stackrel{\&CenterDot;}{B}}_w>}{n}---\left(6\right)$

In formula, for current all summations epoch; N is number epoch;

Wide lane ambiguity B _wfor real number, do not have integer characteristic, cause primarily of hardware delay deviation and initial phase deviation two parts, these two parts are referred to as non-calibration hardware to postpone, i.e. UPD (Uncalibrated Phase Delays).Wide lane real number blur level B _wcan be write as following form:

B _w＝N _w+b _r-b ^s(7)

In formula, N _wfor by rounding the wide lane integer ambiguity obtained; b _rfor receiver end UPD; b ^sfor satellite end UPD.

Can find out, b _rand b ^sallow B _wthere is no integer characteristic, but b _rand b ^sintegral part and N _wcannot be separated, also can ensure that it is integer, therefore, we think that the integral part in UPD does not affect blur level, and fraction part wherein, be called fractional phase deviation, namely FCBs (Fractional Carrier Bias) causes the non-integral reason of blur level.FCBs can be divided into receiver end and satellite end two parts, if by decimal separation out, just can recover the integer characteristic of blur level.

Step (13), by wide lane real number blur level B _wbe divided into three parts, as shown in formula (8):

B _w＝N _w+f _w，r-f _w ^s(8)

In formula, N _wfor by rounding the wide lane integer ambiguity obtained; f _{w, r}for the wide lane FCBs of receiver end; f _w ^sfor the wide lane FCBs of satellite end;

According to step (11) to step (12), obtain the wide lane real number blur level of n base station, and write as matrix form according to formula (4), as shown in formula (9):

$\left[\begin{array}{c}{B}_{w1}\\ B_{w2}\\ .\\ .\\ .\\ B_{\mathrm{wn}}\end{array}\right]=\left[\begin{array}{c}{N}_{w1}\\ N_{w2}\\ .\\ .\\ .\\ N_{\mathrm{wn}}\end{array}\right]+\left[\begin{array}{cc}{R}_{w1}& S_{w1}\\ R_{w2}& S_{w2}\\ .& .\\ .& .\\ .& .\\ R_{\mathrm{wn}}& S_{\mathrm{wn}}\end{array}\right]\left[\begin{array}{c}{f}^{\mathrm{wr}}\\ f^{\mathrm{ws}}\end{array}\right]---\left(9\right)$

F in formula (9) ^wrand f ^wsbe unknown number, B _wifor the wide lane real number ambiguity vector of base station i, comprise the value of 32 satellites; N _wifor base station i rounds the wide lane integer ambiguity obtained, comprise the value of 32 satellites equally; R _withe matrix of coefficients of the wide lane FCBs of the receiver end for base station i, it is 1 entirely that i-th corresponding base station matrix one arranges, and the corresponding columns of all the other base stations is 0; S _withe matrix of coefficients of the wide lane FCBs of the satellite end for base station i, i-th corresponding satellite place of base station is-1, and all the other satellites are 0; f ^wrfor receiver end wide lane FCBs matrix, comprise n base station; f ^wsfor satellite end wide lane FCBs matrix, comprise 32 satellites;

The FCBs arranging a base station is a benchmark, solves rank defect problem, estimates, obtain each base station f by least square method to unknown number in formula (5) _{w, r}value and 32 satellites value;

Step (14), be averaged the wide lane FCBs value of the whole day resolved satellite all epoch every, using the value of mean value as the wide lane FCBs of satellite end, the correctness of Bing Duikuan lane FCBs is verified;

Step (15), is brought into wide lane real number blur level B by the satellite end FCBs that the survey station receiver end FCBs obtained according to step (13) and step (14) obtain _w, by wide lane real number blur level B _wbe fixed into integer.

Step (2): according to the accurate coordinates that CORS base station is known, using position as constraint condition, adopt non-difference without ionospheric combination PPP model, carry out parameter estimation to without ionosphere blur level, obtain non-difference without ionospheric combination real number blur level, concrete steps are:

Set up non-difference without ionospheric combination Static Precise Point Positioning model, its observation equation is as shown in formula (10):

$\begin{array}{c}{P}_{\mathrm{IF}}=\frac{f_1^2}{f_1^2-f_2^2}{P}_1-\frac{f_2^2}{f_1^2-f_2^2}{P}_2={\mathrm{\&rho;}}_0+c(\mathrm{dt}-\mathrm{ds})+{\mathrm{\&rho;}}_{\mathrm{trop}}+\mathrm{dm}+{\mathrm{\&epsiv;}}_P\\ L_{\mathrm{IF}}=\frac{f_1^2}{f_1^2-f_2^2}{L}_1-\frac{f_2^2}{f_1^2-f_2^2}{L}_2={\mathrm{\&rho;}}_0+c(\mathrm{dt}-\mathrm{ds})+{\mathrm{\&rho;}}_{\mathrm{trop}}+\mathrm{\&lambda;}{B}_{\mathrm{IF}}+\mathrm{\&delta;m}+{\mathrm{\&epsiv;}}_L\end{array}---\left(10\right)$

In formula, P _iFfor the pseudorange value without ionospheric combination; L _iFfor the carrier phase value without ionospheric combination; Dm is the multipath effect of combined pseudorange observed reading; ε _pfor combined pseudorange observation noise; B _iFfor non-difference is without ionosphere real number blur level; δ m is the multipath effect of combinatorial phase observed reading; ε _lfor combinatorial phase observation noise; Non-difference is solved without ionosphere real number blur level B by kalman filter method _iF;

Step (3): the non-difference that the wide lane ambiguity of integer step (1) obtained and step (2) obtain combines without ionosphere real number blur level and obtains Fei Chazhai lane real number blur level, then be benchmark by introducing survey station, adopt the narrow lane FCBs of least-squares estimation receiver, satellite end, concrete steps are:

Step (31), by wide lane integer ambiguity N _wwith non-difference without ionosphere real number blur level B _iFaccording to formula (11) combination, obtain narrow lane real number blur level

${\stackrel{\&CenterDot;}{B}}_n=\frac{f_1+f_2}{f_1}{B}_{\mathrm{IF}}-\frac{f_2}{f_1-f_2}{N}_w---\left(11\right)$

In formula, B _iFfor without ionosphere real number blur level; N _wfor the fixing wide lane ambiguity of integer;

Step (32), to narrow lane real number blur level smoothing, obtain metastable narrow lane real number blur level B _n;

By smoothing processing Hou Zhai lane real number blur level B _nbe divided into three parts:

B _n＝N _n+f _n，r-f _n ^s(12)

In formula, N _nfor narrow lane integer ambiguity; f _{n, r}for the narrow lane FCBs of receiver end; f _n ^sfor the narrow lane FCBs of satellite end;

Step (33), according to step (31) to step (32), obtains the narrow lane real number blur level of n base station, and is write as matrix form according to formula (12), as shown in formula (13):

$\left[\begin{array}{c}{B}_{n1}\\ B_{n2}\\ .\\ .\\ .\\ B_{\mathrm{nn}}\end{array}\right]=\left[\begin{array}{c}{N}_{n1}\\ N_{n2}\\ .\\ .\\ .\\ N_{\mathrm{nn}}\end{array}\right]+\left[\begin{array}{cc}{R}_{n1}& S_{n1}\\ R_{n2}& S_{n2}\\ .& .\\ .& .\\ .& .\\ R_{\mathrm{nn}}& S_{\mathrm{nn}}\end{array}\right]\left[\begin{array}{c}{f}^{\mathrm{nr}}\\ f^{\mathrm{ns}}\end{array}\right]---\left(13\right)$

In formula, B _nifor the Fei Chazhai lane real number ambiguity vector of base station i, comprise the value of 32 satellites; N _nifor base station i is by rounding the wide lane integer ambiguity obtained to wide lane real number blur level, comprise the value of 32 satellites equally; R _nithe matrix of coefficients of the narrow lane FCBs of the receiver end for base station i, it is 1 entirely that i-th corresponding base station matrix one arranges, and the corresponding columns of all the other base stations is 0; S _nisatellite end for base station i narrow lane FCBs matrix of coefficients, i-th corresponding satellite place of base station is-1, and all the other satellites are 0; f ^nrfor receiver end narrow lane FCBs matrix, comprise n survey station; f ^nsfor narrow lane satellite end FCBs matrix, comprise 32 satellites;

Step (34), narrow lane wavelength wide lane wavelength is about 86cm, and narrow lane wavelength is only less than 11cm, and values of ambiguity fluctuation is comparatively large, and identical with wide lane FCBs resolve way if adopted, with the data estimation of whole day, the narrow lane FCBs drawn is very unstable.But short-term narrow lane is known in existing research, and FCBs is more stable, therefore staging treating is carried out to the narrow lane ambiguity of whole day, every 10min average computation one Ge Zhai lane value, then least square method is adopted to the narrow lane ambiguity of every 10min, the f of each base station is estimated according to formula (9) _{n, r}the f of value and 32 satellites _n ^svalue;

Step (4): the wide lane f of every satellite that non-for least square difference method is resolved _w ^swith narrow lane f _n ^sbroadcast to rover station, the wide lane ambiguity N of rover station _winteger is fixed as, the narrow lane ambiguity N of rover station by rounding _nbe fixed as integer by LAMBDA algorithm, then both are reassembled into without ionosphere blur level according to formula (10), are called that non-difference is without ionosphere blur level static solution.

$N_{\mathrm{IF}}=\frac{f_1{f}_2}{{f_1}^2-{f_2}^2}{N}_w+\frac{f_1}{f_1+f_2}{N}_n---\left(10\right)$

By fixing non-difference without ionosphere blur level back substitution to PPP observation equation, by adding the form of virtual observation equation, carry out PPP to resolve, obtain location parameter, receiver clock-offsets, Zenith tropospheric wet stack emission and new blur level item, realize PPP static solution, effectively improve positioning precision, shorten convergence time.

The present embodiment adopts Chongqing CORS data, and gather Chongqing CORS whole day data on November 20th, 2010, sampling rate is spaced apart 15s, and website distribution plan as shown in Figure 2.Chongqing CORS has 24 survey stations, and circle marker survey station is base station, and totally 5, survey station is respectively BISH, CHSH, DIJI, KAXI, YOYA; Wherein triangle is masked as rover station, totally 4, is respectively FUDU, NACH, SHZH, WULO; Squarely be masked as all the other survey stations of Chongqing CORS.

Calculate the real number blur level of each base station respectively, solve according to non-poor least square method the wide lane FCBs value that wide lane FCBs, Fig. 3 are part satellites, can find out, the wide lane FCBs of whole day is highly stable, and except the short time period that satellite just rises, losing lock disappears, maximum fluctuation is about 0.2 week.The FCBs value of all for whole day epoch is averaged the value obtained, as the FCBs standard value of this day, thinks that the data differed within 0.15 week are correctly with standard value.The number num total epoch that statistics satellite occurs _p, and meet number num epoch of 0.15 week deviation _0.15, two epoch number more as shown in Figure 4, both bases epoch this quite.Both ratio is estimated as power as wide lane FCBs, and concrete numerical value is listed in Table 1 in detail, and table 1 is that satellite FCBs is estimated as power.In table 1,8,11,20,22, No. 25 satellites be estimated as power all below 90%, compared with other satellites, success ratio is lower slightly, if but will think that fixing successful ranges is successively loosened to 0.2 week from 0.15, these several satellite FCBs are estimated as power and are then changed to respectively: 92.60%, 98.61%, 94.28%, 94.35%, 95.88%, are fixed into power all more than 90%.Therefore, wide lane FCBs estimates correct, within one day, can estimate that a class value is as Long-term forecasting.Utilize receiver end and satellite end FCBs that wide for real number lane ambiguity is fixed as integer.

Tradition obtains non-poor real number without ionosphere blur level without ionospheric combination PPP Models computed, and in conjunction with the wide lane ambiguity of integer, both combinations obtain narrow lane ambiguity.Because narrow lane ambiguity fluctuation is comparatively large, the one group of data adopting every 10min to be averaged, resolve narrow lane FCBs by the data of every 10min, adopt and calculate identical method with wide lane FCBs.Fig. 5 is the narrow lane FCBs value of wherein 5 satellites, and every 10min mono-group, whole day has 144 groups of data, due to first several hours blur level instability, does not calculate respective value.Can find out in figure, compared to Kuan Xiang, narrow lane FCBs fluctuates slightly large, and maximum have 0.3 ~ 0.4 week, but think stable in time adjacent segments, and therefore narrow lane is generally used for short-term and fixes.When rover station fixes narrow lane ambiguity, choose immediate narrow lane FCBs according to time series and substitute into, fixing blur level.Due to narrow lane FCBs short-term stability, FCBs whole day in image width lane is unstable is a value, and narrow lane FCBs does not have stationary value as standard, can only judge that it is estimated as power by the entirety fluctuation situation of narrow lane FCBs.

So far, the task of base station all completes.Wide lane, narrow lane FCBs are broadcast rover station, and self wide lane, narrow lane ambiguity are fixed as integer by rover station.Wide lane, narrow lane FCBs are substituted into wide lane, narrow lane ambiguity respectively, by the real number blur level that obtains and nearest integer poor, thinking that the blur level of deviation within 0.25 week is fixed successfully, directly can be fixed as integer by rounding.By the epoch number and the ratio of satellite total epoch number of deviation in 0.25 week, the blur level as each satellite is fixed into power.Fig. 6 and Fig. 7 is respectively the wide lane of rover station, narrow lane ambiguity is fixed into power.Fig. 6 can find out, the wide lane ambiguity of satellite of each survey station is fixed into power substantially more than 90%, except stand No. 29 satellites, SHZH of NACH stands No. 3 satellite fixed rates lower than 90%, but still more than 85%.Through statistics, the wide lane fixed rate mean value of 4 rover station satellites is respectively 96.44%, 96.71%, 96.78%, 95.83%.The blur level deviation of about 96% is all within 0.25 week, and therefore, wide lane ambiguity directly can be fixed as integer by rounding.Fig. 7 finds out, all satellites narrow lane fixed rate is all between 85% ~ 90%, and through statistics, rover station narrow lane fixed rate mean value is respectively 87.15%, 86.63%, 87.02%, 87.23%.Because narrow lane wavelength is short, narrow lane ambiguity stability is not as wide lane, and fixed rate is naturally also be not as high as wide lane.Be fixed as the wide lane of integer, the combination of narrow lane ambiguity obtains without ionosphere blur level, namely blur level is fixing, by fixing blur level back substitution, re-starts PPP location, realizes static solution.Fig. 8 is the NEU positioning result of rover station tradition without ionospheric combination PPP model, and be commonly referred to as floating-point solution, with regard to floating-point solution positioning result, 4 rover station N direction site errors are about 2 ~ 3mm; E direction is about 1.1 ~ 1.2cm; U direction is about 1.9 ~ 2.1cm.Fig. 9 is the positioning result of static solution, and compared with floating-point solution result, NEU tri-deflection error curves are steady, three directions also can very rapid convergence in 0.1m, 4 rover station static solution N deflection errors are about 4 ~ 7mm, E direction 0.11 ~ 1cm, U direction 0.9 ~ 1.9cm.Using the positioning result of last epoch of floating-point solution and static solution as respective positioning precision index, both NEU directional precisions as shown in Figure 10.Compared with floating-point solution, the N directional precision of static solution result can variation in various degree, and E direction and U directional precision have raising in various degree.Concrete positioning precision is listed in table 2 in detail, and table 2 is that floating-point solution and the concrete error of static solution contrast.Can see, N directional precision is deteriorated, but is probably because the N directional precision of floating-point solution is very high, improve precision to be on the original basis difficult to realize, and found by contrast, static solution N directional precision is also 4 ~ 7mm substantially, not far short of what is expected with floating-point solution 2 ~ 3; E directional precision has lifting in various degree, is substantially risen to the 6.5mm of static solution by the 1.2cm of floating-point solution; U directional precision also has and promotes in various degree, is substantially promoted to 1.4cm by original 2cm.NEU tri-direction positioning precisioies are all reached the 10cm time used, and as the index of convergence time, floating-point solution and each survey station convergence time of static solution are listed in table 3 in detail, and table 3 is that floating-point solution and static solution convergence time contrast.The convergence time average out to 64min of floating-point solution, static solution is 41min, on average promotes 36%, visible, and static solution can not only improve positioning precision, also has remarkable result for shortening convergence time aspect.

Table 1 satellite FCBs is estimated as power

Table 1 can be found out, it is higher that satellite wide lane FCBs is fixed into power, and wide lane FCBs resolves correctly.

Table 2 floating-point solution and the concrete error of static solution contrast

Compared with floating-point solution, static solution E direction and U directional precision obviously promote.

Table 3 floating-point solution and static solution convergence time contrast

Compared with floating-point solution, the convergence time of static solution promotes about 36%.Therefore, the non-poor blur level taking FCBs into account fixes algorithm, can not only improve positioning precision, in speed of convergence, also have remarkable lifting.

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 (1)

1. take the quick fixing means of Static Precise Point Positioning blur level of FCBs into account, it is characterized in that: comprise the following steps:

Step (1): choose CORS base station portion survey station as base station, adopts MW combination to carry out parameter estimation to the wide lane ambiguity of non-difference, and by average method smoothes blur level many epoch, obtains stable wide lane real number blur level; Then be benchmark by introducing survey station FCBs, adopt least-squares estimation, solve the wide lane FCBs of receiver, satellite end, further wide lane ambiguity is fixed as integer, concrete steps are:

Step (11), for base station i, adopts MW combined method, in conjunction with carrier phase frequency f ₁, f ₂on pseudorange and carrier phase observation data, form pseudorange, carrier phase observation data equation respectively, as shown in formula (1) formula (2):

$P_w=\frac{f_1{P}_1+f_2{P}_2}{f_1+f_2}={\mathrm{\&rho;}}_0+c(\mathrm{dt}+\mathrm{ds})+{\mathrm{\&rho;}}_{\mathrm{ion}}+{\mathrm{\&rho;}}_{\mathrm{trop}}+{\mathrm{\&epsiv;}}_{P,s}---\left(1\right)$

${\mathrm{\&Phi;}}_w=\frac{f_1{\mathrm{\&Phi;}}_1-f_2{\mathrm{\&Phi;}}_2}{f_1-f_2}={\mathrm{\&rho;}}_0+c(\mathrm{dt}-\mathrm{ds})+{\mathrm{\&rho;}}_{\mathrm{ion}}+{\mathrm{\&rho;}}_{\mathrm{trop}}+{\mathrm{\&lambda;}}_w{B}_w+{\mathrm{\&epsiv;}}_{\mathrm{\&Phi;},s}---\left(2\right)$

In formula, P _wand Φ _wbe respectively pseudorange wide lane combined value and carrier phase wide lane combined value; f ₁and f ₂be respectively L ₁and L ₂carrier phase frequency; P ₁and P ₂be respectively L ₁and L ₂the Pseudo-range Observations of frequency range; Φ ₁and Φ ₂be respectively L ₁and L ₂the carrier phase observation data of frequency range; ρ ₀for the distance between survey station and satellite; C is the light velocity; Dt is receiver clock-offsets; Ds is satellite clock correction; ρ _ionfor ionospheric delay values; ρ _tropfor tropospheric delay error; ε _{p, s}for other errors of pseudorange observation; λ _wfor wide lane wavelength; B _wfor wide lane real number blur level; ε _{Φ, s}for other errors of carrier phase observation;

Described formula (1) and formula (2) are subtracted each other, obtains wide lane real number blur level

$\stackrel{\&CenterDot;}{B_w}=\frac{{\mathrm{\&Phi;}}_w-P_w}{{\mathrm{\&lambda;}}_w}---\left(3\right)$

Step (12), the method adopting many epoch average is to described wide lane real number blur level smoothing process, obtains level and smooth Hou Kuan lane real number blur level B _w;

Step (13), by described wide lane real number blur level B _wbe divided into three parts, as shown in formula (4):

B _w＝N _w+f _w，r-f _w ^s(4)

In formula, N _wfor by rounding the wide lane integer ambiguity obtained; f _{w, r}for the wide lane FCBs of receiver end; f _w ^sfor the wide lane FCBs of satellite end;

According to step (11) to step (12), obtain the wide lane real number blur level of n base station, and write as matrix form according to formula (4), as shown in formula (5):

$\left[\begin{array}{c}{B}_{w1}\\ B_{w2}\\ .\\ .\\ .\\ B_{\mathrm{wn}}\end{array}\right]=\left[\begin{array}{c}{N}_{w1}\\ N_{w2}\\ .\\ .\\ .\\ N_{\mathrm{wn}}\end{array}\right]+\left[\begin{array}{cc}{R}_{w1}& S_{w1}\\ R_{w2}& S_{w2}\\ .& .\\ .& .\\ .& .\\ R_{\mathrm{wn}}& S_{\mathrm{wn}}\end{array}\right]\left[\begin{array}{c}{f}^{\mathrm{wr}}\\ f_{\mathrm{ws}}\end{array}\right]---\left(5\right)$

In formula, B _wifor the wide lane real number ambiguity vector of base station i, comprise the value of 32 satellites; N _wifor base station i rounds the wide lane integer ambiguity obtained, comprise the value of 32 satellites equally; R _withe matrix of coefficients of the wide lane FCBs of the receiver end for base station i, it is 1 entirely that i-th corresponding base station matrix one arranges, and the corresponding columns of all the other base stations is 0; S _withe matrix of coefficients of the wide lane FCBs of the satellite end for base station i, i-th corresponding satellite place of base station is-1, and all the other satellites are 0; f ^wrfor receiver end wide lane FCBs matrix, comprise n base station; f ^wsfor satellite end wide lane FCBs matrix, comprise 32 satellites;

The FCBs arranging a base station is a benchmark, estimates, obtain each base station f by least square method to unknown number in formula (5) _{w, r}value and 32 satellites value;

Step (14), is averaged, using the value of mean value as the wide lane FCBs of satellite end the wide lane FCBs value of the whole day resolved satellite all epoch every;

Step (15), is brought into described wide lane real number blur level B by the satellite end FCBs that the survey station receiver end FCBs obtained according to described step (13) and step (14) obtain _w, by wide lane real number blur level B _wbe fixed into integer;

Step (2): according to the accurate coordinates that CORS base station is known, using position as constraint condition, adopt non-difference without ionospheric combination PPP model, carry out parameter estimation to without ionosphere blur level, obtain non-difference without ionospheric combination real number blur level, concrete steps are:

Set up non-difference without ionospheric combination Static Precise Point Positioning model, its observation equation is as shown in formula (6):

$P_{\mathrm{IF}}=\frac{{f_1}^2}{{f_1}^2-{f_2}^2}{P}_1-\frac{{f_2}^2}{{f_1}^2-{f_2}^2}{P}_2={\mathrm{\&rho;}}_0+c(\mathrm{dt}+\mathrm{ds})+{\mathrm{\&rho;}}_{\mathrm{trop}}+\mathrm{dm}+{\mathrm{\&epsiv;}}_P$ (6)

$L_{\mathrm{IF}}=\frac{{f_1}^2}{{f_1}^2-{f_2}^2}{L}_1-\frac{{f_2}^2}{{f_1}^2-{f_2}^2}{L}_2={\mathrm{\&rho;}}_0+c(\mathrm{dt}+\mathrm{ds})+{\mathrm{\&rho;}}_{\mathrm{trop}}+{\mathrm{\&lambda;B}}_{\mathrm{IF}}+\mathrm{\&delta;m}+{\mathrm{\&epsiv;}}_L$

In formula, P _iFfor the pseudorange value without ionospheric combination; L _iFfor the carrier phase value without ionospheric combination; Dm is the multipath effect of combined pseudorange observed reading; ε _pfor combined pseudorange observation noise; B _iFfor non-difference is without ionosphere real number blur level; δ m is the multipath effect of combinatorial phase observed reading; ε _lfor combinatorial phase observation noise; Described non-difference is solved without ionosphere real number blur level B by kalman filter method _iF;

Step (3): the non-difference that the wide lane ambiguity of integer described step (1) obtained and step (2) obtain combines without ionosphere real number blur level and obtains Fei Chazhai lane real number blur level, then be benchmark by introducing survey station, adopt the narrow lane FCBs of least-squares estimation receiver, satellite end, concrete steps are:

Step (31), by described wide lane integer ambiguity N _wwith non-difference without ionosphere real number blur level B _iFaccording to formula (7) combination, obtain narrow lane real number blur level

${\stackrel{\&CenterDot;}{B}}_n=\frac{f_1+f_2}{f_1}{B}_{\mathrm{IF}}-\frac{f_2}{f_1-f_2}{N}_w---\left(7\right)$

In formula, B _iFfor without ionosphere real number blur level; N _wfor the fixing wide lane ambiguity of integer;

Step (32), to described narrow lane real number blur level smoothing, obtain metastable narrow lane real number blur level B _n;

By the described narrow lane real number blur level B after smoothing processing _nbe divided into three parts:

B _n＝N _n+f _n，r-f _n ^s(8)

In formula, N _nfor narrow lane integer ambiguity; f _{n, r}for the narrow lane FCBs of receiver end; f _n ^sfor the narrow lane FCBs of satellite end;

Step (33), according to step (31) to step (32), obtains the narrow lane real number blur level of n base station, and is write as matrix form according to formula (8), as shown in formula (9):

$\left[\begin{array}{c}{B}_{n1}\\ B_{n2}\\ .\\ .\\ .\\ B_{\mathrm{nn}}\end{array}\right]=\left[\begin{array}{c}{N}_{n1}\\ N_{n2}\\ .\\ .\\ .\\ N_{\mathrm{nn}}\end{array}\right]+\left[\begin{array}{cc}{R}_{n1}& S_{n1}\\ R_{n2}& S_{n2}\\ .& .\\ .& .\\ .& .\\ R_{\mathrm{nn}}& S_{\mathrm{nn}}\end{array}\right]\left[\begin{array}{c}{f}^{\mathrm{nr}}\\ f^{\mathrm{ns}}\end{array}\right]---\left(9\right)$

In formula, B _nifor the Fei Chazhai lane real number ambiguity vector of base station i, comprise the value of 32 satellites; N _nifor base station i is by rounding the wide lane integer ambiguity obtained to wide lane real number blur level, comprise the value of 32 satellites equally; R _nithe matrix of coefficients of the narrow lane FCBs of the receiver end for base station i, it is 1 entirely that i-th corresponding base station matrix one arranges, and the corresponding columns of all the other base stations is 0; S _nisatellite end for base station i narrow lane FCBs matrix of coefficients, i-th corresponding satellite place of base station is-1, and all the other satellites are 0; f ^nrfor receiver end narrow lane FCBs matrix, comprise n survey station; f ^nsfor narrow lane satellite end FCBs matrix, comprise 32 satellites;

Step (34), carries out staging treating to the narrow lane ambiguity of whole day, every 10min average computation one Ge Zhai lane value, then adopts least square method to the narrow lane ambiguity of every 10min, estimates the f of each base station according to formula (9) _{n, r}the f of value and 32 satellites _n ^svalue;

Step (4): the wide lane f of every satellite that non-for least square difference method is resolved _w ^swith narrow lane f _n ^sbroadcast to rover station, the wide lane ambiguity N of rover station _winteger is fixed as, the narrow lane ambiguity N of rover station by rounding _nbe fixed as integer by LAMBDA algorithm, then both are reassembled into without ionosphere blur level according to formula (10), are called that non-difference is without ionosphere blur level static solution.

$N_{\mathrm{IF}}=\frac{f_1{f}_2}{{f_1}^2-{f_2}^2}{N}_w+\frac{f_1}{f_1+f_2}{N}_n---\left(10\right)$