CN102096084A - Precise point positioning (PPP) method based on inter-satellite combination difference - Google Patents

Abstract

The invention discloses a precise point positioning (PPP) method based on inter-satellite combination difference, comprising the following steps: firstly subtracting by utilizing an observation equation among different satellites with the same epoch so as to form a primary inter-satellite difference observation equation; then on the basis of primary inter-satellite difference, subtracting again by utilizing an observation equation between adjacent epoches so as to form a secondary difference observation equation among the inter-satellite epochs; and finally taking an observation station coordinate and a weight matrix which are solved based on the secondary difference equation as an initial value of a Kalman filter and taking a primary inter-satellite difference as a function solving model, using a Kalman filter method to solve the parameters such as the observation station coordinate and ambiguity and the like, and realizing PPP based on the inter-satellite combination difference. In the method disclosed by the invention, the resolving of PPP can be realized in short time, and the engineering realization is fast, stable and easy; and tests show that as a new model for positioning, the centimeter level can be achieved, and the convergence time is improved by 30% compared with the that of conventional model.

Description

Accurate one-point positioning method based on combination difference between star

Technical field

The present invention relates to choosing of function model in the GPS Static Precise Point Positioning, relate in particular to Static Precise Point Positioning (PPP) difference model and resolve localization method, belong to GPS Static Precise Point Positioning field.

Background technology

GPS Static Precise Point Positioning technology is the hot technology in present satnav field, is that another research is popular after GPS network differential location technology, has broad application prospects.

The Static Precise Point Positioning technology only needs a receiver just can carry out static state or dynamic independently working in the world, reach the purpose of precision positioning, aspects such as characteristics such as low cost, high-level efficiency make that it is kept at regional high-precision coordinate framework, high precision navigation and location all have limitless application prospect.The extensive base station of operation continuously covering the whole world need be set up with respect to the network differential location technology and global location could be realized, can carry out large-scale application in case Static Precise Point Positioning technology acquisition of technology breaks through, be the opportunity that world level is caught up with and surpassed in Chinese positioning service.

In the GPS Static Precise Point Positioning technology, because the equation of positioning calculation and unknown number is more, operand is big is selected a suitable mathematics to resolve model and can be simplified calculating greatly, raising locating speed and precision.Therefore, the Static Precise Point Positioning technology problem of choosing that critical difficult point is a function model.Domestic and international many experts and scholars have carried out many research work to the problem of choosing of the function model of Static Precise Point Positioning, mainly contain following several method:

1, Zumberge adopts the deion layer of sign indicating number and phase place to make up as observed quantity, and every satellite is listed two observation equations.This is the most frequently used function model of Static Precise Point Positioning, and advantage is easy realization, and the convergence back is more stable, eliminated the influence of the single order item of ionosphere correction, but this model can not be eliminated the influence of high-order ionosphere; The non-linear unknown-value formed by L1, L2 carrier phase ambiguity of blur level in this model in addition, this combination can not keep the complete cycle characteristic of carrier phase ambiguity, can only obtaining a floating-point, to separate and measure noise be 3 times of original noise, therefore, it is slower that its disadvantage is calculated convergence exactly, generally needs just can reach more than 30 minutes the bearing accuracy of centimetre-sized;

2, on the basis of conventional model, the Gao Yang of Canadian Calgary university proposed the Uofc model in 2002.The UofC model is to adopt the sign indicating number of L1 and L2 wave band and mean value the replenishing as the carrier phase combined value that no ionospheric refraction is postponed of phase observations value.The advantage of UofC model is to have reduced noise error and residual error, and the deion layer combination in the model kept the integer characteristic of two frequency ambiguity degree, has reduced the number of unknown parameter; Shortcoming is the model complexity, and has fluctuation to exist in the process of positioning calculation, and its speed of convergence also needs about 30 minutes.

Summary of the invention

Technical matters: the present invention is directed to the deficiency of prior art, proposed a kind of fast and be easy to the Static Precise Point Positioning function model of Project Realization, promptly based on the accurate one-point positioning method of combination difference between star.

Technical scheme: the present invention at first utilizes the observation equation between same epoch of the different satellites to ask poor, forms first difference observation equation between star; On the basis of first difference between star, it is poor that the observation equation between adjacent epoch is asked again then, second difference observation equation between epoch between the composition star; Last a survey station coordinate and the initial value of power battle array as Kalman filter with the second difference equation solution, with first difference between star is that function resolves model, find the solution parameters such as survey station coordinate and blur level with the method for adaptive Kalman filter, realize based on combination difference Static Precise Point Positioning between star.

Specifically according to the following steps:

1) the observation file that obtains according to the GPS receiver, list the observation equation of the GPS Static Precise Point Positioning of deion layer combination:

1. the observed reading for double-frequency GPS receiver mainly contains C1, L1, L2, P2 four classes; Wherein L1, L2 represent the phase observations value on gps satellite signal modulating wave L1, the L2 carrier wave respectively, C1 represents the thick catch code pseudorange observed reading on the L1 carrier wave, P2 represents the precision code pseudorange observed reading on the L2 carrier wave respectively, and the observation equation of GPS Static Precise Point Positioning is:

$L_i^s\left({\mathrm{\Φ}}_j\right)={\mathrm{\ρ}}^s\left(i\right)-\mathrm{cd}{T}^s\left(i\right)+{\mathrm{\λ}}_j{N}_j^s\left(i\right)+d_{\mathrm{ion}}^s\left(i\right)+d_{\mathrm{trop}}^s\left(i\right)+d_{\mathrm{Relativity}}^s\left(i\right)+d_e^s\left(i\right)+{\mathrm{\ϵ}}^s\left(i\right)$

In the following formula,

Represent the carrier phase observation data of i satellite s epoch on the Lj carrier wave, j=1,2;

ρ ^s(i) geometric distance between expression i survey station epoch and satellite s, be signal x time satellite in inertial system coordinate and the distance between the coordinate of the signal survey station time of reception in inertial system;

DT ^s(i) the satellite clock correction of expression i satellite s epoch and receiver clock correction is poor;

C represents the light velocity, is constant; λ _jThe wavelength of expression Lj carrier wave;

Represent i epoch, the integer ambiguity of the carrier phase observation data on the Lj carrier wave of satellite s;

The tropospheric delay of representing i satellite s epoch corrects, and can correct or as unknown parameter by relevant formula;

The ionosphere delay of representing i satellite s epoch corrects, and available no ionospheric model corrects;

The relativistic effect of representing i satellite s epoch corrects, and can correct by relevant formula;

Represent the earth rotation influence correction of i satellite s epoch, can correct by relevant formula;

ε ^s(i) not modeled error effects such as the multipath effect of expression i satellite s epoch and observation noise;

2. utilize the double frequency combined method to eliminate the ionospheric error influence, the deion layer observation equation after the combination:

$L_i^s\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)=\frac{f_1^2\·L_i^s\left({\mathrm{\Φ}}_1\right)-f_1\·f_2\·L_i^s\left({\mathrm{\Φ}}_2\right)}{f_1^2-f_2^2}$

$={\mathrm{\ρ}}^s\left(i\right)-{\mathrm{cdT}}^s\left(i\right)+{\mathrm{\λ}}_{\mathrm{IF}}{N}^s\left(i\right)+d_{\mathrm{trop}}^s\left(i\right)+d_{\mathrm{Relativity}}^s\left(i\right)+d_e^s\left(i\right)+{\mathrm{\ϵ}}^s\left(i\right)$

Wherein, f ₁, f ₂The frequency of representing gps satellite signal modulating wave L1, L2 carrier wave respectively, λ _IFAnd N ^s(i) represent wavelength and integer ambiguity after the double frequency combination respectively, eliminated the ionospheric error correction member in the formula;

(2) form first difference observation equation between star

The satellite of choosing elevation angle maximum in epoch is as the reference satellite, and via satellite and ask difference to obtain the observation equation of first difference between star between the reference satellite, its form is as follows:

$L_i^{\▿s}\left(P_{\mathrm{IF}}\right)=L_i^s\left(P_{\mathrm{IF}}\right)-L_i^r\left(P_{\mathrm{IF}}\right)$

$L_i^{\▿s}\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)=L_i^s\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)-L_i^r\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)$

Represent that i satellite s epoch is with respect to difference observed reading between the pseudo-determinative star in the no ionosphere of reference satellite;

Represent difference observed reading between the pseudo-determinative star in no ionosphere of satellite r of i elevation angle maximum in epoch;

Represent that i satellite s epoch is with respect to difference observed reading between the no ionosphere carrier phase star of reference satellite;

Represent difference observed reading between the no ionosphere carrier phase star of satellite r of i elevation angle maximum in epoch;

(3) form between star second difference observation equation between epoch

Carry out again asking poor between epoch on the basis of first difference between based on star.Its observation equation is as follows:

$L_{\mathrm{\Δi}}^{\▿s}\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)=L_i^{\▿s}\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)-L_{i-1}^{\▿s}\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)$

Wherein,

The no ionosphere carrier phase of representing i satellite s epoch difference observed reading between epoch;

Utilize between star second difference observation equation between epoch, needn't consider the influence of receiver clock correction and blur level, operand is little, get final product each unknown parameter of rapid solving after the linearization, comprise the power battle array between survey station coordinate and the observed quantity, because there is stronger correlativity in second difference, can not be as finally resolving the result, but can be used as the initial value in the first difference observation equation, can reach like this and improve precision and quick convergent purpose;

(4) resolving the survey station coordinate and the initial value of power battle array as Kalman filter that obtains with secondary, is parameters such as model solution survey station coordinate and blur level with first difference between star;

Concrete form based on the PPP model of first difference between star is as follows:

$L_i^{\▿s}\left(P_{\mathrm{IF}}\right)=L_i^s\left(P_{\mathrm{IF}}\right)-L_i^r\left(P_{\mathrm{IF}}\right)$

$=({\mathrm{\ρ}}^s\left(i\right)-{\mathrm{\ρ}}^r\left(i\right))+(d_{\mathrm{trop}}^s\left(i\right)-d_{\mathrm{trop}}^r\left(i\right))+(d_{\mathrm{Relativity}}^s\left(i\right)-d_{\mathrm{Relativity}}^r\left(i\right))$

Will Combinational fuzzy degree and tropospheric zenith delay parameter are considered as unknown number, respectively with above-mentioned two equations at survey station apparent position x _R0Place's linearization keeps the single order item, can obtain conventional error equation matrix form: V=Ax-l; Wherein, V is the observed reading residual vector; A is a design matrix; X is the unknown number vector; L is a constant vector;

This moment, the coordinate of first difference waited that the initial value of estimating initial parameter value and observed reading weight matrix P thereof tries to achieve by the second difference model, at last, can find the solution survey station coordinate unknown parameter number by least square adjustment method combining adaptive kalman filter method, realize GPS Static Precise Point Positioning based on combination difference between star.

Beneficial effect:

(1) the present invention can be used for the realization of Static Precise Point Positioning technology, can obtain resolving the result fast, and test shows, reaches the precision of centimetre-sized equally, adopts the present invention can shorten 30% calculating convergence time.

(2) the present invention is realized promoting the Static Precise Point Positioning technology in Application for Field such as Surveying Engineering greatly at Static Precise Point Positioning software.

Description of drawings

Fig. 1 is based on the accurate one-point positioning method process flow diagram that makes up difference between star among the present invention;

Fig. 2 is the Static Precise Point Positioning of combination difference between culminant star of the present invention, in the residual error of volume coordinate XYZ;

Fig. 3 adopts traditional function model to resolve, in the residual error of volume coordinate XYZ;

Fig. 4 adopts the function model of first difference between star to resolve, in the residual error of volume coordinate XYZ;

Fig. 5 adopts between star that the function model of second difference resolves between epoch, in the residual error of volume coordinate XYZ

Embodiment

(1) the observation file that obtains according to the GPS receiver, list the observation equation of the GPS Static Precise Point Positioning of deion layer combination:

1. the observed reading of double-frequency GPS receiver mainly contains C1, L1, L2, P2 four classes.L1 wherein, L2 represents L1 respectively, and the carrier phase observation data on the L2 carrier wave, C1 are represented the C/A sign indicating number pseudorange observed reading on the L1 carrier wave, and P2 represents the P sign indicating number pseudorange observed reading on the L2 carrier wave respectively.The observation equation of GPS Static Precise Point Positioning is:

$L_i^s\left({\mathrm{\Φ}}_j\right)={\mathrm{\ρ}}^s\left(i\right)-\mathrm{cd}{T}^s\left(i\right)+{\mathrm{\λ}}_j{N}_j^s\left(i\right)+d_{\mathrm{ion}}^s\left(i\right)+d_{\mathrm{trop}}^s\left(i\right)+d_{\mathrm{Relativity}}^s\left(i\right)+d_e^s\left(i\right)+{\mathrm{\ϵ}}^s\left(i\right)$

In the following formula,

Represent i epoch, the carrier phase observation data (j=1,2) of satellite s on the Lj carrier wave;

ρ ^s(i) represent i epoch, the geometric distance between survey station and satellite s can be expressed as

Be the coordinate of signal x time satellite in inertial system,

Be the coordinate of the signal survey station time of reception in inertial system;

DT ^s(i) expression i epoch, the satellite clock correction of satellite s and receiver clock correction poor;

C represents the light velocity (constant); λ _jThe wavelength (j=1,2) of expression Lj carrier wave;

Represent i epoch, the integer ambiguity of the carrier phase observation data on the Lj carrier wave of satellite s (j=1,2);

Represent i epoch, the tropospheric delay of satellite s corrects, and can correct or as unknown parameter by relevant formula;

Represent i epoch, the ionosphere delay of satellite s corrects, and available no ionospheric model corrects;

Represent i epoch, the relativistic effect of satellite s corrects, and can correct by relevant formula;

Represent i epoch, the earth rotation of satellite s corrects, and can correct by relevant formula;

ε ^s(i) represent i epoch, not modeled error effects such as observation noise such as the multipath effect of satellite s.

2. utilize the double frequency combined method to eliminate the ionospheric error influence, the deion layer observation equation after the combination:

$L_i^s\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)=\frac{f_1^2\·L_i^s\left({\mathrm{\Φ}}_1\right)-f_1\·f_2\·L_i^s\left({\mathrm{\Φ}}_2\right)}{f_1^2-f_2^2}$

$={\mathrm{\ρ}}^s\left(i\right)-{\mathrm{cdT}}^s\left(i\right)+{\mathrm{\λ}}_{\mathrm{IF}}{N}^s\left(i\right)+d_{\mathrm{trop}}^s\left(i\right)+d_{\mathrm{Relativity}}^s\left(i\right)+d_e^s\left(i\right)+{\mathrm{\ϵ}}^s\left(i\right)$

Wherein,

${\mathrm{\λ}}_{\mathrm{IF}}=\frac{c\·f_1}{f_1^2{-f}_2^2};$ $N^s\left(i\right)=\frac{1}{{\mathrm{\λ}}_1}\·N_1^s\left(i\right)-\frac{1}{{\mathrm{\λ}}_2}\·N_2^s\left(i\right)$

(2) form first difference observation equation between star

The PPP model of first difference is to obtain observation equation after the deion layer combination according to conventional model between star, and the satellite of choosing elevation angle maximum in epoch is as the reference satellite, via satellite and ask difference to obtain observation equation between the reference satellite.Its form is as follows:

$L_i^{\▿s}\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)=L_i^s\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)-L_i^r\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)$

Represent i epoch, satellite s is with respect to difference observed reading between the no ionosphere carrier phase star of reference satellite.

Represent difference observed reading between the no ionosphere carrier phase star of satellite r of i elevation angle maximum in epoch.

(3) form between star second difference observation equation between epoch

Carry out again asking poor between epoch on the PPP model based of first difference between based on star.Its concrete form is as follows:

$L_{\mathrm{\Δi}}^{\▿s}\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)=L_i^{\▿s}\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)-L_{i-1}^{\▿s}\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)$

Wherein,

Represent i epoch, the no ionosphere carrier phase of satellite s difference observed reading between epoch.

Utilize between star second difference observation equation between epoch, needn't consider the influence of receiver clock correction and blur level, operand is little, can each unknown parameter of rapid solving after the linearization, comprise the power battle array between survey station coordinate and the observed quantity.

(4) survey station coordinate and power battle array are parameters such as model solution survey station coordinate and blur level only as the initial value of Kalman filter with first difference between star.

Concrete form based on the PPP model of first difference between star is as follows:

$L_i^{\▿s}\left(P_{\mathrm{IF}}\right)=L_i^s\left(P_{\mathrm{IF}}\right)-L_i^r\left(P_{\mathrm{IF}}\right)$

$=({\mathrm{\ρ}}^s\left(i\right)-{\mathrm{\ρ}}^r\left(i\right))+(d_{\mathrm{trop}}^s\left(i\right)-d_{\mathrm{trop}}^r\left(i\right))+(d_{\mathrm{Relativity}}^s\left(i\right)-d_{\mathrm{Relativity}}^r\left(i\right))$

$+(d_e^s\left(i\right)-d_e^r\left(i\right))+({\mathrm{\ϵ}}^s\left(i\right)-{\mathrm{\ϵ}}^r\left(i\right))$

$L_i^{\▿s}\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)=L_i^s\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)-L_i^r\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)$

$=({\mathrm{\ρ}}^s\left(i\right)-{\mathrm{\ρ}}^r\left(i\right))+{\mathrm{\λ}}_{\mathrm{IF}}(N^s\left(i\right)-N^r\left(i\right))+(d_{\mathrm{trop}}^s\left(i\right)-d_{\mathrm{trop}}^r\left(i\right))$

$+(d_{\mathrm{Relativity}}^s\left(i\right)-d_{\mathrm{Relativity}}^r\left(i\right))+(d_e^s\left(i\right)-d_e^r\left(i\right))+({\mathrm{\ϵ}}^s\left(i\right)-{\mathrm{\ϵ}}^r\left(i\right))$

Respectively with above-mentioned two equations at the survey station apparent position

Place's linearization can obtain:

$V_i^{\▿s}\left(P_{\mathrm{IF}}\right)=[l_i^s-l_i^r,m_i^s-m_i^r,n_i^s-n_i^r]\·{\left[\begin{array}{ccc}{\mathrm{\δx}}_r& {\mathrm{\δy}}_r& {\mathrm{\δz}}_r\end{array}\right]}^T-L_i^{\▿s}\left(P_{\mathrm{IF}}^0\right)$

$V_i^{\▿s}\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)=[l_i^s-l_i^r,m_i^s-m_i^r,n_i^s-n_i^r,-{\mathrm{\λ}}_{\mathrm{IF}}]\·{\left[\begin{array}{cccc}{\mathrm{\δx}}_r& {\mathrm{\δy}}_r& {\mathrm{\δz}}_r& {\mathrm{\δN}}^s\left(i\right)-{\mathrm{\δN}}^r\left(i\right))\end{array}\right]}^T$

$-L_i^{\▿s}\left({\mathrm{\Φ}}_{\mathrm{IF}}^0\right)$

Wherein:

$L_i^{\▿s}\left(P_{\mathrm{IF}}^0\right)=({\mathrm{\ρ}}^{s0}\left(i\right)-{\mathrm{\ρ}}^{r0}\left(i\right))+(d_{\mathrm{trop}}^s\left(i\right)-d_{\mathrm{trop}}^r\left(i\right))+(d_{\mathrm{Relativity}}^s\left(i\right)-d_{\mathrm{Relativity}}^r\left(i\right))$

$+(d_e^s\left(i\right)-d_e^r\left(i\right))+({\mathrm{\ϵ}}^s\left(i\right)-{\mathrm{\ϵ}}^r\left(i\right))$

$L_i^{\▿s}\left({\mathrm{\Φ}}_{\mathrm{IF}}^0\right)=({\mathrm{\ρ}}^{s0}\left(i\right)-{\mathrm{\ρ}}^{r0}\left(i\right))+{\mathrm{\λ}}_{\mathrm{IF}}(N^{s0}\left(i\right)-N^{r0}\left(i\right))+(d_{\mathrm{trop}}^s\left(i\right)-d_{\mathrm{trop}}^r\left(i\right))$

$+(d_{\mathrm{Relativity}}^s\left(i\right)-d_{\mathrm{Relativity}}^r\left(i\right))+(d_e^s\left(i\right)-d_e^r\left(i\right))+({\mathrm{\ϵ}}^s\left(i\right)-{\mathrm{\ϵ}}^r\left(i\right))$

So promptly be converted into conventional error equation matrix form: V=Ax-l.Wherein, V is the observed reading residual vector, has

A is a design matrix, has

X is the unknown number incremental vector, and [δ x is arranged _rδ y _rδ z _r] ^T, [δ x _rδ y _rδ z _rδ N ^s(i)-δ N ^r(i))] ^TL is a constant vector, has

If wait to estimate parameter as the cum rights observed reading, observed reading weight matrix P is tried to achieve by prior second difference model, can find the solution unknown number by the least square adjustment method and be:

x＝(A ^TPA) ^-1A ^TPl

Can obtain thus being estimated parameter and be:

Association's factor battle array of unknown number is:

Q _xx＝(A ^TPA) ^-1

Can obtain unknown parameters such as comprising coordinate, clock correction, blur level efficiently with this kind method, realize Static Precise Point Positioning.

Referring to Fig. 1, among the present invention between reference station baseline integer ambiguity network calculation method mainly undertaken by following flow process:

(1) the observation file that obtains according to the GPS receiver is listed the observation equation of the GPS Static Precise Point Positioning of deion layer combination;

(2) on the basis of the observation equation that the deion layer makes up, form first difference observation equation between star;

(3) on the basis of first difference observation equation between star, form between star second difference observation equation between epoch, ask the power battle array of survey station coordinate and observed reading;

(4) survey station coordinate and power battle array are parameters such as model solution survey station coordinate and blur level with first difference between star, as net result only as the initial value of Kalman filter.

Use the static observation data of LEICA530 receiver as example below.In April, 2007, on No. 8 points of school district, lake, Nanjing Southeast China University Kowloon, gather static observation data with the GPS receiver of LEICA530, be spaced apart 5s epoch, number of satellite is 6～8 stars during observation, satellite is 10 degree by elevation angle.The method that adopts the present invention to propose is done Static Precise Point Positioning and is resolved, and the result that resolves of end product and other classic methods is compared.

At first need to download precise ephemeris and the accurate clock correction file of same period from the IGS website, the Static Precise Point Positioning software of writing with oneself, correct through data pre-service and every error, use different models to carry out resolving of single-point location respectively, and be analyzed resolving the result.

Fig. 2 is the Static Precise Point Positioning result statistics that has adopted built-up pattern between star, because of being the difference model of employing, bounce-back is arranged near being converged in 1000 seconds, reaches the centimetre-sized precision in the time of less than 2000 seconds.

Fig. 3 adopts conventional model to carry out the volume coordinate convergence situation of Static Precise Point Positioning.As seen from Figure 3, after 1000 seconds, volume coordinate is tending towards convergence, and concrete data show, after about 2500 seconds, this some position bearing accuracy on three directions of XYZ reaches centimetre-sized.

Fig. 4 is that the first difference model carries out the coordinate convergence statistical graph that Static Precise Point Positioning is resolved between the employing star.Owing to eliminated the influence of receiver clock correction, unknown parameter only remaining position coordinate, blur level and tropospheric delay.Compare with conventional model, stability is not enough, and the directions X residual error has the change megatrend near 600 seconds, converges to a centimetre meter precision near 2000 seconds, and convergence time is compared conventional model and wanted fast.

Fig. 5 adopts between star second difference model between epoch, than conventional model and first difference model, between star between epoch the parameter item of second order difference model still less, no blur level item, no receiver clock correction item is the simplest observation model.The result shows: the directions X residual error had bounce-back near 1000 seconds, and did not also converge to centimetre-sized 3000 seconds the time, and the convergence of YZ direction is more stable fast.This mainly is because the correlativity between the second difference observed reading strengthens greatly, is unfavorable for resolving.

Table 1 is the time statistics that several test models converge to the centimetre-sized precision.According to data in the table, the conventional model convergence time is long, first difference model convergence time is shorter between star, and between star between epoch the second order difference model in 3000 seconds, also do not converge to the centimetre-sized precision, built-up pattern is faster than first difference convergence time between star between star, nearly 30 minutes time just can reach the centimetre-sized accuracy requirement, and the time ratio conventional model improves 30%.

Table 1 is the statistical that different function models is converged to the used time of centimetre-sized precision.

Table 1

Claims (2)

1. the accurate one-point positioning method based on combination difference between star is characterized in that: at first utilize the observation equation between same epoch of the different satellites to ask poor, form first difference observation equation between star; On the basis of first difference between star, it is poor that the observation equation between adjacent epoch is asked again then, second difference observation equation between epoch between the composition star; Last a survey station coordinate and the initial value of power battle array as Kalman filter with the second difference equation solution, with first difference between star is that function resolves model, find the solution parameters such as survey station coordinate and blur level with the method for adaptive Kalman filter, realize based on combination difference Static Precise Point Positioning between star.

2. the accurate one-point positioning method based on combination difference between star according to claim 1 is characterized in that this method is specific as follows:

1) the observation file that obtains according to the GPS receiver, list the observation equation of the GPS Static Precise Point Positioning of deion layer combination:

1. the observed reading for double-frequency GPS receiver mainly contains C1, L1, L2, P2 four classes; Wherein L1, L2 represent the phase observations value on gps satellite signal modulating wave L1, the L2 carrier wave respectively, C1 represents the thick catch code pseudorange observed reading on the L1 carrier wave, P2 represents the precision code pseudorange observed reading on the L2 carrier wave respectively, and the observation equation of GPS Static Precise Point Positioning is:

$L_i^s\left({\mathrm{\Φ}}_j\right)={\mathrm{\ρ}}^s\left(i\right)-\mathrm{cd}{T}^s\left(i\right)+{\mathrm{\λ}}_j{N}_j^s\left(i\right)+d_{\mathrm{ion}}^s\left(i\right)+d_{\mathrm{trop}}^s\left(i\right)+d_{\mathrm{Relativity}}^s\left(i\right)+d_e^s\left(i\right)+{\mathrm{\ϵ}}^s\left(i\right)$

In the following formula,

Represent the carrier phase observation data of i satellite s epoch on the Lj carrier wave, j=1,2;

ρ ^s(i) geometric distance between expression i survey station epoch and satellite s, be signal x time satellite in inertial system coordinate and the distance between the coordinate of the signal survey station time of reception in inertial system;

DT ^s(i) the satellite clock correction of expression i satellite s epoch and receiver clock correction is poor;

C represents the light velocity, is constant; λ _jThe wavelength of expression Lj carrier wave;

Represent i epoch, the integer ambiguity of the carrier phase observation data on the Lj carrier wave of satellite s;

The tropospheric delay of representing i satellite s epoch corrects, and can correct or as unknown parameter by relevant formula;

The ionosphere delay of representing i satellite s epoch corrects, and available no ionospheric model corrects;

The relativistic effect of representing i satellite s epoch corrects, and can correct by relevant formula;

Represent the earth rotation influence correction of i satellite s epoch, can correct by relevant formula;

ε ^s(i) not modeled error effects such as the multipath effect of expression i satellite s epoch and observation noise;

2. utilize the double frequency combined method to eliminate the ionospheric error influence, the deion layer observation equation after the combination:

$L_i^s\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)=\frac{f_1^2\·L_i^s\left({\mathrm{\Φ}}_1\right)-f_1\·f_2\·L_i^s\left({\mathrm{\Φ}}_2\right)}{f_1^2-f_2^2}$

$={\mathrm{\ρ}}^s\left(i\right)-{\mathrm{cdT}}^s\left(i\right)+{\mathrm{\λ}}_{\mathrm{IF}}{N}^s\left(i\right)+d_{\mathrm{trop}}^s\left(i\right)+d_{\mathrm{Relativity}}^s\left(i\right)+d_e^s\left(i\right)+{\mathrm{\ϵ}}^s\left(i\right)$

Wherein, f ₁, f ₂The frequency of representing gps satellite signal modulating wave L1, L2 carrier wave respectively, λ _IFAnd N ^s(i) represent wavelength and integer ambiguity after the double frequency combination respectively, eliminated the ionospheric error correction member in the formula;

(2) form first difference observation equation between star

The satellite of choosing elevation angle maximum in epoch is as the reference satellite, and via satellite and ask difference to obtain the observation equation of first difference between star between the reference satellite, its form is as follows:

$L_i^{\▿s}\left(P_{\mathrm{IF}}\right)=L_i^s\left(P_{\mathrm{IF}}\right)-L_i^r\left(P_{\mathrm{IF}}\right)$

$L_i^{\▿s}\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)=L_i^s\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)-L_i^r\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)$

Represent that i satellite s epoch is with respect to difference observed reading between the pseudo-determinative star in the no ionosphere of reference satellite;

Represent difference observed reading between the pseudo-determinative star in no ionosphere of satellite r of i elevation angle maximum in epoch;

Represent that i satellite s epoch is with respect to difference observed reading between the no ionosphere carrier phase star of reference satellite;

Represent difference observed reading between the no ionosphere carrier phase star of satellite r of i elevation angle maximum in epoch;

(3) form between star second difference observation equation between epoch

Carry out again asking poor between epoch on the basis of first difference between based on star.Its observation equation is as follows:

$L_{\mathrm{\Δi}}^{\▿s}\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)=L_i^{\▿s}\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)-L_{i-1}^{\▿s}\left({\mathrm{\Φ}}_{\mathrm{IF}}\right)$

Wherein,

The no ionosphere carrier phase of representing i satellite s epoch difference observed reading between epoch;

Utilize between star second difference observation equation between epoch, needn't consider the influence of receiver clock correction and blur level, operand is little, get final product each unknown parameter of rapid solving after the linearization, comprise the power battle array between survey station coordinate and the observed quantity, because there is stronger correlativity in second difference, can not be as finally resolving the result, but can be used as the initial value in the first difference observation equation, can reach like this and improve precision and quick convergent purpose;

(4) resolving the survey station coordinate and the initial value of power battle array as Kalman filter that obtains with secondary, is parameters such as model solution survey station coordinate and blur level with first difference between star;

Concrete form based on the PPP model of first difference between star is as follows:

$L_i^{\▿s}\left(P_{\mathrm{IF}}\right)=L_i^s\left(P_{\mathrm{IF}}\right)-L_i^r\left(P_{\mathrm{IF}}\right)$

$=({\mathrm{\ρ}}^s\left(i\right)-{\mathrm{\ρ}}^r\left(i\right))+(d_{\mathrm{trop}}^s\left(i\right)-d_{\mathrm{trop}}^r\left(i\right))+(d_{\mathrm{Relativity}}^s\left(i\right)-d_{\mathrm{Relativity}}^r\left(i\right))$

Will

Layer combinational fuzzy degree and tropospheric zenith delay parameter are considered as unknown number, respectively with above-mentioned two equations at survey station apparent position x _R0Place's linearization keeps the single order item, can obtain conventional error equation matrix form: V=Ax-l; Wherein, V is the observed reading residual vector; A is a design matrix; X is the unknown number vector; L is a constant vector;

This moment, the coordinate of first difference waited that the initial value of estimating initial parameter value and observed reading weight matrix P thereof tries to achieve by the second difference model, at last, can find the solution survey station coordinate unknown parameter number by least square adjustment method combining adaptive kalman filter method, realize GPS Static Precise Point Positioning based on combination difference between star.

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