CN104502935B - A kind of network RTK Ambiguity Solution Methods based on the non-combined model of non-difference - Google Patents

Abstract

The invention discloses a kind of network RTK Ambiguity Solution Methods based on the non-combined model of non-difference.The Dan Zhanfei difference fuzzinesses of the whole network are estimated using non-difference non-combined model, and using satellite clock as unknown parameter, real-time satellite clock correction product is added as pseudo- observed quantity.According to customer location, the non-poor fuzziness of user's adjacent sites being extracted, one being selected in adjacent sites as reference station, the integer characteristic for obtaining double difference fuzziness using difference operator reduction, single epoch obtain the double difference fuzziness result with integer characteristic.Using method proposed by the present invention, calculating performance can be effectively lifted in large-scale reference station, weaken the impact that atmosphere errors and length are fixed to double difference fuzziness simultaneously, reduce the pathosis of double difference model, improve model robustness and fuzziness fixes success rate.

Description

A kind of network RTK Ambiguity Solution Methods based on the non-combined model of non-difference

Technical field

The present invention relates to GLONASS (GNSS) field of satellite location, the non-combined essence of the non-differences of more particularly to GNSS Close One-Point Location.

Background technology

With base station quantity gradually increase and multisystem multiple-frequency signal compatibility, CORS on a large scale (Continuous Operational Reference System：Continuous operation reference system) system extensively built simultaneously It is increasingly becoming national important infrastructure to support hi-Fix application, user can be obtained li in real time using many reference station networks The positioning precision of meter level.

In the application of current network RTK, it is necessary to assure double difference fuzziness is computed correctly, so that the differential correcting of the whole network is believed Breath and VRS observations are generated, so that it is guaranteed that locating effect.Therefore, most of CORS systems soft wares adopt Baseline solution Calculation method is realizing the whole network ambiguity resolution.Although Baselines method reduces unknown parameter number, solves to a certain extent The rank defect problem for solving, but generally there is relativity problem that is complicated and being difficult to definite solution.Simultaneously as atmosphere errors and The impact of satellite orbital error, during Baselines, the length of base is restricted, it has to consider that new atmosphere errors are estimated Model is widening the length of base.And the increase with base station quantity, the baseline amount of required resolving exponentially increases.Cause This is unfavorable for building and transporting for the distributed structure/architecture of CORS systems on a large scale based on the whole network ambiguity resolution of Baselines method OK, CORS systematic differences on a large scale are limited.

At the same time, with the successful Application of non-poor PPP, a kind of PPP-RTK methods of innovation have obtained widely studied.? In non-combined observational equation, the carrier wave pseudorange biases item degree of being blurred of receiver and satellite is absorbed so that non-differential mode paste loses Integer characteristic.But using fixed double difference fuzziness and correct benchmark fuzziness, the integer of reducible non-poor fuzziness is special Property, and there is numerical equivalence with double-difference equation, but relativity problem need not be faced.Therefore, the fuzziness of the whole network is fixed It is worth further investigation, and the development of CORS systems on a large scale will be greatly facilitated.

Content of the invention

Goal of the invention：For above-mentioned prior art, a kind of network RTK solution of fuzzy degree based on the non-combined model of non-difference is proposed Calculation method, can solve the problem that current network RTK by and the length of base, quantity the are limited problem affected by relativity problem, and will be big Be conducive to greatly the development of CORS systems on a large scale.

Technical scheme：A kind of network RTK Ambiguity Solution Methods based on the non-combined model of non-difference, non-first by non-difference Built-up pattern is estimated to the Dan Zhanfei difference fuzzinesses of the whole network, wherein using satellite clock as unknown parameter, real-time satellite clock correction Product is added as pseudo- observed quantity；Then the non-poor fuzziness of user's adjacent sites, according to customer location, is extracted, in adjacent sites Used as reference station, the integer characteristic for obtaining double difference fuzziness using difference operator reduction, single epoch are had for middle selection one There is the double difference fuzziness result of integer characteristic.

Further, described included based on the network RTK Ambiguity Solution Methods of the non-combined model of non-difference following concrete Step：

Step 1), using the raw observation of each website, the Dan Zhanfei difference fuzzinesses of each website are estimated, and will Satellite clock correction is estimated as unknown parameter, as shown in formula (1.1)：

Wherein：S represents satellite, and k represents reference receiver, and j represents each observation frequency, j=1,2；Represent satellite Pseudo range observed quantity between s and site k in frequency j,The phase observations amount in frequency j between satellite s and site k is represented,Represent satellite to the geometric distance of receiver antenna phase center, δ t_kRepresent receiver clock-offsets, δ t^sRepresent satellite clock correction, Represent tropospheric delay,Represent ionosphere delay；α_jIt is frequency ratio,Represent the value of frequency j；The hardware delay of receiver and satellite frequency j in is represented respectively；It is that other can modeled error；The phase place decimal deviation of receiver and satellite frequency j in is represented respectively；λ_jIt is the carrier wavelength in frequency j, N_j It is the phase ambiguity in frequency j；It is the Pseudo-range Observations and carrier phase observable noise in frequency j；C represents light Speed；

According to formula (1.1), unknown parameter is estimated using Kalman filtering, obtain non-poor float ambiguities, including Following concrete steps：

Step a), arranges unknown parameter vector X_i, as shown in formula (1.2)：

Wherein, unknown parameter X_iBe divided into time-varying and when constant two parts, time-varying part includes Zenith wet delay ZTD_{W, k}； Receiver is absorbed without ionosphere hardware delayReceiver clock-offsets δ t_k',WhereinAbsorb the n dimension ionosphere tilts of receiver and satellite frequency related hardware decay part Postpone WhereinN is the epoch observation satellite number, inhales Receiving satellite is without ionosphere hardware delayN dimension satellite clock correction δ t^s', When constant part include that n ties up the initial N1 integer ambiguities of non-differenceThe initial N2 integer ambiguities of non-difference are tieed up with n

Step b), arranges the design matrix B of Kalman filtering_iWith observation vector L_i, as shown in formula (1.3)：

Wherein, the observation vector L_iComprising four un-differenced observationsAnd a real-time satellite Clock correction product resultAs false observed value,Represent between satellite s and site k respectively in frequency 1 respectively, on 2 Phase observations amount,Represent between satellite s and site k respectively in frequency 1, the pseudo range observed quantity on 2 respectively；

N represents the epoch observation satellite number, θⁿRepresent the elevation of satellite of n-th satellite epoch, MF_w(θ) it is zenith wet Postpone the mapping function related to elevation of satellite, c represents the light velocity, λ₁, λ₂The wavelength of frequency 1,2 is represented respectively；

According to unknown parameter vector X_iAnd design matrix B_iWith observation vector L_i, carry out Kalman filtering obtain non- Difference float ambiguities

Step 2), according to customer location and the distance of website, the non-poor fuzziness of at least three user's adjacent sites is extracted, The non-poor fuzziness of each user's adjacent sitesAs shown in formula (1.5)：

Wherein,Non- difference basis fuzziness N1 of in adjacent sites 1 to the n-th satellite is respectively corresponded to；Non- difference basis fuzziness N2 of in adjacent sites 1 to the n-th satellite is respectively corresponded to；

Step 3), a website is selected first in each user's adjacent sites as reference station, other neighbor stations Point is used as non-referenced website；Then difference operator C between the station of the reference station and non-referenced website is set_kdWith reference satellite with Difference operator C between the star of non-reference satellite^sd, according to difference operator C_kdAnd C^sdThere is integer characteristic between star between reduction station Double difference fuzziness, shown in the reduction step such as formula (1.6)：

Wherein, k1, k2 are respectively reference station and non-referenced website, and r is reference satellite, and s is non-reference satellite, For double difference fuzziness between star between station,The non-poor fuzziness of respectively site k 1 and k2,Respectively For double difference basis fuzziness N1, N2；

Step 4), ambiguity search is carried out using LAMBDA algorithms and fixed, specially：First by double difference basis fuzziness N1, N2 are converted to wide lane ambiguityWith N1 fuzzinesses partThe integer width lane being fixed using LAMBDA algorithms again Fuzziness, finally uses wide lane ambiguity as given value, determines N1 fuzziness integer values.

Beneficial effect：A kind of network RTK Ambiguity Solution Methods based on the non-combined model of non-difference proposed by the present invention, melt Enter real-time satellite clock correction product as pseudo- observed quantity, improve the resolving effect of real-time PPP, improve the robustness journey of model Degree.Non- poor fuzziness reduction is obtained double difference integer ambiguity using difference operator, during constant fuzzy when only introducing Degree parameter carries out the whole network adjustment, reduces the impact of the length of base and atmosphere delay to result, improves computational efficiency, be conducive to The development of extensive CORS systems.

Description of the drawings

Fig. 1 is the inventive method flow chart；

Fig. 2 is embodiment reference station net scattergram；

Fig. 3 is embodiment real-time satellite clock correction Product Precision cartogram；

Fig. 4 is the satellite clock correction deviation map of PRN8 satellites and PRN14 satellites；

Fig. 5 is the conditional number variation diagram under different Satellite Product clock precision；

Fig. 6 is the ADOP variation diagrams under different Satellite Product clock precision；

Fig. 7 is the observation residual error without ionospheric combination model, non-combined model, the non-combined model for estimating satellite clock Figure；

Fig. 8 is the conditional number variation diagram of the double difference fuzziness obtained using non-poor mode and using double difference mode；

Fig. 9 is the floating-point deviation of the double difference width lane ambiguity obtained using non-poor mode and using double difference mode；

Figure 10 is the floating-point deviation of the double difference N1 fuzziness obtained using non-poor mode and using double difference mode.

Specific embodiment

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

As shown in figure 1, a kind of network RTK Ambiguity Solution Methods based on the non-combined model of non-difference, first by non-difference Non-combined model is estimated to the Dan Zhanfei difference fuzzinesses of the whole network, wherein using satellite clock as unknown parameter, real-time satellite clock Difference product is added as pseudo- observed quantity；Then the non-poor fuzziness of user's adjacent sites, according to customer location, is extracted, in neighbor stations One is selected in point as reference station, and the integer characteristic for obtaining double difference fuzziness using difference operator reduction, single epoch are obtained There is the double difference fuzziness result of integer characteristic.The inventive method is comprised the following specific steps that：

Step 1), using the raw observation of each website, the Dan Zhanfei difference fuzzinesses of each website are estimated, and will Satellite clock correction is estimated as unknown parameter；Shown in the non-combined observational equation such as formula (1.1) of each website：

Wherein：S represents satellite, and k represents reference receiver, and j represents each observation frequency, j=1,2；Represent satellite Pseudo range observed quantity between s and site k in frequency j,The phase observations amount in frequency j between satellite s and site k is represented,Represent satellite to the geometric distance of receiver antenna phase center, δ t_kRepresent receiver clock-offsets, δ t^sRepresent satellite clock correction, Represent tropospheric delay,Represent ionosphere delay；α_jIt is frequency ratio,Represent the value of frequency j；The hardware delay of receiver and satellite frequency j in is represented respectively；Be other can modeled error, such as Tide correction, Ghandler motion error；The phase place decimal deviation of receiver and satellite frequency j in is represented respectively；λ_jIt is frequency Carrier wavelength in rate j, N_jIt is the phase ambiguity in frequency j；It is the Pseudo-range Observations in frequency j and phase place Observation noise；C represents the light velocity；

According to formula (1.1), unknown parameter is estimated using Kalman filtering, obtain non-poor float ambiguities, including Following concrete steps：

Step a), arranges unknown parameter vector X_j, as shown in formula (1.2)：

Wherein, unknown parameter X_iBe divided into time-varying and when constant two parts, time-varying part includes Zenith wet delay ZTD_{W, k}； Receiver is absorbed without ionosphere hardware delayReceiver clock-offsets δ t_k',WhereinThe n dimension ionosphere tilts for absorbing receiver and satellite frequency related hardware decay part prolong Late WhereinN is the epoch observation satellite number, absorbs Satellite is without ionosphere hardware delayN dimension satellite clock correction δ t^s', When constant part include that n ties up the initial N1 integer ambiguities of non-differenceThe initial N2 integer ambiguities of non-difference are tieed up with n

Step b), arranges the design matrix B of Kalman filtering_iWith observation vector L_i, as shown in formula (1.3)：

Wherein, the observation vector L_iComprising four un-differenced observationsAnd a real-time satellite Clock correction product resultAs false observed value,Represent between satellite s and site k respectively in frequency 1 respectively, on 2 Phase observations amount,Represent between satellite s and site k respectively in frequency 1, the pseudo range observed quantity on 2 respectively.It may be noted that , as real-time satellite clock correction product is used as false observed value, affected substantially by interpolation precision, Product Precision, by satellite clock correction Estimated as unknown parameter, while the addition of imitation observation equation can reduce the pathosis of equation.Wherein：

N represents the epoch observation satellite number, θⁿRepresent the elevation of satellite of n-th satellite epoch, MF_w(θ) it is zenith wet Postpone the mapping function related to elevation of satellite, c represents the light velocity, λ₁, λ₂The wavelength of frequency 1,2 is represented respectively；

According to unknown parameter vector X_iAnd design matrix B_iWith observation vector L_i, carry out Kalman filtering obtain non- Difference float ambiguitiesWherein, shown in Kalman filtering form such as formula (1.5)：

In formula, Φ_{I, i-1}It is the state-transition matrix of (4n+2) × (4n+2), as shown in formula (1.6)：

Q_iIt is (4n+2) × (4n+2) dynamic noise covariance matrixs, is expressed as follows：

Wherein, The correlation time of respectively corresponding stochastic process,E_nUnit matrix for n × n.

In formula 1.7, Zenith wet delay, the dynamic model that receiver, satellite clock correction and ionosphere tilt postpone depend on each From dynamic characteristic.For Zenith wet delay parameter, it is believed that be first-order Markov process：q_ZWD=1 ～9cm²/ h, Δ t are epoch time intervals.And white noise can simply and effectively describe the stochastic process of receiver, satellite clock correction. For ionosphere tilt delay parameter, it is also possible to be considered the random walk relevant with the zenith angle z ' of ionosphere point of puncture position：Invariant parameter when fuzziness is considered as： Represent Kronecker product.

Step c), from fuzziness covariance conditional number, three indexs of ADOP values and observation residual error, verifies ambiguity resolution Model, comprises the following steps that：

The reaction of fuzziness covariance conditional number is internal relations between fuzziness, and conditional number is less, and its robustness is got over By force, model structure is more stable, and in addition to model coefficient matrix architectural feature itself, different carrier wave pseudorange accuracy ratio and puppet are seen Surveying equation precision can the generation impact of conditional number result.Model normal equation is evaluated, as its fuzziness normal equation is right Claim positive definite matrix, using conditional number as metric, calculate as shown in formula (1.8)：

Wherein,It is the covariance matrix of fuzziness float-solution；| | | | represent norm sign；λ_maxAnd λ_minIt is special respectively The maximum of value indicative and minima.

ADOP values are for the mold strength for evaluating the inside for resolving fuzziness success rate, defend for judgement similar to PDOP Impact of the star receiver geometric position to positioning result, ADOP are used for itself accuracy value for evaluating fuzziness filter solution.Which is received respectively The result that item Index Influence is comprehensively obtained, in this method, in addition to being affected by epoch number, satellite number, is also subject to imitation observation equation essence Degree and number of parameters to be estimated affect.Which is calculated as shown in formula (1.9)：

Observation residual error direct reaction be model posteriori error, can intuitively embody observation noise pair under distinct methods As a result impact, while the characteristics of need to considering carrier noise in the case of differing heights angle.

Step 2), according to customer location and the distance of website, the non-poor fuzziness of at least three user's adjacent sites is extracted, The non-poor fuzziness of each user's adjacent sitesAnd its covariance matrixAs shown in formula (1.10)：

Wherein,Non- difference basis fuzziness N1 of in adjacent sites 1 to the n-th satellite is respectively corresponded to；Non- difference basis fuzziness N2 of in adjacent sites 1 to the n-th satellite is respectively corresponded to；

Step 3), a website is selected first in each user's adjacent sites as reference station, other neighbor stations Point is used as non-referenced website；Then difference operator C between the station of the reference station and non-referenced website is set_kdWith reference satellite with Difference operator C between the star of non-reference satellite^sd, as shown in formula (1.11)：

Between star in difference operator, the sorting position of the position by reference satellite in observation satellite of " -1 " row determines；

According to difference operator C_kdAnd C^sdThere is between star between reduction station the double difference fuzziness of integer characteristic, the reduction Shown in step such as formula (1.12), (1.13)：

Wherein, k1, k2 are respectively reference station and non-referenced website, and r is reference satellite, and s is non-reference satellite； For double difference fuzziness between star between station, corresponding covariance matrix isThe non-differential mode of respectively site k 1 and k2 Paste degree,Respectively double difference basis fuzziness N1, N2；

Step 4), ambiguity search is carried out using LAMBDA algorithms and fixed, comprise the steps：

A), double difference basis fuzziness N1, N2 is converted to wide lane ambiguityWith N1 fuzzinesses partFor Transition observation battle arrayAnd covariance matrixMatrix of a linear transformation C_linearAs shown in formula (1.14)：

Wherein,RespectivelyWithCorresponding covariance matrix.

B), the integer width lane ambiguity being fixed using LAMBDA algorithms, uses wide lane ambiguity as given value, really Determine N1 fuzziness integer values, as shown in formula (1.15)：

In formula (1.15),Respectively N1 fuzzinesses, the integer value of wide lane ambiguity,ForCorresponding Covariance matrix.

The integer characteristic double difference fuzziness between customer location adjacent sites is obtained, wherein adopts the method for fractional steps to reduce fuzziness Quantity, improve the whole network search efficiency of LAMBDA algorithms.

24 hour RINEX observation files and navigation file of the present embodiment using U.S. CORS, and coupling observation file IGS realtime products.In experiment, the whole network includes that nine reference stations, reference station are distributed net figure as shown in Figure 2.

In order to simulate sparse network RTK, if website on the basis of p332 stations, constitutes average baselining length and is about 150km's Eight baselines, as shown in table 1：

Eight baselines of nine base station compositions in 1 U.S. CORS of table nets

From figure 3, it can be seen that the mean square deviation of most of satellite clock corrections is within 0.25s, but still there is part satellite error Larger, at the same time, from fig. 4, it can be seen that in real time data there is system deviation and loss of data in clock correction, therefore non-in non-difference Need to estimate satellite clock correction in built-up pattern to guarantee the when invariant feature of fuzziness.Fig. 5-7 is given to satellite clock The contrast of the lower conditional number of the different estimation strategy of difference, ADOP values and observation residual error, it can be seen that though satellite clock correction is estimated So need to sacrifice more time to guarantee the reliability of ambiguity resolution, but reduce conditional number and phase residual error, it is ensured that The stability of model and robustness.From figure 8, it is seen that non-difference method reduction double difference fuzziness compares double difference method, to floating Fuzzy degree has more preferable estimation effect.From Fig. 9,10 as can be seen that compare traditional MW methods, the non-combined method of non-difference is to width The fixed success rate of lane ambiguity and N1 fuzzinesses is significantly improved.

The above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should It is considered as protection scope of the present invention.

Claims (2)

1. a kind of network RTK Ambiguity Solution Methods based on the non-combined model of non-difference, it is characterised in that non-first by non-difference Built-up pattern is estimated to the Dan Zhanfei difference fuzzinesses of the whole network, wherein using satellite clock correction as unknown parameter, real-time satellite clock Difference product is added as pseudo- observed quantity；Then the non-poor fuzziness of user's adjacent sites, according to customer location, is extracted, in neighbor stations One is selected in point as reference station, and the integer characteristic for obtaining double difference fuzziness using difference operator reduction, single epoch are obtained There is the double difference fuzziness result of integer characteristic.

2. network RTK Ambiguity Solution Methods based on the non-combined model of non-difference according to claim 1, its feature exist In comprising the following specific steps that：

Step 1), using the raw observation of each website, the Dan Zhanfei difference fuzzinesses of each website are estimated, and by satellite clock Difference is estimated as unknown parameter, as shown in formula (1.1)：

$\begin{array}{c}{P}_{j,k}^s={\mathrm{\ρ}}_k^s+{\mathrm{c\δt}}_k-{\mathrm{c\δt}}^s+T_k^s+{\mathrm{\α}}_j{I}_k^s+d_{k,P_j}-d_{P_j}^s+{\mathrm{\ϵ}}_{k,others}^s+{\mathrm{\ϵ}}_{k,P_j}^s\\ {\mathrm{\Φ}}_{j,k}^s={\mathrm{\ρ}}_k^s+{\mathrm{c\δt}}_k-{\mathrm{c\δt}}^s+T_k^s-{\mathrm{\α}}_j{I}_k^s+b_{k,{\mathrm{\Φ}}_j}-b_{{\mathrm{\Φ}}_j}^s+{\mathrm{\ϵ}}_{k,others}^s+{\mathrm{\λ}}_j{N}_j+{\mathrm{\ϵ}}_{k,{\mathrm{\Φ}}_j}^s\end{array}---\left(1.1\right)$

Wherein：S represents satellite, and k represents reference receiver, and j represents each observation frequency, j=1,2；Represent satellite s and station Pseudo range observed quantity between point k in frequency j,The phase observations amount in frequency j between satellite s and site k is represented,Represent Geometric distance of the satellite to receiver antenna phase center, δ t_kRepresent receiver clock-offsets, δ t^sRepresent satellite clock correction,It is right to represent Tropospheric delay,Represent ionosphere delay；α_jIt is frequency ratio,f_jRepresent the value of frequency j；Respectively Represent the hardware delay of the receiver and satellite in frequency j；It is that other can modeled error；Difference table Show the phase place decimal deviation of the receiver and satellite in frequency j；λ_jIt is the carrier wavelength in frequency j, N_jIt is the phase place in frequency j Fuzziness；It is the Pseudo-range Observations and carrier phase observable noise in frequency j；C represents the light velocity；

According to formula (1.1), unknown parameter is estimated using Kalman filtering, obtain non-poor float ambiguities, including as follows Concrete steps：

Step a), arranges unknown parameter vector X_i, as shown in formula (1.2)：

$X_i={\left[\begin{array}{cccccc}{\mathrm{ZTD}}_{w,k}& {{\mathrm{\δt}}_k}^{\′}& {I_k^s}^{\′}& {{\mathrm{\δt}}^s}^{\′}& N_1^s& N_2^s\end{array}\right]}^T,(s=1...n)---\left(1.2\right)$

Wherein, unknown parameter X_iBe divided into time-varying and when constant two parts, time-varying part includes Zenith wet delay ZTD_w,k；Absorb receiver Without ionosphere hardware delayReceiver clock-offsets δ t_k',Wherein The n dimension ionosphere tilts for absorbing receiver and satellite frequency related hardware decay part postpone WhereinN is the epoch observation satellite number, absorbs satellite without ionosphere hardware delay N dimension satellite clock correction δ t^s',When constant part include n tie up The initial N1 integer ambiguities of non-differenceThe initial N2 integer ambiguities of non-difference are tieed up with n

Step b), arranges the design matrix B of Kalman filtering_iWith observation vector L_i, as shown in formula (1.3)：

$L_i=\left[\begin{array}{c}{\mathrm{\Φ}}_{1,k}^s\\ P_{1,k}^s\\ {\mathrm{\Φ}}_{2,k}^s\\ P_{2,k}^s\\ {\mathrm{\δt}}_{IGS}^s\end{array}\right],B_i=\left[\begin{array}{cccccc}{B}_{{\mathrm{MF}}_w}& B_{{{\mathrm{\δt}}_k}^{\′}}& B_I& -B_{{{\mathrm{\δt}}^s}^{\′}}& 0& 0\\ B_{{\mathrm{MF}}_w}& B_{{{\mathrm{\δt}}_k}^{\′}}& \frac{f_1^2}{f_2^2}{B}_I& -B_{{{\mathrm{\δt}}^s}^{\′}}& 0& 0\\ B_{{\mathrm{MF}}_w}& B_{{{\mathrm{\δt}}_k}^{\′}}& -B_I& -B_{{{\mathrm{\δt}}^s}^{\′}}& B_{N_1}& 0\\ B_{{\mathrm{MF}}_w}& B_{{{\mathrm{\δt}}_k}^{\′}}& -\frac{f_1^2}{f_2^2}{B}_I& -B_{{{\mathrm{\δt}}^s}^{\′}}& 0& B_{N_2}\\ 0& 0& 0& B_{{{\mathrm{\δt}}^s}^{\′}}& 0& 0\end{array}\right]---\left(1.3\right)$

Wherein, the observation vector L_iComprising four un-differenced observationsAnd a real-time satellite clock correction is produced Product resultAs false observed value,Represent that the phase place on 2 is seen respectively in frequency 1 between satellite s and site k respectively Measurement,Represent between satellite s and site k respectively in frequency 1, the pseudo range observed quantity on 2 respectively；

N represents the epoch observation satellite number, θⁿRepresent the elevation of satellite of n-th satellite epoch, MF_w(θ) it is Zenith wet delay The mapping function related to elevation of satellite, c represent the light velocity, λ₁,λ₂The wavelength of frequency 1,2 is represented respectively；

According to unknown parameter vector X_iAnd design matrix B_iWith observation vector L_i, carry out Kalman filtering and obtain the non-difference of n dimensions Initial N1, N2 integer ambiguity

Step 2), according to customer location and the distance of website, the non-poor fuzziness of at least three user's adjacent sites is extracted, each use The non-poor fuzziness of family adjacent sitesAs shown in formula (1.5)：

$\underset{2n\×1}{X_k^s}={\left[\begin{array}{cccccc}{N}_{1,k}^1& ...& N_{1,k}^n& N_{2,k}^1& ...& N_{2,k}^n\end{array}\right]}^T---\left(1.5\right)$

Wherein,Non- difference basis fuzziness N1 of in adjacent sites 1 to the n-th satellite is respectively corresponded to；Non- difference basis fuzziness N2 of in adjacent sites 1 to the n-th satellite is respectively corresponded to；

Step 3), first in each user's adjacent sites, select a website as reference station, other adjacent sites are made For non-referenced website；Then difference operator C between the station of the reference station and non-referenced website is set_kdWith reference satellite and non-ginseng Examine difference operator C between the star of satellite^sd, according to difference operator C_kdAnd C^sdThere is between star between reduction station the double difference of integer characteristic Fuzziness, shown in the reduction step such as formula (1.6)：

$\underset{2\left(n-1\right)\×1}{X_{k1,k2}^{s,r}}=C^{sd}\·C_{kd}\·\left[\begin{array}{c}{X}_{k1}^s\\ X_{k2}^s\end{array}\right]={\left[\begin{array}{cc}{N}_{1,k1,k2}^{s,r}& N_{2,k1,k2}^{s,r}\end{array}\right]}^T---\left(1.6\right)$

Wherein, k1, k2 are respectively reference station and non-referenced website, and r is reference satellite, and s is non-reference satellite,For between station Double difference fuzziness between star,The non-poor fuzziness of respectively site k 1 and k2,Respectively double difference base Plinth fuzziness N1, N2；

Step 4), ambiguity search is carried out using LAMBDA algorithms and fixed, specially：First by the double difference basis fuzziness N1, N2 is converted to wide lane ambiguityWith N1 fuzzinesses partThe integer width lane ambiguity being fixed using LAMBDA algorithms again Degree, finally uses wide lane ambiguity as given value, determines N1 fuzziness integer values.