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

Network RTK ambiguity resolution method based on non-differential non-combination model

Technical Field

The invention relates to the field of Global Navigation Satellite System (GNSS) satellite positioning, in particular to GNSS non-differential non-combination precise point positioning.

Background

With the increasing number of Reference stations and the compatibility of multi-System multi-frequency signals, a large-scale CORS (Continuous operation Reference System) System has been widely established and gradually becomes a national important basic facility to support high-precision positioning application, and a user can obtain centimeter-level positioning precision in real time by using a multi-Reference station network.

In the current network RTK application, the correct calculation of the double-difference ambiguity must be ensured so that the difference correction information and the VRS observed value of the whole network can be generated, thereby ensuring the positioning effect. Therefore, most CORS system software adopts a baseline solution method to realize the whole-network ambiguity solution. Although the number of unknown parameters is reduced in the baseline solution method, and the problem of rank deficiency in solution is solved to a certain extent, a correlation problem which is complex and difficult to solve exactly exists. Meanwhile, due to the influence of atmospheric errors and satellite orbit errors, the base length is limited in the base line resolving process, and a new atmospheric error estimation model has to be considered to widen the base length. And as the number of reference stations increases, the number of baselines that need to be resolved grows exponentially. Therefore, the whole-network ambiguity resolution based on the baseline resolution method is not beneficial to the construction and operation of a distributed architecture of a large-range CORS system, and the application of the large-range CORS system is limited.

Meanwhile, with the successful application of non-poor PPP, an innovative PPP-RTK method is widely studied. In the non-combinatorial observation equation, the carrier pseudorange bias terms of the receiver and the satellite are absorbed by the ambiguity, so that the integer property is lost by the non-differential ambiguity. But with fixed double-difference ambiguities and correct reference ambiguities, integer properties of non-differential ambiguities can be restored and there is numerical equivalence to the double-difference equation, but without facing the correlation problem. Therefore, the ambiguity fixation of the whole network deserves further research and will greatly facilitate the development of a large-scale CORS system.

Disclosure of Invention

The purpose of the invention is as follows: aiming at the prior art, a network RTK ambiguity resolving method based on a non-differential non-combination model is provided, the problems that the existing network RTK is affected by correlation problems and the base length and the number are limited can be solved, and the method is greatly beneficial to the development of a large-scale CORS system.

The technical scheme is as follows: a network RTK ambiguity resolving method based on a non-differential non-combination model comprises the steps of firstly, estimating single-station non-differential ambiguity of a whole network by using the non-differential non-combination model, wherein a satellite clock is used as an unknown parameter, and a real-time satellite clock error product is added as a pseudo observed quantity; and then extracting the non-differential ambiguity of the adjacent sites of the user according to the position of the user, selecting one of the adjacent sites as a reference site, reducing by using a difference operator to obtain the integer characteristic of the double-differential ambiguity, and obtaining the double-differential ambiguity result with the integer characteristic by using a single epoch.

Further, the network RTK ambiguity resolution method based on the non-differential non-combination model includes the following specific steps:

step 1), estimating single-station non-differential ambiguity of each station by using an original observation value of each station, and estimating a satellite clock error as an unknown parameter, wherein the formula (1.1) is as follows:

wherein: s denotes a satellite, k denotes a reference station receiver, j denotes each observation frequency, and j is 1 or 2;representing pseudorange observations between satellite s and station k at frequency j,representing the phase observation at frequency j between satellite s and site k,representing the geometric distance, t, of the satellite to the phase center of the receiver antenna_kRepresenting the receiver clock error, t^sWhich represents the clock error of the satellite or satellites,the delay in the troposphere is indicated,indicating ionospheric delay α_jIs the ratio of the frequencies at which the signals are,a value representing frequency j;respectively representing the hardware delays of the receiver and the satellite at frequency j;is other error that can be modeled;respectively representing the phase fractional deviations of the receiver and the satellite at frequency j; lambda [ alpha ]_jIs the carrier wavelength, N, at frequency j_jIs the phase ambiguity at frequency j;is the pseudorange observation and the phase observation noise at frequency j; c represents the speed of light;

according to the formula (1.1), the unknown parameters are estimated by using Kalman filtering to obtain the non-difference floating ambiguity, and the method comprises the following specific steps:

step a), setting unknown parameter vector X_iAs shown in formula (1.2):

wherein the unknown parameter X_iThe time-varying part comprises zenith wet delay ZTD_w，k(ii) a Absorbing receiver ionosphere-free hardware delayOf the receiver clock difference t_k′，WhereinAbsorbing n-dimensional ionospheric tilt delays for receiver and satellite frequency dependent hardware delay components Whereinn is the satellite number observed by the epoch, and absorbs the hardware delay of satellite without ionosphereN-dimensional satellite clock error t^s′，The time-invariant portion includes an n-dimensional non-differenceInitial N1 integer ambiguitysum-N dimensional non-differential initial N2 integer ambiguity

Step B), setting a design matrix B of Kalman filtering_iAnd an observation vector L_iAs shown in formula (1.3):

wherein the observation vector L_iComprising four non-differential observationsAnd a real-time satellite clock error product resultAs a result of the pseudo-observed value,respectively representing the phase observations at frequencies 1, 2 between satellite s and site k,respectively representing pseudo-range observed quantities between the satellite s and the station k on frequencies 1 and 2 respectively;

n represents the epoch observation satelliteNumber of stars, thetaⁿSatellite altitude, MF, representing the epoch of the nth satellite_w(theta) is a mapping function of zenith wet delay with respect to satellite altitude, c represents the speed of light, lambda₁，λ₂Represent wavelengths at frequencies 1, 2, respectively;

according to the unknown parameter vector X_iAnd design matrix B_iAnd an observation vector L_iPerforming Kalman filtering to obtain non-difference floating-point ambiguity

Step 2), extracting the non-differential ambiguity of at least three user adjacent sites according to the distance between the user position and the site, and the non-differential ambiguity of each user adjacent siteAs shown in formula (1.5):

wherein,non-differential base ambiguities N1 for the 1 st to nth satellites in the corresponding neighboring sites, respectively;non-differential base ambiguities N2 for the 1 st to nth satellites in the corresponding neighboring sites, respectively;

step 3), firstly, selecting one site from the adjacent sites of each user as a reference site, and taking other adjacent sites as non-reference sites; then setting an inter-station difference operator C of the reference station and the non-reference station_kdAnd inter-satellite difference operator C of reference satellite and non-reference satellite^sdAccording to said difference operator C_kdAnd C^sdDouble with integral character between reduction stationsPoor ambiguity, the reduction step is as shown in equation (1.6):

wherein k1 and k2 are respectively a reference station and a non-reference station, r is a reference satellite, s is a non-reference satellite,is the double-difference ambiguity between the satellites of the station,the non-differential ambiguities of sites k1 and k2 respectively,double-difference base ambiguities N1, N2, respectively;

step 4), carrying out ambiguity search fixing by using an LAMBDA algorithm, which specifically comprises the following steps: firstly, the double-difference basic ambiguities N1 and N2 are converted into wide lane ambiguitiesAnd N1 ambiguity partAnd obtaining a fixed integer widelane ambiguity by adopting an LAMBDA algorithm, and finally determining an N1 ambiguity integer value by using the widelane ambiguity as a known value.

Has the advantages that: the network RTK ambiguity resolution method based on the non-difference non-combination model provided by the invention is integrated with a real-time satellite clock error product as a pseudo observation quantity, so that the resolution effect of real-time PPP is improved, and the robustness degree of the model is improved. The non-differential ambiguity is reduced by using a differential operator to obtain double-differential integer ambiguity, and only time-invariant ambiguity parameters are introduced in the process to carry out full-net adjustment, so that the influence of the length of a base line and atmospheric delay on the result is reduced, the calculation efficiency is improved, and the development of a large-scale CORS system is facilitated.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

FIG. 2 is an embodiment reference site net map;

FIG. 3 is a graph of an embodiment real-time satellite clock error product accuracy statistic;

FIG. 4 is a graph of satellite clock offset for satellite PRN8 and satellite PRN 14;

FIG. 5 is a graph of condition number variation for different satellite product clock accuracies;

FIG. 6 is a graph of ADOP variation at clock accuracy for different satellite products;

FIG. 7 is a graph of observed value residuals for a non-ionospheric combination model, a non-combination model, and a non-combination model of an estimated satellite clock;

FIG. 8 is a graph of condition number variation for double difference ambiguities obtained using a non-difference mode and using a double difference mode;

FIG. 9 is a graph of double-differenced widelane ambiguity floating-point bias using a non-differenced mode and using a double-differenced mode;

FIG. 10 is a graph of floating point biases for double-differenced N1 ambiguities obtained using a non-differenced mode and using a double-differenced mode.

Detailed Description

The present invention will be further described with reference to the accompanying drawings.

As shown in fig. 1, a network RTK ambiguity resolution method based on a non-differential non-combination model includes estimating single-station non-differential ambiguities of a whole network by using the non-differential non-combination model, wherein a satellite clock is used as an unknown parameter, and a real-time satellite clock difference product is added as a pseudo observed quantity; and then extracting the non-differential ambiguity of the adjacent sites of the user according to the position of the user, selecting one of the adjacent sites as a reference site, reducing by using a difference operator to obtain the integer characteristic of the double-differential ambiguity, and obtaining the double-differential ambiguity result with the integer characteristic by using a single epoch. The method comprises the following specific steps:

step 1), estimating single-station non-differential ambiguity of each station by using an original observation value of each station, and estimating by using a satellite clock error as an unknown parameter; the non-combined observation equation of each station is shown as the formula (1.1):

wherein: s denotes a satellite, k denotes a reference station receiver, j denotes each observation frequency, and j is 1 or 2;representing pseudorange observations between satellite s and station k at frequency j,representing the phase observation at frequency j between satellite s and site k,representing the geometric distance, t, of the satellite to the phase center of the receiver antenna_kRepresenting the receiver clock error, t^sWhich represents the clock error of the satellite or satellites,the delay in the troposphere is indicated,indicating ionospheric delay α_jIs the ratio of the frequencies at which the signals are,a value representing frequency j;respectively representing the hardware delays of the receiver and the satellite at frequency j;other modeling errors, such as tide correction and polar migration errors;respectively representing the phase fractional deviations of the receiver and the satellite at frequency j; lambda [ alpha ]_jIs the carrier wavelength, N, at frequency j_jIs the phase ambiguity at frequency j;is the pseudorange observation and the phase observation noise at frequency j; c represents the speed of light;

according to the formula (1.1), the unknown parameters are estimated by using Kalman filtering to obtain the non-difference floating ambiguity, and the method comprises the following specific steps:

step a), setting unknown parameter vector X_jAs shown in formula (1.2):

wherein the unknown parameter X_iThe time-varying part comprises zenith wet delay ZTD_w，k(ii) a Absorbing receiver ionosphere-free hardware delayOf the receiver clock difference t_k′，WhereinAbsorbing n-dimensional ionospheric tilt delays for receiver and satellite frequency dependent hardware delay components Whereinn is the satellite number observed by the epoch, and absorbs the hardware delay of satellite without ionosphereN-dimensional satellite clock error t^s′，The time-invariant portion includes an N-dimensional non-differential initial N1 integer ambiguitysum-N dimensional non-differential initial N2 integer ambiguity

Step B), setting a design matrix B of Kalman filtering_iAnd an observation vector L_iAs shown in formula (1.3):

wherein the observation vector L_iComprising four non-differential observationsAnd a real-time satellite clock error product resultAs a result of the pseudo-observed value,respectively representing the phase observations at frequencies 1, 2 between satellite s and site k,respectively, represent pseudorange observations between satellite s and station k at frequencies 1, 2, respectively. It should be noted that, because the real-time satellite clock error product is used as a pseudo-observation value and is obviously affected by interpolation precision and product precision, the satellite clock error is used as an unknown parameter for estimation, and meanwhile, the addition of a pseudo-observation equation can reduce the ill-posed property of the equation. Wherein:

n represents the number of satellites observed by the epoch, thetaⁿSatellite altitude, MF, representing the epoch of the nth satellite_w(theta) is a mapping function of zenith wet delay with respect to satellite altitude, c represents the speed of light, lambda₁，λ₂Represent wavelengths at frequencies 1, 2, respectively;

according to the unknown parameter vector X_iAnd design matrix B_iAnd an observation vector L_iPerforming Kalman filtering to obtain non-difference floating-point ambiguityWherein, the Kalman filtering form is shown as formula (1.5):

in the formula phi_i，i-1Is the state transition matrix of (4n +2) × (4n +2), as shown in equation (1.6):

Q_iis a (4n +2) × (4n +2) dynamic noise covariance matrix, expressed as follows:

wherein, respectively the associated time of the corresponding random process,E_nis an identity matrix of n × n.

In equation 1.7, the dynamic models of zenith wet delay, receiver, satellite clock bias, and ionospheric tilt delay depend on the respective dynamics. For the zenith wet delay parameter, one can consider a first order Markov process:q_ZWD＝1～9cm²and/h, Δ t is the epoch time interval. And white noise can simply and effectively describe the random process of the clock error of the receiver and the satellite. To pairThe ionospheric tilt delay parameter can also be considered as a random walk associated with the zenith angle z' of the ionospheric puncture site location:the ambiguity is considered as a time-invariant parameter: representing the kronecker product.

Step c), verifying an ambiguity resolution model from three indexes of an ambiguity covariance condition number, an ADOP value and an observed value residual error, and specifically comprising the following steps:

the ambiguity covariance condition number reflects the internal relation among ambiguities, the smaller the condition number is, the stronger the robust capability of the ambiguity covariance condition number is, the more stable the model structure is, and except the coefficient matrix structure characteristics of the model, the condition number results are affected by different carrier pseudorange precision ratios and pseudo-observation equation precision. Evaluating a model method equation, wherein the ambiguity method equation is a symmetric positive definite matrix, and the condition number is used as a measurement index, so that the calculation is shown as a formula (1.8):

wherein,is a covariance matrix of the ambiguity floating solution; | l | · | | represents a norm symbol; lambda [ alpha ]_maxAnd λ_minRespectively, a maximum value and a minimum value of the characteristic value.

The ADOP value is the internal model strength used to assess the success rate of resolving ambiguities, similar to PDOP used to determine the effect of satellite receiver geometry on the positioning results, and ADOP is used to assess the native accuracy of the ambiguity filter solution. The method is influenced by various indexes, and the method is influenced by the accuracy of a pseudo-observation equation and the quantity of parameters to be estimated besides the number of epochs and satellites. The calculation is shown in formula (1.9):

the observed value residual directly reflects the posterior error of the model, the influence of observed value noise on the result under different methods can be visually reflected, and the characteristics of carrier noise under different altitude angles need to be considered.

Step 2), extracting the non-differential ambiguity of at least three user adjacent sites according to the distance between the user position and the site, and the non-differential ambiguity of each user adjacent siteAnd covariance matrix thereofAs shown in formula (1.10):

wherein,non-differential base ambiguities N1 for the 1 st to nth satellites in the corresponding neighboring sites, respectively;non-differential base ambiguities N2 for the 1 st to nth satellites in the corresponding neighboring sites, respectively;

step 3), firstly, selecting one site from the adjacent sites of each user as a reference site, and taking other adjacent sites as non-reference sites; then setting an inter-station difference operator C of the reference station and the non-reference station_kdAnd inter-satellite difference operator C of reference satellite and non-reference satellite^sdAs shown in formula (1.11):

in the inter-satellite difference operator, the position of the "-1" column is determined by the ordered position of the reference satellite in the observation satellite;

according to the difference operator C_kdAnd C^sdReducing double-difference ambiguity with integer characteristics between the satellites of the station, wherein the reduction steps are shown as formulas (1.12) and (1.13):

wherein k1 and k2 are respectively a reference station and a non-reference station, r is a reference satellite, and s is a non-reference satellite;for the inter-station inter-satellite double-difference ambiguity, the corresponding covariance matrix isThe non-differential ambiguities of sites k1 and k2 respectively,double-difference base ambiguities N1, N2, respectively;

step 4), carrying out ambiguity search fixing by using an LAMBDA algorithm, and comprising the following steps:

a) converting the double-difference base ambiguities N1, N2 into widelane ambiguitiesAnd N1 ambiguity partFor transforming observation arraysSum-covariance matrixLinear transformation matrix C of_linearAs shown in formula (1.14):

wherein,are respectively asAndcorresponding covariance matrix.

b) Obtaining a fixed integer widelane ambiguity by adopting an LAMBDA algorithm, and determining an N1 ambiguity integer value by using the widelane ambiguity as a known value, as shown in formula (1.15):

in the formula (1.15), the compound,respectively are integer values of N1 ambiguity and widelane ambiguity,is composed ofCorresponding covariance matrix.

And obtaining integer characteristic double-difference ambiguity between adjacent sites of the user position, wherein a step method is adopted to reduce the number of ambiguities, and the whole network searching efficiency of the LAMBDA algorithm is improved.

This example uses 24-hour RINEX observation files and navigation files from CORS in the united states, and IGS real-time products that match the observation files. The entire net in the experiment included nine reference stations, which were distributed as a net graph as shown in fig. 2.

In order to simulate sparse network RTK, let the p332 station be the reference station, and form eight baselines with an average baseline length of about 150km, as shown in table 1:

TABLE 1 eight base lines consisting of nine base stations in the CORS network of USA

As can be seen from fig. 3, the mean square error of most satellite clock differences is within 0.25s, but some satellite errors are still large, and at the same time, as can be seen from fig. 4, there are system bias and data loss in the clock differences in real-time data, so that the satellite clock differences need to be estimated in a non-differential non-combination model to ensure the time-invariant property of ambiguity. 5-7 show the comparison of the condition number, ADOP value and observation residual under different estimation strategies for satellite clock error, it can be seen that, although more time is sacrificed to ensure the reliability of ambiguity resolution, the condition number and phase residual are reduced to ensure the stability and robust capability of the model. As can be seen from fig. 8, the non-difference method restores the double-difference ambiguities, and has a better estimation effect on the floating ambiguities than the double-difference method. As can be seen from fig. 9 and 10, compared to the conventional MW method, the non-differential non-combination method has a significantly improved fixing success rate for widelane ambiguities and N1 ambiguities.

The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims (2)

1. A network RTK ambiguity resolution method based on a non-differential non-combination model is characterized in that the non-differential non-combination model is used for estimating single-station non-differential ambiguity of a whole network, wherein satellite clock error is used as an unknown parameter, and a real-time satellite clock error product is added as a pseudo observed quantity; and then extracting the non-differential ambiguity of the adjacent sites of the user according to the position of the user, selecting one of the adjacent sites as a reference site, reducing by using a difference operator to obtain the integer characteristic of the double-differential ambiguity, and obtaining the double-differential ambiguity result with the integer characteristic by using a single epoch.

2. The non-differential non-combination model based network RTK ambiguity resolution method of claim 1, comprising the specific steps of:

step 1), estimating single-station non-differential ambiguity of each station by using an original observation value of each station, and estimating a satellite clock error as an unknown parameter, wherein the formula (1.1) is as follows:

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

wherein: s denotes a satellite, k denotes a reference station receiver, j denotes each observation frequency, and j is 1 or 2;representing pseudorange observations between satellite s and station k at frequency j,representing the phase observation at frequency j between satellite s and site k,representing the geometric distance, t, of the satellite to the phase center of the receiver antenna_kRepresenting the receiver clock error, t^sWhich represents the clock error of the satellite or satellites,the delay in the troposphere is indicated,indicating ionospheric delay α_jIs the ratio of the frequencies at which the signals are,f_ja value representing frequency j;respectively representing the hardware delays of the receiver and the satellite at frequency j;is other error that can be modeled;respectively representing the phase fractional deviations of the receiver and the satellite at frequency j; lambda [ alpha ]_jIs the carrier wavelength, N, at frequency j_jIs the phase ambiguity at frequency j;is the pseudorange observation and the phase observation noise at frequency j; c represents the speed of light;

according to the formula (1.1), the unknown parameters are estimated by using Kalman filtering to obtain the non-difference floating ambiguity, and the method comprises the following specific steps:

step a), setting unknown parameter vector X_iAs 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 the unknown parameter X_iThe time-varying part comprises zenith wet delay ZTD_w,k(ii) a Absorbing receiver ionosphere-free hardware delayOf the receiver clock difference t_k'，WhereinAbsorbing n-dimensional ionospheric tilt delays for receiver and satellite frequency dependent hardware delay components Whereinn is the satellite number observed by the epoch, and absorbs the hardware delay of satellite without ionosphereN-dimensional satellite clock error t^s'，The time-invariant portion includes an N-dimensional non-differential initial N1 integer ambiguitysum-N dimensional non-differential initial N2 integer ambiguity

Step B), setting a design matrix B of Kalman filtering_iAnd an observation vector L_iAs 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 non-differential observationsAnd a real-time satellite clock error product resultAs a result of the pseudo-observed value,respectively representing the phase observations at frequencies 1, 2 between satellite s and site k,respectively representing pseudo-range observed quantities between the satellite s and the station k on frequencies 1 and 2 respectively;

n represents the number of satellites observed by the epoch, thetaⁿThe satellite representing the epoch of the nth satelliteHeight angle, MF_w(theta) is a mapping function of zenith wet delay with respect to satellite altitude, c represents the speed of light, lambda₁,λ₂Represent wavelengths at frequencies 1, 2, respectively;

according to the unknown parameter vector X_iAnd design matrix B_iAnd an observation vector L_iPerforming Kalman filtering to obtain N-dimensional non-difference initial N1 and N2 integer ambiguities

Step 2), extracting the non-differential ambiguity of at least three user adjacent sites according to the distance between the user position and the site, and the non-differential ambiguity of each user adjacent siteAs 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-differential base ambiguities N1 for the 1 st to nth satellites in the corresponding neighboring sites, respectively;non-differential base ambiguities N2 for the 1 st to nth satellites in the corresponding neighboring sites, respectively;

step 3), firstly, selecting one site from the adjacent sites of each user as a reference site, and taking other adjacent sites as non-reference sites; then setting an inter-station difference operator C of the reference station and the non-reference station_kdAnd inter-satellite difference operator C of reference satellite and non-reference satellite^sdAccording to said difference operator C_kdAnd C^sdRestoring double-difference ambiguity with integer characteristics between the satellites of the station, wherein the restoring step is shown as the 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 and k2 are respectively a reference station and a non-reference station, r is a reference satellite, s is a non-reference satellite,is the double-difference ambiguity between the satellites of the station,the non-differential ambiguities of sites k1 and k2 respectively,double-difference base ambiguities N1, N2, respectively;

step 4), carrying out ambiguity search fixing by using an LAMBDA algorithm, which specifically comprises the following steps: firstly, the double-difference basic ambiguities N1 and N2 are converted into wide lane ambiguitiesAnd N1 ambiguity partAnd obtaining a fixed integer widelane ambiguity by adopting an LAMBDA algorithm, and finally determining an N1 ambiguity integer value by using the widelane ambiguity as a known value.