WO2019062030A1

WO2019062030A1 - Star network-based bds/gps broadcast network rtk algorithm

Info

Publication number: WO2019062030A1
Application number: PCT/CN2018/078492
Authority: WO
Inventors: 潘树国; 王彦恒; 张瑞成; 尚睿; 汪登辉
Original assignee: 东南大学
Priority date: 2017-09-26
Filing date: 2018-03-09
Publication date: 2019-04-04
Also published as: CN107797126B; CN107797126A

Abstract

Disclosed is a star network-based BDS/GPS broadcast network RTK algorithm. All base stations form a triangulation network by using Delaunay triangulation algorithm; and a controllable full-region star network formed by a plurality of star network elements is generated on the basis of the triangulation network. Data of the base stations is obtained in real time and network element calculation is performed to generate a baseline atmospheric error. In addition, on the basis of on a UDP protocol, a server broadcasts a master station observation value, base station coordinates, and the baseline atmospheric error to a user by using the star network as a unit; the user selects, according to an approximate location thereof and the location of the master station, a network element where the user is located; and interpolation is performed on an inter-station single-difference atmospheric error of the baseline formed by the user and the master station, and the obtained atmospheric error is corrected to the master station observation value to perform baseline calculation. The user can also upload approximate coordinates by means of two-way communication and the server broadcasts differential data of the network element where the user is located. In addition, differential data broadcasting by equipment such as ground equipment, an airplane, or a satellite is also supported.

Description

BDS/GPS broadcast network RTK algorithm based on star network

Technical field

The invention relates to a star network based BDS/GPS broadcast network RTK algorithm, in particular to a star network based BDS compatible GPS broadcast mode and compatible with two-way communication network RTK (Real Time Kinematic, real-time dynamic positioning technology Implementation technology, belongs to the field of GNSS real-time high-precision fast positioning.

Background technique

Network RTK technology has become one of the most widely used GNSS precision positioning technologies, and can provide users with multi-scale positioning services such as meter, decimeter and centimeter in real time ^[1-3] . According to the differential data distribution method, the mainstream network RTK technology can be divided into VRS (Virtual Reference Station) technology, MAC (Master Auxiliary Concept) technology and FKP (Flachen Korrektur Parameter). Technology ^[4] .

In the VRS technology, the user first uploads its own probability coordinates, and the CORS (Continuously Operating Reference System) central solution software (hereinafter referred to as the central software) generates a virtual reference station in the vicinity of the user according to the user probability position, the user and the user The virtual reference station forms an ultra-short baseline for solution. The disadvantages of this technology are: 1 requires two-way communication, increases data delay 2 When the user position changes greatly (more than 5km), the virtual reference station will change, the user needs to re-initialize; 3 the center software needs to be based on the user's approximate location Generate virtual reference station information for each user, limiting user capacity; 4 because the virtual information is used, the differential correction information cannot be tracked; 5 although the VRS technology itself does not limit the number of reference stations in the network element, the current The software is basically based on triangulation, lacking redundant information; 6 atmospheric error processing is only determined by the central software, so that users can not use better algorithms ^[4] ; 7 need to upload user's general location information, exposing the user's location, especially In some special areas, this method is not even desirable, such as the military field.

MAC technology supports single two-way communication. In two-way communication, the user uploads his own approximate location information. The central software selects the reference station closest to the user as the primary reference station according to the user's location, and broadcasts the differential correction information to the user; in one-way communication, The user needs to know the predefined network element in which he is located, and then obtain the corresponding differential correction information. In the two-way communication, this technology still has the same shortcomings as the VRS technology. In the one-way communication, although the shortcomings of the VRS technology are overcome, the user himself needs to know the network element in which he is located, which is for the user. It is difficult to implement, especially when users enter unfamiliar areas. Currently, software using MAC technology uses non-difference algorithms for network solution, with many parameters and complex models, which makes the solution efficiency of network elements. Low, network initialization time (from boot to network RTK service available) long.

In FKP technology, the central software uses non-difference algorithm to realize network solution, extracts non-difference error, and performs regional modeling on spatial correlation error, parameterizes non-difference space correlation error of mobile station, broadcasts by broadcast mode, and rover Real-time positioning based on these parameters and their location. The disadvantages of this technology are as follows: 1 The central software uses the non-difference algorithm for network solution, with many parameters and complex models, which makes the settlement efficiency low and the network initialization time long; 2 The establishment of the spatial correlation error model is completed by the central software, which limits the user's use. A more optimized algorithm.

Summary of the invention

In order to overcome the deficiencies in the existing network RTK technology, the present invention provides a BDS/GPS broadcast network RTK algorithm based on a star network, and is compatible with two-way communication, and supports differential correction data by ground equipment, aviation aircraft or satellite broadcasting. . The server uses the UDP protocol to broadcast the differential correction data of all the star network elements in the whole network in real time, and the users in the broadcast mode receive the data, and then perform network element selection, atmospheric interpolation and baseline solution. The user who uses the two-way communication uploads its own approximate location through the Ntrip protocol or the TCP/IP protocol, and the server broadcasts the user's network element differential correction data to the user, and the user obtains the data and performs atmospheric interpolation and baseline solution. When the server broadcasts the differential correction number to the two-way communication user, the data broadcasted according to the broadcast mode is still uninterrupted.

The present invention adopts the following technical solutions to solve the above technical problems:

The invention provides a star network-based BDS/GPS broadcast network RTK algorithm, which comprises the following specific steps:

Step 1: Obtain the base station coordinates from the database, use the Delaunay triangulation algorithm to generate the Delaunay triangulation, and generate a star-shaped network composed of several star network elements and control the whole region on the basis of the triangulation network, wherein each A star network element consists of a primary station and a number of secondary stations corresponding thereto;

Step 2: Obtain the base station data in real time, form a double-difference observation with the baseline in the Delaunay triangulation, construct a first Kalman filter, estimate the baseline double-difference ambiguity and the zenith tropospheric wet delay ZTD in real time, and then generate each Baseline double difference atmospheric error of the baseline;

Step 3: Assign the baseline double-difference atmospheric error generated in step 2 to the corresponding star network element baseline, and use the star-shaped network element as a unit to unify the reference star, and generate a single-element atmosphere between each baseline satellite station of the star-shaped network element. error;

Step 4: Using a star-shaped network element as a unit, encoding a single-difference atmospheric error, all base station coordinates, and a master station observation value of each baseline satellite station of the star network element, and the encoded data is performed by using a UDP protocol. Broadcast or use two-way communication for broadcast, in which UDP protocol broadcasts all data and then proceeds to step 5; when using two-way communication, firstly, the user uploads the approximate location information, and then the central software broadcasts only to the user according to the user's location through Ntrip protocol or TCP/IP. The data of the star network element where the user is located, proceeds to step 6;

Step 5, the user receives the data in real time and judges the network element where it is located, according to the differential data of the network element in which the network element is interpolated to obtain the single-difference atmospheric error between the station and the primary station, and corrects the observation value to the primary station, and proceeds to step 7;

Step 6, the user receives the data in real time, according to the differential data of the network element, the inter-station single difference atmospheric error between the station and the main station is interpolated, and corrected to the observation value of the main station, and proceeds to step 7;

In step 7, the user constructs a double-difference observation value by using the corrected observation value of the primary station and the user observation value corrected by step 5 or 6, and constructs a second Kalman filter including the user position parameter and the ambiguity parameter to perform baseline solution.

As a further optimization of the present invention, the step 1 includes the following steps:

Step 11, generating a triangulation network by using a Delaunay triangulation algorithm;

Step 12: extracting a triangulation network boundary reference station and a non-boundary reference station, wherein if the sum of the angles of the inner angles of the vertices of the base station in all the triangles connected to a reference station is greater than a set threshold, the base station a non-boundary base station, otherwise a boundary reference station;

Step 13, initializing the star network element set: all the non-boundary base stations are used as the primary station, and all the base stations connected thereto are used as the corresponding auxiliary stations;

Step 14: Find a set of base stations that do not participate in the star network networking in the boundary reference station;

Step 15, selecting the base station with the largest number of base stations connected to it as the new primary station in the base station set not participating in the networking, and the base station connected thereto as the corresponding secondary station, updating the star network set and not a set of base stations participating in a star network network;

Step 16. Repeat step 15 until the number of base stations that are not participating in the star network networking is zero.

As a further optimization of the present invention, the step 2 includes the following steps:

Step 21: The base station k receives the pseudorange and carrier observation signals of the satellite s, and the carrier and pseudorange observation equations are expressed as:

In the formula:

Indicates the carrier observation value in weeks on the jth frequency point of the satellite s received by the base station k, j=1, 2,

Indicates the station star distance from the base station k to the satellite s,

Indicates the full-circumference ambiguity at the j-th frequency point of the satellite s received by the reference station k, c represents the speed of light, dT _k represents the receiver clock difference of the reference station k, and dT ^s represents the satellite clock difference of the satellite s,

Indicates the tropospheric delay of the satellite s received by the base station k,

Indicates the ionospheric delay at the first frequency of the satellite s received by the base station k,

f _j represents the frequency value at the jth frequency point of the satellite system corresponding to the satellite s, f ₁ represents the frequency value at the 1st frequency point of the satellite system corresponding to the satellite ^s , and rel ^s represents the relativistic effect of the satellite s,

Means the carrier multipath effect in meters on the jth frequency of the satellite s received by the base station k,

Indicates the receiver-side carrier deviation in meters of the j-th frequency point of the base station k,

Indicates the satellite-side carrier deviation in meters on the j-th frequency point on the satellite s.

Indicates the carrier observation noise in meters per unit j of the satellite s received by the base station k,

Indicates the pseudo-range observation value in meters on the j-th frequency point of the satellite s received by the base station k,

Represents the pseudorange multipath effect in meters at the jth frequency of the satellite received by the base station k,

Indicates the receiver-side pseudorange deviation in meters per unit received by the jth frequency point of the reference station k,

Indicates the pseudorange deviation of the satellite end in meters at the jth frequency point of the satellite s,

Representing the pseudorange observation noise in meters at the jth frequency point of the satellite s received by the reference station k, and λ _j indicating the wavelength of the jth frequency point of the satellite system corresponding to the satellite s;

Step 22, according to the carrier observation value obtained by step 21 and the pseudorange observation value constitute a double difference observation value, the double difference carrier observation equation and the double difference pseudo range observation equation of the reference station k and the reference station y are respectively:

Where the superscript r represents the reference satellite,

a double-difference carrier observation indicating the j-th frequency point,

Indicates the star distance of the double-difference station,

Indicates the double-difference full-circumference ambiguity at the jth frequency point,

Indicates double-difference tropospheric delay,

Indicates the doubled ionospheric delay at the first frequency point,

Means the double-difference carrier multipath effect in meters on the jth frequency point,

Indicates the double-difference carrier observation noise in meters on the jth frequency point,

Indicates the double-difference pseudorange observation at the jth frequency point,

Representing the double-difference pseudorange multipath effect at the jth frequency point,

Representing the double difference pseudorange observation noise at the jth frequency point;

Step 23: Combine the double-difference observations formed in step 22 into a double-difference wide lane combined observation value, and calculate the wide lane combined ambiguity:

Using the MW combination to solve the wide-altitude combination ambiguity, the solution equation is:

In the formula:

Indicates the combined observation of double-difference wide lanes,

Indicates the wide lane combination ambiguity, λ _WL represents the wide lane wavelength;

For the wide lane combination ambiguity, multi-epoch smoothing is rounded off, and the specific formula is as follows:

In the formula:

The wide-altitude combined ambiguity floating-point solution obtained by the i-th observation epoch is calculated, z represents the total number of observation epochs, and round represents a rounding-and-rounding operator;

Step 24, using a combination of no ionosphere, constructing a narrow lane filter, and separating the base ambiguity by using a combination of no ionosphere and wide lane

versus

Includes the following steps:

In step 241, a combined observation of the double-difference ionosphere is formed:

In the formula:

Represents a double-difference ionospheric combined observation,

Represents no ionospheric combined ambiguity, λ _NL = c / (f ₁ + f ₂ );

Step 242, constructing a first Kalman filter:

Where E(g) represents the mathematical expectation and Cov(g) represents the covariance.

State vectors representing the i-th epoch and the i-th epoch, respectively;

Representing a state transition matrix;

Represents a dynamic noise vector,

Representing a dynamic noise covariance matrix;

Represents the i-th eigen observation vector,

Representing the design matrix,

Representing the i-th eigen observation noise vector;

Expressed as the i-th epoch observed noise covariance matrix,

Representing the i-th epoch state vector covariance matrix,

Representing a state vector prediction covariance matrix,

Representing the i-th epoch state vector variance-covariance matrix,

Representing the gain matrix,

Express the unit matrix;

Based on the i-th epoch, the base station k and the reference station y have n GPS satellites and g BDS satellites, wherein the nth GPS satellite and the g-th BDS satellite are reference stars of each system. The estimation parameters include double-difference ambiguity and baseline relative zenith tropospheric wet delay. The filter model to be estimated parameter vector, observation vector and design matrix are expressed as:

among them:

In the formula:

A state vector representing the n+g-1 dimension (the parameter vector to be estimated), including a relative zenith tropospheric wet delay parameter RZTD and n+g-2 dimensional double difference whole-circumference ambiguity parameter vector

a vector of double-difference carrier observations representing n+g-2 dimensions,

Indicates GPS double-difference carrier observations, o=1, 2, L, n-1,

Indicates the GPS narrow lane wavelength,

Indicates the wavelength of the first frequency point of GPS,

Indicates the GPS double-difference ionosphere-free combined carrier observation,

Indicates the GPS star distance,

Represents the GPS satellite double-difference tropospheric dry delay,

Indicates the full-circumference ambiguity of the GPS double-difference wide lane

Indicates the frequency value of the first frequency point of GPS.

Indicates the frequency value of the second frequency point of GPS.

Indicates the BDS double-difference carrier observation, s = 1, 2, L, g-1,

Indicates the BDS narrow lane wavelength,

Indicates the wavelength of the first frequency of the BDS,

Indicates the BDS double-difference ionosphere-free combined carrier observation,

Indicates the star distance of the BDS double-difference station,

Indicates the double-difference tropospheric dry delay of the BDS satellite,

Indicates the full-circumference ambiguity of the BDS double-difference wide lane,

Indicates the frequency value of the first frequency point of the BDS.

Indicates the frequency value of the 2nd frequency point of the BDS.

Indicates the tropospheric mapping function of the GPS system satellite o on the base station k,

Indicates the tropospheric mapping function of the GPS system reference satellite n on the base station y,

Indicates the tropospheric mapping function of the BDS system satellite s on the base station k,

Indicates the tropospheric mapping function of the reference satellite g of the BDS system on the base station y,

a design matrix representing (n+g-2)×(n+g-1) dimensions;

Step 243: Perform filtering according to the first Kalman filter established in step 242, and solve a basic carrier ambiguity vector parameter.

Extracting the ambiguity parameter vector floating point solution from the filter

And the variance-covariance matrix is searched by the lambda algorithm to obtain the first frequency double-difference full-circumference ambiguity

(BDS) and

(GPS), further obtain the double difference whole-circumference ambiguity of the second frequency point

versus

Step 25, according to the result of step 24, generating a baseline double difference atmospheric error:

In the formula,

versus

Representing the double-difference tropospheric delay between GPS and BDS,

versus

Representing the GPS and BDS first frequency double-difference carrier observations,

versus

Representing the second frequency difference observation of GPS and BDS respectively,

versus

It indicates the 1st frequency doubled ionospheric delay of GPS and BDS respectively.

As a further optimization of the present invention, the step 3 includes the following steps:

Step 31: The primary station and the secondary station of the star network element form a baseline, and the baseline consisting of the same base station is searched in the baseline list of the entire network of the triangular network. If the two baseline directions are opposite, the baseline commutation is required, thereby obtaining Baseline double-difference atmospheric error for each type of star network element;

Step 32: Check whether the baseline reference stars of the star network elements are consistent. If they are inconsistent, the reference star is unified and the reference star transformation is performed on the atmospheric error;

Step 33: Generate a single-difference atmospheric error between the star-type network elements: the single-difference atmospheric error between the reference satellite stations is 0, and the single-difference atmospheric error value of the other satellites is equal to the double-difference atmospheric error;

Step 34: Extract satellites of each star-shaped network element that can be shared by the baseline, and generate a single-difference atmospheric error between the satellite stations of the star-shaped network element.

As a further optimization scheme of the present invention, the method for determining the network element where the step 5 is located is: the user decodes the received data and calculates the linear distance of the user to each primary station, represented by the primary station with the smallest distance. The NE is the NE of the user.

As a further optimization scheme of the present invention, the step 5 or 6 interpolates the difference between the station and the primary station according to the differential data of the network element in which the network element is located, and corrects the observation to the primary station observation value, including the following steps:

Step 1. Using the linear interpolation algorithm to interpolate the user's atmospheric error, the single-difference atmospheric error between the user and the primary station is calculated as follows:

Where subscript m denotes the primary station, u denotes the user, α ₁ , α ₂ , α ₃ denote the tropospheric interpolation coefficient, β ₁ , β ₂ denote the ionospheric interpolation coefficient, and w denote the number of secondary stations,

Indicates the inter-station single-difference tropospheric delay of the satellite s, Δx _{m, u} , Δy _{m, u} , Δh _{m, u} represent the coordinate difference between the primary station and the user _, respectively.

Indicates the single-difference ionospheric delay between stations;

The tropospheric interpolation coefficients and ionospheric interpolation coefficients are calculated as follows:

Where: Δx _m,t , Δy _m,t , Δh _m,t represents the coordinate difference between the primary station and the secondary station, t=1, 2, L, w;

In step 2, the atmospheric error value obtained by the interpolation is corrected to the observation value of the primary station, and the pseudorange and the carrier observation value are respectively as follows:

In the formula:

It shows the pseudorange and carrier observation values of the jth frequency point of the satellite s after the correction of the atmospheric error on the primary station.

Representing the original pseudorange and carrier observations of the jth frequency point of the satellite s on the primary station,

Indicates the inter-station tropospheric delay of the satellite s obtained by interpolation,

Indicates the inter-site ionospheric delay of the satellite s obtained by interpolation.

As a further optimization of the present invention, the double difference observation in the step 7 is expressed as:

In the formula,

Representing GPS satellite double-difference pseudorange observations,

Indicates the satellite distance of the GPS satellite double-difference station,

Representing GPS satellite double-difference pseudorange multipath effect,

Representing GPS satellite double-difference pseudorange observation noise,

Indicates the GPS satellite double-difference carrier observation, and λ ^G represents the wavelength of the GPS observation corresponding to the frequency point.

Represents the GPS satellite double-difference ambiguity,

Represents the GPS satellite double-difference carrier multipath effect in weeks,

Representing GPS satellite double-difference carrier observation noise in weeks,

Indicates the double-difference pseudorange observation of the BDS satellite,

Indicates the star distance of the BDS satellite double-difference station,

Representing the double-signal pseudorange multipath effect of BDS satellites,

Representing BDS satellite double-difference pseudorange observation noise,

Indicates the BDS satellite double-difference carrier observation, and λ ^C represents the wavelength of the BDS observation corresponding to the frequency point.

Indicates the double-difference ambiguity of the BDS satellite,

Representing the double-signal carrier multipath effect of the BDS satellite in weeks,

Indicates the BDS satellite double-difference carrier observation noise in weeks.

As a further optimization of the invention, the second Kalman filter in step 7 is constructed as follows:

Based on the i-th epoch, the user and the star network have n GPS satellites and g BDS satellites, of which the nth GPS satellite and the gth BDS satellite are reference stars of each system, and all satellites are combined. L1 carrier and P1 pseudorange observation data, filter model to be estimated parameter matrix

Observation matrix

Design matrix

Expressed as:

In the formula,

An estimated parameter vector representing n+g+1 dimensions, including a 3-dimensional positional parameter vector

Double-difference whole-circumference ambiguity parameter vector with n+g-2

Representing a 2(n+g-2) dimensional double difference observation vector, including pseudorange and carrier observations;

Represents a 2(n+g-2)×(n+g+1) dimensional design matrix, where l ^o,n,G ,p ^o,n,G ,q ^o,n,G represent the cosine of the GPS satellite direction (superscript o=1,2L,n-1),l ^s,g,C ,p ^s,g,C ,q ^s,g,C (superscript s=1,2L,t-1) represent the cosine of the BDS satellite direction,

Means the GPS satellite double-difference carrier observation in meters,

Representing GPS satellite double-difference pseudorange observations,

Indicates the star distance of the BDS satellite double-difference station,

Indicates the BDS satellite double-difference carrier observations in meters,

Indicates the double-difference pseudorange observation of the BDS satellite;

The above parameters are assigned and brought into the second Kalman filter to solve the epoch epoch, then the floating ambiguity vector and its variance-covariance matrix are extracted, and the ambiguity fixed solution can be obtained by searching with the lambda algorithm;

After fixing the ambiguity, the fixed solution of the user's three-dimensional coordinates is solved by the following formula:

among them,

Three-dimensional coordinate parameter vector and floating-point ambiguity parameter vector,

The coordinate parameter vector after fixing the ambiguity,

To fix the ambiguity parameter vector,

Corresponding to each parameter filtering solution covariance matrix.

Compared with the prior art, the present invention has the following technical effects:

(1) The present invention uses a star network for atmospheric interpolation to provide redundant observations;

(2) The present invention truly realizes the broadcast mode network RTK, and takes into consideration two-way communication, and the user capacity is not limited;

(3) The broadcast mode adopted by the present invention, the differential data can be broadcasted by ground equipment or by air plane or satellite, and can be used for wide-area differential and satellite-based enhanced data broadcast.

DRAWINGS

1 is a flow chart of a BDS/GPS broadcast network RTK algorithm based on a star network according to the present invention.

2 is a flow chart of a star network element generation algorithm.

Detailed ways

The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings:

The invention designs a BDS/GPS broadcast network RTK algorithm based on a star network, as shown in FIG. 1 , comprising the following steps:

Step 1: Obtain the base station coordinates from the database, use the Delaunay triangulation algorithm to generate the Delaunay triangulation, and generate a star-shaped network composed of several star network elements and control the whole region on the basis of the triangulation network, wherein each A star network element consists of a primary station and a number of secondary stations corresponding to it.

As shown in FIG. 2, the step 1 includes the following steps:

Step 11, using a Delaunay triangulation algorithm to generate a triangulation, wherein the maximum angle threshold of the triangle is 165° (the threshold is set according to personal experience);

Step 12: extracting a triangulation network boundary reference station and a non-boundary reference station, wherein if the sum of the angles of the inner angles of the vertices of the base station in all the triangles connected to a reference station is greater than a set threshold of 195°, then The base station is a non-boundary base station, otherwise it is a boundary base station;

Step 14. Find a set of base stations that are not participating in the star network networking in the border reference station (neither the primary station nor the primary station);

Step 2: Obtain the base station data in real time, form a double-difference observation with the baseline in the Delaunay triangulation, construct a first Kalman filter, estimate the baseline double-difference ambiguity and the zenith tropospheric wet delay ZTD in real time, and then generate each Baseline double difference atmospheric error for the baseline.

Step 2 includes the following steps:

In the formula:

Indicates the station star distance from the base station k to the satellite s,

It represents the pseudorange observation noise in meters at the jth frequency point of the satellite s received by the reference station k, and λ _j represents the wavelength of the jth frequency point of the satellite system corresponding to the satellite s.

Step 22, according to the carrier observation value obtained by step 21 and the pseudorange observation value to form a double difference observation value, the double difference carrier observation equation and the double difference pseudo range observation equation of the reference station k and the reference station y are respectively:

Where the superscript r represents the reference satellite,

a double-difference carrier observation indicating the j-th frequency point,

Indicates the star distance of the double-difference station,

Indicates double-difference tropospheric delay,

Indicates the doubled ionospheric delay at the first frequency point,

Indicates the double-difference pseudorange observation noise at the jth frequency point.

In step 23, the double-difference observations formed in step 22 are combined into a double-difference wide lane combined observation value to solve the wide lane combined ambiguity.

In the formula:

Indicates the combined observation of double-difference wide lanes,

Indicates the wide lane combination ambiguity, and λ _WL represents the wide lane wavelength.

Because the MW combination is used to solve the wide lane ambiguity, it is only affected by the carrier and pseudorange observation noise (ignoring multipath), and the observation noise obeys the Gaussian white noise distribution. Therefore, the multi-epoch smoothing rounding can be adopted for the wide lane combination ambiguity. The specific formula is as follows:

In the formula:

It represents the wide-altitude combined ambiguity floating-point solution obtained by the i-th observation epoch, z represents the total number of observation epochs, and round represents the rounding-and-rounding operator.

versus

Includes the following steps:

In the formula:

Represents a double-difference ionospheric combined observation,

Indicates that there is no ionospheric combined ambiguity, which does not have an integer characteristic. This combination eliminates the influence of the first-order term of the ionospheric delay, λ _NL = c / (f ₁ + f ₂ ).

Step 242, constructing a first Kalman filter:

State vectors representing the i-th epoch and the i-th epoch, respectively;

Representing a state transition matrix;

Represents a dynamic noise vector,

Representing a dynamic noise covariance matrix;

Represents the i-th eigen observation vector,

Representing the design matrix,

Representing the i-th eigen observation noise vector;

Expressed as the i-th epoch observed noise covariance matrix,

Representing the i-th epoch state vector covariance matrix,

Representing a state vector prediction covariance matrix,

Representing the i-th epoch state vector variance-covariance matrix,

Representing the gain matrix,

Represents the identity matrix.

among them:

In the formula:

Indicates GPS double-difference carrier observations, o=1, 2, L, n-1,

Indicates the GPS narrow lane wavelength,

Indicates the wavelength of the first frequency point of GPS,

Indicates the GPS star distance,

Represents the GPS satellite double-difference tropospheric dry delay,

Indicates the frequency value of the first frequency point of GPS.

Indicates the frequency value of the second frequency point of GPS.

Indicates the BDS double-difference carrier observation, s = 1, 2, L, g-1,

Indicates the BDS narrow lane wavelength,

Indicates the wavelength of the first frequency of the BDS,

Indicates the star distance of the BDS double-difference station,

Indicates the double-difference tropospheric dry delay of the BDS satellite,

Indicates the frequency value of the first frequency point of the BDS.

Indicates the frequency value of the 2nd frequency point of the BDS.

A design matrix representing (n + g - 2) × (n + g - 1) dimensions.

Step 243: Filter according to the first Kalman filter established in step 242, and solve the basic carrier ambiguity vector parameter.

And the variance-covariance matrix is searched by the lambda algorithm, and the ambiguity parameter vector fixed solution can be obtained.

(The ambiguity obtained here is the full-circumference ambiguity at the first frequency point).

For observation noise, satellites with different elevation angles adopt a weighting method based on satellite elevation angle. The zenith tropospheric wet delay adopts random walk. The receiver observation noise obeys Gaussian white noise distribution, and the ambiguity is determined as time-invariant parameter.

Obtain the first frequency double-difference full-circumference ambiguity

(BDS) and

After (GPS), the double-difference ambiguity of the second frequency point can be obtained.

versus

In the formula,

versus

Representing the double-difference tropospheric delay between GPS and BDS,

versus

In step 3, the generated baseline atmospheric error is assigned to the corresponding star network baseline, and the baseline direction transformation is performed if necessary. The star-shaped network is used as a unit to unify the reference star and carry out the reference star transformation to generate a single-difference atmospheric error between the star-shaped network elements and the satellite stations.

In the step 3, generating a single-difference atmospheric error between the star network stations includes the following steps:

In step 41, a star network primary station and a secondary station form a baseline, and a baseline consisting of the same base station is searched in the entire network baseline list. If the two baseline directions are opposite, a baseline commutation is required. This results in a baseline atmospheric error for the star network.

Step 42: Check whether the baseline reference stars of the star network elements are consistent. If they are inconsistent, select a unified reference star and perform a reference star transformation on the atmospheric error.

In step 43, a single difference atmospheric error between the star network elements is generated. If the single-difference atmospheric error between the reference satellite stations is 0, the inter-station single-difference atmospheric error value of other satellites is equal to the double-difference atmospheric error.

Step 44: Extract all the satellites of the star network element that are common to each baseline, and generate a single-difference atmospheric error between the satellite stations of the star-shaped network element.

Step 4: Using the star network element as a unit, encoding the single-difference atmospheric error, all base station coordinates, and the observation value of the primary station for each baseline satellite station of the star network element, and broadcasting by using the UDP protocol (broadcasting The mode can be broadcasted by equipment such as ground equipment, aviation aircraft or satellite) or two-way communication (the user can upload the approximate location information, and only broadcast the data of the user's star network element to the user through Ntrip protocol or TCP/IP according to the user's location) .

When the user uses two-way communication, only the differential data of the network element in which the user is located is broadcast to the user, and the data broadcasted in the broadcast mode is still advertised without interruption.

The Beidou/Global Satellite Navigation System (GNSS) Receiver Differential Data Format (II), which was released on October 19, 2015 and implemented on November 1, 2015, is encoded as a standard, including the following messages:

电文号Message number	电文作用描述Description of the role of the message	备注Remarks
11241124	BDS MSM4观测值BDS MSM4 observations
10501050	BDS电离层改正值站间单差BDS ionospheric correction value single difference between stations
10511051	BDS几何改正值站间单差BDS geometric correction value single difference between stations	本发明中所述对流层延迟Tropospheric delay in the present invention
10741074	GPS MSM4观测值GPS MSM4 observations
10151015	GPS电离层改正值站间单差GPS ionospheric correction value single difference between stations
10161016	GPS几何改正值站间单差GPS geometric correction value single difference between stations	本发明中所述对流层延迟Tropospheric delay in the present invention
10061006	主站ECEF坐标信息Master station ECEF coordinate information
10331033	主站接收机与天线信息说明Master station receiver and antenna information
10141014	辅站坐标信息Secondary station coordinate information	辅站与主站大地坐标差Coordinate difference between the auxiliary station and the main station
10131013	电文播发的状态和频度信息Status and frequency information of message broadcast

Step 5: The user receives the data in real time and judges the network element where it is located, and interpolates the difference between the station and the primary station according to the difference data of the network element in which the network element is located, and corrects the error to the observation value of the primary station, and proceeds to step 7. Wherein, when the user decodes the received data and calculates the linear distance of the rover to each primary station, the network element represented by the primary station with the smallest distance is used as the network element where the mobile station is located.

In step 6, the user receives the data in real time, and interpolates the difference between the station and the main station according to the differential data of the network element in which the network element is located, and corrects the error to the observation value of the primary station, and proceeds to step 7.

In step 5 or 6, according to the differential data of the network element in which the network element is interpolated, the single-difference atmospheric error between the station and the primary station is obtained, and corrected to the observation value of the primary station, including the following steps:

Indicates the single-difference ionospheric delay between stations;

In the formula:

In step 7, the user constructs a double-cavity observation using the observation of the primary station corrected by step 5 and the user observation (received by the user receiver itself) to construct a second Kalman filter including the user position parameter and the ambiguity parameter. , perform a baseline solution.

The baseline solution in step 7 includes the following steps:

In step 71, a double difference observation equation is formed, and the pseudorange and carrier double difference observation equation can be expressed as:

In the formula,

Representing GPS satellite double-difference pseudorange observations,

Representing GPS satellite double-difference pseudorange multipath effect,

Representing GPS satellite double-difference pseudorange observation noise,

Represents the GPS satellite double-difference ambiguity,

Indicates the double-difference pseudorange observation of the BDS satellite,

Indicates the star distance of the BDS satellite double-difference station,

Representing the double-signal pseudorange multipath effect of BDS satellites,

Representing BDS satellite double-difference pseudorange observation noise,

Indicates the double-difference ambiguity of the BDS satellite,

Indicates the BDS satellite double-difference carrier observation noise in weeks. Since the atmospheric error has been corrected at the observations of the primary station, the atmospheric error is ignored in the above-mentioned double-difference observation equation.

Step 72, constructing a Kalman filter, comprising the following steps:

Observation matrix

Design matrix

Expressed as:

In the formula,

Double-difference whole-circumference ambiguity parameter vector with n+g-2

Means the GPS satellite double-difference carrier observation in meters,

Representing GPS satellite double-difference pseudorange observations,

Indicates the star distance of the BDS satellite double-difference station,

Indicates the BDS satellite double-difference carrier observations in meters,

Indicates the double-difference pseudorange observation of the BDS satellite. The above parameters are assigned and brought into the Kalman filter to calculate by epoch, then the floating-point ambiguity vector and its variance-covariance matrix are extracted, and the ambiguity fixed solution can be obtained by searching with the lambda algorithm.

For observation noise, the satellites with different elevation angles adopt the weighting method based on the satellite elevation angle. The three-dimensional coordinate parameters adopt random walk. The receiver observation noise obeys the Gaussian white noise distribution, and the ambiguity is determined as the time-invariant parameter.

Step 72, after fixing the ambiguity, using the following formula to solve the fixed solution of the user's three-dimensional coordinates:

among them,

The coordinate parameter vector after fixing the ambiguity,

To fix the ambiguity parameter vector,

Corresponding to each parameter filtering solution covariance matrix. In the establishment of the Kalman filter model, in the case of a medium-long baseline with a number of secondary stations less than 2, the filtering solution of the medium-long baseline can be realized by designing the wide lane and narrow lane filtering model, taking into account the tropospheric delay and the ionosphere.

Network RTK technology is one of the most widely used technologies in the field of high precision real-time positioning. Based on the star network, the method uses the double difference mode for network solution, and the model is simple and the parameters are few. The broadcast mode RTK differential correction number is used in the broadcast mode, and the two-way communication is taken into consideration, and the network RTK of the broadcast mode is truly realized. Support differential data broadcasting from ground equipment, aviation aircraft, satellite and other equipment. In the aspect of atmospheric error processing, the role of the rover is fully utilized, so that the rover can use a more optimized algorithm. In terms of baseline solution, taking into account the network RTK and the traditional RTK mode, it can ensure that the central solution solver does not complete the network initialization, the rover uses the original observation of the primary station for single baseline solution. The invention satisfies both the ordinary network RTK users and the special domain users, such as the military field in which the user coordinates cannot be exposed, and the user capacity is not limited. In broadcast mode, differential data can be broadcast either by ground equipment or by air or satellite. There are no shortcomings of VRS technology, FKP technology, and MAC technology.

The above is only the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand the alteration or replacement within the scope of the technical scope of the present invention. The scope of the invention should be construed as being included in the scope of the invention.

Claims

The star network-based BDS/GPS broadcast network RTK algorithm is characterized by the following specific steps:

Step 1: Obtain the base station coordinates from the database, use the Delaunay triangulation algorithm to generate the Delaunay triangulation, and generate a star-shaped network composed of several star network elements and control the whole region on the basis of the triangulation network, wherein each A star network element consists of a primary station and a number of secondary stations corresponding thereto;

Step 2: Obtain the base station data in real time, form a double-difference observation with the baseline in the Delaunay triangulation, construct a first Kalman filter, estimate the baseline double-difference ambiguity and the zenith tropospheric wet delay ZTD in real time, and then generate each Baseline double difference atmospheric error of the baseline;

Step 3: Assign the baseline double-difference atmospheric error generated in step 2 to the corresponding star network element baseline, and use the star-shaped network element as a unit to unify the reference star, and generate a single-element atmosphere between each baseline satellite station of the star-shaped network element. error;

Step 4: Using a star-shaped network element as a unit, encoding a single-difference atmospheric error, all base station coordinates, and a master station observation value of each baseline satellite station of the star network element, and the encoded data is performed by using a UDP protocol. Broadcast or use two-way communication for broadcast, in which UDP protocol broadcasts all data and then proceeds to step 5; when using two-way communication, firstly, the user uploads the approximate location information, and then the central software broadcasts only to the user according to the user's location through Ntrip protocol or TCP/IP. The data of the star network element where the user is located, proceeds to step 6;

Step 5, the user receives the data in real time and judges the network element where it is located, according to the differential data of the network element in which the network element is interpolated to obtain the single-difference atmospheric error between the station and the primary station, and corrects the observation value to the primary station, and proceeds to step 7;

Step 6, the user receives the data in real time, according to the differential data of the network element, the inter-station single difference atmospheric error between the station and the main station is interpolated, and corrected to the observation value of the main station, and proceeds to step 7;

In step 7, the user constructs a double-difference observation value by using the corrected observation value of the primary station and the user observation value corrected by step 5 or 6, and constructs a second Kalman filter including the user position parameter and the ambiguity parameter to perform baseline solution.
The star network-based BDS/GPS broadcast network RTK algorithm according to claim 1, wherein the step 1 comprises the following steps:

Step 11, generating a triangulation network by using a Delaunay triangulation algorithm;

Step 12: extracting a triangulation network boundary reference station and a non-boundary reference station, wherein if the sum of the angles of the inner angles of the vertices of the base station in all the triangles connected to a reference station is greater than a set threshold, the base station a non-boundary base station, otherwise a boundary reference station;

Step 13, initializing the star network element set: all the non-boundary base stations are used as the primary station, and all the base stations connected thereto are used as the corresponding auxiliary stations;

Step 14: Find a set of base stations that do not participate in the star network networking in the boundary reference station;

Step 15, selecting the base station with the largest number of base stations connected to it as the new primary station in the base station set not participating in the networking, and the base station connected thereto as the corresponding secondary station, updating the star network set and not a set of base stations participating in a star network network;

Step 16. Repeat step 15 until the number of base stations that are not participating in the star network networking is zero.
The star network-based BDS/GPS broadcast network RTK algorithm according to claim 1, wherein the step 2 includes the following steps:

Step 21: The base station k receives the pseudorange and carrier observation signals of the satellite s, and the carrier and pseudorange observation equations are expressed as:

In the formula:
Indicates the carrier observation value in weeks on the jth frequency point of the satellite s received by the base station k, j=1, 2,
Indicates the station star distance from the base station k to the satellite s,
Indicates the full-circumference ambiguity at the j-th frequency point of the satellite s received by the reference station k, c represents the speed of light, dT k represents the receiver clock difference of the reference station k, and dT s represents the satellite clock difference of the satellite s,
Indicates the tropospheric delay of the satellite s received by the base station k,
Indicates the ionospheric delay at the first frequency of the satellite s received by the base station k,
f j represents the frequency value at the jth frequency point of the satellite system corresponding to the satellite s, f 1 represents the frequency value at the 1st frequency point of the satellite system corresponding to the satellite s , and rel s represents the relativistic effect of the satellite s,
Means the carrier multipath effect in meters on the jth frequency of the satellite s received by the base station k,
Indicates the receiver-side carrier deviation in meters of the j-th frequency point of the base station k,
Indicates the satellite-side carrier deviation in meters on the j-th frequency point on the satellite s.
Indicates the carrier observation noise in meters per unit j of the satellite s received by the base station k,
Indicates the pseudo-range observation value in meters on the j-th frequency point of the satellite s received by the base station k,
Represents the pseudorange multipath effect in meters at the jth frequency of the satellite received by the base station k,
Indicates the receiver-side pseudorange deviation in meters per unit received by the jth frequency point of the reference station k,
Indicates the pseudorange deviation of the satellite end in meters at the jth frequency point of the satellite s,
Representing the pseudorange observation noise in meters at the jth frequency point of the satellite s received by the reference station k, and λ j indicating the wavelength of the jth frequency point of the satellite system corresponding to the satellite s;

Step 22, according to the carrier observation value obtained by step 21 and the pseudorange observation value constitute a double difference observation value, the double difference carrier observation equation and the double difference pseudo range observation equation of the reference station k and the reference station y are respectively:

Where the superscript r represents the reference satellite,
a double-difference carrier observation indicating the j-th frequency point,
Indicates the star distance of the double-difference station,
Indicates the double-difference full-circumference ambiguity at the jth frequency point,
Indicates double-difference tropospheric delay,
Indicates the doubled ionospheric delay at the first frequency point,
Means the double-difference carrier multipath effect in meters on the jth frequency point,
Indicates the double-difference carrier observation noise in meters on the jth frequency point,
Indicates the double-difference pseudorange observation at the jth frequency point,
Representing the double-difference pseudorange multipath effect at the jth frequency point,
Representing the double difference pseudorange observation noise at the jth frequency point;

Step 23: Combine the double-difference observations formed in step 22 into a double-difference wide lane combined observation value, and calculate the wide lane combined ambiguity:

Using the MW combination to solve the wide-altitude combination ambiguity, the solution equation is:

In the formula:
λ WL =c/(f 1 -f 2 ),
Indicates the combined observation of double-difference wide lanes,
Indicates the wide lane combination ambiguity, λ WL represents the wide lane wavelength;

For the wide lane combination ambiguity, multi-epoch smoothing is rounded off, and the specific formula is as follows:

In the formula:
The wide-altitude combined ambiguity floating-point solution obtained by the i-th observation epoch is calculated, z represents the total number of observation epochs, and round represents a rounding-and-rounding operator;

Step 24, using a combination of no ionosphere, constructing a narrow lane filter, and separating the base ambiguity by using a combination of no ionosphere and wide lane
versus
Includes the following steps:

In step 241, a combined observation of the double-difference ionosphere is formed:

In the formula:
Represents a double-difference ionospheric combined observation,
Represents no ionospheric combined ambiguity, λ NL = c / (f 1 + f 2 );

Step 242, constructing a first Kalman filter:

Where E(g) represents the mathematical expectation and Cov(g) represents the covariance.
State vectors representing the i-th epoch and the i-th epoch, respectively;
Representing a state transition matrix;
Represents a dynamic noise vector,
Representing a dynamic noise covariance matrix;
Represents the i-th eigen observation vector,
Representing the design matrix,
Representing the i-th eigen observation noise vector;
Expressed as the i-th epoch observed noise covariance matrix,
Representing the i-th epoch state vector covariance matrix,
Representing a state vector prediction covariance matrix,
Representing the i-th epoch state vector variance-covariance matrix,
Representing the gain matrix,
Express the unit matrix;

Based on the i-th epoch, the base station k and the reference station y have n GPS satellites and g BDS satellites, wherein the nth GPS satellite and the g-th BDS satellite are reference stars of each system. The estimation parameters include double-difference ambiguity and baseline relative zenith tropospheric wet delay. The filter model to be estimated parameter vector, observation vector and design matrix are expressed as:

among them:

In the formula:
A state vector representing the n+g-1 dimension (the parameter vector to be estimated), including a relative zenith tropospheric wet delay parameter RZTD and n+g-2 dimensional double difference whole-circumference ambiguity parameter vector
a vector of double-difference carrier observations representing n+g-2 dimensions,
Indicates GPS double-difference carrier observations, o=1, 2, L, n-1,
Indicates the GPS narrow lane wavelength, λ 1 G represents the wavelength of the GPS first frequency point,
Indicates the GPS double-difference ionosphere-free combined carrier observation,
Indicates the GPS star distance,
Represents the GPS satellite double-difference tropospheric dry delay,
Indicates the full-circumference ambiguity of the GPS double-difference wide lane, and f 1 G represents the frequency value of the first frequency point of the GPS.
Indicates the frequency value of the second frequency point of GPS.
Indicates the BDS double-difference carrier observation, s = 1, 2, L, g-1,
Indicates the BDS narrow lane wavelength,
Indicates the wavelength of the first frequency of the BDS,
Indicates the BDS double-difference ionosphere-free combined carrier observation,
Indicates the star distance of the BDS double-difference station,
Indicates the double-difference tropospheric dry delay of the BDS satellite,
Indicates the full-circumference ambiguity of the BDS double-difference wide lane, and f 1 C represents the frequency value of the first frequency point of the BDS.
Indicates the frequency value of the 2nd frequency point of the BDS.
a tropospheric mapping function representing the GPS system satellite o on the base station k,
Indicates the tropospheric mapping function of the GPS system reference satellite n on the base station y,
Indicates the tropospheric mapping function of the BDS system satellite s on the base station k,
Indicates the tropospheric mapping function of the reference satellite g of the BDS system on the base station y,
a design matrix representing (n+g-2)×(n+g-1) dimensions;

Step 243: Perform filtering according to the first Kalman filter established in step 242, and solve a basic carrier ambiguity vector parameter.

Extracting the ambiguity parameter vector floating point solution from the filter
And the variance-covariance matrix is searched by the lambda algorithm to obtain the first frequency double-difference full-circumference ambiguity
versus
Further obtaining the double-difference full-circumference ambiguity of the second frequency point
versus

Step 25, according to the result of step 24, generating a baseline double difference atmospheric error:

In the formula,
versus
Representing the double-difference tropospheric delay between GPS and BDS,
versus
Representing the GPS and BDS first frequency double-difference carrier observations,
versus
Representing the second frequency difference observation of GPS and BDS respectively,
versus
It indicates the 1st frequency doubled ionospheric delay of GPS and BDS respectively.
The star network-based BDS/GPS broadcast network RTK algorithm according to claim 1, wherein the step 3 includes the following steps:

Step 31: The primary station and the secondary station of the star network element form a baseline, and the baseline consisting of the same base station is searched in the baseline list of the entire network of the triangular network. If the two baseline directions are opposite, the baseline commutation is required, thereby obtaining Baseline double-difference atmospheric error for each type of star network element;

Step 32: Check whether the baseline reference stars of the star network element are consistent. If they are inconsistent, the reference star is unified and the reference star transformation is performed on the atmospheric error;

Step 33: Generate a single-difference atmospheric error between the star-type network elements: the single-difference atmospheric error between the reference satellite stations is 0, and the single-difference atmospheric error value of the other satellites is equal to the double-difference atmospheric error;

Step 34: Extract satellites of each star-shaped network element that can be shared by the baseline, and generate a single-difference atmospheric error between the satellite stations of the star-shaped network element.
The star network-based BDS/GPS broadcast network RTK algorithm according to claim 1, wherein the step 5 determines that the network element is located by the user: the user decodes the received data and calculates the user to The linear distance of each primary station is the network element represented by the primary station with the smallest distance as the user's network element.
The star network-based BDS/GPS broadcast network RTK algorithm according to claim 1, wherein the step 5 or 6 interpolates between the station and the master station according to the differential data of the network element in which the network element is located. Single difference atmospheric error, and corrected to the observation of the primary station, including the following steps:

Step 1. Using the linear interpolation algorithm to interpolate the user's atmospheric error, the single-difference atmospheric error between the user and the primary station is calculated as follows:

Where subscript m denotes the primary station, u denotes the user, α 1 , α 2 , α 3 denote the tropospheric interpolation coefficient, β 1 , β 2 denote the ionospheric interpolation coefficient, and w denote the number of secondary stations,
Indicates the inter-station single-difference tropospheric delay of the satellite s, Δx m, u , Δy m, u , Δh m, u represent the coordinate difference between the primary station and the user , respectively.
Indicates the single-difference ionospheric delay between stations;

The tropospheric interpolation coefficients and ionospheric interpolation coefficients are calculated as follows:

Where: Δx m,t , Δy m,t , Δh m,t represents the coordinate difference between the primary station and the secondary station, t=1, 2, L, w;

In step 2, the atmospheric error value obtained by the interpolation is corrected to the observation value of the primary station, and the pseudorange and the carrier observation value are respectively as follows:

In the formula:
It shows the pseudorange and carrier observation values of the jth frequency point of the satellite s after the correction of the atmospheric error on the primary station.
Representing the original pseudorange and carrier observations of the jth frequency point of the satellite s on the primary station,
Indicates the inter-station tropospheric delay of the satellite s obtained by interpolation,
Indicates the inter-site ionospheric delay of the satellite s obtained by interpolation.
The star network-based BDS/GPS broadcast network RTK algorithm according to claim 1, wherein the double difference observation value in the step 7 is expressed as:

In the formula,
Representing GPS satellite double-difference pseudorange observations,
Indicates the satellite distance of the GPS satellite double-difference station,
Representing GPS satellite double-difference pseudorange multipath effect,
Representing GPS satellite double-difference pseudorange observation noise,
Indicates the GPS satellite double-difference carrier observation, and λ G represents the wavelength of the GPS observation corresponding to the frequency point.
Represents the GPS satellite double-difference ambiguity,
Represents the GPS satellite double-difference carrier multipath effect in weeks,
Representing GPS satellite double-difference carrier observation noise in weeks,
Indicates the double-difference pseudorange observation of the BDS satellite,
Indicates the star distance of the BDS satellite double-difference station,
Representing the double-signal pseudorange multipath effect of BDS satellites,
Representing BDS satellite double-difference pseudorange observation noise,
Indicates the BDS satellite double-difference carrier observation, and λ C represents the wavelength of the BDS observation corresponding to the frequency point.
Indicates the double-difference ambiguity of the BDS satellite,
Representing the double-signal carrier multipath effect of the BDS satellite in weeks,
Indicates the BDS satellite double-difference carrier observation noise in weeks.
The star network-based BDS/GPS broadcast network RTK algorithm according to claim 1, wherein the second Kalman filter in step 7 is constructed as follows:

Based on the i-th epoch, the user and the star network have n GPS satellites and g BDS satellites, of which the nth GPS satellite and the gth BDS satellite are reference stars of each system, and all satellites are combined. L1 carrier and P1 pseudorange observation data, filter model to be estimated parameter matrix
Observation matrix
Design matrix
Expressed as:

among them,

In the formula,
An estimated parameter vector representing n+g+1 dimensions, including a 3-dimensional positional parameter vector
Double-difference whole-circumference ambiguity parameter vector with n+g-2
Representing a 2(n+g-2) dimensional double difference observation vector, including pseudorange and carrier observations;
Represents a 2(n+g-2)×(n+g+1) dimensional design matrix, where l o,n,G ,p o,n,G ,q o,n,G represent the cosine of the GPS satellite direction (superscript o=1,2L,n-1),l s,g,C ,p s,g,C ,q s,g,C denotes the cosine of the BDS satellite direction, s=1, 2L, t-1,
Means the GPS satellite double-difference carrier observation in meters,
Representing GPS satellite double-difference pseudorange observations,
Indicates the satellite distance of the GPS satellite double-difference station,
Indicates the star distance of the BDS satellite double-difference station,
Indicates the BDS satellite double-difference carrier observations in meters,
Indicates the double-difference pseudorange observation of the BDS satellite;

The above parameters are assigned and brought into the second Kalman filter to solve the epoch epoch, then the floating ambiguity vector and its variance-covariance matrix are extracted, and the ambiguity fixed solution can be obtained by searching with the lambda algorithm;

After fixing the ambiguity, the fixed solution of the user's three-dimensional coordinates is solved by the following formula:

among them,
Three-dimensional coordinate parameter vector and floating-point ambiguity parameter vector,
The coordinate parameter vector after fixing the ambiguity,
To fix the ambiguity parameter vector,
Corresponding to each parameter filtering solution covariance matrix.