CN109932735B - Positioning method for resolving Beidou short baseline single-frequency single epoch - Google Patents
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Abstract
The invention discloses a Beidou short baseline single-frequency single-epoch resolving positioning method, which comprises the following steps: (1) carrying out Beidou single-frequency pseudo range single-point positioning; (2) preprocessing data; (3) Constructing a Kalman filtering precise n-dimensional dynamic model based on prior historical data and considering the influence of the signal-to-noise ratio and the satellite altitude angle on an observed value; (4) initializing a model; (5) Carrying out Beidou single-frequency partial ambiguity estimation to obtain a fixed value of each hierarchical ambiguity; (6) Cycle slip epoch-by-epoch detection is carried out by combining the single-frequency ambiguity fixed value and the updated value; (7) And carrying out baseline vector calculation and coordinate covariance matrix updating based on fixed ambiguity, and substituting a carrier phase observation equation after the ambiguity is fixed to obtain a baseline vector. The method can automatically eliminate the influence of troposphere errors and multipath errors in real time, realizes the accurate fixation of the Beidou single-frequency ambiguity, greatly reduces the monitoring cost while ensuring the monitoring real-time performance and precision, and is favorable for popularization and application of the Beidou positioning technology.
Description
Technical Field
The invention relates to the field of Beidou deformation monitoring of engineering measurement, in particular to a Beidou short baseline single-frequency single-epoch resolving positioning method.
Background
At present, a Beidou Satellite Navigation System (BeiDou Navigation Satellite System, abbreviated as Beidou) can provide Navigation, time service and short message information service for the whole world, and the application of the Beidou positioning technology in the field of deformation monitoring increasingly becomes one of research hotspots. The cost is the key problem that big dipper deformation monitoring needs to be solved, and big dipper deformation monitoring adopts multifrequency multimode geodesic type receiver usually, and too high cost has seriously restricted big dipper in the popularization and application of deformation monitoring field, to engineering facilities local deformation monitoring, the basic line length of reference station and monitoring station is generally shorter (less than or equal to 10 km). Therefore, the research of the Beidou short baseline single-frequency single-epoch high-precision relative positioning algorithm based on the low-cost receiver has important practical significance.
Many scholars at home and abroad carry out a great deal of research on the Beidou positioning algorithm. Odolinski R, teunissen P J G and Odijk D (First combined COMPASS/BeiDou-2and GPS positioning results in Australia. Part I; hu Zhigang (performance evaluation theory and experimental verification [ D ] of Beidou satellite navigation system, wuhan: wuhan university, 2013) by analyzing the actual measurement data of the Beidou system, comparing and analyzing the results of the short baseline relative positioning and the precise single point positioning of the Beidou and the GPS under the same environment, finding that the relative positioning precision of the short baseline of the Beidou can reach the mm level, the precise single point PPP can reach the cm level precision, and the positioning performance is basically close to that of the GPS; gao Xingwei and the like (the unified Beidou and GPS based on a space-time system, namely the survey and drawing, 2012,41 (5): 743-748, 755) research the unification of time systems/coordinate systems of the Beidou and the GPS, realize the data fusion and high-precision combined positioning of the carrier phases of the Beidou and the GPS, and finally prove that the Beidou has the three-dimensional high-precision positioning capability preliminarily through the actually measured data and the processing result; the single epoch GPS/big dipper single frequency and double frequency RTK (Real Time Kinematic) combined positioning model is provided by Tennissen P J G and the like (instant BeiDou + GPS RTK positioning with high cut-off angles [ J ]. Journal of geodety, 2014,88 (4): 335-350), and the GPS/big dipper double frequency combined model can still realize high-precision positioning under the condition that the satellite height cut-off angle is 40 degrees.
However, the researches are directed at the combined positioning of the big dipper, the big dipper and the GPS of the multi-frequency multi-mode receiver, and the research on the high-precision positioning of the big dipper single-frequency receiver, particularly the research on the static positioning method for the big dipper short baseline single-frequency epoch solution is less.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, construct a Beidou single-frequency precise function and a random weighting model, and provide a Beidou single-frequency single-epoch Kalman filtering solution positioning method.
Therefore, the technical scheme of the invention is as follows:
a Beidou short baseline single-frequency single-epoch resolving positioning method comprises the following steps:
(1) Big dipper single-frequency pseudo range single point location:
calculating the initial coordinates of the mobile station by using a Bancroft algorithm according to a pseudo-range double-difference equation, correcting errors of an ionosphere and a troposphere by using Klobuchar and Saastamoinen models, then performing least square linearization on the result as an approximate coordinate to calculate the coordinates of a monitoring station, a reference station and a satellite altitude angle:
P(t)＝ρ(t)+I(t)+T(t)+v(t)
wherein P is a pseudo-range observation value at epoch T, ρ is a distance between a Beidou satellite and a survey station, I is an ionosphere error, T is a troposphere error, v is observation noise, the unit of each parameter is m,
(2) Data preprocessing:
setting a satellite height cut-off angle based on the fact that the observation value of the Beidou single-frequency receiver is susceptible to errors such as cycle slip and multipath, calculating the height angle of the satellite according to the step (1), eliminating the satellite lower than the height angle, and initially detecting and repairing the cycle slip by adopting a polynomial fitting carrier phase observation value. In one embodiment of the invention, the satellite height cut-off angle is set to 20 °.
(3) The method comprises the following steps of constructing a Kalman filtering precise n-dimensional dynamic model based on prior historical data and considering the influence of a signal-to-noise ratio and a satellite altitude angle on an observation value, and comprises the following steps:
1) And (3) combining the prior data to construct a system dynamic model:
estimating a vector and a floating solution of a current base line by using prior historical data, selecting a base line vector, a velocity vector and a double ambiguity as a system state vector, and expressing an n-dimensional dynamic model as follows:
wherein the content of the first and second substances,
is the coordinate of the monitoring station and has the unit of m->
For dynamic model noise error in units of m, & gt>
The double-difference ambiguity is expressed in cycles, n is different types of motion models, n =0 represents that a monitoring station is in a static state or a creep state, n =1 is in a uniform motion state, n =2 represents that the monitoring station is in an accelerated motion state, r represents a reference station, rm represents the monitoring station, P represents a reference satellite, and s represents an observable Beidou satellite except the reference satellite;
when the monitoring station is in a creep state, the value of n is zero, and the system state transposition model of the system dynamic model is defined as follows:
2) The method for constructing the Beidou single-frequency precise function model and the precise random weighting model based on the Beidou single-frequency carrier phase observed value and considering the influence of the signal-to-noise ratio and the satellite altitude angle on the observed value comprises the following steps:
based on the correlation and error statistical characteristics of the Beidou satellite observation values, distributing a proper weight ratio for each satellite observation value, considering the influence of the Beidou satellite altitude and the observation value signal-to-noise ratio, constructing a Beidou precise random weighting model, and obtaining the optimal linear unbiased estimation:
wherein CN0 is the signal-to-noise ratio of the Beidou satellite signal, e is the satellite altitude angle, the unit is DEG, s1 is the signal-to-noise ratio threshold, the unit is db, generally set to 50db, and when CN0 is larger than or equal to s1, the weight D of the observed value CN0,e Setting the value to be 1, wherein the observed value quality is considered to be better at the moment, the signal-to-noise ratio s0 is determined by an empirical parameter A, and the values of the empirical parameters A, a and s0 are respectively 30, 20 and 10;
(4) Model initialization:
taking the result of the step (1) as an initial state variable [ X ] of a Kalman model r (0)Y r (0)Z r (0)]Velocity vector of
Initializing to zero, assuming that a monitoring station starts to move from a static state or the speed is a constant value, and calculating the ambiguity of an initial epoch by using a least square calculation floating point solution for rounding or combining an approximate distance between the satellite stations and a carrier phase double-difference observed value for calculation; estimating and updating a state vector, a double-difference observed value and a floating ambiguity covariance matrix according to a double-difference equation, and if the equation observed value is insufficient, calculating ambiguity and corresponding variance by combining the double-satellite space and the carrier phase:
in the formula (I), the compound is shown in the specification,
is a double-differential star-station spacing calculated by approximate coordinates and has the unit of m, and is combined with the unit of more than one sun-station spacing>
The unit of the estimated error for approximate coordinate error propagation is m,
estimating ambiguities
Comprises the following steps:
initial state vector covariance matrix
Is defined as: />
In the formula (I), the compound is shown in the specification,
estimate variance for initial coordinates in m 2 Provided by a coordinate covariance matrix;
is the velocity variance, in m 2 /s 2 ；/>
Is to start upThe variance of the ambiguity estimate is in cycles 2 ；
(5) Carrying out Beidou single-frequency partial ambiguity estimation through additional structure body deformation characteristics and maximum displacement variation constraint to obtain fixed values of all graded ambiguities;
(6) Cycle slip epoch-by-epoch detection is carried out by combining a single-frequency ambiguity fixed value and an updated value, and a cycle slip satellite needs to be initialized again when the cycle slip occurs:
for a low-cost receiver, a carrier phase observed value is susceptible to errors such as multipath, antenna phase deviation, noise caused by electronic components and the like, and the positioning accuracy of the low-cost receiver is seriously affected along with the occurrence of cycle slip. The Kalman filtering post-processing can eliminate the influence of errors such as multipath and the like on the positioning precision, and the key for realizing high-precision positioning is whether the cycle slip can be accurately detected.
Based on the Kalman dynamical model, the ambiguity does not change with time, so the ambiguity of epoch t update is:
according to covariance matrix
Obtaining updated ambiguity variance from ambiguity variance corresponding to medium satellite s
The ambiguity update estimate at epoch t is calculated by:
the variance corresponding to the ambiguity is
To detect cycle slip, the following formula was used for the test:
in the formula (I), the compound is shown in the specification,
can be selected empirically, based on>
If the cycle slip is detected, the corresponding satellite can be used as a newly added satellite of the epoch to process, and the ambiguity of the satellite is fixed again; if the reference satellite generates cycle slip, all double-difference observation values and the ambiguity of the epoch are reinitialized to return to the step (1), and Kalman filtering single-epoch baseline vector calculation is carried out again;
(7) Performing baseline vector calculation and coordinate covariance matrix updating based on the ambiguity fixed in the step (5), wherein the coordinate covariance matrix is expressed as
After the ambiguity is fixed, a carrier phase observation equation is replaced to obtain a baseline vector:
wherein H Φ A coefficient matrix that is a baseline vector; r Φ Determining a covariance matrix of the double-difference carrier phase observed values according to the precise random model in the step (3);
is a double difference carrier phase estimate in m, <' > based on>
Is a double-difference ambiguity fixed value and has the unit of cycles.
In the step 2), the method for constructing the big Dipper single-frequency precise function model comprises the following steps:
k big dipper satellites can be observed by the epoch t base station m and the monitoring station r, and if the satellite p is taken as a reference satellite, the big dipper single-frequency carrier phase function double-difference model of each satellite s relative to the reference satellite is expressed as follows:
wherein s =1 … k, s ≠ p, λ is the Beidou single-frequency carrier phase wavelength, unit is m,
is a double difference ambiguity in cycles, is claimed>
Observing noise for double-difference carrier phase in m->
The unit is m, and the unit is the geometric distance between double-difference survey station satellites, double-difference ionosphere and troposphere errors.
For a base line length of less than 10km, the ionosphere and the troposphere are completely eliminated through double difference energy, and a function model is simplified as follows:
the Beidou single-frequency Kalman observation model is linearly constructed by the function model, and the observation vector is expressed as:
wherein the content of the first and second substances,
are respectively the linearization coefficients of the geometric distance of the phases of the double-difference carrier, [ X' r Y' r Z' r ]And the speed vectors are respectively corresponding to the coordinates of the monitoring station, and the unit is m/s.
In the step (5), the method for constructing the big dipper single-frequency precision function model comprises the following steps:
(1) solving an ambiguity floating-point solution variance-covariance matrix according to a least square variance estimation criterion, based on the ambiguity resolution, using (2,1, …, 1) k-1 Carrying out step-by-step dimensionality reduction calculation in a hierarchical mode;
(2) combining pseudo range and carrier phase observation vectors, constructing an error observation equation corresponding to each stage of ambiguity group, searching 50 groups of optimal ambiguities in sequence by using LAMBDA, and removing a priori baseline vector and calculating an ambiguity group outside a vector value range based on the maximum displacement of the structure and deformation characteristics determined by numerical simulation;
(3) and searching the minimum residual square and the corresponding whole-cycle ambiguity vector in the residual ambiguity candidate value, and selecting the ambiguity candidate value which passes the Ratio test as the fixed value of each hierarchical ambiguity.
In the step 1), assuming that the monitoring station is in a creep state, and n is zero, the model is also applicable to other motion states of the monitoring station, and the system state transposition model of the system dynamic model is defined as follows:
in the step 2), the SNR threshold s1 is 50db, and when CN0 is greater than or equal to s1, the weight D of the observed value is CN0,e Assuming that 1 is set, the observed values are considered to be of good quality at this time, and the empirical parameters a, and s0 take values of 30, 20, and 10, respectively.
The invention has the following beneficial effects:
1. the positioning algorithm disclosed by the invention greatly reduces the monitoring cost while ensuring the real-time performance and the precision of monitoring, and is beneficial to promoting the popularization and application of the Beidou positioning technology in the field of deformation monitoring.
2. The algorithm effectively solves the problem that the Beidou satellite has a poor configuration, the Beidou single-frequency least square result has large deviation or can not be calculated, can automatically eliminate the influence on troposphere errors and multipath errors in real time, realizes the accurate fixation of the Beidou B1 frequency single-frequency ambiguity, can effectively detect the structural body displacement change and the occurrence time period, and provides effective data and technical support for the safe operation of the infrastructure in China.
Drawings
FIG. 1 is a flow chart of a positioning method of the present invention;
FIG. 2 is a schematic view of the point location arrangement of a reference station and a monitoring station;
FIG. 3 is a graph of a Beidou single-frequency single epoch static resolving result;
FIG. 4 is a Beidou single-frequency positioning accuracy analysis chart of different resolving periods;
fig. 5 is an elevation direction displacement detection accuracy analysis diagram.
Detailed Description
For better understanding of the technical solution of the present invention, the following detailed description of the positioning algorithm of the present invention is provided with reference to the accompanying drawings and specific embodiments.
Example one
As shown in fig. 2, the reference station and the monitoring station are respectively arranged on the roof of a CORS station of a surveying and mapping institute of china railway design group limited and on the roof of a total institute of china railway design group limited 3, and the receiver is internally provided with a UM440 big dipper single-frequency board card and can receive satellite signals with B1 frequency and sample frequency of 1HZ.
Referring to fig. 1 and 2, in the embodiment, the positioning method for resolving the beidou short baseline single-frequency epoch includes the following steps
(1) Reading a Beidou single-frequency satellite ephemeris and an observation file, and calculating a satellite altitude angle based on a Beidou single-frequency pseudo-range equation;
(2) Setting a satellite height cut-off angle of 20 degrees, removing satellites lower than the height angle, performing observation value cycle slip detection and restoration pretreatment by adopting a polynomial fitting method based on a Beidou single-frequency pseudo-range single-point positioning result and a Beidou carrier phase observation equation, and setting a threshold value to be 1 cycle.
(3) And (4) combining the prior epoch data to construct a system dynamic model, wherein the value of n is 0, and the monitoring station is in a static or creep state.
A Beidou single-frequency function and a precise random model are constructed on the basis of a Beidou single-frequency carrier phase observation value and the consideration of the influence of a signal-to-noise ratio and a satellite altitude angle on the observation value, the threshold value s1 of the signal-to-noise ratio is set to be 50db, and the values of empirical parameters A, a and s0 are respectively 30, 20 and 10. The final calculated precision stochastic model is:
(4) The initial epoch needs model initialization, coordinate and ambiguity resolution is carried out by combining a pseudo range and a carrier phase observation equation, an initial epoch coordinate and ambiguity covariance matrix is obtained, and if equation redundancy is insufficient, ambiguity and corresponding variance are calculated by combining a double-satellite-station spacing and a carrier phase.
Initial standard deviation of ambiguityThe unit is 1000, the unit is cycles, the initial standard deviation of the B1 frequency pseudo range is set to be 0.3m, the initial standard deviation of the carrier phase is set to be 0.003m, a state transpose matrix of the base line vector coordinate and the ambiguity is constructed, and T = I 38×38 Setting the minimum number of observation satellites as 4, setting the number of Beidou visible satellites in the current test to be 8, calculating the initial epoch coordinate of the monitoring station according to the pseudo range and the carrier phase equation to be (-2263559.6610,4404125.3541,4006546.6488) respectively, wherein the unit is m, and the coordinate covariance matrix of the monitoring station is
A square meter per unit and a double-difference ambiguity variance-covariance matrix of->
The unit is cycle 2 The initial state vector coordinates and floating ambiguity are [ -2263559.6610 4404125.3541 4006546.6488-20.6211-2.3515-16.1747.1479.8535-7.5936.2049 0-0.3629 00] T The state transition matrix is a 17 multiplied by 17 unit matrix;
(5) Carrying out partial ambiguity step-by-step search on the floating ambiguity, and simultaneously constraining and fixing the Beidou single-frequency double-difference ambiguity to be [ -20-3-16 06 74 0-1 0] by the additional structure deformation characteristics and the maximum displacement variation;
(6) Estimating a ambiguity approximation based on the double-difference pseudoranges and the carrier phase observations as follows:
[ -20.5622-2.3397-16.1558.2501.9794-7.5802 4.2114 0 0-0.3592 0], comparing with the fixed value in the step (5), finding that the cycle slip of the Beidou satellite PRN5 occurs, and the double-difference ambiguity of the satellite needs to be initialized again; (7) Based on the Beidou single-frequency ambiguity fixed value in the step (6), calculating an initial epoch baseline vector fixed solution as [ -2263559.5267 4404125.1375 4006546.6214], combining the observation values and the state vector variance matrix in the steps (2) and (4), performing Kalman filtering to obtain a next epoch filtering update value and a state vector covariance, and performing baseline vector calculation on an epoch-by-epoch basis, wherein the result is shown in fig. 3, and after the ambiguity is fixed, the positioning accuracy can reach 5mm and is far higher than the traditional RTK positioning accuracy.
Data verification:
to further prove that the method can be applied to the field of high-precision deformation monitoring, as shown in fig. 4, the final fixed epoch coordinate of different resolving periods is selected for precision analysis, and it is found that with the increase of convergence time, the software GNSSMonitor v1.0 hour big dipper single frequency resolving precision corresponding to the method reaches 1.4mm, which is much higher than that of Bernese v5.2 software; compared with the plane, the elevation direction is susceptible to errors such as multipath and observation noise, as shown in fig. 5, the calculation cycle is 12 hours, the displacement is loaded for 6mm in the 7 th time period, the average value of the elevation coordinates in the 4 previous time periods before the loading displacement is selected as the initial displacement loading coordinate, the average value of the coordinates in the 4 later time periods is selected as the final displacement loading coordinate, and through comparison analysis with the actual loading displacement, the GNSSMonitor v1.0 software displacement detection precision is found to be 1mm, the Bernese v5.2 software precision is found to be 3mm, meanwhile, the specific time period when the displacement occurs can be accurately detected, and the superiority of the algorithm is further clarified.
Claims (6)
1. A Beidou short baseline single-frequency single-epoch resolving positioning method comprises the following steps:
(1) Big dipper single-frequency pseudo range single point location:
calculating the initial coordinates of the mobile station by using a Bancroft algorithm according to a pseudo-range double-difference equation, correcting errors of an ionosphere and a troposphere by using Klobuchar and a Saastamoinen model, then taking the initial coordinates after correcting the errors of the ionosphere and the troposphere as approximate coordinates, and performing least square linearization to calculate the coordinates of a monitoring station, a reference station and the height angle of a satellite:
P(t)＝ρ(t)+I(t)+T(t)+v(t)
wherein P is a pseudo-range observation value at epoch T, ρ is a distance between a Beidou satellite and a survey station, I is an ionosphere error, T is a troposphere error, v is observation noise, the unit of each parameter is m,
(2) Data preprocessing:
setting a satellite height cut-off angle, calculating the height angle of the satellite according to the step (1), eliminating the satellite lower than the height angle, adopting a polynomial fitting carrier phase observed value, preliminarily detecting and repairing cycle slip,
(3) The method comprises the following steps of constructing a Kalman filtering precise n-dimensional dynamic model based on prior historical data and considering the influence of a signal-to-noise ratio and a satellite altitude angle on an observation value, wherein the method comprises the following steps:
1) And (3) combining the prior data to construct a system dynamic model:
estimating the vector and floating solution of the current baseline by using prior historical data, selecting a baseline vector, a velocity vector and a double ambiguity as a system state vector, and expressing an n-dimensional dynamic model as follows:
wherein, the first and the second end of the pipe are connected with each other,
is a coordinate of a monitoring station in the unit of m->
For dynamic model noise error in units of m, & gt>
The double-difference ambiguity is expressed in cycles, n is different types of motion models, n =0 represents that a monitoring station is in a static state or a creep state, n =1 is in a uniform motion state, n =2 represents that the monitoring station is in an accelerated motion state, r represents a reference station, m represents the monitoring station, P represents a reference satellite, and s represents an observable Beidou satellite except the reference satellite;
2) The method for constructing the Beidou single-frequency precise function model and the precise random weighting model based on the Beidou single-frequency carrier phase observed value and considering the influence of the signal-to-noise ratio and the satellite altitude angle on the observed value comprises the following steps:
based on the correlation and error statistical characteristics of the Beidou satellite observation values, distributing a proper weight ratio for each satellite observation value, considering the influence of the Beidou satellite altitude and the observation value signal-to-noise ratio, constructing a Beidou precise random weighting model, and obtaining the optimal linear unbiased estimation:
wherein CN0 is the signal-to-noise ratio of the Beidou satellite signal, e is the satellite altitude angle, the unit is DEG, s1 is the signal-to-noise ratio threshold value, the unit is db, the value is set to 50db, and when CN0 is larger than or equal to s1, the weight D of the observed value CN0,e Setting the value to be 1, considering the quality of the observed value at the moment, determining the signal-to-noise ratio value s0 by an empirical parameter A, wherein the values of the empirical parameters A, a and s0 are respectively 30, 20 and 10;
(4) Initializing a model:
taking the result of the step (1) as an initial state variable [ X ] of a Kalman model r (0) Y r (0) Z r (0)]Velocity vector of
Initializing to zero, assuming that a monitoring station starts to move from a static state or the speed is a constant value, and calculating the ambiguity of an initial epoch by using a least square calculation floating point solution for rounding or combining an approximate distance between the satellite stations and a carrier phase double-difference observed value for calculation; estimating and updating a state vector, a double-difference observed value and a floating ambiguity covariance matrix according to a double-difference equation, and if the equation observed value is insufficient, calculating ambiguity and corresponding variance by combining double-satellite station spacing and carrier phase:
in the formula (I), the compound is shown in the specification,
is a double-differential star-station spacing calculated by approximate coordinates and has the unit of m, and is combined with the unit of more than one sun-station spacing>
The unit of the estimated error for approximate coordinate error propagation is m,
estimating ambiguities
Comprises the following steps: />
In the formula (II)>
To estimate the mean error of the ambiguities, σ e The intermediate error of the pseudo-range double-difference observed value is obtained;
initial state vector covariance matrix
Is defined as:
in the formula (I), the compound is shown in the specification,
the variance is estimated for the initial coordinates in m 2 Provided by a coordinate covariance matrix; />
Is the velocity variance, in m 2 /s 2 ；/>
Estimate variance for initial ambiguities in cycles 2 ；
(5) Carrying out Beidou single-frequency partial ambiguity estimation through additional structure body deformation characteristics and maximum displacement variation constraint to obtain fixed values of all graded ambiguities;
(6) Cycle slip epoch-by-epoch detection is carried out by combining a single-frequency ambiguity fixed value and an updated value, and a cycle slip satellite needs to be initialized again when the cycle slip occurs:
based on the Kalman dynamical model, the ambiguity does not change with time, so the ambiguity of epoch t update is:
according to covariance matrix
The ambiguity variance corresponding to the medium satellite s acquires the updated ambiguity variance->
Wherein T is t A conversion matrix of epoch t; />
The ambiguity update estimate at epoch t is calculated by:
the variance corresponding to the ambiguity at epoch t is
To detect cycle slip, the following formula was used for the test:
in the formula (I), the compound is shown in the specification,
selected empirically, based on>
If the cycle slip is detected, the corresponding satellite can be used as a newly added satellite at the epoch t moment for processing, and the ambiguity of the corresponding satellite is fixed again; if the reference satellite generates cycle slip, all double-difference observation values and the ambiguity at epoch t moment are initialized again to return to the step (1), and Kalman filtering single-epoch baseline vector calculation is carried out again;
(7) Performing baseline vector calculation and coordinate covariance matrix updating based on the ambiguity fixed in the step (5), wherein the coordinate covariance matrix is expressed as
After the ambiguity is fixed, a carrier phase observation equation is replaced to obtain a base line vector: :
wherein H Φ A coefficient matrix that is a baseline vector; r Φ Determining a covariance matrix of the double-difference carrier phase observed values according to the precise random model in the step (3);
is a double difference carrier phase estimate in m, <' > based on>
Is a double-difference ambiguity fixed value and has the unit of cycles.
2. The positioning method according to claim 1, wherein in step 2), the method for constructing the big dipper single frequency precision function model is as follows:
k big dipper satellites can be observed to epoch t reference station m and monitoring station r, and with satellite p as the reference satellite, the big dipper single-frequency carrier phase function double-difference model of each satellite s relative to the reference satellite is expressed as:
wherein s =1 … k, s is not equal to p, lambda is the Beidou single-frequency carrier phase wavelength, the unit is m,
are double-difference ambiguities in cycles>
Observe noise for double-difference carrier phase in m->
Respectively the geometric distance between the double-difference survey station satellites, the double-difference ionosphere and the troposphere error, and the unit is m;
for a base line length of less than 10km, the ionosphere and the troposphere are completely eliminated through double difference energy, and a function model is simplified as follows:
the Beidou single-frequency Kalman observation model is established in a linearized mode through a function model, and the observation vector is expressed as follows:
wherein, Y t phase Is a vector of double-difference carrier-phase observations,
is a double-difference carrier phase coefficient matrix, is greater than or equal to>
For a coordinate vector to be ascertained at a monitoring station>
Are respectively the linearization coefficients of the geometric distance of the phases of the double-difference carrier, [ X' r Y′ r Z′ r ]Respectively are velocity vectors corresponding to the coordinates of the monitoring station, and the unit is m/s.
3. The positioning method according to claim 1, wherein in the step (5), the step of performing Beidou single frequency part ambiguity estimation is as follows:
(1) solving an ambiguity floating-point solution variance-covariance matrix according to a least square variance estimation criterion, based on the ambiguity resolution, using (2,1, …, 1) k-1 Step-by-step dimensionality reduction calculation is carried out in a grading mode;
(2) combining pseudo range and carrier phase observation vectors, constructing an error observation equation corresponding to each stage of ambiguity group, searching 50 groups of optimal ambiguities in sequence by using LAMBDA, removing a priori baseline vector and calculating an ambiguity group outside a vector value range based on the maximum displacement of the structure body and deformation characteristics determined by numerical simulation;
(3) and searching the minimum residual square and the corresponding whole-cycle ambiguity vector in the residual ambiguity candidate value, and selecting the ambiguity candidate value which passes the Ratio test as the fixed value of each hierarchical ambiguity.
4. The positioning method according to claim 1, wherein in step 1), it is assumed that the monitoring station is in a creep state, and n is zero, and meanwhile, the beidou single-frequency pseudorange single-point positioning method is also applicable to other motion states of the monitoring station, and a system state transpose model of a system dynamic model is defined as follows:
5. the positioning method according to any one of claims 1-4, wherein in step (2), a satellite height cutoff angle is set to 20 °.
6. The positioning method according to claim 5, wherein in step 2), the SNR threshold s1 is 50db, and when CN0 ≧ s1, the observed value weight D is CN0,e The observed value quality is considered to be optimal at this time, and the empirical parameters a, a and s0 are respectively 30, 20 and 10.
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