CN114545461A - Beidou tri-band fine resolving method with coordinate prior fused with GPS - Google Patents

Beidou tri-band fine resolving method with coordinate prior fused with GPS Download PDF

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CN114545461A
CN114545461A CN202210366620.1A CN202210366620A CN114545461A CN 114545461 A CN114545461 A CN 114545461A CN 202210366620 A CN202210366620 A CN 202210366620A CN 114545461 A CN114545461 A CN 114545461A
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常四平
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Abstract

The method aims at the characteristic that the current global navigation satellite system short baseline double-difference relative positioning technology still resolves the main task into cycle slip detection and ambiguity resolution, and when the measurement environment is poor, cycle slips frequently occur and ambiguity is difficult to fix, the method cannot obtain reliable accuracy; the invention provides a Beidou tri-band fine calculation method with coordinates fused with a GPS in a priori mode on the basis of utilizing a GPS to carry out a high-precision monitoring model, and the method aims to utilize Beidou tri-band signals to establish combined measurement values with long wavelength, weak ionosphere delay and small noise, and realize gradual refinement of a rover coordinate initial value with lower precision according to the GPS high-precision monitoring model principle, so that a high-precision positioning result can be obtained while cycle slip detection and ambiguity calculation are avoided, the degree of automation is high, the speed is high, and the Beidou tri-band fine calculation method has remarkable innovation and outstanding advantages.

Description

Beidou tri-band fine resolving method with coordinate prior fused with GPS
Technical Field
The invention relates to a Beidou tri-band short baseline fine calculation method, in particular to a Beidou tri-band fine calculation method with coordinates integrated with a GPS in a priori mode, and belongs to the technical field of Beidou fine data processing.
Background
The global navigation satellite system has been widely applied to various fields of human production and life, greatly changes the global economic and social development mode, and becomes an epoch-making aerospace and information technology historically for human. In the new century, the satellite navigation positioning technology is developed rapidly, and the global navigation satellite positioning system not only becomes a major modernized information infrastructure of each country, but also becomes an important mark for reflecting comprehensive national strength. The future global navigation satellite system will enter a new development stage, the usability, reliability and other aspects will be greatly improved, and the situation that hundreds of navigation satellites are shared will be met.
The GPS is the first global satellite navigation positioning system established in 1973 by the United states, and can realize sea, land and air real-time all-weather global satellite navigation positioning services. As satellite navigation positioning systems play an increasing role in various fields, countries are actively developing their own satellite navigation systems or augmentation systems.
The Beidou satellite navigation system (Beidou) is a global satellite navigation system which is independently researched and developed and operates in China, and mainly comprises a space section, a ground section and a user section. The space segment is mainly composed of 35 orbiting satellites, of which 5 geostationary orbiting satellites, 27 medium circular orbiting satellites and 3 inclined geostationary orbiting satellites. The ground section mainly comprises a main control station, a monitoring station, an injection station and a communication auxiliary system. The user section mainly comprises equipment or a terminal capable of receiving Beidou satellite signals. At present, a Beidou regional satellite navigation system is established and implemented from regional operation to global expansion. With the implementation of the modernization of the GPS, the re-perfection of the GLONASS and the establishment of the Chinese Beidou satellite navigation system and the Galileo system, in the near future, the global system forms a coexistence pattern of four global navigation satellite systems, more than 100 satellites are in orbit, the application field of the global navigation satellite system is necessarily greatly expanded, and the completeness, the fineness, the stability and the real-time performance of satellite orbit determination, positioning and navigation services are improved.
In the prior art, the global navigation satellite system baseline processing generally adopts carrier phase measurement values, so that the problems of cycle slip detection, integer ambiguity resolution and the like are introduced. In the aspect of data preprocessing, the cycle slip detection and restoration method of the carrier phase measurement value mainly includes a wavelet analysis method, a high-order difference method, a kalman filtering method and the like, and the methods are respectively suitable for different data processing modes. However, as a more classical cycle slip detection method, it also has some obvious defects, such as that the MW combination measurement has large measurement noise, so when a small cycle slip occurs (such as a small cycle slip of 1 to 2 weeks), the MW combination cannot be effectively detected; the LG combination has close relation with ionosphere change, and when the data sampling rate is low or the ionosphere activity is active, the LG combination can fail the cycle slip of the special combination.
The integer ambiguity resolution method in the prior art mainly comprises an ambiguity function method, an integer taking method, a least square search method, a fast decomposition FARA method, an integer least square reduction correlation adjustment method and the like. The methods can be generally divided into two modes of a coordinate domain and an ambiguity domain, but the two modes are equivalent in theory, and the solved optimal integer ambiguity vectors are the same. However, the methods do not fully utilize the covariance matrix of the ambiguity vector, and the success rate of ambiguity resolution is low. The integer ambiguity fixing may be incorrect, and the integer ambiguity fixing may be considered to be correct only with a certain probability.
The prior art also provides methods for eliminating the ambiguity of the whole cycle, so that the problems of whole cycle jumping, ambiguity resolution and the like are not considered, starting from a measurement equation, the problems of cycle jumping detection and ambiguity resolution are avoided, and a mathematical model is simple and has high operation speed. However, these methods all require initial coordinates with higher accuracy, so that the use of the method in short baseline data processing of the global navigation satellite system is limited to some extent, more accurate a priori information is required, and the method may fail when the initial coordinates are less accurate.
In the aspect of three-frequency data processing of a global navigation satellite system, at present, four global positioning systems all start to provide signals with three or more than three frequencies, and the main reason is that a plurality of frequency signals can form a plurality of combined measurement values with better characteristics, so that a better solution is provided for cycle slip detection, ambiguity resolution, tropospheric delay, ionospheric delay and the like. Under the condition of a short baseline, the fast and efficient ambiguity fixing can be realized, and the possibility is provided for realizing the real-time navigation positioning with various accuracies. The Beidou satellite navigation system provides three-frequency signals, so that the delay of an ionized layer and a troposphere can be weakened, and the limit on the distance between measuring stations is weakened; the existence of three signal frequencies can quickly fix the integer ambiguity and effectively shorten the measurement time; meanwhile, the method is beneficial to weakening accidental errors and the influence of local environment.
In summary, the prior art has some obvious defects, which are shown in the following aspects:
firstly, in the Beidou tri-band combined measurement theory in the prior art, the influence of the Beidou tri-band combined measurement value on the ionosphere delay, the troposphere delay and the measurement noise error after combination is not fully analyzed, and the combined measurement value with better characteristics is not screened out according to the conditions of long wavelength, weak ionosphere influence and smaller noise, so that a theoretical basis cannot be provided for the Beidou tri-band short baseline data processing method;
secondly, the short baseline double-difference relative positioning technology of the global navigation satellite system in the prior art still resolves the main task into cycle slip detection and ambiguity resolution, when the measurement environment is poor, cycle slip frequently occurs, and ambiguity is difficult to fix, the method cannot obtain the characteristic of reliable accuracy, cannot utilize Beidou tri-frequency signals to construct a combined measurement value with long wavelength, weak ionospheric delay and small noise, and cannot gradually refine the initial value of the mobile station coordinate with lower accuracy according to the GPS high-accuracy monitoring model principle, so that cycle slip detection and ambiguity resolution cannot be avoided, the automation degree is low, and the speed is slow;
the prior art does not have a Beidou dual-mode fine data calculation method fused with a GPS, does not have a dual-mode fine data calculation method, cannot respectively combine the respective advantages of two satellite positioning systems, and has low data processing precision, low data processing precision and reliability of the Beidou three-frequency fine data calculation method, and the prior art is very sensitive to noise data and low in efficiency and has certain loss in data processing;
fourth, data processing software of the Beidou three-frequency fine solution method is lacked in the prior art, data processing cost is high, the quality and precision of Beidou three-frequency fine solution are low, the operation efficiency of an algorithm is low, the elimination precision and accuracy of data are low, and the quality and precision of Beidou three-frequency fine solution are low.
Disclosure of Invention
The invention provides a Beidou tri-band fine solution method for coordinate prior fusion GPS, which aims at the characteristics that the prior global navigation satellite system short baseline double-difference relative positioning technology still attributes the main tasks to cycle slip detection and ambiguity solution, and when the measurement environment is poor, cycle slips frequently occur and ambiguity is difficult to fix, the method can not obtain reliable accuracy, the invention provides the Beidou tri-band fine solution method for coordinate prior fusion GPS on the basis of a high-accuracy monitoring model by utilizing GPS, aiming at utilizing Beidou tri-band signals to establish combined measurement values of long wavelength, weak ionosphere delay and small noise, and realizing gradual refinement of a mobile station coordinate initial value with lower accuracy according to the GPS high-accuracy monitoring model principle, thereby obtaining a high-accuracy positioning result while avoiding cycle slip detection and ambiguity solution, the Beidou tri-band fine solution method has the advantages of high automation degree and high speed, and is remarkable in innovation and outstanding in advantages.
In order to achieve the technical effects, the technical scheme adopted by the invention is as follows:
according to the Beidou three-frequency fine resolving method with coordinate priori fusion GPS, a GPS high-precision monitoring model is utilized, short baseline vector resolving of the GPS is expanded, initial values of baseline vectors are built step by step, fine processing is performed step by step, the short baseline of a Beidou three-frequency combined measurement value is resolved based on coordinate priori constraint, and dual-mode resolving is performed by fusing Beidou and GPS;
the Beidou tri-band fine resolving method based on coordinate prior fusion GPS comprises a base line resolving framework based on coordinate prior constraint, Beidou tri-band short base line resolving based on coordinate prior constraint and Beidou navigation tri-band phase combination measurement value refining, wherein the Beidou tri-band short base line resolving based on coordinate prior constraint comprises resolving bearing conditions, high-precision pseudo-range double-difference base line resolving and Beidou navigation tri-band phase combination measurement value refining;
the invention specifically comprises the following contents: firstly, screening out a combined measurement value with better characteristics according to the conditions which are favorable for fixing the integer ambiguity and improving the positioning precision based on the Beidou three-frequency combined measurement theory; analyzing the influence of the Beidou tri-band combined measurement value on ionospheric delay, tropospheric delay and measurement noise errors starting from multi-frequency phase combination definition, and screening out a typical combined measurement value with longer wavelength and weak ionospheric delay characteristics by long wavelength, weak ionospheric delay and small noise standards; secondly, a Beidou tri-band fine resolving method of coordinate prior fusion GPS is provided, and resolving carrying conditions of each step of fine process are given by analyzing the positioning precision of pseudo-range double differences in short baseline data processing, the relation between a coordinate initial value and integer ambiguity; selecting a proper phase combination measurement value based on the Beidou tri-band combination theory; based on a GPS high-precision monitoring model, the initial coordinates are refined step by step, and the accurate coordinates of the rover station are finally obtained.
The Beidou tri-band fine resolving method with the coordinate prior fused with the GPS further comprises the following concrete implementation processes: according to the decimetric point position coordinates provided by pseudo-range double differences, an ultra-wide lane combination (0, 1, -1) is utilized to obtain a first refined value of the rover coordinates through a global navigation satellite system data processing method based on coordinate prior constraints; performing secondary refinement treatment by using the first-step refined value of the initial coordinate as the combined refined initial value of (1, 1-2), (1, 0-1) and (1-1, 0) to obtain centimeter-level rover position coordinates; and taking the point location coordinate reaching the centimeter level after the secondary refining processing as an initial value of a global navigation satellite system data processing method based on coordinate prior constraint on the W1 measured value, and performing the tertiary refining processing to obtain the point location coordinate at the millimeter level.
The Beidou tri-band fine solution method based on coordinate prior fusion GPS further comprises a baseline solution framework based on coordinate prior constraint, wherein the baseline solution framework comprises the following specific steps: in the short-baseline relative positioning of the global navigation satellite system, the influence of the residual errors of the ionosphere and the troposphere after double difference can be eliminated, and the influence of multipath effect is weakened; when a certain cut-off height angle is set and a choke coil is adopted, the influence of multipath effect is nearly zero, so that the GPS double-difference phase measurement equation is as follows:
Figure BDA0003586135350000041
in the formula:
Figure BDA0003586135350000042
representing a double difference operator; a is the phase measurement in cycles; b is the geometric distance of the satellite survey station in meters, c is the wavelength of the carrier phase measured value in meters; m is the carrier phase integer ambiguity with the unit of cycle; dφThe unit is meter for phase measurement noise and unmodeled error, subscript m represents the satellite, and subscript r represents the receiver; when the deformation is less than a certain amount, determining the whole cycle number in the measured double difference values according to the whole cycle number in the calculated double difference values, wherein F is a reference station, G is a monitoring station, G' is the position of a G point after deformation, q and p are synchronous measurement satellites, and a satellite p with a larger altitude angle is taken as a reference satellite;
f, G the two-station phase double difference measurement is:
Figure BDA0003586135350000043
before deformation, the coordinates of the monitoring station G point are known, and the double difference distance calculation value is obtained by using the coordinates of F, G two points and the satellite position calculated by the satellite ephemeris:
Figure BDA0003586135350000044
the calculated double difference phase from equation 3 is:
Figure BDA0003586135350000051
in the short baseline data processing, after double differences, errors of an ionized layer, a troposphere and a multipath effect are well eliminated, and then a formula 2 and a formula 4 are substituted into a formula 1 to form a double difference measurement equation:
Figure BDA0003586135350000052
double-difference ambiguity when the G-point coordinates are precisely known
Figure BDA0003586135350000053
By passing
Figure BDA0003586135350000054
Directly rounding to obtain:
Figure BDA0003586135350000055
if the monitoring station G is deformed and generates displacement
Figure BDA00035861353500000518
After G', the double difference measurement values calculated by using the coordinates of the G point cannot satisfy equation 5, and their difference values are used
Figure BDA0003586135350000056
Represents:
Figure BDA0003586135350000057
then
Figure BDA0003586135350000058
In that it contains deformation information
Figure BDA0003586135350000059
According to the algorithm thought of no cycle slip and no ambiguity, the deformation amount
Figure BDA00035861353500000510
Less than a certain amount, formula 7 equal sign right end
Figure BDA00035861353500000511
Double-difference ambiguity determined by direct rounding
Figure BDA00035861353500000512
Is still correctDouble-difference ambiguity, namely the deformation does not affect the integer part of the phase double-difference measurement value, and only affects the decimal part of the measurement value;
Figure BDA00035861353500000513
contains only a fractional part of less than one band, exactly
Figure BDA00035861353500000514
The error equation is listed according to equation 1, and the deformation is calculated:
Figure BDA00035861353500000515
in the formula, a subscript m represents a satellite, a subscript r represents a receiver, and w, n and m are direction cosines in three directions of x, y and z.
According to the Beidou tri-band fine calculation method with the coordinate priori fused with the GPS, further, Beidou tri-band short baseline calculation with the coordinate priori constraint realizes short baseline data processing based on the coordinate priori constraint, integer ambiguity calculation and cycle slip detection are avoided, the initial coordinates of the rover station are firstly obtained by utilizing pseudo-range double differences, then the combined measurement value with longer wavelength and smaller noise is selected to gradually refine the calculation result according to the precision of the initial coordinates and the relation between the coordinate priori precision and the integer ambiguity, and finally high-precision rover coordinate information is obtained.
According to the Beidou tri-band fine solution method with the coordinate priori fused with the GPS, further, a solution receiving condition is based on a baseline solution framework based on coordinate priori constraint, when an initial coordinate has certain precision, the deviation between the initial coordinate and a real coordinate only affects the decimal part of double-difference ambiguity and does not affect the integer part of a phase double-difference measurement value, correct phase double-difference integer ambiguity can be obtained by utilizing the initial coordinate calculation of a rover station, and the search process of the integer ambiguity is avoided; however, the key to realize this process is that the initial coordinate needs to ensure a certain precision so that the deviation value between the initial value and the true value does not affect the phase double difference whole-cycle part, i.e. there is a certain relationship between the deviation value and the whole-cycle ambiguity; the invention obtains the relation between the deviation value and the integer ambiguity through deduction;
difference between two difference distance measurements
Figure BDA00035861353500000516
Amount of deformation and
Figure BDA00035861353500000517
the mathematical relationship of (1) is as follows:
Figure BDA0003586135350000061
Figure BDA0003586135350000062
representing a double difference operator; a is the phase measurement in cycles; b is the geometric distance of the satellite survey station in meters, c is the wavelength of the carrier phase measured value in meters; m is the carrier phase integer ambiguity with the unit of cycle; dφThe unit is meter for phase measurement noise and unmodeled error, subscript m represents the satellite, and subscript r represents the receiver; f is a reference station, G is a monitoring station, G' is the position of a deformed G point, q and p are synchronous measurement satellites, and a satellite p with a larger altitude angle is taken as a reference satellite; if the monitoring station G is deformed and generates displacement
Figure BDA0003586135350000063
After to point G', their difference is used
Figure BDA0003586135350000064
Represents;
amount of deformation
Figure BDA0003586135350000065
Further expressed as:
Figure BDA0003586135350000066
wherein,
Figure BDA0003586135350000067
is composed of
Figure BDA0003586135350000068
A unit vector in the direction;
carrying out the following steps of:
Figure BDA0003586135350000069
taking into account formula 4:
Figure BDA00035861353500000610
if the integer ambiguity is not considered, then:
Figure BDA00035861353500000611
the conditions need to be satisfied: formula 11 right side is less than 1 week, i.e.:
Figure BDA00035861353500000612
due to the fact that
Figure BDA00035861353500000613
So that:
Figure BDA00035861353500000614
then when the condition is satisfied:
Figure BDA00035861353500000615
when the formula 16 is satisfied, the condition of avoiding integer ambiguity resolution can be satisfied; the residual error of the carrier phase measurement value measured by the short baseline after double difference is very small, and when the residual error of the double difference is considered, the residual error term of the double difference should be added to the left term of the formula 16.
In the coordinate prior fusion GPS Beidou tri-band fine resolving method, further, in high-precision pseudo-range double-difference baseline resolving, pseudo-range double-difference resolving is firstly performed to solve the initial coordinate of a rover station by considering coordinate prior constraint; the method is based on a pseudo-range double-difference baseline resolving method, and the accuracy of the pseudo-range double-difference can be resolved to be used as a reference for selecting a subsequent three-frequency linear combination measured value;
the non-differenced pseudorange measurement equation is:
Figure BDA0003586135350000071
in the formula,
Figure BDA0003586135350000072
is a measurement of the pseudorange,
Figure BDA0003586135350000073
the geometric distance from the station to the satellite, o is the speed of light propagation in vacuum, in m/s, fj(t) is the satellite clock error, bF(t) is the receiver clock difference,
Figure BDA0003586135350000074
in order to be a tropospheric delay parameter,
Figure BDA0003586135350000075
for ionospheric errors, a single difference equation can be composed as follows:
Figure BDA0003586135350000076
the double difference equation is:
Figure BDA0003586135350000077
wherein:
Figure BDA0003586135350000078
after linearizing equation 19, the measurement equation is constructed:
Figure BDA0003586135350000079
and solving a pseudo-range double-difference solution of the baseline through indirect adjustment or Kalman filtering.
Further, the invention simulates and analyzes the double-difference precision of the short baseline pseudo range in three latitudes, namely high, medium and low, and the conclusion is that: the error in the short baseline resolved point locations was between 10cm and 20cm, with an average of 15.1cm and a maximum of 22.1 cm.
The invention utilizes the measured data of the Beidou deformation monitoring network to analyze the precision of pseudo-range double differences, the deformation monitoring network consists of a reference station (JZ01) and four monitoring stations (JC01, JC02, JC03 and JZ02), the length of a base line is 29m to 280m, the data processing adopts two groups of data of GPS and Beidou of a whole day to carry out four-hour time interval solution respectively, six time intervals are solved totally, the solution result is differed with the real value of each measuring station, residual values in X, Y, Z three directions are solved, and the result is as follows: the Beidou pseudo-range double-difference calculation result of the solution in four hour periods is better than the result of the GPS; the error of the Beidou pseudorange double difference in the point position is 9cm to 39cm under the condition of a short baseline, and the precision of the error of 9cm to 39cm in the point position is enough as the initial value of the Beidou tri-band short baseline data processing method based on coordinate constraint.
The invention carries out single epoch resolving test on the Beidou pseudorange double-difference positioning to obtain the resolving result of the single epoch pseudorange double-difference positioning, the test carries out single epoch pseudorange double-difference processing by utilizing one of four baselines in a network, and the result is as follows: under the condition of a short baseline, the fluctuation range of the pseudo-range double-difference single-epoch calculation result is within 1.46 meters, and most of the pseudo-range double-difference single-epoch calculation result is within 0.48 meters, so that the positioning accuracy of the Beidou short baseline pseudo-range double-difference in the single-epoch calculation mode is in the decimeter level.
In the refinement of the coordinate prior-fused GPS Beidou tri-band fine solution, further, when the deviation of the coordinate prior value of the rover station is required to be less than c/2 by a Beidou navigation tri-band phase combination measurement value, a Beidou navigation tri-band phase combination measurement value short baseline data processing method constrained by the coordinate prior, the whole cycle number in the measured double difference value can be determined according to the whole cycle number in the double difference value obtained by the initial coordinate of the rover station, so that the problems of cycle slip detection and repair and whole cycle ambiguity solution are avoided only by considering the part less than one whole cycle during data processing, and the range of the determined deformation amount is determined by the size of the carrier wave length;
the point position precision of the pseudo-range double-difference calculation result is in the decimeter level under the static condition, and the precision is within 2 meters under the dynamic single epoch condition, so that a combined measurement value with the wavelength of 4 meters and the noise of about 1 decimeter can be selected during one-time refinement; the ultra-wide lane combination (0, 1, -1) with the wavelength of 4.88 meters and the noise of only 0.057 meters is very suitable for being used as a combined measurement value of one-time refinement; when the combination is used for refining, the initial value deviation of the coordinates can reach 2.43 meters, namely the initial value deviation of the coordinates is within 2.43 meters, and the combination can be refined accurately.
After the ultra-wide lane combination is refined for one time, the point position coordinate precision is poor, the noise is in the decimeter level, and other combination measurement values are required to be refined for the second time; the wavelengths of the combined measurement values of (1, 1, -2), (1, 0, -1) and (1, -1, 0) are all about 1m, the noise is centimeter-level, the point location coordinates can be further refined to centimeter-level, more accurate point location coordinates can be obtained, and the method is suitable for refining the point location coordinates obtained by the ultra-wide roadway combined measurement values.
After the secondary refinement is completed, the precision of the point location coordinate is centimeter level, at the moment, the three refinements are performed, and the point location coordinate can be improved to millimeter level only by using the W1 original measurement value to perform the same data processing method; a global navigation satellite system data processing algorithm based on coordinate prior constraint provides an initial value through pseudo-range double differences, and millimeter-level results can be obtained through three-step refining processing.
The Beidou tri-band fine resolving method with the coordinate prior fused with the GPS further comprises the following specific algorithm for refining the Beidou navigation tri-band phase combination measurement value:
step one, according to point position coordinates provided by pseudo-range double differences, an ultra-wide lane combination (0, 1, -1) is utilized to obtain a first refined value of the rover coordinate through a global navigation satellite system data processing method based on coordinate prior constraint;
step two, taking the primary refined value of the initial coordinate obtained in the step one as the combined refined initial value of (1, 1-2), (1, 0-1) and (1-1, 0), and performing secondary refined value to obtain the centimeter-level rover position coordinate;
taking the centimeter-level point coordinate subjected to secondary refining as an initial value of a global navigation satellite system data processing method based on coordinate prior constraint on the W1 measured value, and performing secondary refining to obtain the millimeter-level point coordinate;
and fourthly, obtaining accurate point location coordinates of the mobile station, then obtaining baseline information, and outputting.
The Beidou tri-band fine resolving method with the coordinate prior fused with the GPS further comprises the steps of adding GPS measurement data in the last refinement process of the refinement of the Beidou combined measurement value, and resolving Beidou dual-mode fine data fused with the GPS;
when the Beidou and GPS are subjected to data fusion processing, firstly, reference unification is carried out, namely unification between a WGS-84 coordinate system and a CGCS2000 coordinate system and unification between GPST and BDT;
the coordinate prior constraint-based short baseline data processing method can directly obtain double-difference ambiguity parameters, so that only three-dimensional position parameters remain in a double-difference measurement equation, and the simplified Beidou/GPS double-difference carrier phase measurement equation is as follows:
Figure BDA0003586135350000091
in the formula:
Figure BDA0003586135350000092
dX represents a relative coordinate correction vector;
Figure BDA0003586135350000093
expressing a double-difference integer ambiguity vector, and directly obtaining a double-difference ambiguity value through a constraint algorithm based on coordinate prior; g is a coefficient matrix corresponding to dX, W is a constant term vector, (x)0,y0,z0) Is the initial position of the rover (x)n，yn，zn) As satellite position, s0The geometric distance between the initial position of the user and the satellite is defined, and n is the measured satellite of the same system; during data processing, the double-difference process is carried out in the same system, n GPS double-difference measurement equations can be obtained by n GPS satellites, m Beidou satellites can obtain m-1 Beidou double-difference measurement equations, n + m-2 measurement equations are in total, and least square or Kalman filtering is adopted in the adjustment process;
the stochastic model is: suppose that
Figure BDA0003586135350000094
The variance of the i satellite phase measurements and the pseudorange measurements for rover station q,
Figure BDA0003586135350000095
variance of the i satellite phase measurement and the pseudorange measurement, respectively, of the reference station s, then:
Figure BDA0003586135350000096
Figure BDA0003586135350000097
the covariance matrix of the double difference measurement values can be obtained according to the error propagation law as follows:
Figure BDA0003586135350000098
in the formula:
Figure BDA0003586135350000099
Figure BDA0003586135350000101
Saa、SQQthe method comprises the following steps of respectively using a double-difference carrier variance-covariance matrix and a double-difference pseudo-range variance-covariance matrix of an i-number satellite as a reference satellite, adopting an altitude weighting rule, and giving the variance of a non-difference original measured value according to an altitude:
Figure BDA0003586135350000102
wherein I represents the satellite altitude, fa0、fQ0Respectively representing standard deviations of the carrier wave and the pseudo range, respectively taking the standard deviations as 0.002 meter and 1 meter, and obtaining a corresponding weight matrix by inverting the square deviation-covariance. After the random model of a single system is determined, the systems have no relevance, so the weight ratio between the GPS and the Beidou system is set to be 1:1, namely a combined measurement value weight array is as follows:
Figure BDA0003586135350000103
SGPS、SBDSand respectively representing measurement value weight arrays of the GPS and the Beidou satellite navigation system.
Compared with the prior art, the invention has the following contributions and innovation points:
firstly, the Beidou tri-band fine calculation method with the coordinate prior fused with the GPS analyzes the influence of Beidou tri-band combined measurement values on ionospheric delay, tropospheric delay and measurement noise errors after combination based on the Beidou tri-band combined measurement theory of the system, screens out combined measurement values with better characteristics according to the long wavelength, weak ionospheric influence and smaller noise conditions, and provides a solid theoretical foundation for the Beidou tri-band short baseline data processing method;
secondly, the invention provides a Beidou tri-band fine solution method for fusing a GPS (global positioning system) with a coordinate prior, aiming at the characteristics that the main tasks of the existing short-baseline double-difference relative positioning technology of the global navigation satellite system are still summarized as cycle slip detection and ambiguity solution, and when the measurement environment is poor, cycle slips frequently occur and ambiguity is difficult to fix, the method can not obtain reliable accuracy, the invention provides the Beidou tri-band fine solution method for fusing the GPS with the coordinate prior on the basis of a high-accuracy monitoring model by utilizing the GPS, aiming at constructing a combined measurement value with long wavelength, weak ionospheric delay and small noise by utilizing a Beidou tri-band signal, realizing gradual refinement of a mobile station coordinate initial value with lower accuracy according to the principle of the GPS high-accuracy monitoring model, and further obtaining a high-accuracy positioning result while avoiding cycle slip detection and ambiguity solution, the Beidou tri-band fine solution method has high automation degree and high speed, is remarkable in innovation and has outstanding advantages;
thirdly, the Beidou tri-band fine solution method for coordinate priori fusion GPS provided by the invention provides a Beidou bi-mode fine data solution method for coordinate priori fusion GPS, is a bi-mode fine data solution method, provides a mathematical model for fusion solution, and combines respective advantages of two satellite positioning systems respectively, so that the data processing precision is effectively improved, and meanwhile, the solution method is applied to the Beidou tri-band fine solution for coordinate priori fusion GPS, so that the data processing precision and reliability of the Beidou tri-band fine solution method for coordinate priori fusion GPS are further improved;
fourthly, the Beidou tri-band fine solution method with the coordinate prior fused with the GPS provided by the invention develops a set of data processing software of the Beidou tri-band fine solution method with the coordinate prior fused with the GPS, develops corresponding short baseline data processing software on the basis of the Beidou tri-band short baseline data processing method with the coordinate prior constrained fused with the GPS, develops test and analysis from multiple aspects by adopting measured data on a group of deformation monitoring platforms, verifies that the Beidou tri-band fine solution method with the coordinate prior fused with the GPS has high data processing precision, greatly reduces the data processing cost, and obviously improves the quality and precision of the Beidou tri-band fine solution.
Drawings
FIG. 1 is a diagram of the deformation vectors of the present invention
Figure BDA0003586135350000111
The effect on the double difference is shown schematically.
Fig. 2 is a schematic diagram of a refinement process of the beidou three-frequency phase combination measurement value of the present invention.
FIG. 3 is a software development flow chart of a Beidou tri-band fine solution method with coordinate prior fusion with a GPS.
Detailed Description
The technical scheme of the Beidou tri-band fine solution method with the coordinate prior fused with the GPS provided by the invention is further described below with reference to the accompanying drawings, so that the technical scheme can be better understood and implemented by the technical personnel in the field.
Cycle slip detection and ambiguity resolution are always the key points in the data processing of the global navigation satellite system, and due to the influence of various errors, the cycle slip cannot be effectively detected, and the ambiguity cannot be fixed, even if the problem is solved, the processing process is still very complicated. The invention provides a high-precision monitoring model by utilizing a GPS (global positioning system), starts from a model measurement equation, avoids the problems of cycle slip detection and restoration and whole-cycle ambiguity resolution, simplifies the data processing process, further expands the short baseline vector resolution of the GPS, constructs accurate initial values of baseline vectors step by step, gradually performs fine processing, successfully avoids the problems of cycle slip detection and ambiguity resolution, has simple mathematical model and high calculation speed, solves the short baseline of Beidou three-frequency combined measurement values based on coordinate prior constraint, and improves the precision and reliability of the resolution result by fusing Beidou and GPS dual-mode resolution.
The invention provides a Beidou tri-frequency short baseline data processing algorithm based on coordinate prior constraint, and a corresponding program is compiled, the correctness of the algorithm and theory involved is analyzed from multiple aspects through measured data, and the accuracy and reliability of the method can be reached, and the specific content is as follows:
the method comprises the steps that firstly, based on the Beidou three-frequency combined measurement theory, the influence of Beidou three-frequency combined measurement values on combined errors is analyzed in detail, and combined measurement values with better characteristics are screened out according to conditions which are beneficial to integer ambiguity fixation and improvement of positioning accuracy;
the invention starts from the definition of multi-frequency phase combination, analyzes the influence of Beidou tri-band combined measurement value on ionosphere delay, troposphere delay and measurement noise error, screens out typical combined measurement value with longer wavelength and weak ionosphere delay characteristics according to long wavelength, weak ionosphere delay and smaller noise standards, mainly comprises ultra-wide lane combined measurement value (0, 1, -1), the wavelength of the combined measurement value is 4.91m, the noise is only 0.06m, the ionosphere amplification factor is only 0.06, and the method is suitable for data processing of short baseline, medium-long baseline and the like; the wavelength of the wide-lane combined measurement value (1, 0, -1) is 0.86m, the noise is 0.01m, and the ionosphere amplification factor is-0.31; (1, -1, 0) combination, wavelength 1.02m, noise 0.01m, ionospheric amplification factor-0.23; the (3, -14, 11) combined ionospheric amplification factor is very small, and therefore the ionospheric effect in data processing can be effectively weakened for weak ionospheric combined measurements.
Secondly, a Beidou tri-band fine resolving method of coordinate prior fusion GPS is provided, and resolving carrying conditions of each step of fine process are given by analyzing the positioning precision of pseudo-range double differences in short baseline data processing, the relation between a coordinate initial value and integer ambiguity; selecting a proper phase combination measurement value based on the Beidou tri-band combination theory; based on a GPS high-precision monitoring model, refining the initial coordinates step by step, and finally obtaining accurate coordinates of the rover station;
the specific implementation process is as follows: according to the decimetric point position coordinates provided by pseudo-range double differences, an ultra-wide lane combination (0, 1, -1) is utilized to obtain a first refined value of the rover coordinates through a global navigation satellite system data processing method based on coordinate prior constraints; performing secondary refinement treatment by using the first-step refined value of the initial coordinate as the combined refined initial value of (1, 1-2), (1, 0-1) and (1-1, 0) to obtain centimeter-level rover position coordinates; and taking the point location coordinate reaching the centimeter level after the secondary refining processing as an initial value of a global navigation satellite system data processing method based on coordinate prior constraint on the W1 measured value, and performing the tertiary refining processing to obtain the point location coordinate at the millimeter level.
Thirdly, according to a Beidou tri-band fine calculation method with coordinate prior fusion GPS, corresponding global navigation satellite system high-precision data processing software is independently developed, and the high precision and the practicability of the invention are verified through analysis of measured data from a plurality of angles. The invention utilizes MATLAB software to compile corresponding high-precision data processing software of the global navigation satellite system in WINDOWS environment, and has the functions of data quality analysis, pseudo-range double-difference positioning, Beidou three-frequency combined measurement value refinement and Beidou and GPS data fusion resolving. Under the static condition, the invention can realize the precision of 1.9mm in the horizontal direction and 4.8mm in the vertical direction; under the dynamic condition, the invention can realize the precision of 3.8mm in the horizontal direction and 0.9cm in the vertical direction. The Beidou tri-band fine resolving method with the coordinate prior fusion GPS has high data processing precision.
First, base line resolving framework based on coordinate prior constraint
In the short-baseline relative positioning of the global navigation satellite system, the residual influence of the ionosphere and the troposphere after double difference can be well eliminated, and the influence of multipath effect is weakened. When a certain cut-off height angle is set and a choke coil is adopted, the influence of multipath effect is nearly zero, so that the GPS double-difference phase measurement equation is as follows:
Figure BDA0003586135350000131
in the formula:
Figure BDA0003586135350000132
representing a double difference operator; a is the phase measurement in cycles; b is the geometric distance of the satellite survey station in meters, c is the wavelength of the carrier phase measured value in meters; m is the carrier phase integer ambiguity with the unit of cycle; dφThe unit is meter for phase measurement noise and unmodeled error, subscript m represents the satellite, and subscript r represents the receiver; the invention provides a cycle slip-free ambiguity-free resolving method by utilizing a GPS high-precision model, and when the deformation is less than a certain amount, the whole cycle number in the measured double difference values is determined according to the whole cycle number in the calculated double difference values, so that the troublesome problems of detection and repair of cycle slip, whole cycle ambiguity determination and the like are avoided. As shown in fig. 1, F is a reference station, G is a monitoring station, G' is a deformed G point position, q and p are synchronous measurement satellites, and a satellite p with a large altitude angle is used as a reference satellite.
F, G the two-station phase double difference measurement is:
Figure BDA0003586135350000133
before deformation, the coordinates of the monitoring station G point are known, and the double difference distance calculation value is obtained by using the coordinates of F, G two points and the satellite position calculated by the satellite ephemeris:
Figure BDA0003586135350000134
the calculated double difference phase from equation 3 is:
Figure BDA0003586135350000135
in the short baseline data processing, after double differences, the errors of the ionosphere, the troposphere and the multipath effect are well eliminated, and then
Formula 2 and formula 4 are substituted for formula 1 to form a double difference measurement equation:
Figure BDA0003586135350000136
double-difference ambiguity when the G-point coordinates are precisely known
Figure BDA0003586135350000137
By passing
Figure BDA0003586135350000138
Directly rounding to obtain:
Figure BDA0003586135350000139
if the monitoring station G is deformed and generates displacement
Figure BDA00035861353500001310
After G', the double difference measurement values calculated by using the coordinates of the G point cannot satisfy equation 5, and their difference values are used
Figure BDA00035861353500001311
Represents:
Figure BDA00035861353500001312
then
Figure BDA00035861353500001313
In that it contains deformation information
Figure BDA00035861353500001314
According to the algorithm thought of no cycle slip and no ambiguity, the deformation amount
Figure BDA00035861353500001315
Less than a certain amount, formula 7 equal sign right end
Figure BDA00035861353500001316
Double-difference ambiguity determined by direct rounding
Figure BDA00035861353500001317
The double-difference ambiguity is still correct, i.e. the amount of deformation does not affect the integer part of the phase double-difference measurement, but only the fractional part of the measurement. Therefore, the temperature of the molten metal is controlled,
Figure BDA00035861353500001318
contains only a fractional part of less than one band, exactly
Figure BDA00035861353500001319
The error equation is listed according to equation 1, and the deformation is calculated:
Figure BDA0003586135350000141
in the formula, a subscript m represents a satellite, a subscript r represents a receiver, and w, n and m are direction cosines in three directions of x, y and z.
Second, coordinate prior constrained Beidou tri-band short baseline solution
The method comprises the steps of firstly obtaining initial coordinates of the rover station by utilizing pseudo-range double differences, then selecting combined measurement values with longer wavelength and smaller noise to gradually refine calculation results according to the precision of the initial coordinates and the relation between the coordinate prior precision and the integer ambiguity, and finally obtaining high-precision rover coordinate information.
Resolving the bearing conditions
According to the baseline resolving framework based on the coordinate prior constraint, when the initial coordinate has certain precision, the deviation between the initial coordinate and the real coordinate only affects the decimal part of the double-difference ambiguity and does not affect the integer part of the phase double-difference measurement value, so that the correct phase double-difference integer ambiguity can be obtained by utilizing the initial coordinate calculation of the rover station, and the searching process of the integer ambiguity is avoided. However, the key to implementing this process is that the initial coordinate needs to ensure a certain precision so that the deviation value between the initial value and the true value does not affect the phase double difference whole-cycle part, i.e. there is a certain relationship between the deviation value and the whole-cycle ambiguity. The invention obtains the relation between the deviation value and the integer ambiguity by derivation.
Difference between two difference distance measurements
Figure BDA0003586135350000142
Amount of deformation and
Figure BDA0003586135350000143
the mathematical relationship of (1) is as follows:
Figure BDA0003586135350000144
Figure BDA0003586135350000145
representing a double difference operator; a is the phase measurement in cycles; b is the geometric distance of the satellite survey station in meters, c is the wavelength of the carrier phase measured value in meters; m is the carrier phase integer ambiguity with the unit of cycle; dφThe unit is meter for phase measurement noise and unmodeled error, subscript m represents the satellite, and subscript r represents the receiver; f is a reference station, G is a monitoring station, G' is the position of a deformed G point, q and p are synchronous measurement satellites, and a satellite p with a larger altitude angle is taken as a reference satellite; if the monitoring station G is deformed and generates displacement
Figure BDA0003586135350000146
After to point G', their difference is used
Figure BDA0003586135350000147
Represents;
amount of deformation
Figure BDA0003586135350000148
Further expressed as:
Figure BDA0003586135350000149
wherein,
Figure BDA00035861353500001410
is composed of
Figure BDA00035861353500001411
A unit vector in the direction;
carrying out the following steps of:
Figure BDA00035861353500001412
taking into account formula 4:
Figure BDA00035861353500001413
if the integer ambiguity is not considered, then:
Figure BDA0003586135350000151
the conditions need to be satisfied: formula 11 is less than 1 week to the right, i.e.:
Figure BDA0003586135350000152
due to the fact that
Figure BDA0003586135350000153
Therefore:
Figure BDA0003586135350000154
then when the condition is satisfied:
Figure BDA0003586135350000155
when the formula 16 is satisfied, the condition of avoiding integer ambiguity resolution can be satisfied; the residual error of the carrier phase measurement value measured by the short baseline after double difference is very small, and when the residual error of the double difference is considered, the residual error term of the double difference should be added to the left term of the formula 16.
High-precision pseudo-range double-difference baseline solution
The short baseline solution considering the coordinate prior constraint is pseudo-range double-difference solution to obtain the initial coordinate of the rover station; the method is based on a pseudo-range double-difference baseline resolving method, and the accuracy of the pseudo-range double-difference can be resolved to be used as a reference for selecting a subsequent three-frequency linear combination measured value.
The non-differenced pseudorange measurement equation is:
Figure BDA0003586135350000156
in the formula,
Figure BDA0003586135350000157
is a measurement of the pseudorange,
Figure BDA0003586135350000158
the geometric distance from the station to the satellite, o is the speed of light propagation in vacuum, in m/s, fj(t) is the satellite clock error, bF(t) is the receiver clock difference,
Figure BDA0003586135350000159
in order to be a tropospheric delay parameter,
Figure BDA00035861353500001510
for ionospheric errors, a single difference equation can be composed as follows:
Figure BDA00035861353500001511
the double difference equation is:
Figure BDA00035861353500001512
wherein:
Figure BDA00035861353500001513
after linearizing equation 19, the measurement equation is constructed:
Figure BDA00035861353500001514
and solving a pseudo-range double-difference solution of the baseline through indirect adjustment or Kalman filtering.
Because the distance between the two measuring stations is short, satellite orbit errors and atmospheric delay errors in short-baseline data processing have strong spatial correlation; through pseudo-range double differences, the errors are better eliminated or weakened, and therefore the accuracy of single-point positioning is improved to a greater extent than the pseudo-range. The invention simulates and analyzes the double-difference precision of the short baseline pseudo range in the high, middle and low latitudes, and the conclusion is that: the error in the short baseline resolved point locations was between 10cm and 20cm, with an average of 15.1cm and a maximum of 22.1 cm.
The invention utilizes the measured data of the Beidou deformation monitoring network to analyze the precision of pseudo-range double differences, the deformation monitoring network consists of a reference station (JZ01) and four monitoring stations (JC01, JC02, JC03 and JZ02), the length of a base line is 29m to 280m, the data processing adopts two groups of data of GPS and Beidou of a whole day to carry out four-hour time interval solution respectively, six time intervals are solved totally, the solution result is differed with the real value of each measuring station, residual values in X, Y, Z three directions are solved, and the result is as follows: the Beidou pseudo-range double-difference calculation result of the solution in four hour periods is better than the result of the GPS; the error of the Beidou pseudo-range double difference in the point location is 9cm to 39cm under the condition of a short baseline, and the precision of the error of 9cm to 39cm in the point location is enough to be used as an initial value of a Beidou tri-band coordinate constraint-based short baseline data processing method.
In order to analyze the double-difference effect of the Beidou pseudoranges under the dynamic condition, the invention carries out single-epoch resolving test on the Beidou pseudorange double-difference positioning to obtain the resolving result of the single-epoch pseudorange double-difference positioning, the test carries out single-epoch pseudorange double-difference processing by utilizing one of four baselines in a network, and the result is as follows: under the condition of a short baseline, the fluctuation range of the pseudo-range double-difference single-epoch calculation result is within 1.46 meters, and most of the pseudo-range double-difference single-epoch calculation result is within 0.48 meters, so that the positioning accuracy of the Beidou short baseline pseudo-range double-difference in the single-epoch calculation mode is in the decimeter level.
(III) refinement of three-frequency phase combination measurement value of Beidou navigation
The short baseline data processing method of the coordinate prior constraint requires that when the deviation of the prior value of the rover coordinate is smaller than c/2, the whole cycle number in the measured double difference value can be determined according to the whole cycle number in the double difference value obtained by the initial coordinate of the rover, so that the problems of detection and repair of cycle slip and whole cycle ambiguity resolution are avoided by only considering the part less than one whole cycle during data processing, and the data processing is simplified. Therefore, the magnitude of the carrier wavelength determines the range of the deformation amount that can be determined.
The point position precision of the pseudo-range double-difference calculation result is in the decimeter level under the static condition, and the precision is within 2 meters under the dynamic single epoch condition, so that the combined measurement value with the wavelength of 4 meters and the noise of about 1 decimeter can be selected during one-time refinement. The ultra-wide lane combination (0, 1, -1) with a wavelength of 4.88 meters and a noise of only 0.057 meters in the specific embodiment is well suited as a combined measurement value for one refinement. When the combination is used for refining, the initial value deviation of the coordinates can reach 2.43 meters, namely the initial value deviation of the coordinates is within 2.43 meters, and the combination can be refined accurately.
However, after one refinement obtained by ultra-wide lane combination, the point location coordinate accuracy is poor, the noise is in the decimeter level, and secondary refinement needs to be performed by using other combined measurement values. In the specific embodiment, the wavelengths of the combined measurement values (1, 1, -2), (1, 0, -1) and (1, -1, 0) are all about 1m, the noise is centimeter-level, the point location coordinates can be further refined to centimeter-level, more accurate point location coordinates can be obtained, and the method is suitable for refining the point location coordinates obtained by the ultra-wide roadway combined measurement values.
After the secondary refinement is completed, the precision of the point location coordinate is centimeter level, at the moment, the three refinements are performed, and the point location coordinate can be improved to millimeter level only by using the W1 original measurement value to perform the same data processing method. A global navigation satellite system data processing algorithm based on coordinate prior constraint provides an initial value through pseudo-range double differences, millimeter-level results can be obtained through three-step fine processing, detection and ambiguity resolution of cycle slip are not involved, and a mathematical model is relatively simple.
The specific algorithm is as follows:
step one, according to point position coordinates provided by pseudo-range double differences, an ultra-wide lane combination (0, 1, -1) is utilized to obtain a first refined value of the rover coordinate through a global navigation satellite system data processing method based on coordinate prior constraint;
step two, taking the primary refined value of the initial coordinate obtained in the step one as the combined refined initial value of (1, 1-2), (1, 0-1) and (1-1, 0), and performing secondary refined value to obtain the centimeter-level rover position coordinate;
taking the centimeter-level point coordinate subjected to secondary refining as an initial value of a global navigation satellite system data processing method based on coordinate prior constraint on the W1 measured value, and performing secondary refining to obtain the millimeter-level point coordinate;
and fourthly, obtaining accurate point location coordinates of the mobile station, then obtaining baseline information, and outputting.
The corresponding algorithm flow chart is shown in fig. 2.
In order to verify the feasibility of the algorithm provided by the invention, three algorithms are adopted respectivelyThe strip baseline test tests the resolving effect of the algorithm in different baseline lengths, the data of three groups of baselines are collected in a static mode, and the GAMIT software is used for obtaining point position coordinates of each base station and the mobile station with the accuracy reaching millimeter level through GPS data for comparison. During test, the resolving effect of an epoch analysis algorithm on three base lines is firstly realized, and the initial coordinate of the mobile station is changed into a coordinate (X) containing errors0+fx，Y0+fy，Z0+fz) The corresponding measurement data is the measurement data of the rover in exact coordinates when there is a displacement (f) of the roverx，fy，fz) (referred to as bias value), the real coordinate of the monitoring point is (X)0，Y0，Z0) The deviation (f) of the rover is obtained from the initial coordinates and the measured data in the real coordinates of the roverx，fy，fz) And the difference value between the deviation amount and the design displacement is the deviation amount precision obtained by the method.
The differences between the deviation amount calculated by the three base lines in the three sets of single-epoch deformation tests and the design deviation are all in millimeter magnitude, and the deviation information in each direction is effectively extracted. When the ultra-wide lane combined data is processed and refined by using the wide lane measured value, the obtained WL corrected value and the obtained W1 corrected value are the same between different deviation amounts in the same direction when the ultra-wide lane combined data is processed and refined by using the W1 measured value. The ultra-wide lane combined measurement value effectively extracts a deviation amount, and the wide lane combined measurement value and the W1 measurement value only process noise in the measurement value in the previous step so as to improve the deviation amount and the accuracy of the position coordinates of the rover station, and therefore the ultra-wide lane combined measurement value is processed in a fine mode.
Third, GPS-fused Beidou dual-mode fine data calculation
The Beidou satellite navigation system can provide independent positioning, navigation and time service for Asia-Pacific areas, so that the interconnection and mutual operation of multiple systems become possible, the fusion data processing among multiple global navigation satellite systems is certainly greatly improved in the aspects of satellite navigation positioning precision, reliability, application efficiency and the like, and the multi-mode multi-system data fusion processing is a trend of high-precision data processing development of the global navigation satellite systems.
GPS measurement data is added in the last refinement process of the refinement of the Beidou combined measurement value, and the Beidou dual-mode refined data of the GPS is resolved.
When the Beidou and GPS are used for data fusion processing, firstly, reference unification is carried out, namely unification between a WGS-84 coordinate system and a CGCS2000 coordinate system and unification between GPST and BDT.
In the relative positioning of a global navigation satellite system, double differences are adopted to resolve and remove satellite clock differences and receiver clock differences, troposphere, ionosphere and satellite orbit errors are well weakened under the condition of a short baseline, and multipath effects can be weakened as much as possible by adopting a better receiver and selecting a better measurement environment, so that the influence of the multipath effects can be ignored in actual processing, but the double differences ambiguity parameters can be directly solved by the coordinate prior constraint-based short baseline data processing method, so that only three-dimensional position parameters remain in a double difference measurement equation, and the simplified Beidou/GPS double difference carrier phase measurement equation is as follows:
Figure BDA0003586135350000181
in the formula:
Figure BDA0003586135350000182
dX represents a relative coordinate correction vector;
Figure BDA0003586135350000183
expressing a double-difference integer ambiguity vector, and directly obtaining a double-difference ambiguity value through a constraint algorithm based on coordinate prior; g is a coefficient matrix corresponding to dX, W is a constant term vector, (x)0,y0,z0) Is the initial position of the rover (x)n，yn，zn) As satellite position, s0The geometric distance between the initial position of the user and the satellite is defined, and n is the measured satellite of the same system; number ofWhen the data is processed, the double-difference process is carried out in the same system, n GPS double-difference measurement equations can be obtained by n GPS satellites, m Beidou satellites can obtain m-1 Beidou double-difference measurement equations, n + m-2 measurement equations are in total, and the adjustment process adopts least square or Kalman filtering.
The stochastic model is: suppose that
Figure BDA0003586135350000184
The variance of the i satellite phase measurements and the pseudorange measurements for rover station q,
Figure BDA0003586135350000185
variance of the i satellite phase measurement and the pseudorange measurement, respectively, of the reference station s, then:
Figure BDA0003586135350000186
Figure BDA0003586135350000187
the covariance matrix of the double difference measurement values can be obtained according to the error propagation law as follows:
Figure BDA0003586135350000191
in the formula:
Figure BDA0003586135350000192
Figure BDA0003586135350000193
Saa、SQQa double difference carrier variance-covariance matrix and a double difference pseudo-range variance-covariance matrix which respectively use the i-number satellite as a reference satellite and adopt an altitude weighting ruleThe variance of the non-poor raw measurements is given in elevation:
Figure BDA0003586135350000194
wherein I represents the altitude of the satellite, fa0、fQ0Respectively representing standard deviations of the carrier wave and the pseudo range, respectively taking the standard deviations as 0.002 meter and 1 meter, and obtaining a corresponding weight matrix by inverting the square deviation-covariance. After the random model of a single system is determined, the systems have no relevance, so the weight ratio between the GPS and the Beidou system is set to be 1:1, namely a combined measurement value weight array is as follows:
Figure BDA0003586135350000195
SGPS、SBDSand respectively representing measurement value weight arrays of the GPS and the Beidou satellite navigation system.
Software development of Beidou tri-band fine calculation method with coordinate prior fused with GPS
According to the Beidou tri-band fine solution method based on the coordinate prior fusion GPS, corresponding software is developed on the basis of the Beidou tri-band fine solution method based on the coordinate prior fusion GPS, example analysis is carried out on the Beidou tri-band fine solution method based on the coordinate prior fusion GPS by utilizing measured data, and meanwhile, the reliability and the practicability of the algorithm are demonstrated by comparing with other software or algorithms.
According to the Beidou tri-band fine solution method and the mathematical model with coordinate prior fusion GPS, the invention develops corresponding solution software by MATLAB software in WINDOWS environment, the software is used for the tri-band static and dynamic short baseline data processing of GPS and Beidou satellite navigation system, and the specific modules mainly comprise:
the first module is used for analyzing the data quality of the measurement value of the global navigation satellite system, wherein the data quality comprises the calculation and analysis of the number of visible satellites, a PDOP value and multipath information and graphic drawing;
modeling the single-pass measurement value, wherein the modeling comprises signal emission time calculation, time delay, satellite position calculation and the single-pass measurement value to measure the station coordinate;
a third module, performing pseudo-range double-difference relative positioning to obtain a rover station approximate coordinate, wherein the rover station approximate coordinate is used as an initial value for subsequent fine calculation, and Kalman filtering is adopted in a pseudo-range relative positioning process;
a fourth module, which is used for respectively forming corresponding single difference and double difference measurement values between stations by using three combinations of an ultra-wide term combination (0, 1-1), a wide term combination (1, 0-1) and a W1 original phase measurement value (1, 0, 0), and checking the continuity of the single difference and double difference measurement values;
and a fifth module, wherein the parameter estimation adopts a network solution mode, and the estimation method is a least square algorithm to obtain the accurate coordinates of the rover station. The main flow is shown in fig. 3.
The method is based on the baseline solution of prior constraint, and the relation between the initial coordinate deviation and the integer ambiguity in the baseline solution of prior constraint is provided as a carrying condition for gradually refining various combined measured values; the accuracy of pseudo-range double-difference baseline calculation is analyzed by using data of a group of Beidou deformation monitoring networks, the data is used as a basis for selecting a combined measured value in Beidou three-frequency short baseline data processing based on prior constraint, the data processing of gradual refinement is carried out on pseudo-range double-difference calculation results according to the combined measured value with better characteristics, the gradual refinement is carried out by respectively using the ultra-wide item combination (0, 1, -1) and (1, 1, -2), (1, 0, -1), (1, -1, 0) combination and the W1 original phase measured value, and finally the Beidou three-frequency high-accuracy short baseline data processing is realized. The invention does not relate to the problems of cycle slip detection, ambiguity resolution and the like, and the calculation process is simpler. Meanwhile, in order to improve the data processing precision and reliability, the invention also provides a Beidou dual-mode fine data calculation method fused with the GPS, provides a mathematical model fused with the calculation, and lays a foundation for the subsequent multi-mode multi-system fused data processing so as to further improve the precision and reliability of the data processing of the Beidou three-mode fine calculation method fused with the GPS by coordinate prior.

Claims (10)

1. The Beidou tri-band fine solution method with the coordinate prior fused with the GPS is characterized in that a GPS high-precision monitoring model is utilized and expanded to short baseline vector solution of the GPS, initial values of baseline vectors are built step by step and are subjected to fine treatment step by step, the short baseline of a Beidou tri-band combined measured value is solved based on coordinate prior constraint, and dual-mode solution is carried out by fusing the Beidou and the GPS;
the Beidou tri-band fine resolving method based on coordinate prior fusion GPS comprises a base line resolving framework based on coordinate prior constraint, Beidou tri-band short base line resolving based on coordinate prior constraint and Beidou navigation tri-band phase combination measurement value refining, wherein the Beidou tri-band short base line resolving based on coordinate prior constraint comprises resolving bearing conditions, high-precision pseudo-range double-difference base line resolving and Beidou navigation tri-band phase combination measurement value refining;
the invention specifically comprises the following contents: firstly, screening out a combined measurement value with better characteristics according to the conditions which are favorable for fixing the integer ambiguity and improving the positioning precision based on the Beidou three-frequency combined measurement theory; analyzing the influence of the Beidou tri-band combined measurement value on ionospheric delay, tropospheric delay and measurement noise errors starting from multi-frequency phase combination definition, and screening out a typical combined measurement value with longer wavelength and weak ionospheric delay characteristics by long wavelength, weak ionospheric delay and small noise standards; secondly, a Beidou tri-band fine resolving method of coordinate prior fusion GPS is provided, and resolving carrying conditions of each step of fine process are given by analyzing the positioning precision of pseudo-range double differences in short baseline data processing, the relation between a coordinate initial value and integer ambiguity; selecting a proper phase combination measurement value based on the Beidou tri-band combination theory; based on a GPS high-precision monitoring model, the initial coordinates are refined step by step, and the accurate coordinates of the rover station are finally obtained.
2. The Beidou tri-band fine solution method for coordinate prior fusion GPS according to claim 1 is characterized by comprising the following concrete implementation processes: according to the decimetric point position coordinates provided by pseudo-range double differences, an ultra-wide lane combination (0, 1, -1) is utilized to obtain a first refined value of the rover coordinates through a global navigation satellite system data processing method based on coordinate prior constraints; performing secondary refinement treatment by using the first-step refined value of the initial coordinate as the combined refined initial value of (1, 1-2), (1, 0-1) and (1-1, 0) to obtain centimeter-level rover position coordinates; and taking the point location coordinate reaching the centimeter level after the secondary refining processing as an initial value of a global navigation satellite system data processing method based on coordinate prior constraint on the W1 measured value, and performing the tertiary refining processing to obtain the point location coordinate at the millimeter level.
3. The Beidou tri-band fine solution method for coordinate prior fusion GPS according to claim 1, characterized in that the baseline solution framework based on coordinate prior constraint is specifically: in the short-baseline relative positioning of the global navigation satellite system, the influence of the residual errors of the ionosphere and the troposphere after double difference can be eliminated, and the influence of multipath effect is weakened; when a certain cut-off height angle is set and a choke coil is adopted, the influence of multipath effect is nearly zero, so that the GPS double-difference phase measurement equation is as follows:
Figure FDA0003586135340000011
in the formula:
Figure FDA0003586135340000012
representing a double difference operator; a is the phase measurement in cycles; b is the geometric distance of the satellite survey station in meters, c is the wavelength of the carrier phase measured value in meters; m is the carrier phase integer ambiguity with the unit of cycle; dφThe unit is meter for phase measurement noise and unmodeled error, subscript m represents the satellite, and subscript r represents the receiver; when the deformation is less than a certain amount, determining the whole cycle number in the measured double difference values according to the whole cycle number in the calculated double difference values, wherein F is a reference station, G is a monitoring station, G' is the position of a G point after deformation, q and p are synchronous measurement satellites, and a satellite p with a larger altitude angle is taken as a reference satellite;
f, G the two-station phase double difference measurement is:
Figure FDA0003586135340000021
before deformation, the coordinates of the monitoring station G point are known, and the double difference distance calculation value is obtained by using the coordinates of F, G two points and the satellite position calculated by the satellite ephemeris:
Figure FDA0003586135340000022
the calculated double difference phase from equation 3 is:
Figure FDA0003586135340000023
in the short baseline data processing, after double differences, errors of an ionized layer, a troposphere and a multipath effect are well eliminated, and then a formula 2 and a formula 4 are substituted into a formula 1 to form a double difference measurement equation:
Figure FDA0003586135340000024
double-difference ambiguity when the G-point coordinates are precisely known
Figure FDA0003586135340000025
By passing
Figure FDA0003586135340000026
Directly rounding to obtain:
Figure FDA0003586135340000027
if the monitoring station G is deformed and generates displacement
Figure FDA0003586135340000028
After G', the double difference measurement values calculated by using the coordinates of the G point cannot satisfy equation 5, and their difference values are used
Figure FDA0003586135340000029
Represents:
Figure FDA00035861353400000210
then
Figure FDA00035861353400000211
In that it contains deformation information
Figure FDA00035861353400000212
According to the algorithm thought of no cycle slip and no ambiguity, the deformation amount
Figure FDA00035861353400000213
Less than a certain amount, formula 7 equal sign right end
Figure FDA00035861353400000214
Double-difference ambiguity determined by direct rounding
Figure FDA00035861353400000215
The double-difference ambiguity is still correct, namely the deformation does not influence the integer part of the phase double-difference measurement value, and only influences the decimal part of the measurement value;
Figure FDA00035861353400000216
contains only a fractional part of less than one band, exactly
Figure FDA00035861353400000217
The error equation is listed according to equation 1, and the deformation is calculated:
Figure FDA00035861353400000218
in the formula, a subscript m represents a satellite, a subscript r represents a receiver, and w, n and m are direction cosines in three directions of x, y and z.
4. The Beidou tri-band fine solution method for coordinate prior fusion GPS according to claim 1, characterized in that Beidou tri-band short baseline solution of coordinate prior constraint realizes short baseline data processing based on coordinate prior constraint, avoids integer ambiguity solution and cycle slip detection, first obtains initial coordinates of the rover station by pseudo-range double difference, then selects combined measurement values with longer wavelength and smaller noise to gradually refine calculation results according to the precision of the initial coordinates and the relation between the coordinate prior precision and the integer ambiguity, and finally obtains high-precision rover coordinate information.
5. The Beidou tri-band fine solution method for coordinate prior fusion GPS according to claim 1 is characterized in that solution carrying conditions are a baseline solution framework based on coordinate prior constraint, when an initial coordinate has a certain precision, the deviation between the initial coordinate and a real coordinate only affects the fractional part of double-difference ambiguity and does not affect the integer part of a phase double-difference measurement value, correct phase double-difference integer ambiguity can be obtained by calculation of the initial coordinate of a rover station, and the search process of the integer ambiguity is avoided; however, the key to realize this process is that the initial coordinate needs to ensure a certain precision so that the deviation value between the initial value and the true value does not affect the phase double difference whole-cycle part, i.e. there is a certain relationship between the deviation value and the whole-cycle ambiguity; the method comprises the steps of obtaining the relation between a deviation value and the integer ambiguity through derivation;
difference between two difference distance measurements
Figure FDA0003586135340000031
Amount of deformation and
Figure FDA0003586135340000032
the mathematical relationship of (1) is as follows:
Figure FDA0003586135340000033
Figure FDA0003586135340000034
representing a double difference operator; a is the phase measurement in cycles; b is the geometric distance of the satellite survey station in meters, c is the wavelength of the carrier phase measured value in meters; m is the carrier phase integer ambiguity with the unit of cycle; dφThe unit is meter for phase measurement noise and unmodeled error, subscript m represents the satellite, and subscript r represents the receiver; f is a reference station, G is a monitoring station, G' is the position of a deformed G point, q and p are synchronous measurement satellites, and a satellite p with a larger altitude angle is taken as a reference satellite; if the monitoring station G is deformed and generates displacement
Figure FDA0003586135340000035
After to point G', their difference is used
Figure FDA0003586135340000036
Represents;
amount of deformation
Figure FDA0003586135340000037
Further expressed as:
Figure FDA0003586135340000038
wherein,
Figure FDA0003586135340000039
is composed of
Figure FDA00035861353400000310
A unit vector in a direction;
carrying out the following steps of:
Figure FDA00035861353400000311
considering formula 4:
Figure FDA00035861353400000312
if the integer ambiguity is not considered, then:
Figure FDA00035861353400000313
the conditions need to be satisfied: formula 11 is less than 1 week to the right, i.e.:
Figure FDA00035861353400000314
due to the fact that
Figure FDA00035861353400000315
Therefore:
Figure FDA00035861353400000316
then when the condition is satisfied:
Figure FDA0003586135340000041
when the formula 16 is satisfied, the condition of avoiding integer ambiguity resolution can be satisfied; the residual error of the carrier phase measurement value measured by the short baseline after double difference is very small, and when the residual error of the double difference is considered, the residual error term of the double difference should be added to the left term of the formula 16.
6. The Beidou tri-band fine solution method for coordinate prior fusion GPS according to claim 5, characterized in that in the pseudo-range double-difference baseline solution with high precision, the short baseline solution considering coordinate prior constraint is pseudo-range double-difference solution firstly to obtain the initial coordinate of the rover station; the method is based on a pseudo-range double-difference baseline resolving method, and the accuracy of the pseudo-range double-difference can be resolved to be used as a reference for selecting a subsequent three-frequency linear combination measured value;
the non-differenced pseudorange measurement equation is:
Figure FDA0003586135340000042
in the formula,
Figure FDA0003586135340000043
is a measurement of the pseudorange,
Figure FDA0003586135340000044
the geometric distance from the station to the satellite, o is the speed of light propagation in vacuum, in m/s, fj(t) is the satellite clock error, bF(t) is the receiver clock difference,
Figure FDA0003586135340000045
in order to be a tropospheric delay parameter,
Figure FDA0003586135340000046
for ionospheric errors, a single difference equation can be composed as follows:
Figure FDA0003586135340000047
the double difference equation is:
Figure FDA0003586135340000048
wherein:
Figure FDA0003586135340000049
after linearizing equation 19, the measurement equation is constructed:
Figure FDA00035861353400000410
and solving a pseudo-range double-difference solution of the baseline through indirect adjustment or Kalman filtering.
7. The Beidou tri-band fine solution method for coordinate prior fusion GPS according to claim 6 is characterized in that the invention simulates and analyzes the double-difference precision of the short baseline pseudo-range in the high, middle and low latitudes, and the conclusion is as follows: the error in the short baseline resolved point locations was between 10cm and 20cm, with an average of 15.1cm and a maximum of 22.1 cm.
The invention utilizes the measured data of the Beidou deformation monitoring network to analyze the precision of pseudo-range double differences, the deformation monitoring network consists of a reference station (JZ01) and four monitoring stations (JC01, JC02, JC03 and JZ02), the length of a base line is 29m to 280m, the data processing adopts two groups of data of GPS and Beidou of a whole day to carry out four-hour time interval solution respectively, six time intervals are solved totally, the solution result is differed with the real value of each measuring station, residual values in X, Y, Z three directions are solved, and the result is as follows: the Beidou pseudo-range double-difference calculation result of the solution in four hour periods is better than the result of the GPS; the error of the Beidou pseudorange double difference in the point position is 9cm to 39cm under the condition of a short baseline, and the precision of the error of 9cm to 39cm in the point position is enough as the initial value of the Beidou tri-band short baseline data processing method based on coordinate constraint.
The invention carries out single epoch resolving test on the Beidou pseudorange double-difference positioning to obtain the resolving result of the single epoch pseudorange double-difference positioning, the test carries out single epoch pseudorange double-difference processing by utilizing one of four baselines in a network, and the result is as follows: under the condition of a short baseline, the fluctuation range of the pseudo-range double-difference single-epoch calculation result is within 1.46 meters, and most of the pseudo-range double-difference single-epoch calculation result is within 0.48 meters, so that the positioning accuracy of the Beidou short baseline pseudo-range double-difference in the single-epoch calculation mode is in the decimeter level.
8. The Beidou tri-band fine solution method for coordinate prior fusion GPS according to claim 5 is characterized in that in the refinement of Beidou navigation tri-band phase combination measurement values, when the deviation of the rover coordinate prior value is required to be less than c/2 by a coordinate prior constrained short baseline data processing method, the whole cycle number in the measured double difference value can be determined according to the whole cycle number in the double difference value obtained by the initial coordinate of the rover, so that the detection and repair of the cycle slip and the whole cycle ambiguity resolution problem are avoided only by considering the part less than one whole cycle during data processing, and the range of the deformation amount which can be determined is determined by the size of the carrier wave length;
the point position precision of the pseudo-range double-difference calculation result is in the decimeter level under the static condition, and the precision is within 2 meters under the dynamic single epoch condition, so that a combined measurement value with the wavelength of 4 meters and the noise of about 1 decimeter can be selected during one-time refinement; the ultra-wide lane combination (0, 1, -1) with the wavelength of 4.88 meters and the noise of only 0.057 meters is very suitable for being used as a combined measurement value of one-time refinement; when the combination is used for refining, the initial value deviation of the coordinates can reach 2.43 meters, namely the initial value deviation of the coordinates is within 2.43 meters, and the combination can be refined accurately.
After the ultra-wide lane combination is used for obtaining the first refinement, the point coordinate precision is poor, the noise is in the decimeter level, and the second refinement needs to be carried out by using other combined measurement values; the wavelengths of the combined measurement values of (1, 1, -2), (1, 0, -1) and (1, -1, 0) are all about 1m, the noise is centimeter-level, the point location coordinates can be further refined to centimeter-level, more accurate point location coordinates can be obtained, and the method is suitable for refining the point location coordinates obtained by the ultra-wide roadway combined measurement values.
After the secondary refinement is completed, the precision of the point location coordinate is centimeter level, at the moment, the three refinements are performed, and the point location coordinate can be improved to millimeter level only by using the W1 original measurement value to perform the same data processing method; a global navigation satellite system data processing algorithm based on coordinate prior constraint provides an initial value through pseudo-range double differences, and millimeter-level results can be obtained through three-step refining processing.
9. The Beidou tri-band fine solution method for coordinate prior fusion GPS according to claim 8, characterized in that the specific algorithm for the refinement of the Beidou navigation tri-band phase combination measurement value is as follows:
step one, according to point position coordinates provided by pseudo-range double differences, an ultra-wide lane combination (0, 1, -1) is utilized to obtain a first refined value of the rover coordinate through a global navigation satellite system data processing method based on coordinate prior constraint;
step two, taking the primary refined value of the initial coordinate obtained in the step one as the combined refined initial value of (1, 1-2), (1, 0-1) and (1-1, 0), and performing secondary refined value to obtain the centimeter-level rover position coordinate;
taking the centimeter-level point coordinate subjected to secondary refining as an initial value of a global navigation satellite system data processing method based on coordinate prior constraint on the W1 measured value, and performing secondary refining to obtain the millimeter-level point coordinate;
and fourthly, obtaining accurate point location coordinates of the mobile station, then obtaining baseline information, and outputting.
10. The Beidou tri-band fine solution method with the coordinate prior fused with the GPS according to claim 1 is characterized in that the Beidou dual-mode fine data solution of the GPS is obtained by adding the GPS measurement data in the last refinement process of the Beidou combined measurement value refinement;
when the Beidou and GPS are subjected to data fusion processing, firstly, reference unification is carried out, namely unification between a WGS-84 coordinate system and a CGCS2000 coordinate system and unification between GPST and BDT;
the coordinate prior constraint-based short baseline data processing method can directly obtain double-difference ambiguity parameters, so that only three-dimensional position parameters remain in a double-difference measurement equation, and the simplified Beidou/GPS double-difference carrier phase measurement equation is as follows:
Figure FDA0003586135340000061
in the formula:
Figure FDA0003586135340000062
dX represents a relative coordinate correction vector;
Figure FDA0003586135340000063
expressing a double-difference integer ambiguity vector, and directly obtaining a double-difference ambiguity value through a constraint algorithm based on coordinate prior; g is a coefficient matrix corresponding to dX, W is a constant term vector, (x)0,y0,z0) Is the initial position of the rover (x)n，yn，zn) As satellite position, s0The geometric distance between the initial position of the user and the satellite is defined, and n is the measured satellite of the same system; during data processing, the double-difference process is carried out in the same system, n GPS double-difference measurement equations can be obtained by n GPS satellites, m Beidou satellites can obtain m-1 Beidou double-difference measurement equations, n + m-2 measurement equations are in total, and least square or Kalman filtering is adopted in the adjustment process;
the stochastic model is: suppose that
Figure FDA0003586135340000064
The variance of the i satellite phase measurements and the pseudorange measurements for rover station q,
Figure FDA0003586135340000065
variance of the i satellite phase measurement and the pseudorange measurement, respectively, of the reference station s, then:
Figure FDA0003586135340000066
Figure FDA0003586135340000067
the covariance matrix of the double difference measurement values can be obtained according to the error propagation law as follows:
Figure FDA0003586135340000071
in the formula:
Figure FDA0003586135340000072
Figure FDA0003586135340000073
Saa、SQQthe method comprises the following steps of respectively using a double-difference carrier variance-covariance matrix and a double-difference pseudo-range variance-covariance matrix of an i-number satellite as a reference satellite, adopting an altitude weighting rule, and giving the variance of a non-difference original measured value according to an altitude:
Figure FDA0003586135340000074
wherein I represents the satellite altitude, fa0、fQ0Respectively representing standard deviations of the carrier wave and the pseudo range, respectively taking the standard deviations as 0.002 meter and 1 meter, and obtaining a corresponding weight matrix by inverting the square deviation-covariance. After the random model of a single system is determined, the systems have no relevance, so the weight ratio between the GPS and the Beidou system is set to be 1:1, namely a combined measurement value weight array is as follows:
Figure FDA0003586135340000075
SGPS、SBDSand respectively representing measurement value weight arrays of the GPS and the Beidou satellite navigation system.
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