CN113253322B - Mobile carrier relative position resolving method based on double antennas - Google Patents
Mobile carrier relative position resolving method based on double antennas Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/43—Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
- G01S19/44—Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
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Abstract
The invention discloses a method for resolving the relative position of a mobile carrier based on double antennas, which is used for resolving the position coordinates of the mobile carrier provided with the double antennas relative to a reference station and comprises the following steps: establishing a double-difference observed quantity random model; establishing a double-difference observation model under the constraint of the base line length between the double antennas by using the pseudo-range original observed quantity and the carrier phase original observed quantity of the double antennas on the mobile carrier, and solving the base line vector and the integer ambiguity parameter between the double antennas according to the double-difference observation model; and establishing a relative positioning model by utilizing the dual-antenna observed quantity and the reference station observed quantity on the mobile carrier, merging the obtained dual-antenna baseline vector and the variance-covariance matrix of the baseline vector obtained by solving into the relative positioning model as prior constraint information, carrying out integer ambiguity solving, and estimating the position coordinate of the mobile carrier relative to the reference station. The invention can effectively utilize the length information of the double-antenna base line, improve the success rate of resolving the integer ambiguity and enhance the reliability and accuracy of relative positioning.
Description
Technical Field
The invention relates to the technical field of satellite navigation, in particular to a mobile carrier relative position resolving method based on double antennas.
Background
The relative positioning technology based on satellite navigation carrier phase difference can accurately solve the three-dimensional position information of the mobile carrier relative to the reference station, the precision can reach centimeter level or even millimeter level, and the relative positioning technology has key effects in the military fields of unmanned aerial vehicle formation flight, aircraft landing, landing and other combat tasks or experimental test, simulation training and other civil fields, as well as in the civil fields of deformation monitoring, precise agriculture and the like. The basic principle of the relative positioning technology based on satellite navigation carrier phase difference is to make difference between satellite original observation data received by an antenna on a mobile carrier and reference station antenna data, thereby establishing an observation equation reflecting a functional relation between the observation quantity and a base line vector of the reference station pointing to the mobile carrier, and solving the base line vector to realize the relative position calculation of the mobile carrier. The core of the high-precision relative positioning is the correct resolving of the integer ambiguity, and the rapidity and the reliability of the integer ambiguity resolving are particularly important for high-safety applications such as unmanned aerial vehicle formation flight, carrier-based aircraft landing and the like.
With the rapid development of global or regional satellite navigation systems, satellite navigation technology has entered the era of multi-system fusion, visible satellites and available frequency resources have been significantly improved, and under typical observation conditions, the number of visible satellites is no longer a key factor for restricting high-precision relative positioning. However, in weak observation environments such as urban canyons, dense mountain forests and the like, the limited number of available satellites is still a prominent problem, so that the success rate of resolving the integer ambiguity may be obviously reduced, and the availability and reliability of high-precision relative positioning are greatly restricted. At present, in order to improve the resolving performance, besides adding other navigation devices such as an inertial sensor to perform integrated navigation, it is effective to increase the number of satellite antennas mounted on a carrier, such as a common dual-antenna device. Because the double antennas are fixed on the carrier, the inherent baseline length information between the antennas can be used as an additional nonlinear constraint condition to be fused into an observation equation, and the effect of parameter estimation is enhanced. Based on the technical conception, in the dual-antenna orientation, the minimum square drop correlation adjustment algorithm (C-LAMBDA algorithm) with the constraint of the base line length is provided in the prior art, and the reliability of the orientation can be obviously improved. Specific C-LAMBDA algorithm steps can be found, for example, in the prior art literature: teunissen P J G. Integer least-squares theory for the GNSS compact. Journal of Geodesy,2010,84 (7): 433-447. Although compared with a single antenna, the dual antennas can increase the observed quantity, enhance the intensity of an observation model and further facilitate parameter estimation, in the field of relative positioning, the dual antennas on the carrier generally only mutually back up, and although the usability in positioning calculation can be improved to a certain extent, the baseline length information among the antennas is not fully utilized, and the effective improvement of the reliability of the whole-cycle ambiguity calculation in high-precision relative positioning is difficult to realize.
Disclosure of Invention
In order to solve part or all of the technical problems in the prior art, the invention provides a mobile carrier relative position resolving method based on double antennas.
The invention discloses a method for resolving the relative position of a mobile carrier based on double antennas, which is used for resolving the position coordinates of the mobile carrier provided with the double antennas relative to a reference station, and comprises the following steps:
establishing a double-difference observed quantity random model;
establishing a double-difference observation model under the constraint of a base line length between double antennas by using the pseudo-range original observed quantity and the carrier phase original observed quantity of the double antennas on the mobile carrier, and solving a base line vector and a whole-cycle ambiguity parameter between the double antennas according to the double-difference observation model;
and establishing a relative positioning model by using the dual-antenna observed quantity and the reference station observed quantity on the mobile carrier, merging the baseline vector between the dual antennas and the variance-covariance matrix of the baseline vector into the relative positioning model as prior constraint information, carrying out integer ambiguity resolution, and estimating the position coordinate of the mobile carrier relative to the reference station.
In some alternative embodiments, the establishing the random model of the double difference observables includes:
setting: the number of visible satellites at a certain moment is s+1, and the two receivers are respectively denoted as a receiver n and a receiver m;
for the receiver n and the receiver m, establishing a double difference observed random model as follows:
wherein Q represents a double difference observance variance-covariance matrix,representing inter-satellite differential matrices, e s S×1 column vector representing 1 for all elements, I s Represents an s-dimensional unit array, O 1 S×1 column vector representing 0 for all elements, O s Representing an s-dimensional zero matrix-> and />Representing the variance of the observed non-differential carrier phase when said receiver n and said receiver m receive the ith satellite signal, respectively,/o> and />Representing the non-differential pseudorange observed quantity variance of the ith satellite signal received by the receiver n and the receiver m, respectively.
In some alternative embodiments, the settings are: the mobile carrier is provided with an antenna m 1 And antenna m 2 The base line length between the two antennas is l, and the accuracy of satellite signal observation of each antenna and each receiver of the mobile carrier and the reference station is consistent;
the method for solving the baseline vector and the integer ambiguity parameter between the double antennas by using the pseudo-range original observed quantity and the carrier phase original observed quantity of the double antennas on the mobile carrier to establish a double-difference observation model under the constraint of the baseline length between the double antennas comprises the following steps:
establishing a double-difference observation equation under the constraint of the base line length between the double antennas according to a formula II by utilizing the pseudo-range original observed quantity and the carrier phase original observed quantity of the double antennas on the mobile carrier;
wherein E represents the expectation operator, D represents the variance operator,for the antenna m 1 And the antenna m 2 Three-dimensional baseline vector between->Representing baseline vector +.>The observation vector comprises an s-dimensional double-difference carrier phase observed quantity and an s-dimensional double-difference pseudo-range observed quantity, < ->Is baseline vector->S-dimensional double-difference integer ambiguity parameter with each element being an integer, A represents coefficient matrix of double-difference integer ambiguity, B represents coefficient matrix of baseline vector, and +.>Representing the observation vector +.>Variance-covariance matrix of (a);
based on the double-difference observation equation, performing integer ambiguity search by adopting a C-LAMBDA algorithm to obtain a double-difference integer ambiguity fixed solution
Fixing the solution according to the double-difference integer ambiguityCalculating a baseline vector between the double antennas by using a formula III;
wherein ,representing the saidBaseline vector between dual antennas.
In some optional embodiments, the establishing a relative positioning model by using the dual-antenna observables and the reference station observables on the mobile carrier, integrating the inter-dual-antenna baseline vector and the variance-covariance matrix of the baseline vector into the relative positioning model as prior constraint information, performing integer ambiguity resolution, and estimating the position coordinates of the mobile carrier relative to the reference station, including:
using the antenna m on the mobile carrier 1 Establishing an antenna m on the mobile carrier as in equation four 1 And a first relative positioning observation equation between the reference station antennas:
wherein ,for the antenna m 1 Three-dimensional baseline vector between the reference station antenna,>representing baseline vector +.>The observation vector comprises an s-dimensional double-difference carrier phase observed quantity and an s-dimensional double-difference pseudo-range observed quantity, < ->Is the baseline vectorS-dimensional double-difference integer ambiguity parameter with all the elements being integers>Representing the observation vector +.>Variance-covariance matrix of (a);
using the antenna m on the mobile carrier 2 Establishing an antenna m on the mobile carrier as in equation five 2 And a second relative positioning observation equation between the reference station antennas:
wherein ,for the antenna m 2 Three-dimensional baseline vector between the reference station antenna,>representing baseline vector +.>The observation vector comprises an s-dimensional double-difference carrier phase observed quantity and an s-dimensional double-difference pseudo-range observed quantity, < ->Is the baseline vectorS-dimensional double-difference integer ambiguity parameter with all the elements being integers>Representing the observation vector +.>Variance-covariance matrix of (a);
using the baseline vectorAnd said double difference integer ambiguity fix solution +.>Correcting the formula five into a formula six;
combining the formula IV and the formula VI to obtain a formula seven;
wherein ,H＝[A T A T ] T ，G＝[B T B T ] T ，represents the Kronecker product;
according to the least square criterion, solving the integer ambiguity parameter in the seventh formula by using the eighth formulaLeast square floating solution and variance-covariance matrix of the least square floating solution;
wherein ,representing the integer ambiguity parameter +.>Least squares floating of (2)Click solution, alleviate->Variance-covariance matrix representing the least squares solution, +.>I represents an identity matrix;
taking a formula six as input, and adopting a least square drop correlation adjustment algorithm to search and test the integer ambiguity to obtain the integer ambiguity parameterInteger solution of->
Based on the integer solutionSolving a position coordinate of the mobile carrier relative to the reference station by using a formula nine;
wherein ,representing the position coordinates of the moving carrier relative to the reference station.
The technical scheme of the invention has the main advantages that:
according to the method for solving the relative position of the mobile carrier based on the double antennas, the baseline vector and the integer ambiguity parameter between the double antennas are solved, and the solved baseline vector and integer ambiguity parameter between the double antennas are used as prior information to be fused into a relative positioning observation equation of the mobile carrier for solving the relative position, so that the baseline length information of the double antennas can be effectively utilized, the success rate of the integer ambiguity solving is improved, and the reliability and accuracy of relative positioning are enhanced.
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The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention and without limitation to the invention. In the drawings:
fig. 1 is a flowchart of a mobile carrier relative position calculating method based on dual antennas according to an embodiment of the present invention;
fig. 2 is a schematic diagram showing a comparison between a resolution success rate of resolving integer ambiguity of relative positioning under different satellite numbers and an unconstrained condition according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to specific embodiments of the present invention and corresponding drawings. It will be apparent that the described embodiments are only some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The following describes in detail the technical scheme provided by the embodiment of the invention with reference to the accompanying drawings.
Referring to fig. 1, an embodiment of the present invention provides a dual-antenna based moving carrier relative position resolving method for resolving position coordinates of a moving carrier mounted with dual antennas with respect to a reference station, including:
establishing a double-difference observed quantity random model;
establishing a double-difference observation model under the constraint of the base line length between the double antennas by using the pseudo-range original observed quantity and the carrier phase original observed quantity of the double antennas on the mobile carrier, and solving the base line vector and the integer ambiguity parameter between the double antennas according to the double-difference observation model;
and establishing a relative positioning model by utilizing the dual-antenna observed quantity and the reference station observed quantity on the mobile carrier, merging the baseline vector between the dual antennas and the variance-covariance matrix of the baseline vector into the relative positioning model as prior constraint information, carrying out integer ambiguity resolution, and estimating the position coordinate of the mobile carrier relative to the reference station.
The following specifically describes the steps and principles of the method for calculating the relative position of a mobile carrier based on dual antennas according to an embodiment of the present invention.
Specifically, in an embodiment of the present invention, a dual difference observed random model is established, including the following steps:
setting: the number of visible satellites at a certain moment is s+1, and the two receivers are respectively denoted as a receiver n and a receiver m;
for receiver n and receiver m, building a double difference observance random model as:
where Q represents a double difference observance variance-covariance matrix,representing inter-satellite differential matrices, e s S×1 column vector representing 1 for all elements, I s Represents an s-dimensional unit array, O 1 S×1 column vector representing 0 for all elements, O s Representing an s-dimensional zero matrix-> and />Representing the variance of the observed non-differential carrier phase when receiver n and receiver m receive the ith satellite signal, respectively,/-> and />Representing the reception of the ith satellite signal by receiver n and receiver m, respectivelyNon-differential pseudorange observed quantity variance at sign.
Wherein the observed quantity variance and />The value of (2) can be obtained by establishing a conventional equal weight model, a satellite elevation model and the like through real-time calculation.
If the antennas and the receivers on the mobile carrier are the same brand or similar brands with the reference station antennas and the receivers, the observed quantity noise generated when the satellite signals are measured by different receivers can be considered to be subjected to the same distribution, and the double-difference observed quantity random model between any two antennas can be represented by using a variance-covariance matrix Q in a formula I.
Further, setting: two antennas are arranged on the mobile carrier, and the two antennas are respectively indicated as an antenna m 1 And antenna m 2 The base line length between the two antennas is l, and the accuracy of satellite signal observation of each antenna and each receiver of the mobile carrier and the reference station is consistent;
based on the setting, a double-difference observation model under the constraint of the base line length between the double antennas is established by using the pseudo-range original observed quantity and the carrier phase original observed quantity of the double antennas on the mobile carrier, and the base line vector and the whole-cycle ambiguity parameter between the double antennas are solved according to the double-difference observation model, and the method comprises the following steps:
establishing a double-difference observation equation under the constraint of the base line length between the double antennas as shown in a formula II by using the pseudo-range original observed quantity and the carrier phase original observed quantity of the double antennas on the mobile carrier;
where E represents the expectation operator, D represents the variance operator,for antenna m 1 And antenna m 2 Three-dimensional baseline vector between->Representing baseline vector +.>The observation vector comprises an s-dimensional double-difference carrier phase observed quantity and an s-dimensional double-difference pseudo-range observed quantity, < ->Is baseline vector->S-dimensional double-difference integer ambiguity parameter with each element being an integer, A represents coefficient matrix of double-difference integer ambiguity, B represents coefficient matrix of baseline vector, and +.>Representing the observation vector +.>Variance-covariance matrix of (a);
based on a double-difference observation equation, a C-LAMBDA algorithm (least square drop correlation adjustment algorithm with base line length constraint) is adopted to search the integer ambiguity, and a double-difference integer ambiguity fixed solution is obtained
Fixed solution based on double difference integer ambiguityCalculating a baseline vector between the double antennas by using a formula III;
in the formula,representing the baseline vector between the dual antennas.
Wherein, since the accuracy of satellite signal observation by each antenna and each receiver of the mobile carrier and the reference station is consistent, there areQ represents the double difference observables variance-covariance matrix in equation one.
Specific C-LAMBDA algorithm steps can be found, for example, in the prior art literature: teunissen P J G. Integer least-squares theory for the GNSS compact. Journal of Geodesy,2010,84 (7): 433-447.
Further, the above-described solution yields a baseline vector between the dual antennasAnd double difference integer ambiguity fix solutionOn the basis of the method, a relative positioning model is established by utilizing the observed quantity of the double antennas and the observed quantity of the reference station on the mobile carrier, the base line vector between the double antennas and the variance-covariance matrix of the base line vector are used as prior constraint information to be fused into the relative positioning model, the whole-cycle ambiguity solution is carried out, and the position coordinates of the mobile carrier relative to the reference station are estimated, and the method comprises the following steps:
using antennas m on a moving carrier 1 The observed quantity of the reference station antenna r and the observed quantity of the reference station antenna r are established as shown in a formula four 1 And a first relative positioning observation equation between the reference station antenna r:
where E represents the expectation operator, D represents the variance operator,for antenna m 1 Three-dimensional baseline vector between reference station antenna r, < >>Representing baseline vector +.>The observation vector comprises an s-dimensional double-difference carrier phase observed quantity and an s-dimensional double-difference pseudo-range observed quantity, < ->Is baseline vector->S-dimensional double-difference integer ambiguity parameter with each element being an integer, A represents coefficient matrix of double-difference integer ambiguity, B represents coefficient matrix of baseline vector, and +.>Representing the observation vector +.>Variance-covariance matrix of (a);
using antennas m on a moving carrier 2 The observed quantity of the reference station antenna r and the observed quantity of the reference station antenna r are established as shown in a formula five 2 And a second relative positioning observation equation between the reference station antenna r:
where E represents the expectation operator, D represents the variance operator,for antenna m 2 Three-dimensional baseline vector between reference station antenna r, < >>Representing baseline vector +.>The observation vector comprises an s-dimensional double-difference carrier phase observed quantity and an s-dimensional double-difference pseudo-range observed quantity, < ->Is baseline vector->S-dimensional double-difference integer ambiguity parameter with each element being an integer, A represents coefficient matrix of double-difference integer ambiguity, B represents coefficient matrix of baseline vector, and +.>Representing the observation vector +.>Variance-covariance matrix of (a);
using baseline vectorsAnd double difference integer ambiguity fix solution +.>Correcting the formula five into a formula six;
due toThe baseline vector +.>And double difference integer ambiguity fix solution +.>Correcting the formula five into a formula six;
combining the formula IV and the formula VI to obtain a formula seven;
in the formula,H＝[A T A T ] T ，G＝[B T B T ] T ，represents the Kronecker product;
since the accuracy of satellite signal observation by each antenna and each receiver of the mobile carrier and the reference station is uniform, there are and />
According to the least square criterion, solving the integer ambiguity parameter in the seventh formula by using the eighth formulaLeast square floating solution and variance-covariance matrix of the least square floating solution;
in the formula,representing integer ambiguity parameter +.>Least squares floating point solution of +.>Variance-covariance matrix representing least squares floating-point solution, +.>I represents an identity matrix;
taking a formula six as input, and adopting a least square drop correlation adjustment algorithm to search and test the integer ambiguity to obtain an integer ambiguity parameterInteger solution of->
Based on integer solutionSolving the position coordinates of the mobile carrier relative to the reference station by using a formula nine;
in the formula,representing the position coordinates of the moving carrier relative to the reference station.
According to the method for solving the relative position of the mobile carrier based on the double antennas, provided by the embodiment of the invention, the baseline vector and the integer ambiguity parameter between the double antennas are solved, the solved baseline vector and integer ambiguity parameter between the double antennas are used as prior information to be fused into a relative positioning observation equation of the mobile carrier for solving the relative position, so that the baseline length information of the double antennas can be effectively utilized, the success rate of the integer ambiguity solving is improved, and the reliability and the accuracy of relative positioning are enhanced.
The following describes the beneficial effects of the mobile carrier relative position resolving method based on dual antennas according to an embodiment of the present invention with reference to specific examples.
Establishing a double-difference observed quantity random model;
taking three antennas of measured data at a time as an example, at time t=1050, 6 GPS satellites (s=5) are observed in total of #2, #6, #12, #17, #19, #28, and the inter-satellite differential matrix is
Constructing an equal-weight random model, and taking the non-differential carrier phase observed quantity precision and the non-differential pseudo-range observed quantity precision as sigma respectively φ,n,i ＝σ φ,m,i＝3mm and σp,n,i ＝σ p,m,i =0.3m, then the double difference observed quantity variance-covariance matrix between any two antennas can be expressed as
Establishing a double-difference observation model under the constraint of the base line length between the double antennas by using the pseudo-range original observed quantity and the carrier phase original observed quantity of the double antennas on the mobile carrier, and solving the base line vector and the integer ambiguity parameter between the double antennas according to the double-difference observation model;
taking the same test as an example, an antenna m 1 And antenna m 2 The inter-baseline length l is known as 3.28m, the double difference observation vector in equation twoCoefficient matrix of double-difference integer ambiguity +.>Coefficient matrix of baseline vector->
Solving by adopting C-LABMA algorithm to obtain double-difference integer ambiguity fixed solutionBaseline vector between double antennas->
Establishing a relative positioning model by utilizing the observed quantity of the double antennas and the observed quantity of the reference station on the mobile carrier, taking the baseline vector between the double antennas and the variance-covariance matrix of the baseline vector as priori constraint information to be fused into the relative positioning model, carrying out integer ambiguity resolution, and estimating the position coordinates of the mobile carrier relative to the reference station;
taking the same test as an example, the antenna m on the mobile carrier 1 The double difference observation vector formed between the reference station antenna r isAntenna m on mobile carrier 2 The double difference observation vector formed between the reference station antenna r isSubstituting the solved fixed solution +.>And baseline vector->Available->
According to the least square criterion, calculating to obtain the ambiguity by using a formula eightThe least squares floating solution and the variance-covariance matrix of (2) are: />
Adopts LAMBDA algorithm (least square drop correlation adjustment algorithm) and is based on least square floating point solutionAnd its variance-covariance matrix->Performing ambiguity search and check to obtain integer solution +.>Solving the integer->Carry over formula nine to get +.>I.e. the exact position coordinates of the moving carrier with respect to the reference station.
Referring to fig. 2, fig. 2 is a schematic diagram showing a comparison between a resolution success rate of a relative positioning integer ambiguity with different satellite numbers and an unconstrained condition in a resolving method according to an embodiment of the present invention, in fig. 2, a horizontal axis represents a visible satellite number, a vertical axis represents a resolution success rate of an integer ambiguity obtained by statistics using a conventional unconstrained method and a resolving method provided by an embodiment of the present invention, and a data duration is 1200s. Obviously, by adopting the resolving method provided by the embodiment of the invention, the resolving success rate of the integer ambiguity is higher than that of the traditional unconstrained method under the condition of different visible satellite numbers, and therefore, the method provided by the embodiment of the invention can effectively improve the integer ambiguity estimating effect and enhance the reliability and accuracy of relative positioning.
It should be noted that in this document, relational terms such as "first" and "second" and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. In this context, "front", "rear", "left", "right", "upper" and "lower" are referred to with respect to the placement state shown in the drawings.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting thereof; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (1)
1. A method for resolving a relative position of a moving carrier based on dual antennas, the method for resolving a position coordinate of the moving carrier mounted with dual antennas with respect to a reference station, the method comprising:
establishing a double-difference observed quantity random model;
establishing a double-difference observation model under the constraint of a base line length between double antennas by using the pseudo-range original observed quantity and the carrier phase original observed quantity of the double antennas on the mobile carrier, and solving a base line vector and a whole-cycle ambiguity parameter between the double antennas according to the double-difference observation model;
establishing a relative positioning model by using the dual-antenna observed quantity and the reference station observed quantity on the mobile carrier, integrating a baseline vector between the dual antennas and a variance-covariance matrix of the baseline vector into the relative positioning model as prior constraint information, carrying out integer ambiguity resolution, and estimating a position coordinate of the mobile carrier relative to the reference station;
the establishing the double difference observed quantity random model comprises the following steps:
setting: the number of visible satellites at a certain moment is s+1, and the two receivers are respectively denoted as a receiver n and a receiver m;
for the receiver n and the receiver m, establishing a double difference observed random model as follows:
wherein Q represents a double difference observance variance-covariance matrix,representing inter-satellite differential matrices, e s S×1 column vector representing 1 for all elements, I s Represents an s-dimensional unit array, O 1 S×1 column vector representing 0 for all elements, O s Representing an s-dimensional zero matrix-> and />Representing the variance of the observed non-differential carrier phase when said receiver n and said receiver m receive the ith satellite signal, respectively,/o> and />Representing non-differential pseudorange observed quantity variances when the receiver n and the receiver m receive the ith satellite signal, respectively;
setting: the mobile carrier is provided with an antenna m 1 And antenna m 2 The base line length between the two antennas is l, and the accuracy of satellite signal observation of each antenna and each receiver of the mobile carrier and the reference station is consistent;
the method for solving the baseline vector and the integer ambiguity parameter between the double antennas by using the pseudo-range original observed quantity and the carrier phase original observed quantity of the double antennas on the mobile carrier to establish a double-difference observation model under the constraint of the baseline length between the double antennas comprises the following steps:
establishing a double-difference observation equation under the constraint of the base line length between the double antennas according to a formula II by utilizing the pseudo-range original observed quantity and the carrier phase original observed quantity of the double antennas on the mobile carrier;
wherein E represents the expectation operator, D represents the variance operator,for the antenna m 1 And the antenna m 2 Three-dimensional baseline vector between->Representing baseline vector +.>The observation vector comprises an s-dimensional double-difference carrier phase observed quantity and an s-dimensional double-difference pseudo-range observed quantity, < ->Is baseline vector->S-dimensional double with all the elements being integersThe difference integer ambiguity parameter, A represents the coefficient matrix of double difference integer ambiguities, B represents the coefficient matrix of the baseline vector,>representing the observation vector +.>Variance-covariance matrix of (a);
based on the double-difference observation equation, performing integer ambiguity search by adopting a C-LAMBDA algorithm to obtain a double-difference integer ambiguity fixed solution
Fixing the solution according to the double-difference integer ambiguityCalculating a baseline vector between the double antennas by using a formula III;
wherein ,representing baseline vectors between the dual antennas;
establishing a relative positioning model by using the dual-antenna observed quantity and the reference station observed quantity on the mobile carrier, integrating the baseline vector between the dual antennas and the variance-covariance matrix of the baseline vector into the relative positioning model as prior constraint information, performing integer ambiguity solving, and estimating the position coordinates of the mobile carrier relative to the reference station, wherein the method comprises the following steps:
using the antenna m on the mobile carrier 1 Establishing an antenna m on the mobile carrier as in equation four 1 And a first relative positioning observation equation between the reference station antennas:
wherein ,for the antenna m 1 Three-dimensional baseline vector between the reference station antenna,>representing baseline vector +.>The observation vector comprises an s-dimensional double-difference carrier phase observed quantity and an s-dimensional double-difference pseudo-range observed quantity, < ->Is baseline vector->S-dimensional double-difference integer ambiguity parameter with all the elements being integers>Representing the observation vector +.>Variance-covariance matrix of (a);
using the antenna m on the mobile carrier 2 Establishing an antenna m on the mobile carrier as in equation five 2 And a second relative positioning observation equation between the reference station antennas:
wherein ,for the antenna m 2 Three-dimensional baseline vector between the reference station antenna,>representing baseline vector +.>The observation vector comprises an s-dimensional double-difference carrier phase observed quantity and an s-dimensional double-difference pseudo-range observed quantity, < ->Is baseline vector->S-dimensional double-difference integer ambiguity parameter with all the elements being integers>Representing the observation vector +.>Variance-covariance matrix of (a);
using the baseline vectorAnd said double difference integer ambiguity fix solution +.>Correcting the formula five into a formula six;
combining the formula IV and the formula VI to obtain a formula seven;
wherein ,H＝[A T A T ] T ，G＝[B T B T ] T ，/> represents the Kronecker product;
according to the least square criterion, solving the integer ambiguity parameter in the seventh formula by using the eighth formulaLeast square floating solution and variance-covariance matrix of the least square floating solution;
wherein ,representing the integer ambiguity parameter +.>Least squares floating point solution of +.>Variance-covariance matrix representing the least squares solution, +.>I represents an identity matrix;
taking a formula six as input, and adopting a least square drop correlation adjustment algorithm to search and test the integer ambiguity to obtain the integer ambiguity parameterInteger solution of->
Based on the integer solutionSolving a position coordinate of the mobile carrier relative to the reference station by using a formula nine;
wherein ,representing the position coordinates of the moving carrier relative to the reference station.
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