CN110531394A - A kind of fuzziness fast resolution algorithm and device based on case theory and least square method - Google Patents
A kind of fuzziness fast resolution algorithm and device based on case theory and least square method Download PDFInfo
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- 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
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Abstract
The present invention proposes a kind of fuzziness fast resolution algorithm and device based on case theory and least square method, and wherein method includes that S1 reads ephemeris file, base station and monitoring station observation file；S2 constructs GNSS double difference carrier phase relative positioning model；S3 is estimated with fuzziness of the least square method to the GNSS double difference carrier phase relative positioning model；S4 converts ambiguity search to the nearest grid search problem of known lattice point in plaid matching；S5 carries out specification to lattice, obtains with minimum possible length and mutually orthogonal lattice vector；S6 goes out optimal fuzziness using nearest grid search algorithm search.Whether the optimal fuzziness that S7 is obtained with RATIO algorithm detecting step S6 is correct；If correct, optimal fuzziness is exported, S1 is otherwise returned to and carries out next epoch search.The present invention not only theoretically improves the search efficiency of fuzziness, while for the following increase with GNSS system, the quick resolving of the system ambiguous degree of multi-frequency multi-mode brings new opportunity.
Description
Technical field
The invention belongs to Technique of Satellite Navigation and Positioning and art of mathematics, and in particular to one kind is based on case theory and least square
The fast calculation method of the fuzziness of method and device.
Background technique
As Technique of Satellite Navigation and Positioning application field constantly expands and the development and construction of a variety of global position systems, use
Requirement of the family to the precision and reliability of positioning result is higher and higher, and high-precision GNSS positioning is normally based on carrier phase sight
What measured value carried out, and quickly and accurately resolving fuzziness shaping value is the key that realize GNSS carrier phase high accuracy positioning.By
In the discreteness of fuzziness unknown parameter, it is typically based on its real solution and covariance matrix constructs certain search space
It scans for obtain the solution of fuzziness.For this problem, domestic and foreign scholars did further investigation to this problem, successively
Propose different Ambiguity Solution Methods, such as THE AMBIGUITY FUNCTION METHOD USED, least square search method and FARA search method, these sides
Method is all the shaping value for directlying adopt the technology acquisition fuzziness of search, since there are strong correlations between fuzziness, so that on
It is lower to state method search efficiency.The LAMBDA algorithm that Teunissen is proposed, basic thought reduce fuzziness by integer transform
Correlation, after obtain optimal fuzziness shaping value in the space of integer transform, then using search technique.Chang is according to changing
Into spherical search algorithm carried out extension propose MLAMBDA algorithm, reduce fuzziness shaping search space, improve mould
The search efficiency of paste degree.But with the increase of GNSS system, the increase of the available number and frequency transmission signal of satellite will increase mould
The quantity of paste degree parameter, when handling higher-dimension ambiguity resolution problem, existing method efficiency is still very slow.
Summary of the invention
In view of the foregoing deficiencies of prior art, the purpose of the present invention is to provide one kind based on case theory and minimum two
The fast calculation method of the fuzziness of multiplication and device.
In order to achieve the above objects and other related objects, the present invention provides a kind of mould based on case theory and least square method
Paste degree fast resolution algorithm, this method comprises:
S1 reads ephemeris file, base station and monitoring station and observes file；
S2 constructs GNSS double difference carrier phase relative positioning model；
S3 is estimated with fuzziness of the least square method to the GNSS double difference carrier phase relative positioning model；
S4 converts ambiguity search to the nearest grid search problem of known lattice point in plaid matching；
S5 carries out specification to lattice, obtains with minimum possible length and mutually orthogonal lattice vector；
S6 goes out optimal fuzziness using nearest grid search algorithm search；
Whether the optimal fuzziness that S7 is obtained with RATIO algorithm detecting step S6 is correct；If correct, export optimal fuzzy
Otherwise degree returns to S1 and carries out next epoch search.
Optionally, fuzziness estimated value table is shown as:
Wherein, a is the float-solution of fuzziness,Real value is weighted for the floating type of a, P is the weight matrix of observation.
Optionally, carrying out specification to lattice includes:
Cholesky decomposition is carried out to matrix P, obtains triangular matrix R；
Gram-Schmidt orthogonalization is carried out to triangular matrix R；
To the coefficient gi of lattice,jGram-Schmidt orthogonalization is carried out, size reduction is carried out to lattice；
Lattice size is reduced；
Base b in plaid matchingiWith base b in latticei+1It is converted.
Optionally, the nearest grid search algorithm includes:
Set R0The initial search radius of particle is tieed up for the n centered on y；
||Ra-y||2≤R0
Since R is upper triangular matrix, inequality has following set relationship:
It may thereby determine that search boundary [Li,Ui]；
Wherein, round (*) expression takes immediate integer value, Rj,kFor R jth row kth column element, ajFor corresponding jth
The integer value of a fixation, yiFor corresponding i-th of observation central point, akFor k-th of fixed integer value, Ri,jFor the i-th row jth column
Element；
Calculate the Euclidean distance square between the lattice point and y searched out；
From [Li,Ui] midpoint in section of each rank starts to scan for, while R0It is set as infinitely great, if section
Midpoint is Mi, then
IfThe sequence then searched for is according to Mi,Mi+1,Mi-1,Mi+2,…；
IfThe sequence then searched for is according to Mi,Mi-1,Mi+1,Mi-2,…；
Search process is since rank i=n, if this rank is the 1st grade, first lattice point of generation is set as aB, obtain offscale
Point aBAfterwards, by search radius R0It is set as distance d2(y,RaB)；
Start the 2nd grade of search, obtains the corresponding minimum search radius R of integral pointi；If Ri< R0, then search radius is updated,
Make R0=Ri；
Successively the 3rd, 4 ..., n grades are scanned for, obtain the corresponding least radius of integral point, and and upper level in order
Obtained search radius is compared, if being less than, is updated to it, and next stage search is otherwise carried out, until failing n-th
When grade finds new integer value, search process stops, then the integral point of minimum search radius is optimal integer solution.
Optionally, Ratio algorithm checks formula are as follows:
Wherein, a indicates fuzziness float-solution, QaIndicate covariance matrix corresponding to a, RthresExpression judges limit value,Table
Show the optimal value of fuzziness,Indicate the secondary figure of merit of fuzziness.
In order to achieve the above objects and other related objects, the present invention provides a kind of mould based on case theory and least square method
The quick resolver of paste degree, the device include:
Data read module, for reading ephemeris file, base station and monitoring observation file；
Module is constructed, for constructing GNSS double difference carrier phase relative positioning model；
Estimation module is estimated with fuzziness of the least square method to the GNSS double difference carrier phase relative positioning model
Meter；
Conversion module, for converting ambiguity search to the nearest grid search problem of known lattice point in plaid matching；
Protocol module is obtained for carrying out specification to lattice with minimum possible length and mutually orthogonal lattice vector；
Search module, for going out optimal fuzziness using nearest grid search algorithm search；
Authentication module, it is whether correct for detecting optimal fuzziness with RATIO algorithm；If correct, export optimal fuzzy
Degree, otherwise carries out next epoch search.
Optionally, fuzziness estimated value table is shown as:
Wherein, a is the float-solution of fuzziness,Real value is weighted for the floating type of a, P is the weight matrix of observation.
Optionally, carrying out specification to lattice includes:
Cholesky decomposition is carried out to matrix P, obtains triangular matrix R；
Gram-Schmidt orthogonalization is carried out to triangular matrix R；
To the coefficient g of latticei,jGram-Schmidt orthogonalization is carried out, to carry out size reduction to lattice；
Lattice size is reduced；
Base b in plaid matchingiWith base b in latticei+1It is converted.
Optionally, the nearest grid search algorithm includes:
Set R0The initial search radius of particle is tieed up for the n centered on y；
||Ra-y||2≤R0
Since R is upper triangular matrix, inequality has following set relationship:
It may thereby determine that search boundary [Li,Ui]；
Wherein, round (*) expression takes immediate integer value, Rj,kFor R jth row kth column element, ajFor corresponding jth
The integer value of a fixation, yiFor corresponding i-th of observation central point, akFor k-th of fixed integer value, Ri,jFor the i-th row jth column
Element；
Calculate the Euclidean distance square between the lattice point and y searched out；
From [Li,Ui] midpoint in section of each rank starts to scan for, while R0It is set as infinitely great, if section
Midpoint is Mi, then
IfThe sequence then searched for is according to Mi,Mi+1,Mi-1,Mi+2,…；
IfThe sequence then searched for is according to Mi,Mi-1,Mi+1,Mi-2,…；
Search process is since rank i=n, if this rank is the 1st grade, first lattice point of generation is set as aB, obtain offscale
Point aBAfterwards, by search radius R0It is set as distance d2(y,RaB)；
Start the 2nd grade of search, obtains the corresponding minimum search radius R of integral pointi；If Ri< R0, then search radius is updated,
Make R0=Ri；
Successively the 3rd, 4 ..., n grades are scanned for, obtain the corresponding least radius of integral point, and and upper level in order
Obtained search radius is compared, if being less than, is updated to it, and next stage search is otherwise carried out, until failing n-th
When grade finds new integer value, search process stops, then the integral point of minimum search radius is optimal integer solution.
Optionally, Ratio algorithm checks formula are as follows:
Wherein, a indicates fuzziness float-solution, QaIndicate covariance matrix corresponding to a, RthresExpression judges limit value,
Indicate the optimal value of fuzziness,Indicate the secondary figure of merit of fuzziness.
As described above, a kind of fast calculation method of fuzziness based on case theory and least square method of the invention and device,
It has the advantages that
The present invention utilizes the features such as nearest lattic point problem and least-squares estimation problem in case theory, passes through and derives minimum
Square law solves fuzziness optimal value and is equivalent to solve nearest lattic point problem in case theory, then passes through the real solution to fuzziness
Covariance carries out triangle decomposition and obtains one group of lattice, to construct lattice corresponding to fuzziness, then is improved by lattice reduction
Fuzziness optimal solution search efficiency finally carries out fast and stable to fuzziness optimal value using nearest grid search algorithm and searches
Rope.The it is proposed of the method not only theoretically improves the search efficiency of fuzziness, while for the following increasing with GNSS system
Add, the quick resolving of the system ambiguous degree of multi-frequency multi-mode brings new opportunity.
Detailed description of the invention
In order to which the present invention is further explained, described content, with reference to the accompanying drawing makees a specific embodiment of the invention
Further details of explanation.It should be appreciated that these attached drawings are only used as typical case, and it is not to be taken as to the scope of the present invention
It limits.
Fig. 1 is a kind of fuzziness fast resolution algorithm overall flow frame based on case theory and least square method proposed
Figure；
Fig. 2 is the whole search routine block diagram of the nearest grid search method (CLP) proposed；
Fig. 3 be propose nearest grid search algorithm (CLP) case 1. -7. to the average search of fuzziness optimal value when
Between scheme；
Fig. 4 is that the nearest grid search algorithm (CLP) proposed and LAMBDA/MLAMBDA algorithm fuzziness optimal value are searched for
Time comparison diagram.
Fig. 5 is the lattice point x audio-visual picture closest to given input point y.
Specific embodiment
Illustrate embodiments of the present invention below by way of specific specific example, those skilled in the art can be by this specification
Other advantages and efficacy of the present invention can be easily understood for disclosed content.The present invention can also pass through in addition different specific realities
The mode of applying is embodied or practiced, the various details in this specification can also based on different viewpoints and application, without departing from
Various modifications or alterations are carried out under spirit of the invention.It should be noted that in the absence of conflict, following embodiment and implementation
Feature in example can be combined with each other.
It should be noted that illustrating the basic structure that only the invention is illustrated in a schematic way provided in following embodiment
Think, only shown in schema then with related component in the present invention rather than component count, shape and size when according to actual implementation
Draw, when actual implementation kenel, quantity and the ratio of each component can arbitrarily change for one kind, and its assembly layout kenel
It is likely more complexity.
As shown in Figure 1, the present invention proposes a kind of fuzziness fast resolution algorithm based on case theory and least square method.Its
In entire method include the verifying nearest grid search problem equivalent of case theory in integer least square estimation problem, construct with most
Small two multiply the lattice of ambiguous estimation degree equivalence, specification are carried out to lattice, finally again using the nearest grid search algorithm search proposed
Optimal fuzziness integer value out.
Specific embodiment is as follows:
S1 reads ephemeris file, base station and monitoring observation file；
S2 constructs GNSS double difference carrier phase relative positioning model；
S3 is estimated with fuzziness of the least square method to the GNSS double difference carrier phase relative positioning model；
S4 converts ambiguity search to the nearest grid search problem of known lattice point in plaid matching；
S5 carries out specification to lattice, obtains with minimum possible length and mutually orthogonal lattice vector；
S6 goes out optimal fuzziness using nearest grid search algorithm search.
Whether the optimal fuzziness that S7 is obtained with RATIO algorithm detecting step S6 is correct；If correct, export optimal fuzzy
Otherwise degree returns to S1 and carries out next epoch search.
Step S2~step S7 is described in detail below.
In step s 2, GNSS double difference carrier phase relative positioning model can be with following linear equation system come general
It includes:
Y=Aa+Bb+e (1)
Wherein, y indicates observation, and b is the real number unknown parameter in observation model, including position, troposphere and ionosphere
Delay parameter, B are its corresponding coefficient matrix, and a is fuzziness unknown parameter, and A is its corresponding coefficient matrix, and e is that observation misses
Difference vector.
In step s3, (1) formula is applied to by least square method, parameter optimal value in estimation equation (1) obtains:
min(y-Aa-Bb)TP(y-Aa-Bb) (2)
Wherein, P is the weight matrix of observation, and the integer characteristic by ignoring fuzziness a directly finds out floating type weighting
Real valueAnd its covariance matrixMinimization problem in formula (2) can be converted to following problem:
In step S4: converting ambiguity search to the nearest grid search problem of known lattice point in plaid matching.
Specifically, based on the nearest lattic point problem in case theory, for set point y ∈ Rn, search for the lattice point x closest to y.
There are a ∈ Zk, so that for x ∈ Λ, x=Ba.Have:
It wherein in mathematics, can be expressed as follows in the matrix form of lattice, Λ (B)={ Ba:a ∈ Zk}。
The least square problem in formula (3) is considered again simultaneously, due to the fuzziness integer value of estimationCovariance square
Battle arrayIt is positive definite, therefore the cholesky of matrix P is decomposed into, P=RTR, so solving the least-squares estimation equation in S1
It can convert are as follows:
Assuming thatThen:
Therefore formula (3) is variable are as follows:
The nearest lattic point problem of solution is demonstrated by formula (4) and formula (7) and is equivalent to least square method solution fuzziness integer value.
Lattice Λ (B) relevant to fuzziness can be wherein constructed, wherein B=R, the ambiguity search of formula (3) can be converted to pair
The nearest grid search problem of known lattice point y in lattice Λ (B).
In step s 5, specification is carried out to lattice, obtained with minimum possible length and mutually orthogonal lattice vector.
Specifically, specification is carried out to lattice based on case theory, three basic steps of lattice reduction: orthogonalization, size subtract
Small and vector exchange.If b1,b2,…,bm∈Rn, (m≤n) is one group of lattice, under decomposing to the cholesky of the matrix P of formula (7)
Triangular matrix R carries out Gram-Schmidt orthogonalization and obtains:
WhereinFor orthogonalization lattice bnSquare of vector norm, then the coefficient g to latticei,jCarry out Gram-
Schmidt orthogonalization meets it all 1 all≤i≤j≤kThis process is known as the reduction of lattice size.
It is reduced to obtain better size, b in latticeiSequence by with corresponding Gram-Schmidt orthogonal basis bi *
Transformation is to change.Corresponding orthogonal basis b in order to obtaini *Shorter value, can be by biAnd bi+1It is converted, vector row
biAnd bi+1Transformation condition it is as follows:
By lattice reduction, specification is carried out to R matrix, is obtained close to orthogonal and minimum length lattice, to accelerate mould
The search of paste degree.
In step s 6, go out optimal fuzziness using nearest grid search algorithm search.The nearest lattice defined first by (4)
Point search problem sets square radius that R0 ties up particle as the n centered on Y, and it is optimal to carry out fuzziness to this piece region of search
Value search.
||Ra-y||2≤R0 (11)
It is upper triangular matrix by R, the search space of step S41 is variable are as follows:
Due to the integer characteristic of a value, if for i+1≤j≤n, ajValue fixed, then variable ai, i=n-1, n-
2 ..., 1 can be in integer range [Li,Ui] it is rounded numerical value.
Wherein, round (*) expression takes immediate integer value, Rj,kFor R jth row kth column element, ajFor corresponding jth
The integer value of a fixation, yiFor corresponding i-th of observation central point, akFor k-th of fixed integer value, Ri,jFor the i-th row jth column
Element.
And a for having fixedj, the point of j=i+1 ..., n is not belonging to the radius centered on ySphere.This
A little points and the Euclidean distance square between y are expressed as:
Using nearest grid search algorithm from [Li,Ui] midpoint in section of each rank starts with Z-shaped row sequence according to item
Part estimation scans in an alternating manner, while R0It is set as infinitely great, if interval midpoint is Mi, then
Wherein search step is as follows:
(1) ifThe sequence then searched for is according to Mi,Mi+1,Mi-1,Mi+2,…；
(2) ifThe sequence then searched for is according to Mi,Mi-1,Mi+1,Mi-2,…；
(3) search process is since rank i=n, if this rank is the 1st grade, first lattice point of generation is set as aB, obtain
aBAfterwards, by R0It is set as distance d2(y,RaB)；
(4) start the 2nd grade of search, and obtain next integer value of the rank according to SS1 and SS2, if newly calculate
Square search radius is less than radius in SS3, then search radius can be updated to new search radius, otherwise continue 3rd level
The search of next integer value, search process will persistently find than the 1st grade small integer value；
(5) when search process fails when finding new integer value for n-th grade, i.e., squared distance value up to the present at this time
Greater than best square apart from when, search process stop, and the integral point of the least radius found be find optimal integer solution.
In the step s 7, whether correct with the integer value of the obtained fuzziness of Ratio algorithm detecting step S4, wherein
Inspection formula of the Ratio algorithm to solution of fuzzy degree are as follows:
Wherein, a indicates the fuzziness float-solution based on least-squares estimation, QaIndicate covariance matrix corresponding to a,
RthresIndicate the judgement limit value of Ratio algorithm,The optimal value of fuzziness,Indicate the secondary figure of merit of fuzziness.
(17) formula is substituted by obtained optimal integer value, sees whether meet the requirements, then available fixed fuzziness is most
The figure of merit.Otherwise float-solution is obtained, next epoch search is carried out.
The present invention proposes a kind of fuzziness fast resolution algorithm based on case theory and least square method, we are mentioning herein
Nearest grid search method out is indicated with initial English capitalization CLP, in order to verify the validity of proposition method, is based on
Verification result has been obtained by 7 groups of simulation case emulation on MATLAB platform.
Go out following 7 kinds different simulation cases according to true fuzziness parametric configuration, first four kinds are based on Qa=LTDL, wherein
It is L unit lower triangular matrix, each lijIt is the random number generated by randn.
(1) case is 1.: D=diag (di),di=rand, wherein rand is MATLAB built-in function, in (0,1)
Generate equally distributed random number；
(2) case is 2.: D=diag (n-1,(n-1)-1,...,1-1)；
(3) case is 3.: D=diag (1-1,2-1,...,n-1)；
(4) case is 4.: D=diag (200,200,0.1,0.1 ..., 0.1).
Other three cases for example under:
(5) case is 5.:U is to decompose to obtain by the QR of the random matrix generated by randn (n, n)
Random orthogonal matrix, D=diag (di), di=rand；
(6) case is 6.:5. identical mode generates U with case,In D
Other diagonal elements are randomly dispersed in d1And dnBetween, n isDimension.ThereforeConditional number be
(7) case is 7.:
Table 1. for dimension be 40, three kinds of algorithms simulation case 1. -7. under average search time
Such as table 1, based on Principle of Statistics to CLP and LAMBDA/MLAMBDA algorithm different cases search time
It is for statistical analysis, it obtains for when fuzziness dimension is 40, the average search time of CLP is about the 97 of LAMBDA, 374,
151,179,64,205,187 times.Even and if this method is in higher-dimension, knot still efficient for the search efficiency of fuzziness
As shown in figure 3, wherein case is 3. exactly consistent with the method for the present invention, other case retrieval times all increase with dimension in finger fruit
Number type increases.Simultaneously in the measured data of same group of more than 300 a epoch, under the GNSS relative positioning model of short baseline, CLP
The fuzziness optimal value search time of one epoch stablizes at 0.01 second or so, and LAMBDA and MLAMBDA are then respectively at 0.052 second
With 0.03 second or so, as a result as shown in Figure 4.The fuzziness based on case theory and least square method of comprehensive analysis, invention is quick
Calculation method has very high timeliness even for the search of fuzziness optimal value.
The present invention also provides a kind of quick resolver of the fuzziness based on case theory and least square method, the device packets
It includes:
Data read module, for reading ephemeris file, base station and monitoring observation file；
Module is constructed, for constructing GNSS double difference carrier phase relative positioning model；
Estimation module is estimated with fuzziness of the small square law to the GNSS double difference carrier phase relative positioning model
Meter；
Conversion module, for converting ambiguity search to the nearest grid search problem of known lattice point in plaid matching；
Protocol module is obtained for carrying out specification to lattice with minimum possible length and mutually orthogonal lattice vector；
Search module, for going out optimal fuzziness using nearest grid search algorithm search.
Authentication module, it is whether correct for detecting optimal fuzziness with RATIO algorithm；If correct, export optimal fuzzy
Degree, otherwise carries out next epoch search.
In one embodiment, fuzziness estimated value table is shown as:
Wherein, a is the float-solution of fuzziness,Real value is weighted for the floating type of a, P is the weight matrix of observation.
In one embodiment, carrying out specification to lattice includes:
Cholesky decomposition is carried out to matrix P, obtains triangular matrix R；
Gram-Schmidt orthogonalization is carried out to triangular matrix R；
To the coefficient gi of lattice,jCarry out Gram-Schmidt orthogonalization；
Lattice size is reduced；
Base b in plaid matchingiWith base b in latticei+1It is converted.
In one embodiment, the nearest grid search algorithm includes:
Set R0The initial search radius of particle is tieed up for the n centered on y；
||Ra-y||2≤R0
Since R is upper triangular matrix, inequality has following set relationship:
It may thereby determine that search boundary [Li,Ui]；
Wherein, round (*) expression takes immediate integer value, Rj,kFor R jth row kth column element, ajFor corresponding jth
The integer value of a fixation, yiFor corresponding i-th of observation central point, akFor k-th of fixed integer value, Ri,jFor the i-th row jth column
Element；
Calculate the Euclidean distance square between the lattice point and y searched out；
From [Li,Ui] midpoint in section of each rank starts to scan for, while R0It is set as infinitely great, if section
Midpoint is Mi, then
IfThe sequence then searched for is according to Mi,Mi+1,Mi-1,Mi+2,…；
IfThe sequence then searched for is according to Mi,Mi-1,Mi+1,Mi-2,…；
Search process is since rank i=n, if this rank is the 1st grade, first lattice point of generation is set as aB, obtain offscale
Point aBAfterwards, by search radius R0It is set as distance d2(y,RaB)；
Start the 2nd grade of search, obtains the corresponding minimum search radius R of integral pointi；If Ri< R0, then search radius is updated,
Make R0=Ri；
Successively the 3rd, 4 ..., n grades are scanned for, obtain the corresponding least radius of integral point, and and upper level in order
Obtained search radius is compared, if being less than, is updated to it, and next stage search is otherwise carried out, until failing n-th
When grade finds new integer value, search process stops, then the integral point of minimum search radius is optimal integer solution.
In one embodiment, Ratio algorithm checks formula are as follows:
Wherein, a indicates fuzziness float-solution, QaIndicate covariance matrix corresponding to a, RthresExpression judges limit value,
Indicate the optimal value of fuzziness,Indicate the secondary figure of merit of fuzziness.
It should be noted that the embodiment due to device part is corresponded to each other with the embodiment of method part, device
The content of partial embodiment refers to the description of the embodiment of method part, wouldn't repeat here.
The present invention also provides a kind of storage mediums, computer program are stored, when the computer program is run by processor
Execute method above-mentioned.
The present invention also provides a kind of electric terminals, comprising:
Memory, for storing computer program；
Processor, for executing the computer program of the memory storage, so that the equipment executes method above-mentioned.
The computer program includes computer program code, the computer program code can for source code form,
Object identification code form, executable file or certain intermediate forms etc..The computer-readable medium may include: that can carry institute
State any entity or device, recording medium, USB flash disk, mobile hard disk, magnetic disk, CD, the computer storage of computer program code
Device, read-only memory (ROM, Read-Only Memory), random access memory ((RAM, Random Access
Memory), electric carrier signal, telecommunication signal and software distribution medium etc..
The processor can be central processing unit (Central Processing Unit, CPU), can also be it
His general processor, digital signal processor (Digital Signal Processor, DSP), specific integrated circuit
(Application Specific Integrated Circuit, ASIC), field programmable gate array (Field
Programmable Gate Array, FPGA) either other programmable logic device, discrete gate or transistor logic,
Discrete hardware components etc..General processor can be microprocessor or the processor is also possible to any conventional processor
Deng.
The memory can be internal storage unit or External memory equipment, such as plug-in type hard disk, intelligent memory card
(Smart Media Card, SMC), safe digital card (Secure Digital, SD), flash card (Flash Card) etc..Into
One step, the memory can also both include internal storage unit, also include External memory equipment.The memory is for depositing
Store up the computer program and other programs and data.The memory can be also used for temporarily storing oneself through output or
The data that will be exported.
It is apparent to those skilled in the art that for convenience of description and succinctly, only with above-mentioned each function
Can unit, module division progress for example, in practical application, can according to need and by above-mentioned function distribution by different
Functional unit, module are completed, i.e., the internal structure of described device is divided into different functional unit or module, more than completing
The all or part of function of description.Each functional unit in embodiment, module can integrate in one processing unit, can also
To be that each unit physically exists alone, can also be integrated in one unit with two or more units, it is above-mentioned integrated
Unit both can take the form of hardware realization, can also realize in the form of software functional units.In addition, each function list
Member, the specific name of module are also only for convenience of distinguishing each other, the protection scope being not intended to limit this application.Above system
The specific work process of middle unit, module, can refer to corresponding processes in the foregoing method embodiment, and details are not described herein.
In the above-described embodiments, it all emphasizes particularly on different fields to the description of each embodiment, is not described in detail or remembers in some embodiment
The part of load may refer to the associated description of other embodiments.
Those of ordinary skill in the art may be aware that list described in conjunction with the examples disclosed in the embodiments of the present disclosure
Member and algorithm steps can be realized with the combination of electronic hardware or computer software and electronic hardware.These functions are actually
It is implemented in hardware or software, the specific application and design constraint depending on technical solution.Professional technician
Each specific application can be used different methods to achieve the described function, but this realization is it is not considered that exceed
The scope of the present invention.
In embodiment provided by the present invention, it should be understood that disclosed device/terminal device and method, it can be with
It realizes by another way.For example, device described above/terminal device embodiment is only schematical, for example, institute
The division of module or unit is stated, only a kind of logical function partition, there may be another division manner in actual implementation, such as
Multiple units or components can be combined or can be integrated into another system, or some features can be ignored or not executed.Separately
A bit, shown or discussed mutual coupling or direct-coupling or communication connection can be through some interfaces, device
Or the INDIRECT COUPLING or communication connection of unit, it can be electrical property, mechanical or other forms.
The above-described embodiments merely illustrate the principles and effects of the present invention, and is not intended to limit the present invention.It is any ripe
The personage for knowing this technology all without departing from the spirit and scope of the present invention, carries out modifications and changes to above-described embodiment.Cause
This, institute is complete without departing from the spirit and technical ideas disclosed in the present invention by those of ordinary skill in the art such as
At all equivalent modifications or change, should be covered by the claims of the present invention.
Claims (10)
1. a kind of fuzziness fast resolution algorithm based on case theory and least square method, which is characterized in that this method comprises:
S1 reads ephemeris file, base station and monitoring station and observes file；
S2 constructs GNSS double difference carrier phase relative positioning model；
S3 is estimated with fuzziness of the least square method to the GNSS double difference carrier phase relative positioning model；
S4 converts ambiguity search to the nearest grid search problem of known lattice point in plaid matching；
S5 carries out specification to lattice, obtains with minimum possible length and mutually orthogonal lattice vector；
S6 goes out optimal fuzziness using nearest grid search algorithm search；
Whether the optimal fuzziness that S7 is obtained with RATIO algorithm detecting step S6 is correct；If correct, optimal fuzziness is exported,
Otherwise it returns to S1 and carries out next epoch search.
2. the fuzziness fast resolution algorithm according to claim 1 based on case theory and least square method, feature exist
In fuzziness estimated value table is shown as:
Wherein, a is the float-solution of fuzziness,Real value is weighted for the floating type of a, P is the weight matrix of observation.
3. the fuzziness fast resolution algorithm according to claim 2 based on case theory and least square method, feature exist
In carrying out specification to lattice includes:
Cholesky decomposition is carried out to matrix P, obtains triangular matrix R；
Gram-Schmidt orthogonalization is carried out to triangular matrix R；
To the coefficient g of latticei,jGram-Schmidt orthogonalization is carried out, size reduction is carried out to lattice；
Lattice size is reduced；
Base b in plaid matchingiWith base b in latticei+1It is converted.
4. the fuzziness fast resolution algorithm according to claim 3 based on case theory and least square method, feature exist
In the nearest grid search algorithm includes:
Set R0The initial search radius of particle is tieed up for the n centered on y；
||Ra-y||2≤R0
Since R is upper triangular matrix, inequality has following set relationship:
It may thereby determine that search boundary [Li,Ui]；
Wherein, round (*) expression takes immediate integer value, Rj,kFor R jth row kth column element, ajFor corresponding j-th of fixation
Integer value, yiFor corresponding i-th of observation central point, akFor k-th of fixed integer value, Ri,jFor the i-th row jth column element；
Calculate the Euclidean distance square between the lattice point and y searched out；
From [Li,Ui] midpoint in section of each rank starts to scan for, while R0It is set as infinitely great, if interval midpoint
For Mi, then
IfThe sequence then searched for is according to Mi,Mi+1,Mi-1,Mi+2,…；
IfThe sequence then searched for is according to Mi,Mi-1,Mi+1,Mi-2,…；
Search process is since rank i=n, if this rank is the 1st grade, first lattice point of generation is set as aB, obtain lattice point aB
Afterwards, by search radius R0It is set as distance d2(y,Ra B)；
Start the 2nd grade of search, obtains the corresponding minimum search radius R of integral pointi；If Ri< R0, then search radius is updated, R is made0=
Ri；
Successively the 3rd, 4 ..., n grades are scanned for, obtain the corresponding least radius of integral point in order, and obtain with upper level
Search radius be compared, if being less than, it is updated, next stage search is otherwise carried out, until fail to look at n-th grade
When to new integer value, search process stops, then the integral point of minimum search radius is optimal integer solution.
5. the fuzziness fast resolution algorithm according to claim 4 based on case theory and least square method, feature exist
In Ratio algorithm checks formula are as follows:
Wherein, a indicates fuzziness float-solution, QaIndicate covariance matrix corresponding to a, RthresExpression judges limit value,Indicate mould
The optimal value of paste degree,Indicate the secondary figure of merit of fuzziness.
6. a kind of quick resolver of fuzziness based on case theory and least square method, which is characterized in that the device includes:
Data read module, for reading ephemeris file, base station and monitoring observation file；
Module is constructed, for constructing GNSS double difference carrier phase relative positioning model；
Estimation module is estimated with fuzziness of the least square method to the GNSS double difference carrier phase relative positioning model；
Conversion module, for converting ambiguity search to the nearest grid search problem of known lattice point in plaid matching；
Protocol module is obtained for carrying out specification to lattice with minimum possible length and mutually orthogonal lattice vector；
Search module, for going out optimal fuzziness using nearest grid search algorithm search；
Authentication module, it is whether correct for detecting optimal fuzziness with RATIO algorithm；If correct, optimal fuzziness is exported, it is no
Then carry out next epoch search.
7. the quick resolver of the fuzziness according to claim 6 based on case theory and least square method, feature exist
In fuzziness estimated value table is shown as:
Wherein, a is the float-solution of fuzziness,Real value is weighted for the floating type of a, P is the weight matrix of observation.
8. the quick resolver of the fuzziness according to claim 7 based on case theory and least square method, feature exist
In carrying out specification to lattice includes:
Cholesky decomposition is carried out to matrix P, obtains triangular matrix R；
Gram-Schmidt orthogonalization is carried out to triangular matrix R；
To the coefficient g of latticei,jGram-Schmidt orthogonalization is carried out, to carry out size reduction to lattice；
Lattice size is reduced；
Base b in plaid matchingiWith base b in latticei+1It is converted.
9. the quick resolver of the fuzziness according to claim 8 based on case theory and least square method, feature exist
In the nearest grid search algorithm includes:
Set R0The initial search radius of particle is tieed up for the n centered on y；
||Ra-y||2≤R0
Since R is upper triangular matrix, inequality has following set relationship:
It may thereby determine that search boundary [Li,Ui]；
Wherein, round (*) expression takes immediate integer value, Rj,kFor R jth row kth column element, ajFor corresponding j-th of fixation
Integer value, yiFor corresponding i-th of observation central point, akFor k-th of fixed integer value, Ri,jFor the i-th row jth column element；
Calculate the Euclidean distance square between the lattice point and y searched out；
From [Li,Ui] midpoint in section of each rank starts to scan for, while R0It is set as infinitely great, if interval midpoint
For Mi, then
IfThe sequence then searched for is according to Mi,Mi+1,Mi-1,Mi+2,…；
IfThe sequence then searched for is according to Mi,Mi-1,Mi+1,Mi-2,…；
Search process is since rank i=n, if this rank is the 1st grade, first lattice point of generation is set as aB, obtain lattice point aB
Afterwards, by search radius R0It is set as distance d2(y,RaB)；
Start the 2nd grade of search, obtains the corresponding minimum search radius R of integral pointi；If Ri< R0, then search radius is updated, R is made0=
Ri；
Successively the 3rd, 4 ..., n grades are scanned for, obtain the corresponding least radius of integral point in order, and obtain with upper level
Search radius be compared, if being less than, it is updated, next stage search is otherwise carried out, until fail to look at n-th grade
When to new integer value, search process stops, then the integral point of minimum search radius is optimal integer solution.
10. the quick resolver of the fuzziness according to claim 9 based on case theory and least square method, feature exist
In Ratio algorithm checks formula are as follows:
Wherein, a indicates fuzziness float-solution, QaIndicate covariance matrix corresponding to a, RthresExpression judges limit value,Indicate mould
The optimal value of paste degree,Indicate the secondary figure of merit of fuzziness.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111381266A (en) * | 2020-05-12 | 2020-07-07 | 泉州信息工程学院 | Integer ambiguity determination method and device, electronic equipment and computer readable medium |
| CN111650615A (en) * | 2020-01-14 | 2020-09-11 | 东华理工大学 | Ambiguity lattice reduction quality evaluation method |
| CN113970774A (en) * | 2021-12-22 | 2022-01-25 | 广东汇天航空航天科技有限公司 | Ambiguity fixing method and device of navigation system |
Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2001086271A2 (en) * | 2000-05-08 | 2001-11-15 | Molecular Simulations, Inc. | Structure factor determinations |
| CN104122566A (en) * | 2014-07-01 | 2014-10-29 | 华东师范大学 | Multi-path error removing method of navigation satellite system and multi-path hemisphere model |
| CN105842721A (en) * | 2016-03-23 | 2016-08-10 | 中国电子科技集团公司第十研究所 | Method for improving resolving success rate of medium and long baseline GPS integral cycle fuzziness |
| EP3163324A1 (en) * | 2014-06-25 | 2017-05-03 | Mitsubishi Electric Corporation | Positioning device, positioning method, and program |
| CN107102346A (en) * | 2017-06-08 | 2017-08-29 | 中国电子科技集团公司第五十四研究所 | A kind of multiple antennas based on dipper system surveys attitude positioning method |
| CN108317949A (en) * | 2018-02-07 | 2018-07-24 | 桂林电子科技大学 | A kind of RTK high-precision differences positioning deformation monitoring system and method |
| CN108828641A (en) * | 2018-06-20 | 2018-11-16 | 成都信息工程大学 | A method of shortening the Fast integer Ambiguity Resolution time |
| CN108871179A (en) * | 2018-05-07 | 2018-11-23 | 桂林电子科技大学 | Deformation monitoring localization method and device based on the fusion of carrier phase difference transfer static state |
| CN108897009A (en) * | 2018-06-08 | 2018-11-27 | 桂林电子科技大学 | A kind of BOC navigation signal receiver and its code tracking method |
| CN109613579A (en) * | 2018-11-23 | 2019-04-12 | 桂林电子科技大学 | A kind of method and system calculating integer ambiguity based on least-squares algorithm |
-
2019
- 2019-08-16 CN CN201910758472.6A patent/CN110531394A/en active Pending
Patent Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2001086271A2 (en) * | 2000-05-08 | 2001-11-15 | Molecular Simulations, Inc. | Structure factor determinations |
| EP3163324A1 (en) * | 2014-06-25 | 2017-05-03 | Mitsubishi Electric Corporation | Positioning device, positioning method, and program |
| CN104122566A (en) * | 2014-07-01 | 2014-10-29 | 华东师范大学 | Multi-path error removing method of navigation satellite system and multi-path hemisphere model |
| CN105842721A (en) * | 2016-03-23 | 2016-08-10 | 中国电子科技集团公司第十研究所 | Method for improving resolving success rate of medium and long baseline GPS integral cycle fuzziness |
| CN107102346A (en) * | 2017-06-08 | 2017-08-29 | 中国电子科技集团公司第五十四研究所 | A kind of multiple antennas based on dipper system surveys attitude positioning method |
| CN108317949A (en) * | 2018-02-07 | 2018-07-24 | 桂林电子科技大学 | A kind of RTK high-precision differences positioning deformation monitoring system and method |
| CN108871179A (en) * | 2018-05-07 | 2018-11-23 | 桂林电子科技大学 | Deformation monitoring localization method and device based on the fusion of carrier phase difference transfer static state |
| CN108897009A (en) * | 2018-06-08 | 2018-11-27 | 桂林电子科技大学 | A kind of BOC navigation signal receiver and its code tracking method |
| CN108828641A (en) * | 2018-06-20 | 2018-11-16 | 成都信息工程大学 | A method of shortening the Fast integer Ambiguity Resolution time |
| CN109613579A (en) * | 2018-11-23 | 2019-04-12 | 桂林电子科技大学 | A kind of method and system calculating integer ambiguity based on least-squares algorithm |
Non-Patent Citations (5)
| Title |
|---|
| B. SHIM, F. ABRISHAMKAR AND I. KANG: "Decision-Feedback Closest Lattice Point Search for UMTS HSPA System", 《IEEE SIGNAL PROCESSING LETTERS》 * |
| D. M. IONESCU AND H. ZHU: "SISO APP Searches in Lattices With Tanner Graphs", 《 IEEE TRANSACTIONS ON INFORMATION THEORY》 * |
| 于兴旺: "多频GNSS精密定位理论与方法研究", 《中国博士学位论文全文数据库 基础科学辑》 * |
| 刘经南: "基于格论的GNSS模糊度解算", 《测绘学报》 * |
| 范龙: "基于格理论的GNSS模糊度估计方法研究", 《中国博士学位论文全文数据库 基础科技辑》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111650615A (en) * | 2020-01-14 | 2020-09-11 | 东华理工大学 | Ambiguity lattice reduction quality evaluation method |
| CN111381266A (en) * | 2020-05-12 | 2020-07-07 | 泉州信息工程学院 | Integer ambiguity determination method and device, electronic equipment and computer readable medium |
| CN113970774A (en) * | 2021-12-22 | 2022-01-25 | 广东汇天航空航天科技有限公司 | Ambiguity fixing method and device of navigation system |
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