CN105182378A - LLL (Lenstra-Lenstra-LovaszLattice) ambiguity decorrelation algorithm - Google Patents
LLL (Lenstra-Lenstra-LovaszLattice) ambiguity decorrelation algorithm Download PDFInfo
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- CN105182378A CN105182378A CN201510426357.0A CN201510426357A CN105182378A CN 105182378 A CN105182378 A CN 105182378A CN 201510426357 A CN201510426357 A CN 201510426357A CN 105182378 A CN105182378 A CN 105182378A
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- blur level
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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
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/13—Receivers
- G01S19/35—Constructional details or hardware or software details of the signal processing chain
- G01S19/37—Hardware or software details of the signal processing chain
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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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- Radar, Positioning & Navigation (AREA)
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- Signal Processing (AREA)
- Complex Calculations (AREA)
Abstract
The invention discloses an LLL (Lenstra-Lenstra-LovaszLattice) ambiguity decorrelation algorithm. According to the algorithm, upper triangular decomposition (U<T>U) is performed on a covariance matrix Qa through utilizing Cholesky decomposition method, so that an upper triangular matrix U<T> can be obtained, and with the above decomposition method adopted, the computational efficiency of the LLL algorithm can be improved; before algorithm decomposition every time, descending sorting is performed on column vectors of the matrix Qa according to the magnitude of inner products, and a coefficient matrix can obtain a minimum integer value, and the decorrelation performance of the decorrelation algorithm is better; and a rounding step in an orthogonal transformation process is shifted to a Z-solving matrix, and therefore, calculation quantity increase and error accumulation caused by repeated rounding in an iteration process can be avoided, and the computational efficiency and success rate of the novel algorithm can be improved.
Description
Technical field
The invention belongs to satellite navigation positioning technical field, relate to a kind of blur level and fall related algorithm, be specifically related to a kind ofly fall related algorithm for the LLL blur level in GNSS Carrier Phase Ambiguity Resolution.
Background technology
When utilizing GNSS carrier phase to carry out high-precision real as observed quantity in position fixing process, integer ambiguity can be solved quickly and accurately and become key issue, fall correlation technique by adopting to fall relevant treatment to the floating-point solution of integer ambiguity and covariance matrix thereof be a kind of conventional and method of function admirable.Correlativity due to blur level covariance directly determines speed and the efficiency of Carrier Phase Ambiguity Resolution, affect effect and the success or failure of ambiguity resolution, therefore, proposing a kind of related algorithm that falls rapidly and efficiently is the key reducing original blur level correlativity, locate when realizing GNSS high-precision real, is also object of the present invention and meaning.
Related algorithm falls in blur level conventional at present three kinds: related algorithm (IntegerGaussianDecorrelationAlgorithm) falls in integer Gauss, related algorithm (InverseIntegerCholeskyDecorrelationAlgorithm) falls in inverse integer Qiao Lesiji, related algorithm (Lenstra-Lenstra-LovaszLatticeDecorrelationAlgorithm) falls in LLL.Wherein, LLL algorithm is that related algorithm falls in a kind of more novel blur level, obtain deep research in recent years and apply widely, but still there are some defects, rounding in the iterative process of round-off error at algorithm such as in integer orthogonal transformation process is constantly added up, can convergence be had influence on, even cause falling and be correlated with unsuccessfully.
In order to realize the relevant processing procedure of fast prompt drop, meeting the target of Efficient Solution blur level, in the urgent need to a kind of transform algorithm of function admirable, the search efficiency of integer ambiguity can be improved, and then the demand of locating when meeting high-precision real.
Summary of the invention
The present invention mainly provides a kind of related algorithm that falls newly to fall relevant treatment to blur level, and this algorithm can reduce iterations, improves ambiguity search speed, and can effectively reduce in iterative process and round accumulation of rounding errors problem.
The technical solution adopted in the present invention is: related algorithm falls in a kind of LLL blur level, it is characterized in that, comprises the following steps:
Step 1: input original blur level covariance matrix Q
awith transformation matrix Z, wherein, Z is unit matrix; Arrange cycle index I=N, N gets positive integer;
Step 2: loop initialization number of times I=0;
Step 3: by blur level covariance matrix Q
acarry out descending sort according to the inner product size of column vector, obtain ordinal matrix H, and the new matrix after descending sort is: Q
b=HQ
ah
t;
Step 4: to matrix Q
bcarry out triangle decomposition on Qiao Lesiji, obtain the upper triangular matrix U after decomposing
tand transposed matrix U, matrix U and U
tall unique solutions;
Step 5: carry out QR decomposition transform to matrix U, obtains triangular transformation matrix R, and orthogonal matrix Q
c;
Step 6: to the element R of transformation matrix R
ijask whole and obtain INTEGER MATRICES [R], by ask whole after matrix inversion obtain new transformation matrix [R]
-1;
Step 7: ask transform matrix Z
i, Z
i=[R]
-1hZ;
Step 8: ask the covariance matrix Qz=Z after transform
iq
az
i t;
Step 9: cycle index I adds 1;
Step 10: judgment matrix [R]
-1whether be whether unit matrix or cycle index I reach the upper limit; If two Rule of judgment meet any one, then finishing iteration process, and redirect performs following step 11; Otherwise by Qz assignment to Qa, i.e. Qa=Qz, by Z
iassignment to Z, i.e. Z=Z
i, and the step 3 described in revolution execution;
Step 11: circulation terminates, exports and falls correlation matrix Z
iwith the covariance matrix Qz through falling relevant treatment.
As preferably, the N=50 described in step 1.
Compared with prior art, contemplated by the invention and existingly fall the problem that the orthogonal transformation existed in related algorithm rounds round-off error, the related algorithm that falls of the present invention is adopted to process integer ambiguity, effectively can reduce iterations, and before each decomposition, descending sort is done to rectangular array vector, rounding operation also moves on to when asking transformation matrix Z and carries out, very large improvement has been had to the accumulation of rounding errors that rounds in iterative process, improve counting yield, add and fall relevant success ratio, accelerate the search speed of blur level, guarantee is provided for locating in real time at a high speed.
Accompanying drawing explanation
Fig. 1: the algorithm flow chart of the embodiment of the present invention.
Embodiment
Understand for the ease of those of ordinary skill in the art and implement the present invention, below in conjunction with drawings and Examples, the present invention is described in further detail, should be appreciated that exemplifying embodiment described herein is only for instruction and explanation of the present invention, is not intended to limit the present invention.
A kind of related algorithm that falls newly is the object of the present invention is to provide to fall relevant treatment to blur level, the method adopts triangle decomposition on Qiao Lesiji, effectively improve the performance of transform matrix, thus improve search speed and the computation success of integer ambiguity.Carry out descending sort to the column vector of upper triangular matrix U according to inner product size, that can improve this algorithm thus falls correlated performance simultaneously, and then improves convergence and success ratio.By rounding operation is carried out when orthogonal process moves on to and asks transform matrix, effectively reduce the cumulative of round-off error in iterative process, improve the stability of this algorithm further.The present invention falls relevant speed and efficiency by improving, thus effectively improves search speed and the success ratio of Carrier Phase Ambiguity Resolution.
Ask for an interview Fig. 1, related algorithm falls in a kind of LLL blur level provided by the invention, comprises the following steps:
Step 1: input original blur level covariance matrix Q
awith transformation matrix Z, wherein, Z is unit matrix; Cycle index I=50 is set;
Step 2: loop initialization number of times I=0;
Step 3: by blur level covariance matrix Q
acarry out descending sort according to the inner product size of column vector, obtain ordinal matrix H, and the new matrix after descending sort is: Q
b=HQ
ah
t;
Step 4: to matrix Q
bcarry out triangle decomposition on Qiao Lesiji, obtain the upper triangular matrix U after decomposing
tand transposed matrix U, matrix U and U
tall unique solutions;
Step 5: carry out QR decomposition transform to matrix U, obtains triangular transformation matrix R, and orthogonal matrix Q
c;
Step 6: to the element R of transformation matrix R
ijask whole and obtain INTEGER MATRICES [R], by ask whole after matrix inversion obtain new transformation matrix [R]
-1;
Step 7: ask transform matrix Z
i, Z
i=[R]
-1hZ;
Step 8: ask the covariance matrix Qz=Z after transform
iq
az
i t;
Step 9: cycle index I adds 1;
Step 10: judgment matrix [R]
-1whether be whether unit matrix or cycle index I reach the upper limit; If two Rule of judgment meet any one, then finishing iteration process, and redirect performs following step 11; Otherwise by Qz assignment to Qa, i.e. Qa=Qz, by Z
iassignment to Z, i.e. Z=Z
i, and the step 3 described in revolution execution;
Step 11: circulation terminates, exports and falls correlation matrix Z
iwith the covariance matrix Qz through falling relevant treatment.
The present invention is first by utilizing Qiao Lesiji decomposition method to covariance matrix Q
acarry out upper triangle decomposition (U
tu) upper triangular matrix U is obtained
t, this isolation can improve the counting yield of LLL algorithm.Secondly, before algorithm decomposes each time, to Q
amatrix column vector carries out descending sort according to inner product size, and now matrix of coefficients can obtain minimum round values thus, now fall related algorithm to fall correlated performance better.Finally, rounding when step moves on to and asks Z matrix in orthogonal transformation process is carried out, so just can avoid repeatedly rounding the calculated amount caused in iterative process increases and error accumulation, thus improves counting yield and the success ratio of new algorithm further.
Should be understood that, the part that this instructions does not elaborate all belongs to prior art.
Should be understood that; the above-mentioned description for preferred embodiment is comparatively detailed; therefore the restriction to scope of patent protection of the present invention can not be thought; those of ordinary skill in the art is under enlightenment of the present invention; do not departing under the ambit that the claims in the present invention protect; can also make and replacing or distortion, all fall within protection scope of the present invention, request protection domain of the present invention should be as the criterion with claims.
Claims (2)
1. a related algorithm falls in LLL blur level, it is characterized in that, comprises the following steps:
step 1: input original blur level covariance matrix Q
a
with transformation matrix Z, wherein, Z is unit matrix; Arrange cycle index I=N, N gets positive integer;
step 2: loop initialization number of times I=0;
step 3: by blur level covariance matrix Q
a
carry out descending sort according to the inner product size of column vector, obtain ordinal matrix H, and the new matrix after descending sort is: Q
b
=HQ
a
h
t
;
step 4: to matrix Q
b
carry out triangle decomposition on Qiao Lesiji, obtain the upper triangular matrix U after decomposing
t
and transposed matrix U, matrix U and U
t
all unique solutions;
step 5: carry out QR decomposition transform to matrix U, obtains triangular transformation matrix R, and orthogonal matrix Q
c
;
step 6: to the element R of transformation matrix R
ij
ask whole and obtain INTEGER MATRICES [R], by ask whole after matrix inversion obtain new transformation matrix [R]
-1
;
step 7: ask transform matrix Z
i
, Z
i
=[R]
-1
hZ;
step 8: ask the covariance matrix Qz=Z after transform
i
q
a
z
i
t
;
Step 9: cycle index I adds 1;
Step 10: judgment matrix [R]
-1whether be whether unit matrix or cycle index I reach the upper limit; If two Rule of judgment meet any one, then finishing iteration process, and redirect performs following step 11; Otherwise by Qz assignment to Qa, i.e. Qa=Qz, by Z
iassignment to Z, i.e. Z=Z
i, and the step 3 described in revolution execution;
Step 11: circulation terminates, exports and falls correlation matrix Z
iwith the covariance matrix Qz through falling relevant treatment.
2. related algorithm falls in LLL blur level according to claim 1, it is characterized in that: the N=50 described in step 1.
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107957586A (en) * | 2017-11-21 | 2018-04-24 | 东华理工大学 | Correlation technique drops in a kind of fuzziness decomposed based on lower triangle Cholesky |
| CN107966718A (en) * | 2017-11-23 | 2018-04-27 | 东华理工大学 | A kind of improved searching for integer cycle method |
| CN110554419A (en) * | 2019-09-11 | 2019-12-10 | 东华理工大学 | Ambiguity reduction correlation evaluation method |
| CN110907975A (en) * | 2019-12-13 | 2020-03-24 | 北京遥测技术研究所 | Ambiguity fixing method based on sequential least squares |
| CN111650615A (en) * | 2020-01-14 | 2020-09-11 | 东华理工大学 | Ambiguity lattice reduction quality evaluation method |
| CN114442131A (en) * | 2022-04-11 | 2022-05-06 | 西南交通大学 | Method, device and equipment for calculating target coordinate and storage medium |
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| CN103487819A (en) * | 2013-09-06 | 2014-01-01 | 哈尔滨工程大学 | Integer ambiguity decorrelation method based on ascending sorting optimization |
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| CN103487819A (en) * | 2013-09-06 | 2014-01-01 | 哈尔滨工程大学 | Integer ambiguity decorrelation method based on ascending sorting optimization |
Non-Patent Citations (3)
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| 徐定杰等: "一种改进的GPS整周模糊度降相关LLL算法", 《哈尔滨工业大学学报》 * |
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Cited By (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107957586A (en) * | 2017-11-21 | 2018-04-24 | 东华理工大学 | Correlation technique drops in a kind of fuzziness decomposed based on lower triangle Cholesky |
| CN107957586B (en) * | 2017-11-21 | 2022-02-01 | 东华理工大学 | Ambiguity reduction correlation method based on lower triangular Cholesky decomposition |
| CN107966718A (en) * | 2017-11-23 | 2018-04-27 | 东华理工大学 | A kind of improved searching for integer cycle method |
| CN107966718B (en) * | 2017-11-23 | 2021-04-20 | 东华理工大学 | Improved integer ambiguity searching method |
| CN110554419A (en) * | 2019-09-11 | 2019-12-10 | 东华理工大学 | Ambiguity reduction correlation evaluation method |
| CN110554419B (en) * | 2019-09-11 | 2023-03-24 | 东华理工大学 | Ambiguity reduction correlation evaluation method |
| CN110907975A (en) * | 2019-12-13 | 2020-03-24 | 北京遥测技术研究所 | Ambiguity fixing method based on sequential least squares |
| CN110907975B (en) * | 2019-12-13 | 2021-10-01 | 北京遥测技术研究所 | Ambiguity fixing method based on sequential least squares |
| CN111650615A (en) * | 2020-01-14 | 2020-09-11 | 东华理工大学 | Ambiguity lattice reduction quality evaluation method |
| CN114442131A (en) * | 2022-04-11 | 2022-05-06 | 西南交通大学 | Method, device and equipment for calculating target coordinate and storage medium |
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Application publication date: 20151223 |