CN110248309A - Wireless signal fingerprint restoration methods based on dynamic sliding window - Google Patents
Wireless signal fingerprint restoration methods based on dynamic sliding window Download PDFInfo
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- CN110248309A CN110248309A CN201910399871.8A CN201910399871A CN110248309A CN 110248309 A CN110248309 A CN 110248309A CN 201910399871 A CN201910399871 A CN 201910399871A CN 110248309 A CN110248309 A CN 110248309A
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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
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/0252—Radio frequency fingerprinting
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/15—Correlation function computation including computation of convolution operations
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
- H04W4/02—Services making use of location information
- H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
Abstract
The wireless signal fingerprint restoration methods based on dynamic sliding window that the present invention provides a kind of, specific steps include: to needing the region for carrying out wireless fingerprint prediction to be split, the region after segmentation is scanned using sliding window, estimated in sliding window using a kind of Stiefel manifold optimization method of fast convergence for the prediction of wireless signal fingerprint, judgement is that have to complete signal estimation to region after completing a scanning, if returning to scanning step without if, unfinished region is predicted using fractional prediction wireless signal fingerprint obtained in scanning process before, until being finally completed the prediction to the wireless signal fingerprint of whole region.The present invention can largely restore matrix using less data；It can be applied under various sampling situations, prediction be able to carry out sampled point is sparse；Method provided by the invention can faster realize convergence for Grassmann manifold method.
Description
Technical field
The present invention relates to communications, technical field of navigation and positioning, and in particular, to a kind of wireless communication based on dynamic sliding window
Number fingerprint restoration methods more particularly to a kind of measurement number that the wireless signal data using limited measurement are more predicted
According to method.
Background technique
Cellular network location is all country's driving all the time for the positioning that carries out to emergency place area
Technology, such as the E911 and European E112 of North America.Present widely applied outdoor positioning technology is mainly GPS, but due to
Venue indoors occurs when many emergencies, due to the complexity of environment in book, GPS can not meet the positioning of E911
Demand, therefore sight is turned to the indoor positioning technologies based on cellular network by many researchers.Since present LTE mobile phone exists
Meeting item data center returns to the data that mobile phone for measuring arrives when communication, just contains to be similar to receive in these data and believe
The wireless signal information of number strength information (RSSI).These information can be counted as a kind of wireless signal being observed a little and refer to
Line can establish a wireless signal fingerprint database using this characteristic, so as to realize the indoor positioning for mobile phone.
In the positioning based on wireless signal fingerprint, maximum problem is exactly the foundation of wireless signal fingerprint database.It is logical
The region positioned for often is very big, therefore in order to carry out high-precision positioning, needs to carry out a large amount of database and refer to
Line measures work.Be currently used to solve this problem means generally have it is following several.
The first, by installing specific cell phone software, the signal received is returned automatically；Such as R.Margolies et al.
Delivered in international computer meeting in 2017 " you can find me now? network-based assessment
It is localized in 4G LTE network "
Proc.IEEE INFOCOM, " the Can you find me now delivered on 2017.? Evaluation of
network-based localization in a 4G LTE network"；For another example A.Ray et al. is in Proc.IEEE
INFOCOM, " the Location of LTE measurement records with missing delivered on 2016.
information"；" being positioned using the LTE data of excalation information "
The second, received signals fingerprint is predicted using the signal propagation model of foundation；As A.Chakraborty et al. exists
" the Network-side positioning of cellular-band devices delivered on Proc.IEEE INFOCOM
with minimal effort"；" the network side positioning of cellular band equipment is carried out with less workload "
Third is matched the data of user with time and route in the way of motion track tracking, to export
The location information of continuous user data.As R.Margolies et al. IEEE/ACM Trans.on Netw. (
IEEE/ACM network periodical) on " the Exploiting mobility in proportional fair that delivers
Cellular scheduling:Measurements and algorithms " " movement is utilized in the scheduling of ratio justice honeycomb
Property: measurement and algorithm "；For another example S.C.Ergen et al. is on IEEE Trans.Veh.Technol. (IEEE Vehicle Technology periodical)
" the RSSI-fingerprinting-based mobile phone localization with route delivered
constraints"." the mobile phone positioning based on RSSI fingerprint recognition is constrained with route "
Although these interesting ideas can help to handle specific condition, extensive outdoor fingerprint is carried out in city level
The systems approach of prediction is still an outstanding question.And propose a kind of wireless signal fingerprint based on dynamic sliding window
Restoration methods can solve the above problems to a certain extent, practical value and meaning with higher, wherein the solution of sliding window
It releases as follows:
Wireless signal fingerprint is considered as a matrix, and two dimensions of matrix indicate the two of wireless signal fingerprint location
Position is tieed up, sliding window indicates that choosing a sampling matrix (referred to as window) is slided from the upper left corner of matrix according to a fixed step size,
The length and width of window indicate a sampled data number.
Summary of the invention
For the defects in the prior art, the object of the present invention is to provide one kind.
A kind of wireless signal fingerprint restoration methods based on dynamic sliding window provided according to the present invention, including walk as follows
It is rapid:
Step 1: will need to carry out the region segmentation of wireless signal fingerprint prediction as N number of subregion according to the method set；
Step 2: any subregion divided in step 1 being scanned using sliding window, and is made in sliding window
It is estimated with wireless signal fingerprint of the optimization method based on Stiefel manifold to this subregion；
Step 3: judging whether to complete the prediction to the wireless signal fingerprint of whole region；
If the judging result of step 3 is to be completed, terminate to scan, otherwise, then return step 2.
Preferably, in step 1, N number of subregion is the square and/or square for setting side length；It is described square and/
Or the side length of square and the measurement accuracy of setting are inversely proportional.
Preferably, step 2 includes following sub-step:
Step 2.1: inputting original sampled data matrix PΩ(A) and the dimension d of initial subspace0；
Wherein, the dimension d of initial sub-spaces0Less than the length and width of sliding window, PΩ(A) non-zero in objective matrix A is indicated
Element；
Step 2.2: according to the initial row columns of sampling matrix or the ranks number of setting, being adopted according to the method building of setting
Sample matrix AwAs sliding window, by sampling matrix AwThe coordinate (row, col) in objective matrix A of middle setting element, which is used as, to be adopted
The position of sample matrix, by sampling matrix AwIt carries out singular value decomposition and makes Aw=U Λ VT, the element on Λ leading diagonal is to adopt
Sample matrix AwSingular value, by sampling matrix AwSingular value be denoted as σi1, and have σi1=Λi2i2, take sampling matrix AwApproximate square
Battle arrayAnd it takesAs AdRemaining information, wherein d be approximation parameters, choose suitable d
Value is so that approximate matrix AdRemaining information and sampling matrix AwInformation it is suitable, enter step 2.5；
Wherein, the line number of sampling matrix, columns are denoted as a respectivelyt、bt, and have at>RANK(Aw), bt>RANK(Aw), that is, it adopts
The length and width of sample matrix are all larger than the dimension RANK (A of subspacew), RANK (Aw) it is matrix AwOrder；Objective matrix A refer to
The wireless signal fingerprint matrices of recovery, objective matrix A and sampling matrix AwInitial phase contraposition be set to setting value；U is at×atRank
Unitary Matrix, V bt×btThe Unitary Matrix of rank, VTFor the transposed matrix of V, Λ is positive semi-definite at×btRank diagonal matrix；
σi1For sampling matrix AwThe i-th 1 big singular values, Λi2i2For the element value of the i-th 2 row of matrix Λ, the i-th 2 column, and there is i1=1,
2,…,m；I2=1,2 ..., m；M=min (at, bt)；D is matrix AdApproximation parameters, Ud、VdIt is the preceding d column of U, V, Λ respectivelyd
It is the preceding d row of Λ and the matrix of preceding d column composition；The information of matrix refers to the quantity of nonzero element in matrix；
Step 2.3: judging sampling matrix AwWhether all rows of objective matrix A are scanned through, if judging result is to have swept
It retouches and finishes, then update at、btThe setting line number new as sampling matrix, columns, and return step 2.2 carries out the iteration of a new round,
If judging result is to complete all rows of objective matrix A without scanning, 2.4 are entered step, and be finished in step 2.4,
Before 2.3 or the step 2.5 of going to step, more newline coordinate row=row0+τrat；
Wherein, a is updatedt、btThe specific method is as follows:
at=at0+a′
bt=bt0+b′
at0For the line number for updating preceding sampling matrix, bt0For the columns for updating preceding sampling matrix；A ' and b ' is the step of setting
Long value；row0For the row coordinate value before update, τrFor the random real number between 0 to 1；If at、btThe number and/or a of updatet、bt
Updated value meets the condition of setting, then stops iteration；
Step 2.4: judging whether sampling matrix has scanned all column for completing current line in objective matrix A, if sampling square
Battle array has scanned all column for completing current line in objective matrix A, then return step 2.3, if sampling matrix does not scan through target
All column of current line in matrix A, then update column coordinate col=col0+τcbt, and guarantee that updated column coordinate col is not more than
The columns of objective matrix A, enters step 2.5；
Wherein, the current line refers to the row of the corresponding objective matrix A of row value；col0For the column coordinate value before update, τc
For the random real number between 0 to 1；
Step 2.5: judge matrix element in present sample matrix whether and meanwhile meet the first formula, the second formula and
Third formula；If not meeting the first formula, the second formula and third formula simultaneously, ungratified element is set as zero, and
2.6 are entered step, if meeting the first formula, the second formula and third formula simultaneously, is directly entered step 2.6；
Wherein, when forefront refers to the column of the corresponding objective matrix A of col value；First formula are as follows:
RANK(Aw)≤at
Second formula are as follows:
RANK(Aw)≤mi3,
The third formula are as follows:
Wherein, mi3Refer to sampling matrix AwIn the i-th 3 column non-sampling wireless received signals fingerprint number,Refer to sampling matrix Aw
Order；
Step 2.6: by sampling matrix AwParameter with Stiefel manifold algorithm passes through sampling matrix A as input valuewWith
Completion matrix A is calculated in the parameter iteration of Stiefel manifold algorithmd, and return step 2.4.
Preferably, in step 2.5, the parameter of Stiefel manifold algorithm is determined as follows:
Step 2.5.1: iteration direction, objective function, iterative formula and the iteration of Stiefel manifold algorithm are determined respectively
Step-length.
Preferably, in step 2.5, it is iterated calculating as follows:
Step 2.5.2: the matrix subspace U after Stiefel manifold algorithm optimization is solvedoptimized；
Step 2.5.3: final completion matrix A is solved according to the matrix subspace U after optimizationd-optimized；
Wherein, step 2.5.2 includes following sub-step:
Step 2.5.2a: the matrix U of the orthogonal m × d of an initial column is inputted respectivelyt, t=0, initial known portions number
According to matrix PΩ(A) and maximum the number of iterations Tmax, enabling t is the number of iterations, initial value 0；
Step 2.5.2b: in PΩ(A) a column [C is randomly selected inq]Ω；
Wherein, CqRefer to matrix PΩ(A) q column, [Cq]ΩRefer to CqIn nonzero element；
Step 2.5.2c: the first intermediate quantity is calculated
Wherein, [Ut]ΩRefer to UtIn nonzero element；
Step 2.5.2d: the first intermediate quantity w is calculatedtIn UtOn projection pt:
pt=Utwt
Step 2.5.2e: the second intermediate quantity r is calculatedt=PΩ(Cq-pt)；
Wherein, PΩ() indicates the known element of the matrix in bracket；
Step 2.5.2f: it calculates
Step 2.5.2g: judging whether t and T is equal, if t ≠ T, updates the number of iterations t=t0+ 1, if t=T, into
Enter step 2.5.2h；
Wherein, t0For the number of iterations before update；
Step 2.5.2h:Uoptimized=Ut；
Step 2.5.3 includes following sub-step:
Step 2.5.3a: third intermediate quantity is calculated
Wherein, nmaxFor total columns value of objective matrix A；
Step 2.5.3b: it calculates
Preferably, in step 2.5.1, the iteration direction of Stiefel manifold algorithm is
Wherein, F is the objective function of Stiefel manifold algorithm,For the gradient of Stiefel manifold algorithm objective function.
Preferably, in step 2.5.1, the objective function of Stiefel manifold algorithm are as follows:
Wherein, UdIt is the d dimension matrix comprising d m dimension orthogonal vectors of necessary requirement；AdIt is finally to need
Matrix after obtained recovery, ΛdD × d the matrix being made of d maximum singular values,It is the reality of d × n
Unitary matrice；Take the 4th intermediate quantityUse wjThe jth column for indicating W, then haveThen xjTo meet objective function F
J-th of column vector；For xjConjugation；CjIt is jth column of the objective matrix A in pivot column.
Preferably, in step 2.5.1, the iterative formula of Stiefel manifold algorithm are as follows:
Wherein, UtAnd Ut+1It is the iteration item of matrix subspace；ηtIndicate the step parameter in the t times iteration, rt=PΩ
(Cq-pt), PΩ() indicates the known element of the matrix in bracket,watRefer to the w in the t times iterative processj。
Preferably, in step 2.5.1, the iteration step length of Stiefel manifold algorithm are as follows:
A kind of computer readable storage medium for being stored with computer program provided according to the present invention, the computer journey
The step of above-mentioned wireless signal fingerprint restoration methods based on dynamic sliding window are realized when sequence is executed by processor.
Compared with prior art, the present invention have it is following the utility model has the advantages that
1, the wireless signal fingerprint restoration methods provided by the invention based on dynamic sliding window, can utilize less data
Matrix is largely restored；
2, the wireless signal fingerprint restoration methods provided by the invention based on dynamic sliding window, can be applied to various samplings
In the case of, prediction is able to carry out sampled point is sparse；
3, the wireless signal fingerprint restoration methods provided by the invention based on dynamic sliding window are flowed relative to Grassmann
Convergence can be faster realized for shape method.
Detailed description of the invention
Upon reading the detailed description of non-limiting embodiments with reference to the following drawings, other feature of the invention,
Objects and advantages will become more apparent upon:
Fig. 1 is a kind of wireless signal fingerprint restoration methods flow diagram based on dynamic sliding window of the invention；
Fig. 2 is the flow diagram of the Stiefel manifold optimization method of fast convergence；
Fig. 3 is the error distribution schematic diagram of the result obtained with preference of the present invention；
Fig. 4 is the distribution schematic diagram of the sampled point in preference of the present invention sampling practice operation；
Fig. 5 is preference of the present invention figure compared with the convergence rate of Grassmann manifold method.
Specific embodiment
The present invention is described in detail combined with specific embodiments below.Following embodiment will be helpful to the technology of this field
Personnel further understand the present invention, but the invention is not limited in any way.It should be pointed out that the ordinary skill of this field
For personnel, without departing from the inventive concept of the premise, several changes and improvements can also be made.These belong to the present invention
Protection scope.
A kind of wireless signal fingerprint restoration methods based on dynamic sliding window provided according to the present invention, including walk as follows
It is rapid:
Step 1: will need to carry out the region segmentation of wireless signal fingerprint prediction as N number of subregion according to the method set；
Step 2: any subregion divided in step 1 being scanned using sliding window, and is made in sliding window
It is estimated with wireless signal fingerprint of the optimization method based on Stiefel manifold to this subregion；
Step 3: judging whether to complete the prediction to the wireless signal fingerprint of whole region；
If the judging result of step 3 is to be completed, terminate to scan, otherwise, then return step 2.
In step 1, N number of subregion is the square and/or square for setting side length；The square and/or pros
The side length of body and the measurement accuracy of setting are inversely proportional.
Preferably, step 2 includes following sub-step:
Step 2.1: inputting original sampled data matrix PΩ(A) and the dimension d of initial subspace0；
Wherein, the dimension d of initial sub-spaces0Less than the length and width of sliding window, PΩ(A) non-zero in objective matrix A is indicated
Element；
Step 2.2: according to the initial row columns of sampling matrix or the ranks number of setting, being adopted according to the method building of setting
Sample matrix AwAs sliding window, by sampling matrix AwThe coordinate (row, col) in objective matrix A of middle setting element, which is used as, to be adopted
The position of sample matrix, by sampling matrix AwIt carries out singular value decomposition and makes Aw=U Λ VT, the element on Λ leading diagonal is to adopt
Sample matrix AwSingular value, by sampling matrix AwSingular value be denoted as σi1, and have σi1=Λi2i2, take sampling matrix AwApproximate square
Battle arrayAnd it takesAs AdRemaining information, wherein d be approximation parameters, choose suitable d
Value is so that approximate matrix AdRemaining information and sampling matrix AwInformation it is suitable, enter step 2.5；
Wherein, the line number of sampling matrix, columns are denoted as a respectivelyt、bt, and have at>RANK(Aw), bt>RANK(Aw), that is, it adopts
The length and width of sample matrix are all larger than the dimension RANK (A of subspacew), RANK (Aw) it is matrix AwOrder；Objective matrix A refer to
The wireless signal fingerprint matrices of recovery, objective matrix A and sampling matrix AwInitial phase contraposition be set to setting value；U is at×atRank
Unitary Matrix, V bt×btThe Unitary Matrix of rank, VTFor the transposed matrix of V, Λ is positive semi-definite at×btRank diagonal matrix；
σi1For sampling matrix AwThe i-th 1 big singular values, Λi2i2For the element value of the i-th 2 row of matrix Λ, the i-th 2 column, and there is i1=1,
2,…,m；I2=1,2 ..., m；M=min (at, bt)；D is matrix AdApproximation parameters, Ud、VdIt is the preceding d column of U, V, Λ respectivelyd
It is the preceding d row of Λ and the matrix of preceding d column composition；The information of matrix refers to the quantity of nonzero element in matrix；
Step 2.3: judging sampling matrix AwWhether all rows of objective matrix A are scanned through, if judging result is to have swept
It retouches and finishes, then update at、btThe setting line number new as sampling matrix, columns, and return step 2.2 carries out the iteration of a new round,
If judging result is to complete all rows of objective matrix A without scanning, 2.4 are entered step, and be finished in step 2.4,
Before 2.3 or the step 2.5 of going to step, more newline coordinate row=row0+τrat；
Wherein, a is updatedt、btThe specific method is as follows:
at=at0+a′
bt=bt0+b′
at0For the line number for updating preceding sampling matrix, bt0For the columns for updating preceding sampling matrix；A ' and b ' is the step of setting
Long value；row0For the row coordinate value before update, τrFor the random real number between 0 to 1；If at、btThe number and/or a of updatet、bt
Updated value meets the condition of setting, then stops iteration；
Step 2.4: judging whether sampling matrix has scanned all column for completing current line in objective matrix A, if sampling square
Battle array has scanned all column for completing current line in objective matrix A, then return step 2.3, if sampling matrix does not scan through target
All column of current line in matrix A, then update column coordinate col=col0+τcbt, and guarantee that updated column coordinate col is not more than
The columns of objective matrix A, enters step 2.5；
Wherein, the current line refers to the row of the corresponding objective matrix A of row value；col0For the column coordinate value before update, τc
For the random real number between 0 to 1；
Step 2.5: judge matrix element in present sample matrix whether and meanwhile meet the first formula, the second formula and
Third formula；If not meeting the first formula, the second formula and third formula simultaneously, ungratified element is set as zero, and
2.6 are entered step, if meeting the first formula, the second formula and third formula simultaneously, is directly entered step 2.6；
Wherein, when forefront refers to the column of the corresponding objective matrix A of col value；First formula are as follows:
RANK(Aw)≤at
Second formula are as follows:
RANK(Aw)≤mi3,
The third formula are as follows:
Wherein, mi3Refer to sampling matrix AwIn the i-th 3 column non-sampling wireless received signals fingerprint number,Refer to sampling matrix Aw
Order；Particularly, " not sampling " mark is position element in matrix herein, rather than the member not covered by sampling matrix
Element；
Step 2.6: by sampling matrix AwParameter with Stiefel manifold algorithm passes through sampling matrix A as input valuewWith
Completion matrix A is calculated in the parameter iteration of Stiefel manifold algorithmd, and return step 2.4.
In step 2.5, the parameter of Stiefel manifold algorithm is determined as follows:
Step 2.5.1: iteration direction, objective function, iterative formula and the iteration of Stiefel manifold algorithm are determined respectively
Step-length.
In step 2.5, it is iterated calculating as follows:
Step 2.5.2: the matrix subspace U after Stiefel manifold algorithm optimization is solvedoptimized；
Step 2.5.3: final completion matrix A is solved according to the matrix subspace U after optimizationd-optimized；
Wherein, step 2.5.2 includes following sub-step:
Step 2.5.2a: the matrix U of the orthogonal m × d of an initial column is inputted respectivelyt, t=0, initial known portions number
According to matrix PΩ(A) and maximum the number of iterations Tmax, enabling t is the number of iterations, initial value 0；
Step 2.5.2b: in PΩ(A) a column [C is randomly selected inq]Ω；
Wherein, CqRefer to matrix PΩ(A) q column, [Cq]ΩRefer to CqIn nonzero element；
Step 2.5.2c: the first intermediate quantity is calculated
Wherein, [Ut]ΩRefer to UtIn nonzero element；
Step 2.5.2d: the first intermediate quantity w is calculatedtIn UtOn projection pt:
pt=Utwt
Step 2.5.2e: the second intermediate quantity r is calculatedt=PΩ(Cq-pt)；
Wherein, PΩ() indicates the known element of the matrix in bracket；
Step 2.5.2f: it calculates
Step 2.5.2g: judging whether t and T is equal, if t ≠ T, updates the number of iterations t=t0+ 1, if t=T, into
Enter step 2.5.2h；
Wherein, t0For the number of iterations before update；
Step 2.5.2h:Uoptimized=Ut；
Step 2.5.3 includes following sub-step:
Step 2.5.3a: third intermediate quantity is calculated
Wherein, nmaxFor total columns value of objective matrix A；
Step 2.5.3b: it calculates
In step 2.5.1, the iteration direction of Stiefel manifold algorithm is
Wherein, F is the objective function of Stiefel manifold algorithm,For the gradient of Stiefel manifold algorithm objective function.
In step 2.5.1, the objective function of Stiefel manifold algorithm are as follows:
Wherein, UdIt is the d dimension matrix comprising d m dimension orthogonal vectors of necessary requirement；AdIt is finally to need
Matrix after obtained recovery, ΛdD × d the matrix being made of d maximum singular values,It is the reality of d × n
Unitary matrice；Take the 4th intermediate quantityUse wjThe jth column for indicating W, then haveThen xjTo meet objective function F
J-th of column vector；For xjConjugation；CjIt is jth column of the objective matrix A in pivot column.
In step 2.5.1, the iterative formula of Stiefel manifold algorithm are as follows:
Wherein, UtAnd Ut+1It is the iteration item of matrix subspace；ηtIndicate the step parameter in the t times iteration, rt=PΩ
(Cq-pt), PΩ() indicates the known element of the matrix in bracket,watRefer to the w in the t times iterative processj。
In step 2.5.1, the iteration step length of Stiefel manifold algorithm are as follows:
A kind of computer readable storage medium for being stored with computer program provided according to the present invention, the computer journey
The step of above-mentioned wireless signal fingerprint restoration methods based on dynamic sliding window are realized when sequence is executed by processor.
Specifically, the simulated environment of the present embodiment are as follows: MATLAB 2012a
Including algorithm parameter obtaining step and iterative calculation step；Wherein
In step 1, selected data acquisition city shown in Fig. 4 freely, 69.8 square kilometres of area, about
8820000 sampled points are carried out using wireless signal fingerprint of the obtained data acquired along city main stem road to branch road
Prediction.Initial sampled data accounts for the 6.7% of overall area.
In step 3, the error distribution of the result of the wireless signal fingerprint prediction finally obtained is as shown in Figure 3.
In the description of the present application, it is to be understood that term " on ", "front", "rear", "left", "right", " is erected at "lower"
Directly ", the orientation or positional relationship of the instructions such as "horizontal", "top", "bottom", "inner", "outside" is orientation based on the figure or position
Relationship is set, description the application is merely for convenience of and simplifies description, rather than the device or element of indication or suggestion meaning are necessary
It with specific orientation, is constructed and operated in a specific orientation, therefore should not be understood as the limitation to the application.
One skilled in the art will appreciate that in addition to realizing system provided by the invention in a manner of pure computer readable program code
It, completely can be by the way that method and step be carried out programming in logic come so that provided by the invention other than system, device and its modules
System, device and its modules are declined with logic gate, switch, specific integrated circuit, programmable logic controller (PLC) and insertion
The form of controller etc. realizes identical program.So system provided by the invention, device and its modules may be considered that
It is a kind of hardware component, and the knot that the module for realizing various programs for including in it can also be considered as in hardware component
Structure；It can also will be considered as realizing the module of various functions either the software program of implementation method can be Hardware Subdivision again
Structure in part.
Specific embodiments of the present invention are described above.It is to be appreciated that the invention is not limited to above-mentioned
Particular implementation, those skilled in the art can make a variety of changes or modify within the scope of the claims, this not shadow
Ring substantive content of the invention.In the absence of conflict, the feature in embodiments herein and embodiment can any phase
Mutually combination.
Claims (10)
1. a kind of wireless signal fingerprint restoration methods based on dynamic sliding window, which comprises the steps of:
Step 1: will need to carry out the region segmentation of wireless signal fingerprint prediction as N number of subregion according to the method set；
Step 2: any subregion divided in step 1 being scanned using sliding window, and uses base in sliding window
The wireless signal fingerprint of this subregion is estimated in the optimization method of Stiefel manifold；
Step 3: judging whether to complete the prediction to the wireless signal fingerprint of whole region；
If the judging result of step 3 is to be completed, terminate to scan, otherwise, then return step 2.
2. the wireless signal fingerprint restoration methods according to claim 1 based on dynamic sliding window, which is characterized in that
In step 1, N number of subregion is the square and/or square for setting side length；It is described square and/or square
Side length and the measurement accuracy of setting are inversely proportional.
3. the wireless signal fingerprint restoration methods according to claim 1 based on dynamic sliding window, which is characterized in that
Step 2 includes following sub-step:
Step 2.1: inputting original sampled data matrix PΩ(A) and the dimension d of initial subspace0；
Wherein, the dimension d of initial sub-spaces0Less than the length and width of sliding window, PΩ(A) nonzero element in objective matrix A is indicated；
Step 2.2: according to the initial row columns of sampling matrix or the ranks number of setting, according to the method building sampling square of setting
Battle array AwAs sliding window, by sampling matrix AwThe coordinate (row, col) in objective matrix A of middle setting element is as sampling square
The position of battle array, by sampling matrix AwIt carries out singular value decomposition and makes Aw=U Λ VT, the element on Λ leading diagonal is to sample square
Battle array AwSingular value, by sampling matrix AwSingular value be denoted as σi1, and have σi1=Λi2i2, take sampling matrix AwApproximate matrixAnd it takesAs AdRemaining information, wherein d be approximation parameters, choose suitable d value
So that approximate matrix AdRemaining information and sampling matrix AwInformation it is suitable, enter step 2.5；
Wherein, the line number of sampling matrix, columns are denoted as a respectivelyt、bt, and have at>RANK(Aw), bt>RANK(Aw), that is, sample square
The length and width of battle array are all larger than the dimension RANK (A of subspacew), RANK (Aw) it is matrix AwOrder；Objective matrix A refers to be restored
Wireless signal fingerprint matrices, objective matrix A and sampling matrix AwInitial phase contraposition be set to setting value；U is at×atRank
Positive matrices, V bt×btThe Unitary Matrix of rank, VTFor the transposed matrix of V, Λ is positive semi-definite at×btRank diagonal matrix；σi1For
Sampling matrix AwThe i-th 1 big singular values, Λi2i2For the element value of the i-th 2 row of matrix Λ, the i-th 2 column, and there is i1=1,2 ..., m；i2
=1,2 ..., m；M=min (at, bt)；D is matrix AdApproximation parameters, Ud、VdIt is the preceding d column of U, V, Λ respectivelydIt is the preceding d of Λ
The matrix of capable and preceding d column composition；The information of matrix refers to the quantity of nonzero element in matrix；
Step 2.3: judging sampling matrix AwWhether all rows of objective matrix A are scanned through, if judging result is to have scanned through
Finish, then updates at、btThe setting line number new as sampling matrix, columns, and return step 2.2 carries out the iteration of a new round, if sentencing
Disconnected result is that all rows of objective matrix A are completed without scanning, then enters step 2.4, and be finished in step 2.4, jump
To step 2.3 or step 2.5, more newline coordinate row=row0+τrat；
Wherein, a is updatedt、btThe specific method is as follows:
at=at0+a′
bt=bt0+b′
at0For the line number for updating preceding sampling matrix, bt0For the columns for updating preceding sampling matrix；A ' and b ' is the step value of setting；
row0For the row coordinate value before update, τrFor the random real number between 0 to 1；If at、btThe number and/or a of updatet、btAfter update
Value meet setting condition, then stop iteration；
Step 2.4: judging whether sampling matrix has scanned all column for completing current line in objective matrix A, if sampling matrix is
All column of current line in objective matrix A are completed in scanning, then return step 2.3, if sampling matrix does not scan through objective matrix A
All column of middle current line then update column coordinate col=col0+τcbt, and guarantee updated column coordinate col no more than target
The columns of matrix A, enters step 2.5；
Wherein, the current line refers to the row of the corresponding objective matrix A of row value；col0For the column coordinate value before update, τcIt is arrived for 0
Random real number between 1；
Step 2.5: judge matrix element in present sample matrix whether and meanwhile meet the first formula, the second formula and third
Formula；If not meeting the first formula, the second formula and third formula simultaneously, ungratified element is set as zero, and enter
Step 2.6, if meeting the first formula, the second formula and third formula simultaneously, it is directly entered step 2.6；
Wherein, when forefront refers to the column of the corresponding objective matrix A of col value；First formula are as follows:
RANK(Aw)≤at
Second formula are as follows:
The third formula are as follows:
Wherein, mi3Refer to sampling matrix AwIn the i-th 3 column non-sampling wireless received signals fingerprint number,Refer to sampling matrix AwOrder；
Step 2.6: by sampling matrix AwParameter with Stiefel manifold algorithm passes through sampling matrix A as input valuewWith
Completion matrix A is calculated in the parameter iteration of Stiefel manifold algorithmd, and return step 2.4.
4. the wireless signal fingerprint restoration methods according to claim 3 based on dynamic sliding window, which is characterized in that step
In 2.5, the parameter of Stiefel manifold algorithm is determined as follows:
Step 2.5.1: iteration direction, objective function, iterative formula and the iteration step of Stiefel manifold algorithm are determined respectively
It is long.
5. the wireless signal fingerprint restoration methods according to claim 3 based on dynamic sliding window, which is characterized in that step
In 2.5, it is iterated calculating as follows:
Step 2.5.2: the matrix subspace U after Stiefel manifold algorithm optimization is solvedoptimize d；
Step 2.5.3: final completion matrix A is solved according to the matrix subspace U after optimizationd-optimize d；
Wherein, step 2.5.2 includes following sub-step:
Step 2.5.2a: the matrix U of the orthogonal m × d of an initial column is inputted respectivelyt, t=0, initial known portions data
Matrix PΩ(A) and maximum the number of iterations Tmax, enabling t is the number of iterations, initial value 0；
Step 2.5.2b: in PΩ(A) a column [C is randomly selected inq]Ω；
Wherein, CqRefer to matrix PΩ(A) q column, [Cq]ΩRefer to CqIn nonzero element；
Step 2.5.2c: the first intermediate quantity is calculated
Wherein, [Ut]ΩRefer to UtIn nonzero element；
Step 2.5.2d: the first intermediate quantity w is calculatedtIn UtOn projection pt:
pt=Utwt
Step 2.5.2e: the second intermediate quantity r is calculatedt=PΩ(Cq-pt)；
Wherein, PΩ() indicates the known element of the matrix in bracket；
Step 2.5.2f: it calculates
Step 2.5.2g: judging whether t and T is equal, if t ≠ T, updates the number of iterations t=t0+ 1, if t=T, enter step
2.5.2h；
Wherein, t0For the number of iterations before update；
Step 2.5.2h:Uoptimize d=Ut；
Step 2.5.3 includes following sub-step:
Step 2.5.3a: third intermediate quantity is calculated
Wherein, nmaxFor total columns value of objective matrix A；
Step 2.5.3b: it calculates
6. the wireless signal fingerprint restoration methods according to claim 4 based on dynamic sliding window, which is characterized in that step
2.5.1 in, the iteration direction of Stiefel manifold algorithm is
Wherein, F is the objective function of Stiefel manifold algorithm,For the gradient of Stiefel manifold algorithm objective function.
7. the wireless signal fingerprint restoration methods according to claim 4 based on dynamic sliding window, which is characterized in that step
2.5.1 in, the objective function of Stiefel manifold algorithm are as follows:
Wherein, UdIt is the d dimension matrix comprising d m dimension orthogonal vectors of necessary requirement；AdBe finally need into
Matrix after the recovery that row obtains, ΛdD × d the matrix being made of d maximum singular values,It is the real tenth of the twelve Earthly Branches square of d × n
Battle array；Take the 4th intermediate quantityUse wjThe jth column for indicating W, then haveThen xjFor the jth for meeting objective function F
A column vector；For xjConjugation；CjIt is jth column of the objective matrix A in pivot column.
8. the wireless signal fingerprint restoration methods according to claim 7 based on dynamic sliding window, which is characterized in that step
2.5.1 in, the iterative formula of Stiefel manifold algorithm are as follows:
Wherein, UtAnd Ut+1It is the iteration item of matrix subspace；ηtIndicate the step parameter in the t times iteration, rt=PΩ(Cq-
pt), PΩ() indicates the known element of the matrix in bracket,watRefer to the w in the t times iterative processj。
9. the wireless signal fingerprint restoration methods according to claim 8 based on dynamic sliding window, which is characterized in that step
2.5.1 in, the iteration step length of Stiefel manifold algorithm are as follows:
10. a kind of computer readable storage medium for being stored with computer program, which is characterized in that the computer program is located
Reason device realizes the wireless signal fingerprint restoration methods described in any one of claims 1 to 9 based on dynamic sliding window when executing
The step of.
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