CN103648106B - WiFi indoor positioning method of semi-supervised manifold learning based on category matching - Google Patents

WiFi indoor positioning method of semi-supervised manifold learning based on category matching Download PDF

Info

Publication number
CN103648106B
CN103648106B CN201310750528.6A CN201310750528A CN103648106B CN 103648106 B CN103648106 B CN 103648106B CN 201310750528 A CN201310750528 A CN 201310750528A CN 103648106 B CN103648106 B CN 103648106B
Authority
CN
China
Prior art keywords
rss
radio map
semi
data
line
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201310750528.6A
Other languages
Chinese (zh)
Other versions
CN103648106A (en
Inventor
谭学治
周才发
马琳
邓仲哲
何晨光
迟永钢
魏守明
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Harbin University of Technology Robot Group Co., Ltd.
Original Assignee
Harbin Institute of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Harbin Institute of Technology filed Critical Harbin Institute of Technology
Priority to CN201310750528.6A priority Critical patent/CN103648106B/en
Publication of CN103648106A publication Critical patent/CN103648106A/en
Application granted granted Critical
Publication of CN103648106B publication Critical patent/CN103648106B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Abstract

The invention discloses a WiFi indoor positioning method of semi-supervised manifold learning based on category matching, and relates to an indoor positioning method. The WiFi indoor positioning method disclosed by the invention is used for solving the problems that a Radio Map database is large and the like in an existing WiFi indoor positioning method. The WiFi indoor positioning method comprises the following steps: 1. collecting Radio Map; 2. carrying out intrinsic dimension analysis on the Radio Map; 3. carrying out clustering analysis on the Radio Map; 4. carrying out dimensionality reduction on the Radio Map; 5. adding RSS in the Radio Map to obtain Radio Mapul; and 6. carrying out dimensionality reduction on the Radio Mapul to obtain a characteristic transformation matrix V, and forming an online positioning database through the Radio Map * and V. The WiFi indoor positioning method also comprises the following steps: 1. online testing RSS; 2. carrying out dimensionality reduction on the RSS to obtain RSS *; 3. outputting a positioning result; and 4. updating the database. The WiFi indoor positioning method disclosed by the invention is applied to the field of network technology.

Description

A kind of WiFi indoor orientation methods of the semi-supervised manifold learning based on categorical match
Technical field
The present invention relates to a kind of indoor orientation method, and in particular to a kind of semi-supervised manifold learning based on categorical match WiFi indoor orientation methods.
Background technology
As WLAN develops rapidly widely available with mobile terminal device worldwide, go out in recent years The related technology of many indoor positionings and application are showed.Due to the complexity of multipath effect, signal attenuation and indoor positioning environment, It is difficult to reach high-precision indoor positioning requirement based on the indoor orientation method of traditional signal propagation model.Based on the time of advent (Time of Arrival), reaching time-difference (Time Difference of Arrival) and angle of arrival (Angles of Arrival) although etc. localization method can substantially meet positioning precision demand, but be required for positioning terminal to have extra hardware Equipment is supported, with compared with big limitation, so as to cause not obtain general based on the indoor locating system of above-mentioned a few class localization methods And.
At present, it is widely applied based on the WiFi indoor orientation methods of WLAN location fingerprint (Finger Print). The network establishing method of the method is with low cost, and which uses 2.4GHz ISM (Industrial Science Medicine) public It is total to frequency range and without the need for adding positioning measurement specialized hardware on existing utility.Only need to wireless network card by mobile terminal and Signal intensity (the Received Signal of the access point (Access Point, AP) that corresponding software measurement is received Strength, RSS), thus building network signal coverage diagram (Radio Map), and then by matching algorithm predicting movement The coordinate of user present position, or relative position.
But the Radio Map for setting up by this way include huge data message, and as positioning region expands, Radio Map may(According to position matching mode and algorithms selection)Exponentially situation increases.Obtain dependency number as much as possible Positioning precision can be lifted for whole system according to characteristic information, but processing substantial amounts of characteristic information increases algorithm expense, Location algorithm cannot be effectively run on the limited mobile terminal of disposal ability, while some characteristic informations are probably for positioning Even there is negative effect without effect, cause matching efficiency to reduce, so as to cause the realization for matching location algorithm to become more multiple It is miscellaneous, and positioning precision decline.
When the reference point that the number of AP increases and positions(Reference Point)During increase, the data letter of Radio Map Breath increases.Now, the information of the AP numbers for representing in Radio Map illustrates the dimension of data.Therefore, when AP numbers increase, Radio Map have reformed into high dimensional data.For mitigate process high dimensional data burden, dimension-reduction algorithm be effective solution it One.High dimensional data may include many features, and these features are all describing same things, and these features are tight to a certain extent It is close connected.Such as when taking pictures from all angles to same object simultaneously, the data for obtaining are just containing the information for overlapping.If Some nonoverlapping expression for simplifying of these data can be obtained, it will the efficiency for being greatly enhanced data processing operation is simultaneously certain Accuracy is improved in degree.The purpose of dimension-reduction algorithm is also exactly the treatment effeciency for improving high dimensional data.
Can be in addition to efficient process except data can be simplified, dimension reduction method can also realize data visualization.Due to Many statistical and machine learning algorithms are very poor for the accuracy of optimal solution, and the visualization application of dimensionality reduction can make user's energy The ability of the space structure and algorithm output of high dimensional data is actually seen enough, with very strong using value.
There are many dimension-reduction algorithms based on different purposes at present, include linearity and non-linearity dimension-reduction algorithm.Wherein PCA (Principal Component Analysis) and LDA (Linear Discriminant Analysis) are typical linear Dimension-reduction algorithm.This class algorithm has good result for the high dimensional data with linear structure, but for non-linear The not no good result of the high dimensional data of structure.Typical nonlinear reductive dimension algorithm is with manifold learning(Manifold Learning) Algorithm.On Science magazines in 2000 the same phase delivered 3 be related to manifold learning arithmetic in propose 2 kinds of classical streams Shape learning algorithm:LLE (Local Linear Embedding) and ISOMAP (Isometric Mapping).Thus, various bases In terms of manifold learning arithmetic in different criterions is suggested and some manifold learning arithmetic is applied to image procossing.LDE (Local Discriminant Embedding)Algorithm is later proposition in manifold learning arithmetic, and it is a kind of typical The manifold learning arithmetic that feature based is extracted, and it is not based only on visualization target.
For above-mentioned dimension-reduction algorithm can not improve dimensionality reduction to the online RSS data for obtaining or newly-increased RSS Precision.Due to the change of indoor positioning environment, not in the same time, particularly after long-time, the dependency between RSS data is just Can reduce.In existing algorithm, there is the class algorithm can be by the RSS data in different time while adding corresponding data with existing In, so as to strengthen the dependency between different pieces of information, improve dimensionality reduction precision.This class algorithm is generally referred to as semi-supervised algorithm.Root The characteristics of according to semi-supervised algorithm, propose that semi-supervised discriminating is embedded(Semi-supervised Discriminant Embedding, SDE)Algorithm.
According to the characteristics of SDE algorithms, the RSS for newly obtaining online is added into existing Radio by the way of categorical match Map, then carries out local and differentiates embedded dimensionality reduction, so as to propose that the semi-supervised local based on categorical match differentiates embedded mobile GIS (Classification Matching Based Semi-supervised Discriminant Embedding, CM- SDE).Dimensionality reduction is carried out to Radio Map using CM-SDE algorithms, the Radio Map after dimensionality reduction is drawn, after to dimensionality reduction Radio Map indoor positionings, so that propose the WiFi indoor positioning algorithms based on CM-SDE algorithms.
The content of the invention
The present invention is to solve Radio Map data bases present in existing WiFi indoor orientation methods are big, and due to Tuning on-line stage computation complexity is high and being difficult to of causing obtains RSS data, is difficult in mobile terminal reality using on-line stage It is existing and it is difficult to ensure that the problems such as the requirement of real-time of positioning, and provide a kind of semi-supervised manifold learning based on categorical match WiFi indoor orientation methods.
Press following based on the WiFi indoor orientation method off-line phases position fixing process of the semi-supervised manifold learning of categorical match Step is realized:
First, to room area arrangement AP to be positioned, make wireless signal cover room area to be positioned, complete WiFi nets Network builds;
The corresponding coordinate of reference point is chosen and is recorded in room area rule to be positioned, measurement simultaneously records reference point successively The RSS signals of all AP for receiving build Radio Map, and store Radio Map as position feature information;
2nd, the intrinsic dimension of the Radio Map using the intrinsic dimension algorithm for estimating of GMST to building in step one is carried out point Analysis, |input paramete one of of the intrinsic dimension for obtaining as CM-SDE algorithms, determines the dimension after Radio Map dimensionality reductions;
3rd, cluster analyses are carried out using KFCM algorithms to Radio Map, realize the category label of the Radio Map of foundation, One of and the |input paramete as CM-SDE, and corresponding initial cluster center and category label are provided;
4th, the category label in the intrinsic dimension and step 3 in step 2 is used as |input paramete, using CM-SDE algorithms To the Radio Map dimensionality reductions built in step one, the RadioMap after corresponding dimensionality reduction is drawn*, RadioMap*As in matching Location database is used for the tuning on-line stage;
5th, by the unmarked RSS that obtains of different user tuning on-line stage test, added by the way of categorical match to In existing Radio Map, obtain including unmarked Radio map RadioMap accordinglyul, by gathering that categorical match updates Class center is used as classification |input paramete new in CM-SDE algorithms;
6th, the cluster centre of the renewal in step 5 is used as |input paramete, using CM-SDE to RadioMapulDimensionality reduction is obtained Eigentransformation matrix V ', V ' and RadioMap*On-line matching location database is collectively formed, is positioned for on-line stage;Wherein, The line phase orientation is specially:
Six(One), on-line testing RSS;
Six(Two), adopt V by RSS dimensionality reductions for RSS*
Six(Three), using KNN algorithms carry out matching positioning output positioning result;
Six(Four), user's positioning terminal location database update;
A kind of off-line phase of the WiFi indoor orientation methods of the semi-supervised manifold learning based on categorical match is completed Implementation.
Under being passed through based on the WiFi indoor orientation method on-line stage position fixing processs of the semi-supervised manifold learning of categorical match State step realization:
First, on-line testing RSS;
2nd, the RSS of the point to be determined for obtaining is obtained into RSS* using the conversion of eigentransformation matrix dimensionality reduction;
3rd, using KNN algorithms to RSS* and Radio Map* match bits, the particular location coordinate of point to be determined is carried out pre- The renewal of online data is surveyed and carries out, which realizes that process is:
(1)On-line stage, the RSS=[AP received at test point1,AP2,…,APn], it is multiplied with eigentransformation matrix V ', from And draw the RSS ' after dimensionality reduction=[AP1,AP2,…APd], wherein d represents intrinsic dimension;
(2)Matching for RSS ' and Radio Map* is realized using KNN algorithms, using the K reference point nearest with RSS ' The meansigma methodss of coordinate as test point (x ', y '), its expression formula are:
In formula, (x ', y ') be test point prediction coordinate, (xi,yi) be i-th Neighbor Points coordinate, K be KNN algorithms in The number of neighbour;
4th, user's positioning terminal location database updates, that is, complete semi-supervised manifold learning based on categorical match WiFi on-line stage indoor orientation methods.
Invention effect:
Need to ask for CM-SDE algorithms proposed by the present invention and background, by Harbin Institute of Technology's research park 2A The indoor positioning region of 12 layers of corridor composition is positioned.It is using association V450 notebook computers and soft with reference to NetStumbler The RSS that part is tested at all reference points, constitutes Radio Map, and using CM-SDE algorithms are to Radio Map dimensionality reductions and adopt KNN algorithms realize indoor positioning.In the emulation of accompanying drawing 4, the dimension of the Radio Map after dimensionality reduction is tieed up for original Radio Map Several 1/3rd.From the point of view of the simulation result of accompanying drawing 4, using the positioning performance of CM-SDE algorithms and the algorithm of initial KNN Can compare, but the positioning complexity of CM-SDE is only 1/3rd, and CM-SDE algorithms can effectively using obtaining in real time New RSS carrys out the density of Radio Map, so as to effectively improve positioning precision.
Description of the drawings
Fig. 1 is offline database positioning implementing procedure figure in the present invention;Solid arrow represents the data transfer between step;
Fig. 2 is online database positioning implementing procedure figure in the present invention;Solid arrow represents the data transfer between step;
Fig. 3 is the structure and experimental situation schematic diagram of the indoor positioning network based on WiFi;
Fig. 4 is sampling network trrellis diagram;
Fig. 5 is using CM-SDE and KNN algorithm positioning performance comparison diagrams;Wherein,Represent CM-SDE,Represent KNN.
Specific embodiment
Specific embodiment one:The WiFi indoor positionings of the semi-supervised manifold learning based on categorical match of present embodiment Method off-line phase position fixing process is realized according to the following steps:
First, to room area arrangement AP to be positioned, make wireless signal cover room area to be positioned, complete WiFi nets Network builds;
The corresponding coordinate of reference point is chosen and is recorded in room area rule to be positioned, measurement simultaneously records reference point successively The RSS signals of all AP for receiving build Radio Map, and store Radio Map as position feature information;
2nd, the intrinsic dimension of the Radio Map using the intrinsic dimension algorithm for estimating of GMST to building in step one is carried out point Analysis, |input paramete one of of the intrinsic dimension for obtaining as CM-SDE algorithms, determines the dimension after Radio Map dimensionality reductions;
3rd, cluster analyses are carried out using KFCM algorithms to Radio Map, realize the category label of the Radio Map of foundation, One of and the |input paramete as CM-SDE, and corresponding initial cluster center and category label are provided;
4th, the category label in the intrinsic dimension and step 3 in step 2 is used as |input paramete, using CM-SDE algorithms To the Radio Map dimensionality reductions built in step one, the RadioMap after corresponding dimensionality reduction is drawn*, RadioMap*As in matching Location database is used for the tuning on-line stage;
5th, by the unmarked RSS that obtains of different user tuning on-line stage test, added by the way of categorical match to In existing Radio Map, obtain including unmarked Radio map RadioMap accordinglyul, by gathering that categorical match updates Class center is used as classification |input paramete new in CM-SDE algorithms;
6th, the cluster centre of the renewal in step 5 is used as |input paramete, using CM-SDE to RadioMapulDimensionality reduction is obtained Eigentransformation matrix V ', V ' and RadioMap*On-line matching location database is collectively formed, is positioned for on-line stage;Wherein, The line phase orientation is specially:
Six(One), on-line testing RSS;
Six(Two), adopt V by RSS dimensionality reductions for RSS*
Six(Three), using KNN algorithms carry out matching positioning output positioning result;
Six(Four), user's positioning terminal location database update;
A kind of off-line phase of the WiFi indoor orientation methods of the semi-supervised manifold learning based on categorical match is completed Implementation.
The off-line phase is completed in positioning terminal with on-line stage.
Specific embodiment two:Present embodiment from unlike specific embodiment one:GMST sheets are adopted in step 2 The intrinsic dimension for levying Radio Map of the dimension algorithm for estimating to building in step one is analyzed, and its computing formula is:
Geodesic distance minimal spanning tree algorithm
In above formulaIn a represent minimum spanning tree linear fit expression formula y=ax+b slope.
Other steps and parameter are identical with specific embodiment one.
Specific embodiment three:Present embodiment from unlike specific embodiment one or two:Generate in step 4 new Dimensionality reduction after Radio map RadioMap*With the V ' expression formulas in step 6 it is:
Radio Map*=V′·X
X is the Radio Map for needing dimensionality reduction.
Other steps and parameter are identical with specific embodiment one or two.
Specific embodiment four:Unlike one of present embodiment and specific embodiment one to three:Class in step 5 The realization not matched, its core process are completed in two steps:
The first step, finds the category attribute of unmarked RSS, completes category attribute labelling by following formula:
Second step:Threshold detection is carried out to RSS:By calculating and judging the relation of generalized symbol value and threshold value, so as to The renewal of Radio Map and category label data is realized, lower two formulas are completed respectively for the renewal of generalized symbol value and cluster centre:
Wherein, threshold value VT=0.9N。
Other steps and parameter are identical with one of specific embodiment one to three.
Specific embodiment five:WiFi on-line stage indoor orientation methods based on the semi-supervised manifold learning of categorical match Realized by following step:
First, on-line testing RSS;
2nd, the RSS of the point to be determined for obtaining is obtained into RSS* using the conversion of eigentransformation matrix dimensionality reduction;
3rd, using KNN algorithms to RSS* and Radio Map* match bits, the particular location coordinate of point to be determined is carried out pre- The renewal of online data is surveyed and carries out, which realizes that process is:
(1)On-line stage, the RSS=[AP received at test point1,AP2,…,APn], it is multiplied with eigentransformation matrix V ', from And draw the RSS ' after dimensionality reduction=[AP1,AP2,…APd], wherein d represents intrinsic dimension;
(2)Matching for RSS ' and Radio Map* is realized using KNN algorithms, using the K reference point nearest with RSS ' The meansigma methodss of coordinate as test point (x ', y '), its expression formula are:
In formula, (x ', y ') be test point prediction coordinate, (xi,yi) be i-th Neighbor Points coordinate, K be KNN algorithms in The number of neighbour;
4th, user's positioning terminal location database updates, that is, complete semi-supervised manifold learning based on categorical match WiFi on-line stage indoor orientation methods;
The off-line phase is completed on the server;On-line stage is completed in positioning terminal.
Specific embodiment six:Present embodiment from unlike specific embodiment five:To point to be determined in step 3 Particular location coordinate be predicted and carry out the renewal of online data by the offline database described in claim 1 and online Database realizing:
The implementation of location database is offline:User will be positioned, and this positions the RSS for measuring as Unlabeled data It is added in Radio Map using categorical match mode, and is realized to local On-line matching location database on mobile terminals Renewal, realization dynamically update local data, so as to realize offline database positioning mode;
The implementation of online database is:After the completion of user's tuning on-line, in the RSS values that this measures online by user The server at tuning on-line data base place is reached, and tuning on-line data base is updated just online calmly in server end Position data pass the positioning terminal for uploading RSS data back.
Other steps and parameter are identical with one of specific embodiment one to five.
Emulation experiment:
First, combine 3 pairs of this emulation experiments of accompanying drawing to be described in detail:It is illustrated as Harbin Institute of Technology's research park 2A 12 The plane graph of layer is illustrated, and is namely based under the experimental situation based on the indoor locating system of WiFi and is set up.In experimental situation, always 27 AP are arranged altogether, and the position of AP arrangements is at blue wireless transmission signal shape tag place.AP is highly 2 from room floors Rice.In off-line phase, NetStumbler softwares are installed on association's V450 notebooks, it is different at four of all reference points In orientation, continuous sampling records 100 RSS values of AP, and the relevant information of AP.By the physical coordinates of all of sampled point and Corresponding physical coordinates and RSS values are stored as the data called by position fixing process, set up Radio Map.It is total in experimental situation 900 reference points, its sampling density are 0.5 meter × 0.5 meter, as shown in Figure 4.Radio Map are defeated as CM-SDE algorithms Enter the input data of parameter and intrinsic dimension algorithm for estimating.
2nd, the acquisition of the intrinsic dimension of Radio Map is realized by following step:
Intrinsic dimension is to carry out independent variable minimum needed for eigenspace dimension and space reconstruction for high dimensional data Number.In concrete Practical Calculation, due to high dimensional data it is intrinsic not substantially, not usually seek to obtain definite intrinsic dimension Number, but seek to estimate the credible value of intrinsic dimension.Specifically, a sample from higher dimensional space, intrinsic dimension are given The central task of number algorithm for estimating and important content are exactly determining the intrinsic dimension of this higher-dimension structure by these sample datas Number.
The estimation of the intrinsic dimension of Radio Map is the important |input paramete of CM-SDE algorithms, and this is related to the knot of dimensionality reduction Whether fruit can represent the feature of the higher dimensional space of Radio Map, therefore the estimation of accurately and effectively intrinsic dimension is most important. At present, commonly use intrinsic dimension algorithm for estimating and be divided into two classes:Partial estimation and global estimation.Estimated to Radio using Global Algorithm The intrinsic dimension of Map estimated, and as the input variable of CM-SDE algorithms.Geodesic curve minimum spanning tree is adopted in this experiment Algorithm(Geodesic Minimum Spanning Tree,GMST)The intrinsic dimension of Radio Map is estimated.
Below the theory of GMST algorithms is analyzed.
Geodesic curve minimum spanning tree (GMST) estimate be depended on based on the length function of geodesic curve minimum spanning tree it is intrinsic Dimension d.GMST refers to the minimum spanning tree of the neighbour's curve being defined on data set X.Length function L (X) of GMST is to survey The corresponding Euclidean distance sum in all edges in ground wire minimum spanning tree.
GMST estimates to construct a neighbour curve G, wherein, each data point x in the X on data set XiAll with it K neighbourIt is connected.Geodesic curve minimum spanning tree T is defined as the minimum curve on X, and it has length
Wherein,It is all subtree collections of curve G, e is an edge for setting T, geThe corresponding Euclideans of edge e away from From its computing formula is shown in formula (2).
ge=||xi-xj||,xi,xj∈e (2)
In GMST estimates, some subsetsIt is made up of all size m, and length L (A) of the GMST of subset A It is also required to calculate.In theory,It is linear, estimates such that it is able to by the function of this forms of y=ax+b, pass through Method of least square is estimated that variable a and b.May certify that, by a estimated value andIntrinsic dimension can be obtained Estimate.The expression formula that intrinsic dimension d is given by GMST algorithms is shown in formula (3).Intrinsic dimension d is another of CM-SDE algorithms Important |input paramete.
3rd, CM-SDE is a kind of semi-supervised manifold learning arithmetic, is needed to all during CM-SDE algorithms are realized Reference point carry out class labelling.In considering WiFi indoor positioning environment up till now, with reference to counting out at nearly 1000 points, not Class labelling is artificially carried out to all of reference point, but the classification of reference point is marked using certain sorting algorithm.
The target of cluster is by data set X={ x1,x2,…,xnBe divided into it is orthogonal between c classes and Various types of data.Base This clustering algorithm is realized as follows:
(1)C cluster centre is generated, v is designated asi, i=1,2 ..., c.
(2)By data set X={ x1,x2,…,xnEach element sort out, using arest neighbors(Nearest Neighbor) The attaching relation of algorithm decision element, its equivalent expression is:
In formula (4), xiFor i-th data point, GiFor the syntopy figure that the i-th class is constituted.D(xi,vj) represent calculating xiWith vjBetween Euclidean distance.
(3)The renewal of cluster centre, for the cluster centre of the i-th class is updated to:
In formula (5), | | represent the number for calculating certain apoplexy due to endogenous wind element.
(4)Convergence is verified and iteration
If one of convergence conditions in the case of meeting following four, iteration stopping, otherwise repeat(2)~(3), Until iteration convergence or reach and maximum perform number of times.Four kinds of convergence test conditions are:
Condition one:Cluster centre is constant;
Condition two:The element of each cluster is constant;
Condition three:Cluster centre change is converged in radius ε;
Condition four:Cluster element change is converged in radius ε.
Generally speaking, above-mentioned convergence test condition can be expressed as following formula:
max||vi-vi′||≤ε,ε≥0 (6)
Wherein, viThe cluster centre of the i-th class after ' expression renewal.
From the basic implementation analysis of above-mentioned clustering algorithm, the Algorithm constitution for the attaching relation of decision element is poly- The core of class.Different types of clustering algorithm proposes different classification indexs, and the function is referred to as the loss function typically(Loss Function).Using Euclidean distance as the loss function in basic clustering method.This patent is using KFCM algorithms to Radio Map carries out the category label that category analysiss draw cluster centre and Radio Map.The theory analysis of KFCM algorithms is as follows:
The target for introducing the Fuzzy c-means Clustering of kernel function is to infinite dimensional by original data set place spatial alternation Hilbert space(Hilbert Space), then corresponding cluster analyses are made to the space after conversion.By the change of kernel function Change, be easier to state after the category feature between initial data is further converted and distinguish.Fuzzy c-means based on kernel function The object function of clustering algorithm is:
In formula (7), Φ (xk)、WiThe data set being illustrated respectively under Hilbert space and corresponding cluster centre.Pass through Derivation can show that the solution of KFCM algorithms is expressed as:
The loss function or similarity function that it is critical only that calculating Hilbert space of the solution of KFCM.Examine herein Consider and introduce gaussian kernel function(Gaussian Kernel Function)FCM(Fuzzy C-Means)The theory analysis of algorithm And its realize.Shown in gaussian kernel function such as formula (9).
In Hilbert space, by formulaState its corresponding loss function, the formula be addressed further under for Formula (10).
In formula (10),<·,·>Represent the kernel function value for calculating corresponding formula.And in fact, the conversion in infinite space is not deposited , therefore, formula (10) is further simplified as shown in formula (11).
The Full-expasion of formula (11) is shown in formula (12).
In formula (12),<Φ(xk),Φ(xj)>Calculated by gaussian kernel function, i.e.,:
In algorithm is realized, cluster centre is not randomly generated, but from data set X={ x1,x2,…,xnIn select at random C element is selected as cluster centre, set Y={ y are constituted1,…,yc}.Therefore, initialized loss function value is calculated such as formula institute Show.
4th, realize carrying out dimensionality reduction to Radio Map with CM-SDE algorithms and obtain under feature weight matrix process passes through State step realization:
CM-SDE algorithms are maximized one kind of divergence in the class scatter based on flag data and Unlabeled data and class Manifold learning arithmetic.The input data that CM-SDE algorithms give is done before theory analysis being carried out to CM-SDE algorithms say as follows It is bright:Input high dimensional data pointData point xiClass be labeled as yi∈ { 1,2 ..., P }, wherein P are represented high dimension According to P submanifold is divided into, the high dimensional data that will be input into is divided into P classes, remembers that the cluster centre of P classes is V={ v1,v2,…,vP}。 The high dimensional data of input is expressed as into the form of matrix:X=[x1,x2,…,xm]∈Rn×m.From the point of view of the form that matrix is represented, square Row in battle array represent a high dimensional data point.
For the RadioMap comprising Unlabeled dataul, wherein all of Unlabeled data Xu=[xu1,xu2,…,xuk]∈ Rn×kCategorical match is carried out, while marked data are designated as Xl=[xl1,xl2,…,xlc]∈Rn×c.For XuIn all data enter Row ordered categories are matched.It is meant that after some Unlabeled data is distributed in order, the cluster centre of respective class can be affected, because This can differentiate to the class of next Unlabeled data and can have an impact.The time sequencing of the collection of consideration signal main in this patent. It is assumed that XuIt is to be sequentially arranged.Ownership x of class is calculated using formula (15)u1, and updated in corresponding cluster using formula (5) The heart.Then all of Unlabeled data is carried out into categorical match successively
The object function of CM-SDE algorithms is:
S in formula (16)w、Sb、StRepresent that divergence, class scatter and total divergence can be calculated by formula (17) in class respectively:
In formula (17),For the average of the i-th class, liFor the number of the sampled point of the i-th class;For the average of all sampled points, numbers of the N for sampled point.
For the object function shown in formula (16) may also indicate that local differentiates the target letter of embedded manifold learning arithmetic Number form formula, its expression formula is:
In formula (18), wijRepresent the weight distribution between homogeneous data, wijWeight distribution between ' expression inhomogeneity data, point W is not expressed asN×NAnd WN×N′.Weight computations are completed by two steps.The first step:Construction Neighborhood Graph.According to high dimensional data point Class label information and its neighbor relationships construct directionless figure G and G '.Wherein neighbor relationships are the criterions be given using KNN algorithms, Used as its neighbour, G is represented and is worked as x K point for selecting data point nearestiWith xjClass label information yi=yjWhen and xi、xjK each other Neighbor relationships;G ' shows and works as xiWith xjClass label information yi≠yjWhen and xi、xjK nearest neighbor relation each other.Second step:Calculate weights square Battle array.The calculating of weight matrix is carried out according to the adjacent map of first step construction using class Gaussian function.Its expression formula (19), (20) are It is shown.W in formulaijRepresent Neighbor Points xiWith xjBetween weights, | | xi-xj||2For Neighbor Points. with xjThe distance between, adopt Matrix-style computed range, t are weights normalized parameter, and U, L represent the number of unmarked and marked sampled point respectively.Root According to analysis it is recognised that WN×NAnd WN×N' can be made up of three parts, it is respectively:Between marked data and marked data The weight between weight and Unlabeled data and Unlabeled data between weight, marked data and Unlabeled data, respectively It is expressed as:
Can be obtained by the property of above-mentioned computing formula and matrix: It is possible thereby to derive WN×NAnd WN×N' form of matrix in block form is expressed as, such as formula (21) institute Show.
According to the calculating formula of matrix:Calculating formula is expressed as the computational methods of the matrix of matrix A, calculating formula The method for being given is consistent with the calculating formula of the mark of matrix, i.e.,:||A||2=tr(AAT).Thus formula (18) can be expressed as matrix The calculation of mark:
Formula (22) can be reduced to:
Real number is by the scalar nature and weights element of the calculating of trace of a matrix, formula (23) can be reduced to:
According to simple mathematical relationship, formula (24) can be reduced to:
J(V)=2tr{VT[X(D′-W′N×N)XT]V} (25)
In formula (25):X is input data, and λ and v is characterized value and characteristic vector, and W and W ' is respectively the corresponding power of G and G ' Value matrix, D and D ' are diagonal matrix, and its diagonal element can be represented by formula (26).
According to the derivation mode of formula (25), the constraints in formula (18) can be write as shape as similar such as formula (25) in the same manner Formula, thus, it is possible to be expressed as form by (18):
To formula (27) application Lagrange(Lagrange)Multiplier Method, it can be deduced that shown in formula (28):
X(D′-W′N×N)XTv=λX(D-WN×N)XTv (28)
Generalized eigenvalue decomposition is carried out to formula (28), eigenvalue and the characteristic vector of its Eigenvalues Decomposition is drawn, is expressed as: λ=[λ12,…,λn]T, its corresponding characteristic vector is:v=[v1,v2,…,vn]T.Take the first d maximum corresponding spy of eigenvalue Levy vector and constitute transformation matrix V=[v1,v2,…,vd].Can be drawn by the output data alternative approach of CM-SDE algorithms, dimensionality reduction Data are afterwards:
zi=VTxi (29)
In formula (29), ziRepresent input high dimensional data point xiLow-dimensional output data after conversion.The content of the invention from this patent The implementation steps of the off-line phase for being given are:The first step is first dropped to all reference point Radio Map using CM-SDE algorithms Dimension process, obtains the Radio Map after the dimensionality reduction of corresponding reference point, i.e., as the matching location database of on-line stage (RadioMap*).Radio Map, i.e. RadioMap of the second step to addition Unlabeled dataulDimension-reduction treatment is carried out, spy is obtained Levy transformation matrix V '.It is possible thereby to set up data base required for off-line phase:RadioMap*With V '.
5th, the RSS obtained by different user's on-line stage positioning stages is unmarked category attribute, its addition Radio Map, and constitute Radio MapulProcess be referred to as classification.Its implementation is as described below:
The unmarked RSS that the test of different user on-line stage positioning stage is obtained, is added by the way of categorical match Into existing Radio Map, obtain including unmarked Radio map RadioMap accordinglyul;Increased by categorical match method Plus the data volume of Radio Map, and then the density of raising Radio Map, new dimensionality reduction data are provided for CM-SDE algorithms, while Cluster centre can be updated, and new categorical data is provided for CM-SDE algorithms.Categorical match method is divided into two steps, and which realizes process It is as described below:
The first step, finds the category attribute of unmarked RSS.Remember that one group of unmarked RSS is RSSi, with the cluster in step 3 Center is matched, and completes RSS by formula (4)iCategory label.
Second step:Threshold detection is carried out to RSS.For cluster centre vi is expressed as vi=(vi1,vi2,…,viN), N is room The number of AP in interior alignment system.RSSiIt is expressed as RSSi=(RSSi1,RSSi2,…,RSSiN).Calculate broad sense defined in following formula Value of symbol:
Wherein, sgn () is defined as:
Work as SiDuring more than setting threshold value, then by RSSiIn adding Radio Map, and cluster centre is updated, otherwise given up RSSi, it is added without in Radio Map.In this patent, threshold value VT=0.9N.The renewal of cluster centre is completed by formula (5):
6th, the offline database implementation based on the WiFi indoor orientation methods of CM-SDE algorithms:
Offline database mode is made up of three parts.First, the foundation of the Radio Map of all reference points, and adopt CM- SDE algorithms obtain RadioMap*.Second, then stochastical sampling U point Unlabeled data be added in original Radio Map, and V ' is obtained with CM-SDE algorithms, and the location database for being formed is downloaded(Storage)To the mobile terminal of positioning.3rd, it is online fixed Position is realized and Radio Map update.Being implemented as follows for Part III is described:
On-line stage, the RSS=[AP received at test point1,AP2,…,APn], n represents the AP of indoor locating system arrangement Number.RSS is multiplied with eigentransformation matrix V ', so as to draw the RSS ' after dimensionality reduction=[AP1,AP2,…,APd], wherein d tables Show intrinsic dimension.RSS ' and RadioMap are realized using KNN algorithms again*Matching.Using the K reference point nearest with RSS ' The meansigma methodss of coordinate as test point (x ', y '), its expression formula are:
The user RSS that measures of this positioning will be positioned Radio is added to using categorical match mode as Unlabeled data In Map, and the renewal to local On-line matching location database is realized on mobile terminals, realization dynamically updates local number According to so as to realize offline database positioning mode, fixed in the WiFi rooms of the semi-supervised manifold learning of 1 be shown in categorical match of accompanying drawing Position method is realized in user's positioning terminal;
7th, the online database implementation based on the WiFi indoor orientation methods of CM-SDE algorithms:
Online database mode is made up of four parts.First, the foundation of the Radio Map of all reference points, and adopt CM- SDE algorithms obtain RadioMap*.Second, then stochastical sampling U point Unlabeled data be added in original Radio Map, and V ' is obtained with CM-SDE algorithms, and the location database for being formed is downloaded(Storage)To the mobile terminal of positioning.3rd, it is online fixed Position is realized and Radio Map update.Being implemented as follows for Part III is described:
On-line stage, the RSS=[AP received at test point1,AP2,…,APn], n represents the AP of indoor locating system arrangement Number.RSS is multiplied with eigentransformation matrix V ', so as to draw the RSS ' after dimensionality reduction=[AP1,AP2,…,APd], wherein d tables Show intrinsic dimension.RSS ' and RadioMap are realized using KNN algorithms again*Matching.Using the K reference point nearest with RSS ' The meansigma methodss of coordinate as test point (x ', y '), its expression formula are:
Part IV:After the completion of user's tuning on-line, the RSS values that this measures online by user are uploaded to tuning on-line number According to place server, and tuning on-line data base be updated into just tuning on-line data in server end pass upload back The positioning terminal of RSS data, i.e. off-line phase shown in accompanying drawing 2 are completed on the server in tuning on-line data base, and The line stage is completed in positioning terminal.

Claims (6)

1. a kind of WiFi indoor orientation methods of the semi-supervised manifold learning based on categorical match, it is characterised in that based on classification The WiFi indoor orientation method off-line phase position fixing processs of the semi-supervised manifold learning matched somebody with somebody are realized according to the following steps:
First, to room area arrangement access point AP to be positioned, make wireless signal cover room area to be positioned, complete wireless Fidelity technology WiFi network builds;
The corresponding coordinate of reference point is chosen and is recorded in room area rule to be positioned, measurement simultaneously records reference point reception successively The signal intensity RSS signals of all AP for arriving build network signal coverage diagram Radio Map, and deposit as position feature information Storage Radio Map;
2nd, the sheet of the Radio Map using the intrinsic dimension algorithm for estimating of geodesic curve minimum spanning tree GMST to building in step one Levy dimension to be analyzed, the intrinsic dimension for obtaining differentiates embedded CM-SDE algorithms as based on the semi-supervised local of categorical match One of |input paramete, determines the dimension after Radio Map dimensionality reductions;
3rd, cluster analyses are carried out to Radio Map using by Fuzzy c-means KFCM algorithms, realize the Radio Map's of foundation One of category label, and the |input paramete as CM-SDE, and corresponding initial cluster center and category label are provided;
4th, the category label in the intrinsic dimension and step 3 in step 2 is used as |input paramete, using CM-SDE algorithms to step The Radio Map dimensionality reductions built in rapid one, draw the network signal coverage diagram RadioMap after corresponding dimensionality reduction*, RadioMap* It is used for the tuning on-line stage as in matching location database;
5th, the unmarked RSS for obtaining the test of different user tuning on-line stage, is added to by the way of categorical match In Radio Map, obtain including unmarked Radio map RadioMap accordinglyul, by the cluster that categorical match updates The heart is used as classification |input paramete new in CM-SDE algorithms;
6th, the cluster centre of the renewal in step 5 is used as |input paramete, using CM-SDE algorithms to RadioMapulDimensionality reduction is obtained Eigentransformation matrix V ', V ' and RadioMap*On-line matching location database is collectively formed, is positioned for on-line stage;Wherein, The line phase orientation is specially:
Six (one), on-line testing RSS;
Six (two), adopt V by RSS dimensionality reductions for the signal intensity RSS after dimensionality reduction*
Six (three), matching positioning output positioning result is carried out using k-nearest neighbor KNN algorithm;
Six (four), user's positioning terminal location database updates;
The off-line phase for completing a kind of WiFi indoor orientation methods of the semi-supervised manifold learning based on categorical match is realized Mode.
2. WiFi indoor orientation methods of a kind of semi-supervised manifold learning based on categorical match according to claim 1, It is characterized in that adopting the intrinsic dimension of Radio Map of the intrinsic dimension algorithm for estimating of GMST to building in step one in step 2 It is analyzed, its computing formula is:
d int r i n s i dim = 1 1 - a ,
In above formulaIn a represent minimum spanning tree linear fit expression formula y=ax+b slope.
3. WiFi indoor orientation methods of a kind of semi-supervised manifold learning based on categorical match according to claim 1, It is characterized in that generating the Radio map RadioMap after new dimensionality reduction in step 4*With the V ' expression formulas in step 6 it is:
Radio Map*=V ' X
X is the Radio Map for needing dimensionality reduction.
4. WiFi indoor orientation methods of a kind of semi-supervised manifold learning based on categorical match according to claim 1, It is characterized in that in step 5 categorical match realization, its core process completed in two steps:
The first step, finds the category attribute of unmarked RSS, completes category attribute labelling by following formula:
Second step:Threshold detection is carried out to RSS:By calculating and judging generalized symbol value and threshold value VTRelation, so as to realize The renewal of Radio Map and category label data, the renewal of generalized symbol value and cluster centre are completed by following two formula respectively:
S i = &Sigma; j = 1 N sgn ( RSS i j - v i j )
v i = 1 | G i | &Sigma; x k &Element; G i x k
Wherein, threshold value VT=0.9N;C is cluster centre number;xiFor i-th data point;GiFor the neighbour that the i-th class is constituted Connect graph of a relation;D(xi,vj) represent calculating xiWith vjBetween Euclidean distance;| | represent the number for calculating certain apoplexy due to endogenous wind element;N is The number of AP in indoor locating system;Sgn () is defined as:
5. WiFi indoor orientation methods of a kind of semi-supervised manifold learning based on categorical match according to claim 1, It is characterized in that being passed through based on the WiFi indoor orientation method on-line stage position fixing processs of the semi-supervised manifold learning of categorical match Following step is realized:
First, on-line testing RSS;
2nd, the RSS of the point to be determined for obtaining is obtained into RSS* using the conversion of eigentransformation matrix dimensionality reduction;
3rd, RSS* and Radio Map* match bits are predicted simultaneously to the particular location coordinate of point to be determined using KNN algorithms The renewal of online data is carried out, which realizes that process is:
(1) on-line stage, the RSS=[AP received at test point1,AP2,…,APn], it is multiplied with eigentransformation matrix V ', so as to Draw the RSS ' after dimensionality reduction=[AP1,AP2,…APd], wherein d represents intrinsic dimension;
(2) matching for RSS ' and Radio Map* is realized using KNN algorithms, using the coordinate of the K reference point nearest with RSS ' Meansigma methodss as test point (x ', y '), its expression formula is:
( x &prime; , y &prime; ) = 1 K &Sigma; i = 1 K ( x i , y i )
In formula, (x ', y ') be test point prediction coordinate, (xi,yi) be i-th Neighbor Points coordinate, K be KNN algorithms in neighbour Number;
4th, user's positioning terminal location database updates, that is, complete the WiFi of the semi-supervised manifold learning based on categorical match On-line stage indoor orientation method.
6. WiFi indoor orientation methods of a kind of semi-supervised manifold learning based on categorical match according to claim 5, It is characterized in that being predicted to the particular location coordinate of point to be determined in step 3 and carrying out the renewal of online data by offline Data base and online database are realized:
The implementation of offline database is:The user RSS that measures of this positioning will be positioned classification is adopted as Unlabeled data Matching way is added in Radio Map, and realizes the renewal to local On-line matching location database on mobile terminals, real Local data are dynamically updated now, so as to realize offline database positioning mode;
The implementation of online database is:After the completion of user's tuning on-line, the RSS values that this measures online by user are uploaded to The server that tuning on-line data base is located, and tuning on-line data base is updated into just tuning on-line number in server end According to the positioning terminal for passing upload RSS data back.
CN201310750528.6A 2013-12-31 2013-12-31 WiFi indoor positioning method of semi-supervised manifold learning based on category matching Active CN103648106B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201310750528.6A CN103648106B (en) 2013-12-31 2013-12-31 WiFi indoor positioning method of semi-supervised manifold learning based on category matching

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201310750528.6A CN103648106B (en) 2013-12-31 2013-12-31 WiFi indoor positioning method of semi-supervised manifold learning based on category matching

Publications (2)

Publication Number Publication Date
CN103648106A CN103648106A (en) 2014-03-19
CN103648106B true CN103648106B (en) 2017-03-22

Family

ID=50253244

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201310750528.6A Active CN103648106B (en) 2013-12-31 2013-12-31 WiFi indoor positioning method of semi-supervised manifold learning based on category matching

Country Status (1)

Country Link
CN (1) CN103648106B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US11818629B2 (en) 2016-11-22 2023-11-14 Aerial Technologies Device-free localization methods within smart indoor environments

Families Citing this family (15)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103906234B (en) * 2014-04-03 2019-04-26 李晨 A kind of indoor orientation method based on WIFI signal
CN104185275B (en) * 2014-09-10 2017-11-17 北京航空航天大学 A kind of indoor orientation method based on WLAN
TWI554136B (en) * 2014-09-24 2016-10-11 緯創資通股份有限公司 Methods for indoor positioning and apparatuses using the same
CN105517143B (en) * 2014-10-17 2019-01-11 深圳航天科技创新研究院 A method of it reducing WLAN indoor positioning and searches for dimension
CN104469932B (en) * 2014-11-21 2018-07-06 北京拓明科技有限公司 A kind of location fingerprint localization method based on support vector machines
CN104507097A (en) * 2014-12-19 2015-04-08 上海交通大学 Semi-supervised training method based on WiFi (wireless fidelity) position fingerprints
CN104540221B (en) * 2015-01-15 2018-06-22 哈尔滨工业大学 WLAN indoor orientation methods based on semi-supervised SDE algorithms
CN104581945B (en) * 2015-02-06 2018-09-07 哈尔滨工业大学 The WLAN indoor orientation methods of semi-supervised APC clustering algorithms based on distance restraint
CN105657823B (en) * 2015-12-16 2020-07-14 吉林大学 WIFI indoor weighted K nearest neighbor positioning algorithm based on kernel function main feature extraction
WO2018094502A1 (en) * 2016-11-22 2018-05-31 Aerial Technologies Device-free localization methods within smart indoor environments
CN106028446B (en) * 2016-07-15 2019-04-02 西华大学 Parking garage localization method
CN107277773B (en) * 2017-07-10 2020-04-17 广东工业大学 Adaptive positioning method combining multiple contextual models
CN107862757A (en) * 2017-11-03 2018-03-30 广东广凌信息科技股份有限公司 A kind of movable attendance checking method and system based on Wi Fi fingerprints
CN108519578A (en) * 2018-03-23 2018-09-11 天津大学 A kind of indoor positioning fingerprint base construction method based on intelligent perception
CN108600002B (en) * 2018-04-17 2021-02-26 浙江工业大学 Mobile edge calculation and distribution decision method based on semi-supervised learning

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103079269A (en) * 2013-01-25 2013-05-01 哈尔滨工业大学 LDE (Linear Discriminant Analysis) algorithm-based WiFi (Wireless Fidelity) indoor locating method

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7515578B2 (en) * 2006-05-08 2009-04-07 Skyhook Wireless, Inc. Estimation of position using WLAN access point radio propagation characteristics in a WLAN positioning system

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103079269A (en) * 2013-01-25 2013-05-01 哈尔滨工业大学 LDE (Linear Discriminant Analysis) algorithm-based WiFi (Wireless Fidelity) indoor locating method

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
基于学习算法的WLAN室内定位技术研究;邓志安;《哈尔滨工业大学博士学位论文》;20121225;1-16,65-67 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US11818629B2 (en) 2016-11-22 2023-11-14 Aerial Technologies Device-free localization methods within smart indoor environments

Also Published As

Publication number Publication date
CN103648106A (en) 2014-03-19

Similar Documents

Publication Publication Date Title
CN103648106B (en) WiFi indoor positioning method of semi-supervised manifold learning based on category matching
CN103096466B (en) Wireless fidelity (Wi-Fi) indoor positioning method
CN105335756B (en) A kind of image classification method and image classification system based on Robust Learning model
CN106604229A (en) Indoor positioning method based on manifold learning and improved support vector machine
CN103079269A (en) LDE (Linear Discriminant Analysis) algorithm-based WiFi (Wireless Fidelity) indoor locating method
Martínez-Ballesteros et al. Selecting the best measures to discover quantitative association rules
CN104540221A (en) WLAN indoor positioning method based on semi-supervised SDE algorithm
CN104504393A (en) SAR (Synthetic Aperture Radar) image semi-supervised classification method based on integrated learning
CN102609944B (en) Hyper-spectral remote sensing image mixed pixel decomposition method based on distance geometry theory
CN114169442B (en) Remote sensing image small sample scene classification method based on double prototype network
CN107292341A (en) Adaptive multi views clustering method based on paired collaboration regularization and NMF
CN103945531B (en) Method for WLAN indoor positioning Radio Map updating based on information entropy
CN107423762A (en) Semi-supervised fingerprinting localization algorithm based on manifold regularization
CN106127179A (en) Based on the Classification of hyperspectral remote sensing image method that adaptive layered is multiple dimensioned
CN106529563A (en) High-spectral band selection method based on double-graph sparse non-negative matrix factorization
CN106970379A (en) Based on distance-measuring and positioning method of the Taylor series expansion to indoor objects
Zhao et al. WiFi indoor positioning algorithm based on machine learning
CN103310237B (en) Handwritten Numeral Recognition Method and system
CN106096622A (en) Semi-supervised Classification of hyperspectral remote sensing image mask method
CN107153839A (en) A kind of high-spectrum image dimensionality reduction processing method
CN107392863A (en) SAR image change detection based on affine matrix fusion Spectral Clustering
CN106952077A (en) The generation method and device of a kind of worksheet strategy
CN105975940A (en) Palm print image identification method based on sparse directional two-dimensional local discriminant projection
Mugglestone et al. Spectral tests of randomness for spatial point patterns
CN112333652B (en) WLAN indoor positioning method and device and electronic equipment

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
C10 Entry into substantive examination
SE01 Entry into force of request for substantive examination
C14 Grant of patent or utility model
GR01 Patent grant
TR01 Transfer of patent right

Effective date of registration: 20190612

Address after: 150000 Heilongjiang Harbin Dalian economic and Trade Zone, the North Road and Xingkai Road intersection

Patentee after: Harbin University of Technology Robot Group Co., Ltd.

Address before: 150001 No. 92 West straight street, Nangang District, Heilongjiang, Harbin

Patentee before: Harbin Institute of Technology

TR01 Transfer of patent right