CN104540221A - WLAN indoor positioning method based on semi-supervised SDE algorithm - Google Patents

Abstract

The invention discloses a WLAN indoor positioning method based on a semi-supervised SDE algorithm, and belongs to the field of indoor positioning. The problems that an existing WiFi indoor positioning method is high in on-line positioning complexity, and a mobile terminal has poor positioning real-time performance are solved. The semi-supervised SDE dimension reduction algorithm is introduced, through using unmarked data easy to collect, the low-dimension manifold of high-dimension data representing position information is found, and while the positioning precision of a WLAN indoor positioning system is guaranteed, the calculation quantity in the positioning process is effectively decreased. Meanwhile, the workloads of collecting data at reference points are reduced, and the WLAN indoor positioning method provides a simple path convenient and easy to implement for real-time updating of a database. The on-line positioning complexity is low, and the mobile terminal has high positioning real-time performance. The WLAN indoor positioning method is suitable for WLAN indoor positioning.

Description

Based on the WLAN indoor orientation method of semi-supervised SDE algorithm

Technical field

The present invention relates to indoor positioning field, be specifically related to a kind of location fingerprint indoor orientation method.

Background technology

Along with wireless network, mobile communication and the extensive of general fit calculation are popularized, location Based service (LBS, Location-based Services) also more and more get more and more people's extensive concerning, wherein how to determine that the position of user is the key realizing LBS.As everyone knows, global positioning satellite (GPS, Global Positioning System) system measures the difference time of advent estimated position from 5 ~ 24 satellite-signals by receiver, can provide the location estimation of degree of precision.But GPS cannot realize location in indoor and that high building is intensive city due to the non line of sight of satellite-signal.Along with the proposition of IEEE 802.11 standard, WLAN (wireless local area network) (WLAN, Wireless Local Area Networks) is extensively distributed in campus, office block and family.And based on received signal strength indoor locating system because of have dispose convenient, cost is low, do not need to add features such as location survey specialized hardware and in widespread attention.

Under WLAN environment, measured from WAP (wireless access point) (AP by the wireless network card of mobile terminal and corresponding software, Access Point) received signal strength (RSS, Received Signal Strength) value, obtain the information relevant with relevant position, and then predict mobile subscriber present position by matching algorithm.Wherein the location algorithm of position-based fingerprint is because positioning precision is high, can make full use of existing utility, and upgrading and maintenance are used widely to advantages such as customer impact are little.Location fingerprint location algorithm is divided into off-line measurement stage and tuning on-line stage two steps, off-line phase mainly sets up the corresponding relation between position and received signal strength, namely in area to be targeted, reference point is set by certain rule, by the different AP signal strength values that witness mark place receives, set up corresponding location fingerprint database Radio Map.In the tuning on-line stage, the RSS value received by test point, is adopted corresponding matching algorithm, mainly comprises nearest neighbor method, k-nearest neighbor, probabilistic method and neural network.Wherein k-nearest neighbor (KNN, K NearestNeighbors) on algorithm complex and positioning precision, all there is some superiority, be widely used in tuning on-line coupling, find position immediate with it in location fingerprint database, as final location estimation result.The Radio Map that off-line phase is set up includes a large amount of data messages, and along with locating area expand, the increase of reference point, cause RadioMap amount of information exponentially situation increase.

The WLAN indoor locating system of position-based fingerprint, gathers data message as much as possible by off-line phase, effectively can improve the positioning precision of system.And the data message that tuning on-line phase process is a large amount of, increase the data operation quantity of position fixing process, limited to its disposal ability of mobile terminal, cause location algorithm to run difficulty.Some characteristic information not only can not provide effective positional information simultaneously, even also can affect the accuracy of positioning result.

When AP number increases, in Radio Map, represent that the dimension information of AP number just becomes high dimensional data, about alleviate the burden of process high dimensional data by dimension.High dimensional data may comprise a lot of feature, and these features are all in the same things of description, and these features are closely be connected to a certain extent.As when taking pictures from multiple angle to same object simultaneously, the data obtained are just containing overlapping information.If some nonoverlapping expression simplified of these data can be obtained, greatly will improve the efficiency of data processing operation and improve accuracy to a certain extent.The object of dimension-reduction algorithm is also the treatment effeciency improving high dimensional data just.

Have at present much based on the dimension-reduction algorithm of different object, comprise linearity and non-linearity dimension-reduction algorithm.Wherein PCA and LDA is typical linear dimension-reduction algorithm.This class algorithm has good dimensionality reduction result for the high dimensional data with linear structure, but is not suitable for the high dimensional data of nonlinear organization.Nonlinear reductive dimension algorithm is then based on manifold learning arithmetic.SDE algorithm proposes based on LDE algorithm in manifold learning arithmetic, and it is the manifold learning arithmetic that a kind of typical feature based extracts.

Summary of the invention

The present invention is high in order to solve the tuning on-line complexity existed in existing WiFi indoor orientation method, the problem of mobile terminal location poor real, thus provides a kind of WLAN indoor orientation method based on semi-supervised SDE algorithm.

Based on the WLAN indoor orientation method of semi-supervised SDE algorithm, it is realized by following steps:

Step one, for indoor environment arrange m access point AP (AP _j, 1≤j≤m), guarantee the quorum sensing inhibitor that in described indoor environment, any point is sent by two or more wireless access point AP; M is positive integer;

Step 2, in indoor environment, evenly reference point is set, choosing a reference point is that initial point sets up rectangular coordinate system, obtain the coordinate position of each reference point in this rectangular coordinate system, and in each reference point, utilize signal receiver collection and record from received signal strength RSS value k time of each AP, and carry out data processing; K is positive integer;

Step 3, according to K means clustering algorithm, indoor positioning environment being divided into Q sub regions, is the reference point marker classification information separately of every sub regions;

Step 4, gather random unmarked RSS data, the characteristic vector of each sub regions obtained with step 3 compares, namely the distance with the characteristic vector of all subregion is asked for, by random data category division in the subregion nearest with its characteristic vector;

Step 5, SDE algorithm is adopted to every sub regions in K sub regions, obtain eigentransformation matrix;

The input parameter of SDE algorithm, the i.e. value of intrinsic dimension, by existing intrinsic dimension algorithm for estimating, RadioMap partition data is estimated, provide the intrinsic dimension estimated value of each area data, determine the eigentransformation matrix in each region, and generate the location fingerprint database Radio Map after dimensionality reduction ^*;

The characteristic vector of each sub regions that step 6, the signal strength signal intensity RSS value obtained by tested point and step 3 obtain compares, namely ask for the distance of the characteristic vector of test point and the characteristic vector of all subregion, test point is positioned in the subregion nearest with its characteristic vector;

Step 7, by the subregion of locating, the RSS value of the eigentransformation matrix utilizing step 5 to draw to tested point carries out dimensionality reduction, obtains the RSS of low-dimensional ^*, with fingerprint database Radio Map ^*mate, adopt k nearest neighbor location fingerprint location algorithm accurately to locate test point.

Described in step 2 in each reference point, utilize signal receiver collection and record from received signal strength RSS value k time of each AP, and the concrete steps of carrying out data processing are:

Step 2 one, k × m rank matrix is obtained to each reference point, the i-th row jth list of matrix show gather for i-th time in the RSS value from a jth AP that receives; K, m, i, j are positive integer;

Elements all in step 2 two, k × m rank rectangular array vector of each reference point being obtained is added and obtains a value, again this value divided by k, then each reference point is obtained for the vector of a 1 × m, for each reference point, this vector is called the characteristic vector of this reference point, and the jth element in vector is as a jth feature of this reference point; If the RSS value of some AP can't detect in a reference point, be then the minimum signal value-100dBm that can receive under this environment by its assignment, so the scope of the received signal strength RSS value v of reference point is-100dBm≤v≤0dBm arbitrarily; This group vector is for realizing the cluster subregion of step three.

Described in step 3 according to K means clustering algorithm to the concrete steps that indoor positioning environment is divided into Q sub regions be:

The characteristic vector of all reference points that step 3 one, input step two or two record and subregion number Q;

Step 3 two, at random obtain choose the RSS of K reference point data from step 2 two, that is: the characteristic vector value of each reference point is as the cluster centre of K sub regions;

Step 3 three, calculate the Euclidean distance of each reference point and K cluster centre characteristic vector, each reference point is distributed to the subregion minimum with its Euclidean distance;

Step 3 four, the RSS value of each reference point in every sub regions to be averaged, obtain new cluster centre;

Step 3 five, repetition step 3 three and step 3 four are until the center of every sub regions no longer changes;

Step 3 six, obtain K sub regions and all subregion corresponding cluster centre vector, that is: the vector of a 1 × m, this vector is claimed to be the characteristic vector of this sub regions, a jth feature of jth this sub regions of element representation of this vector is also the RSS average from a jth AP that this sub regions obtains.

The detailed process of the category division of the random RSS data of step 4 is:

The Unlabeled data of step 4 one, input random acquisition, described Unlabeled data only has signal strength values and does not have positional information;

Step 4 two, the characteristic vector of each sub regions Unlabeled data and step 3 obtained compare, namely the distance with the characteristic vector of all subregion is asked for, random data is distributed in the subregion nearest with its characteristic vector, as the classification belonging to it.

Adopt SDE algorithm to carry out dimensionality reduction to the every sub regions in K sub regions described in step 5, determine the eigentransformation matrix in each region, and the concrete grammar generating new location fingerprint database be:

Step May Day, structure adjacent map:

Directionless figure G and G' is constructed according to the class label information of high dimensional data point and neighbor relationships thereof; Wherein neighbor relationships is the criterion adopting KNN algorithm to provide, and puts as its neighbours for K that namely selects data point nearest, and G represents and works as x _iwith x _jclass label information y _i=y _jtime and x _i, x _jk nearest neighbor relation each other; G' shows and works as x _iwith x _jclass label information y _i≠ y _jtime and x _i, x _jk nearest neighbor relation each other;

Step 5 two, calculating weight matrix:

According to the adjacent map of step structure on May Day, adopt class Gaussian function to carry out the calculating of weight matrix, its expression formula is for shown in (1):

$\left\{\begin{array}{c}{w}_{\mathrm{ij}}=\left\{\begin{array}{c}\exp (-{\left|\right|x_i-x_j\left|\right|}^2/t);\\ 0;\end{array}\mathrm{if}{x}_i,x_j\∈G\right.\\ w_{\mathrm{ij}}^{\′}=\left\{\begin{array}{c}\exp (-{\left|\right|x_i-x_j\left|\right|}^2/t)\\ 0;\end{array}\right.\mathrm{if}{x}_i,x_j\∈G^{\′}\end{array}\right.---\left(1\right)$

Wherein: w _ijrepresent Neighbor Points x _iwith x _jbetween weights, || x _i-x _j|| ²for Neighbor Points x _iwith x _jbetween norm distance, adopt matrix-style to calculate norm distance, t is weights normalized parameter;

Step 5 three, determine target function and solve:

Target according to SDE algorithm: minimize divergence in class while maximizing class scatter; Divergence adopts the norm distance representing similar and non-like numbers strong point to represent;

Draw its corresponding optimization object function by the target of SDE algorithm, shown in (2), eigentransformation matrix P is optimal solution to be asked:

$\left\{\begin{array}{c}\mathrm{Maximze\; J}\left(V\right)=\underset{i,j}{\mathrm{\Σ}}{\left|\right|P^T{x}_i-P^T{x}_j\left|\right|}^2{w}_{\mathrm{ij}}^{\′}\\ \mathrm{subject\; to}\underset{i,j}{\mathrm{\Σ}}{\left|\right|P^T{x}_i-P^T{x}_j\left|\right|}^2{w}_{\mathrm{ij}}=1\end{array}\right.---\left(2\right)$

Optimization object function according to formula (2) provides:

The calculating formula of known matrix norm the calculating formula of this formula and matrix trace || A|| ²=tr (AA ^t) consistent, therefore formula (2) is expressed as matrix trace:

$J\left(V\right)=\underset{i,j}{\mathrm{\Σ}}\left\{\mathrm{tr}\right[(P^T{x}_i-P^T{x}_j){(P^T{x}_i-P^T{x}_j)}^T{w}_{\mathrm{ij}}^{\′}\left]\right\}---\left(3\right)$

Formula (3) is reduced to further:

$J\left(V\right)=\underset{i,j}{\mathrm{\Σ}}\left\{\mathrm{tr}\right[P^T(x_i-x_j){(x_i-x_j)}^{T}P\left]w_{\mathrm{ij}}^{\′}\right\}---\left(4\right)$

Be real number by the calculating scalar nature of trace of a matrix and weights element, formula (4) be reduced to:

J(V)＝2tr{P ^T[X(D′-W′)X ^T]P} (5)

In like manner, formula (2) is simplified to:

$\left\{\begin{array}{c}\mathrm{Maximize\; J}\left(V\right)=2\mathrm{tr}\left\{P^T\right[X(D^{\′}-W^{\′})X^T\left]P\right\}\\ \mathrm{subject\; to}2\mathrm{tr}\left[P^{T}X(D-W)X^{T}P\right]=1\end{array}\right.---\left(6\right)$

In formula (6), X is input high dimensional data, and W, W' are respectively weight matrix corresponding to G and G'; D and D' is diagonal matrix, and its diagonal element is tried to achieve by formula (7):

$\left\{\begin{array}{c}{d}_{\mathrm{ii}}=\underset{j}{\mathrm{\Σ}}{w}_{\mathrm{ij}}\\ d_{\mathrm{ii}}^{\′}=\underset{j}{\mathrm{\Σ}}{w}_{\mathrm{ij}}^{\′}\end{array}\right.---\left(7\right)$

To formula (6) application lagrange's method of multipliers, draw shown in formula (8):

X(D′-W′)X ^TP＝λX(D-W)X ^TP (8)

Generalized eigenvalue decomposition is carried out to formula (8), draws the eigenvalue λ=[λ of its Eigenvalues Decomposition ₁, λ ₂..., λ _n] ^tand characteristic vector p=[p ₁, p ₂..., p _n] ^t;

Step the May 4th, intrinsic dimension are estimated:

The characteristic value obtained according to step 5 three and characteristic vector thereof, estimate intrinsic dimension according to formula (9):

$\frac{\underset{i=1}{\overset{d}{\mathrm{\Σ}}}{\mathrm{\λ}}_i}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\λ}}_i}\≥{\mathrm{\η}}^{*}---\left(9\right)$

Wherein: η ^*be the threshold value that projector space retains information, usual value is greater than 80%, namely chooses front d eigenvalue of maximum sum and is not less than 80% with the ratio of All Eigenvalues summation, namely meets and embeds the good low-dimensional of primary data information (pdi);

Step 5 five, calculating embed result:

Estimate threshold value according to step the May 4th setting intrinsic dimension, the d chosen a characteristic value characteristic of correspondence vector forms transformation matrix P=[p ₁, p ₂..., p _d], input high dimensional data point x is being calculated by formula (10) _idata Z after dimensionality reduction _ifor:

Z _i＝P ^Tx _i(10)

Drawn received signals fingerprint data and the eigentransformation matrix of low-dimensional by SDE algorithm, be designated as Radio Map respectively ^*and P.

Described in step 7 to the every sub regions in K sub regions, utilize the low-dimensional RadioMap that step 5 is tried to achieve respectively ^*and eigentransformation matrix, employing k neighbor positions fingerprinting localization algorithm to the concrete grammar that test point positions is:

Test point is positioned in subregion by step July 1st, step 6, and the RSS signal that test point receives is higher-dimension live signal, is expressed as R _test=[r ₁, r ₂..., r _n]; Utilize formula (10) to be multiplied with the eigentransformation matrix P in this region, calculate the signal value after dimensionality reduction ${\tilde{R}}_{\mathrm{test}}=[{\tilde{r}}_1,{\tilde{r}}_2,...,{\tilde{r}}_d];$

The low dimensional feature vector of step 7 two, test point with this region low-dimensional Radio Map ^*in i-th reference point between distance tried to achieve by formula (11):

${\mathrm{Dis}}_i={\left(\underset{j=1}{\overset{d}{\mathrm{\Σ}}}{|{\tilde{r}}_j-{\mathrm{rss}}_{\mathrm{ij}}|}^2\right)}^{\frac{1}{2}}---\left(11\right)$

Step 7 three, from result, choose nearest with the test point characteristic vector reference point of k from small to large, by the location estimation coordinate of formula (12) calculating test point

$(\hat{x},\hat{y})=\frac{1}{k}\underset{i=1}{\overset{k}{\mathrm{\Σ}}}(x_{\mathrm{ix}},y_{\mathrm{iy}})---\left(12\right)$

Complete the location to test point.

The present invention is by introducing semi-supervised SDE dimension-reduction algorithm, by utilizing the Unlabeled data being easy to gather, find out the low dimensional manifold of the high dimensional data characterizing positional information, while the positioning precision ensureing WLAN indoor locating system, effectively reduce the amount of calculation of position fixing process.Decrease the workload of reference point data acquisition, the real-time update for database provides simple and easy to do approach simultaneously.Tuning on-line complexity of the present invention is low, and mobile terminal location is real-time.

Accompanying drawing explanation

Fig. 1 is the indoor scene schematic diagram described in the specific embodiment of the present invention three.

Embodiment

The position fixing process of the WLAN indoor orientation method of the semi-supervised SDE algorithm described in embodiment one, present embodiment is:

Step one, for indoor environment arrange m AP (AP _j, 1≤j≤m), guarantee the quorum sensing inhibitor that in described environment, any point is sent by two or more AP;

Step 2, in indoor environment, evenly reference point is set, choosing a reference point is that initial point sets up rectangular coordinate system, obtain the coordinate position of each reference point in this rectangular coordinate system, and in each reference point, utilize signal receiver collection and record from each AP received signal strength RSS value k time and carry out corresponding data processing;

Step 3, according to K means clustering algorithm, indoor positioning environment being divided into Q sub regions, is the reference point marker classification information separately of every sub regions.In every sub regions, the received signal strength RSS value of each reference point has similar feature, and namely the characteristic vector of each reference point is similar;

Step 4, gather random unmarked RSS data (distinguish with reference point and be only to have signal strength values and do not have positional information), the characteristic vector of each sub regions obtained with step 3 compares, namely the distance with the characteristic vector of all subregion is asked for, by random data category division in the subregion nearest with its characteristic vector;

Step 5, SDE algorithm is adopted to every sub regions in K sub regions.Input parameter as SDE algorithm: the value of intrinsic dimension (Intrinsic Dimensionality), by existing intrinsic dimension algorithm for estimating, Radio Map partition data is estimated, provide the intrinsic dimension estimated value of each area data.Determine the eigentransformation matrix in each region, and generate location fingerprint database (the Radio Map after dimensionality reduction ^*);

The characteristic vector of each sub regions that step 6, the signal strength signal intensity RSS value obtained by tested point and step 3 obtain compares, namely ask for the distance of the characteristic vector of test point and the characteristic vector of all subregion, test point is positioned in the subregion nearest with its characteristic vector;

Step 7, by the subregion of locating, the RSS value of the eigentransformation matrix utilizing step 5 to draw to tested point carries out dimensionality reduction, obtains the RSS of low-dimensional ^*, with fingerprint database Radio Map ^*mate, adopt k nearest neighbor location fingerprint location algorithm accurately to locate test point.

Embodiment two, present embodiment are further illustrating the WLAN indoor orientation method of the semi-supervised SDE algorithm described in embodiment one, in embodiment one described in step 2 in each reference point, utilize signal receiver collection and record from received signal strength RSS value k time of each AP and the concrete steps of carrying out corresponding data processing be:

Step 2 one, k × m rank matrix is obtained to each reference point, the i-th row jth list of matrix show gather for i-th time in the RSS value from a jth AP that receives;

Elements all in step 2 two, k × m rank rectangular array vector of each reference point being obtained is added and obtains a value, again this value divided by k, each like this reference point is obtained for the vector of a 1 × m, for each reference point, this vector is called the characteristic vector of this reference point, and the jth element in vector is (namely from AP _jthe signal strength signal intensity RSS average obtained) can as the jth of this reference point feature.In a reference point, the RSS value of some AP can't detect sometimes, be then the minimum signal value-100dBm that can receive under this environment by its assignment, so the scope of the received signal strength RSS value v of reference point is-100dBm≤v≤0dBm arbitrarily.This group vector will be used for the cluster subregion realizing step three.

Present embodiment is that follow-up embodiment provides fingerprint database sample.

Embodiment three, present embodiment are further illustrating the WLAN indoor orientation method of the semi-supervised SDE algorithm described in embodiment one, in embodiment one described in step 3 according to K means clustering algorithm to the concrete steps that indoor positioning environment is divided into Q sub regions are:

The characteristic vector of all reference points that step 3 one, input step two or two record and subregion number Q;

Step 3 two, at random obtain choose the cluster centre of RSS (i.e. the characteristic vector of each reference point) value as K sub regions of K reference point data from step 2 two;

Step 3 three, calculate the Euclidean distance of each reference point and K cluster centre characteristic vector, each reference point is distributed to the subregion minimum with its Euclidean distance;

Step 3 four, the RSS value of each reference point in every sub regions to be averaged, obtain new cluster centre;

Step 3 five, repetition step 3 three and step 3 four are until the center of every sub regions no longer changes;

Step 3 six, obtain K sub regions and cluster centre vector (the i.e. vector of a 1 × m corresponding to all subregion, this vector is claimed to be the characteristic vector of this sub regions, a jth feature of jth this sub regions of element representation of this vector is also the RSS average from a jth AP that this sub regions obtains).

Present embodiment can ensure to carry out effective subregion to localizing environment, the signal strength signal intensity RSS value from each AP that reference point in every sub regions is received, namely the characteristic vector similarity degree of a reference point is greater than the characteristic vector similarity of the reference point from two different subregions, and this also lays the foundation for the random RSS data category in step 4 divides.

Test in the indoor scene shown in Fig. 1, have 19 laboratories, 1 meeting room and 1 table tennis room, represent elevator, the material of wall is fragment of brick, aluminium alloy window and metallic door, and wireless access point AP is LinksysWAP54G-CN, and with AP1, AP2 ..., AP27 indicate 1 to No. 27 AP, each AP be fixed on apart from ground 2m height position.Signal receiver is 1.2m overhead, and in figure, arrow mark is the position that 1 to No. 27 AP places, and select corridor as experiment place, the latticed region namely in figure, is spaced apart 1m between neighboring reference point, totally 247 reference points.

Use the wireless network card of Intel PRO/Wireless 3945ABG network connection to connect to network, association V450 notebook installs NetStumbler software, gathers the signal strength signal intensity RSS value from 27 access point AP; Off-line phase, in four of all reference points different orientation, with 2/second sample frequencys, 100 RSS values of continuous sampling record AP, and the relevant information of AP.The physical coordinates of all reference points and RSS value are stored as the data that position fixing process calls, set up Radio Map.The RSS data of random acquisition locating area 580 points, direction is random and with 2/second frequencies, each point sampling 10 seconds, gets average as the Unlabeled data in SDE algorithm, these data tracer signal intensity level and do not have more specific location information.As the input data of SDE algorithm together with Radio Map.

Embodiment four, present embodiment are further illustrating the WLAN indoor orientation method of the semi-supervised SDE algorithm described in embodiment one, and in embodiment one, the detailed process of the category division of the random RSS data of step 4 is:

The Unlabeled data (only have signal strength values and do not have positional information) of step 4 one, input random acquisition;

Step 4 two, the characteristic vector of each sub regions Unlabeled data and step 3 obtained compare, namely the distance with the characteristic vector of all subregion is asked for, random data is distributed in the subregion nearest with its characteristic vector, as the classification belonging to it.

Present embodiment can divide the classification belonging to the Unlabeled data of random acquisition, provides classification information for the SDE algorithm in step 5 builds total data adjacent map matrix.

Embodiment five, present embodiment are further illustrating the WLAN indoor orientation method of the semi-supervised SDE algorithm described in embodiment one, SDE algorithm is adopted to carry out dimensionality reduction to the every sub regions in K sub regions in embodiment one described in step 5, determine the eigentransformation matrix in each region, and generate new location fingerprint database and be specifically described:

SDE algorithm is based on the maximized a kind of manifold learning arithmetic of divergence in class scatter and class.Before theory analysis is carried out to SDE algorithm, following explanation is done to input data: input higher-dimension flag data and Unlabeled data the two class data main distinctions are: the data that the former corresponding reference point place gathers, containing positional information (x _ix, y _iy) and class mark y _i∈ 1,2 ..., c}.Wherein c represents high dimensional data is divided into c submanifold, and the high dimensional data being about to input is divided into c class.Unlabeled data also obtains corresponding category information after step 4.

Step May Day, structure adjacent map

Directionless figure G and G' is constructed according to the class label information of high dimensional data point and neighbor relationships thereof.Wherein neighbor relationships is the criterion adopting KNN algorithm to provide, and puts as its neighbours for K that namely selects data point nearest, and G represents and works as x _iwith x _jclass label information y _i=y _jtime and x _i, x _jk nearest neighbor relation each other; G' shows and works as x _iwith x _jclass label information y _i≠ y _jtime and x _i, x _jk nearest neighbor relation each other.

Step 5 two, calculating weight matrix

According to the adjacent map of step structure on May Day, class Gaussian function is adopted to carry out the calculating of weight matrix.Its expression formula is for shown in (1).W in formula (1) _ijrepresent Neighbor Points x _iwith x _jbetween weights, || x _i-x _j|| ²for Neighbor Points x _iwith x _jbetween norm distance, adopt matrix-style to calculate norm distance, t is weights normalized parameter.

$\left\{\begin{array}{c}{w}_{\mathrm{ij}}=\left\{\begin{array}{c}\exp (-{\left|\right|x_i-x_j\left|\right|}^2/t);\\ 0;\end{array}\mathrm{if}{x}_i,x_j\∈G\right.\\ w_{\mathrm{ij}}^{\′}=\left\{\begin{array}{c}\exp (-{\left|\right|x_i-x_j\left|\right|}^2/t)\\ 0;\end{array}\right.\mathrm{if}{x}_i,x_j\∈G^{\′}\end{array}\right.---\left(1\right)$

Step 5 three, determine target function and solve

Target according to SDE algorithm: minimize divergence in class while maximizing class scatter.Divergence adopts the norm distance representing similar and non-like numbers strong point to represent.Can draw its corresponding optimization object function by the target of SDE algorithm, shown in (2), eigentransformation matrix P is optimal solution to be asked.

$\left\{\begin{array}{c}\mathrm{Maximze\; J}\left(V\right)=\underset{i,j}{\mathrm{\Σ}}{\left|\right|P^T{x}_i-P^T{x}_j\left|\right|}^2{w}_{\mathrm{ij}}^{\′}\\ \mathrm{subject\; to}\underset{i,j}{\mathrm{\Σ}}{\left|\right|P^T{x}_i-P^T{x}_j\left|\right|}^2{w}_{\mathrm{ij}}=1\end{array}\right.---\left(2\right)$

In formula: Maximize represents: maximize, subject to represents: obey;

Following analysis is done according to the optimization object function that formula (2) provides:

The calculating formula of known matrix norm the calculating formula of this formula and matrix trace || A|| ²=tr (AA ^t) consistent, therefore formula (2) can be expressed as matrix trace:

$J\left(V\right)=\underset{i,j}{\mathrm{\Σ}}\left\{\mathrm{tr}\right[(P^T{x}_i-P^T{x}_j){(P^T{x}_i-P^T{x}_j)}^T{w}_{\mathrm{ij}}^{\′}\left]\right\}---\left(3\right)$

Formula (3) is reduced to further:

$J\left(V\right)=\underset{i,j}{\mathrm{\Σ}}\left\{\mathrm{tr}\right[P^T(x_i-x_j){(x_i-x_j)}^{T}P\left]w_{\mathrm{ij}}^{\′}\right\}---\left(4\right)$

Be real number by the calculating scalar nature of trace of a matrix and weights element, formula (4) can be reduced to:

J(V)＝2tr{P ^T[X(D′-W′)X ^T]P} (5)

In like manner, formula (2) is simplified to:

$\left\{\begin{array}{c}\mathrm{Maximize\; J}\left(V\right)=2\mathrm{tr}\left\{P^T\right[X(D^{\′}-W^{\′})X^T\left]P\right\}\\ \mathrm{subject\; to}2\mathrm{tr}\left[P^{T}X(D-W)X^{T}P\right]=1\end{array}\right.---\left(6\right)$

In formula (6), X is input high dimensional data, and W, W' are respectively weight matrix corresponding to G and G'.D and D' is diagonal matrix, and its diagonal element can be tried to achieve by formula (7):

$\left\{\begin{array}{c}{d}_{\mathrm{ii}}=\underset{j}{\mathrm{\Σ}}{w}_{\mathrm{ij}}\\ d_{\mathrm{ii}}^{\′}=\underset{j}{\mathrm{\Σ}}{w}_{\mathrm{ij}}^{\′}\end{array}\right.---\left(7\right)$

To formula (6) application lagrange's method of multipliers, can draw shown in formula (8):

X(D′-W′)X ^TP＝λX(D-W)X ^TP (8)

Generalized eigenvalue decomposition is carried out to formula (8), draws the eigenvalue λ=[λ of its Eigenvalues Decomposition ₁, λ ₂..., λ _n] ^tand characteristic vector p=[p ₁, p ₂..., p _n] ^t.

Step the May 4th, intrinsic dimension are estimated

The number of the characteristic value that intrinsic dimension retains when being low-dimensional embedding and characteristic of correspondence vector thereof.Characteristic vector character pair value is larger, and between class distance corresponding to this direction is larger, also just means that retained feature more has judgement index.Intrinsic dimension d is an important parameter of algorithm, and it is whether accurate that its value is estimated, determine amount of information contained by low-dimensional data number, thus affect positioning precision.The characteristic value obtained according to step 5 three and characteristic vector thereof, estimate intrinsic dimension according to formula (9):

$\frac{\underset{i=1}{\overset{d}{\mathrm{\Σ}}}{\mathrm{\λ}}_i}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\λ}}_i}\≥{\mathrm{\η}}^{*}---\left(9\right)$

Wherein η ^*be the threshold value that projector space retains information, usual value is greater than 80%, namely chooses front d eigenvalue of maximum sum and is not less than 80% with the ratio of All Eigenvalues summation, can meet and embed the good low-dimensional of primary data information (pdi).

Step 5 five, calculating embed result

Estimate threshold value according to step 4 setting intrinsic dimension, the d chosen a characteristic value characteristic of correspondence vector forms transformation matrix P=[p ₁, p ₂..., p _d], input high dimensional data point x is being calculated by formula (10) _idata Z after dimensionality reduction _ifor:

Z _i＝P ^Tx _i(10)

The theory deduction of SDE algorithm is provided by formula (2) ~ (8).Received signals fingerprint data and the eigentransformation matrix of low-dimensional can be drawn by SDE algorithm, be designated as Radio Map respectively ^*and P.

Embodiment six, present embodiment are further illustrating the WLAN indoor orientation method of the semi-supervised SDE algorithm described in embodiment one, in embodiment one described in step 7 to the every sub regions in K sub regions, utilize the low-dimensional Radio Map that step 5 is tried to achieve respectively ^*and eigentransformation matrix, adopt k neighbor positions fingerprinting localization algorithm to position test point and be specifically described:

Test point is positioned in subregion by step July 1st, step 6, and the RSS signal that test point receives is higher-dimension live signal, is expressed as R _test=[r ₁, r ₂..., r _n].Utilize formula (10) to be multiplied with the eigentransformation matrix P (obtaining in step 5 five) in this region, calculate the signal value after dimensionality reduction

The low dimensional feature vector of step 7 two, test point with this region low-dimensional Radio Map ^*i-th reference point in (obtaining in step 5 five) between distance can be tried to achieve by formula (11):

${\mathrm{Dis}}_i={\left(\underset{j=1}{\overset{d}{\mathrm{\Σ}}}{|{\tilde{r}}_j-{\mathrm{rss}}_{\mathrm{ij}}|}^2\right)}^{\frac{1}{2}}---\left(11\right)$

Step 7 three, from result, choose nearest with the test point characteristic vector reference point of k from small to large, by the location estimation coordinate of formula (12) calculating test point

$(\hat{x},\hat{y})=\frac{1}{k}\underset{i=1}{\overset{k}{\mathrm{\Σ}}}(x_{\mathrm{ix}},y_{\mathrm{iy}})---\left(12\right)$

Complete the location to test point.

Claims (6)

1., based on the WLAN indoor orientation method of semi-supervised SDE algorithm, it is characterized in that: it is realized by following steps:

Step one, for indoor environment arrange m access point AP (AP _j, 1≤j≤m), guarantee the quorum sensing inhibitor that in described indoor environment, any point is sent by two or more wireless access point AP; M is positive integer;

Step 2, in indoor environment, evenly reference point is set, choosing a reference point is that initial point sets up rectangular coordinate system, obtain the coordinate position of each reference point in this rectangular coordinate system, and in each reference point, utilize signal receiver collection and record from received signal strength RSS value k time of each AP, and carry out data processing; K is positive integer;

Step 3, according to K means clustering algorithm, indoor positioning environment being divided into Q sub regions, is the reference point marker classification information separately of every sub regions;

Step 4, gather random unmarked RSS data, the characteristic vector of each sub regions obtained with step 3 compares, namely the distance with the characteristic vector of all subregion is asked for, by random data category division in the subregion nearest with its characteristic vector;

Step 5, SDE algorithm is adopted to every sub regions in K sub regions, obtain eigentransformation matrix;

The input parameter of SDE algorithm, the i.e. value of intrinsic dimension, by existing intrinsic dimension algorithm for estimating, RadioMap partition data is estimated, provide the intrinsic dimension estimated value of each area data, determine the eigentransformation matrix in each region, and generate the location fingerprint database Radio Map after dimensionality reduction ^*;

The characteristic vector of each sub regions that step 6, the signal strength signal intensity RSS value obtained by tested point and step 3 obtain compares, namely ask for the distance of the characteristic vector of test point and the characteristic vector of all subregion, test point is positioned in the subregion nearest with its characteristic vector;

Step 7, by the subregion of locating, the RSS value of the eigentransformation matrix utilizing step 5 to draw to tested point carries out dimensionality reduction, obtains the RSS of low-dimensional ^*, with fingerprint database Radio Map ^*mate, adopt k nearest neighbor location fingerprint location algorithm accurately to locate test point.

2. the WLAN indoor orientation method based on semi-supervised SDE algorithm according to claim 1, it is characterized in that, described in step 2 in each reference point, utilize signal receiver collection and record from received signal strength RSS value k time of each AP, and the concrete steps of carrying out data processing are:

Step 2 one, k × m rank matrix is obtained to each reference point, the i-th row jth list of matrix show gather for i-th time in the RSS value from a jth AP that receives; K, m, i, j are positive integer;

Elements all in step 2 two, k × m rank rectangular array vector of each reference point being obtained is added and obtains a value, again this value divided by k, then each reference point is obtained for the vector of a 1 × m, for each reference point, this vector is called the characteristic vector of this reference point, and the jth element in vector is as a jth feature of this reference point; If the RSS value of some AP can't detect in a reference point, be then the minimum signal value-100dBm that can receive under this environment by its assignment, so the scope of the received signal strength RSS value v of reference point is-100dBm≤v≤0dBm arbitrarily; This group vector is for realizing the cluster subregion of step three.

3. the WLAN indoor orientation method of semi-supervised SDE algorithm according to claim 1, it is characterized in that described in step 3 according to K means clustering algorithm to the concrete steps that indoor positioning environment is divided into Q sub regions be:

The characteristic vector of all reference points that step 3 one, input step two or two record and subregion number Q;

Step 3 two, at random obtain choose the RSS of K reference point data from step 2 two, that is: the characteristic vector value of each reference point is as the cluster centre of K sub regions;

Step 3 three, calculate the Euclidean distance of each reference point and K cluster centre characteristic vector, each reference point is distributed to the subregion minimum with its Euclidean distance;

Step 3 four, the RSS value of each reference point in every sub regions to be averaged, obtain new cluster centre;

Step 3 five, repetition step 3 three and step 3 four are until the center of every sub regions no longer changes;

Step 3 six, obtain K sub regions and all subregion corresponding cluster centre vector, that is: the vector of a 1 × m, this vector is claimed to be the characteristic vector of this sub regions, a jth feature of jth this sub regions of element representation of this vector is also the RSS average from a jth AP that this sub regions obtains.

4. the WLAN indoor orientation method of semi-supervised SDE algorithm according to claim 1, is characterized in that the detailed process of the category division of the random RSS data of step 4 is:

The Unlabeled data of step 4 one, input random acquisition, described Unlabeled data only has signal strength values and does not have positional information;

Step 4 two, the characteristic vector of each sub regions Unlabeled data and step 3 obtained compare, namely the distance with the characteristic vector of all subregion is asked for, random data is distributed in the subregion nearest with its characteristic vector, as the classification belonging to it.

5. the WLAN indoor orientation method of semi-supervised SDE algorithm according to claim 1, it is characterized in that adopting SDE algorithm to carry out dimensionality reduction to the every sub regions in K sub regions described in step 5, determine the eigentransformation matrix in each region, and the concrete grammar generating new location fingerprint database is:

Step May Day, structure adjacent map:

Directionless figure G and G' is constructed according to the class label information of high dimensional data point and neighbor relationships thereof; Wherein neighbor relationships is the criterion adopting KNN algorithm to provide, and puts as its neighbours for K that namely selects data point nearest, and G represents and works as x _iwith x _jclass label information y _i=y _jtime and x _i, x _jk nearest neighbor relation each other; G' shows and works as x _iwith x _jclass label information y _i≠ y _jtime and x _i, x _jk nearest neighbor relation each other;

Step 5 two, calculating weight matrix:

According to the adjacent map of step structure on May Day, adopt class Gaussian function to carry out the calculating of weight matrix, its expression formula is for shown in (1):

$\left\{\begin{array}{c}{w}_{\mathrm{ij}}=\left\{\begin{array}{c}\exp (-{\left|\right|x_i-x_j\left|\right|}^2/t)\\ 0;\end{array}\right.;\begin{array}{cc}\mathrm{if}& x_i,x_j\∈G\end{array}\\ w_{\mathrm{ij}}^{\′}=\left\{\begin{array}{c}\exp (-{\left|\right|x_i-x_j\left|\right|}^2/t)\\ 0;\end{array}\right.;\begin{array}{cc}\mathrm{if}& x_i,x_j\∈G^{\′}\end{array}\end{array}\right.---\left(1\right)$

Wherein: w _ijrepresent Neighbor Points x _iwith x _jbetween weights, || x _i-x _j|| ²for Neighbor Points x _iwith x _jbetween norm distance, adopt matrix-style to calculate norm distance, t is weights normalized parameter;

Step 5 three, determine target function and solve:

Target according to SDE algorithm: minimize divergence in class while maximizing class scatter; Divergence adopts the norm distance representing similar and non-like numbers strong point to represent;

Draw its corresponding optimization object function by the target of SDE algorithm, shown in (2), eigentransformation matrix P is optimal solution to be asked:

$\left\{\begin{array}{c}\mathrm{Maximize\; J}\left(V\right)=\underset{i,j}{\mathrm{\Σ}}{\left|\right|P^T{x}_i-P^T{x}_j\left|\right|}^2{w}_{\mathrm{ij}}^{\′}\\ \mathrm{subject\; to}\underset{i,j}{\mathrm{\Σ}}{\left|\right|P^T{x}_i-P^T{x}_j\left|\right|}^2{w}_{\mathrm{ij}}=1\end{array}\right.---\left(2\right)$

Optimization object function according to formula (2) provides:

The calculating formula of known matrix norm the calculating formula of this formula and matrix trace || A|| ²=tr (AA ^t) consistent, therefore formula (2) is expressed as matrix trace:

$J\left(V\right)=\underset{i,j}{\mathrm{\Σ}}\left\{\mathrm{tr}\right[(P^T{x}_i-P^T{x}_j){(P^T{x}_i-P^T{x}_j)}^T{w}_{\mathrm{ij}}^{\′}\left]\right\}---\left(3\right)$

Formula (3) is reduced to further:

$J\left(V\right)=\underset{i,j}{\mathrm{\Σ}}\left\{\mathrm{tr}\right[P^T(x_i-x_j){(x_i-x_j)}^{T}P\left]w_{\mathrm{ij}}^{\′}\right\}---\left(4\right)$

Be real number by the calculating scalar nature of trace of a matrix and weights element, formula (4) be reduced to:

J(V)＝2tr{P ^T[X(D′-W′)X ^T]P} (5)

In like manner, formula (2) is simplified to:

$\left\{\begin{array}{c}\mathrm{Maximize\; J}\left(V\right)=2\mathrm{tr}\left\{P^T\right[X(D^{\′}-W^{\′})X^T\left]P\right\}\\ \mathrm{subject\; to}2\mathrm{tr}\left[P^{T}X(D-W)X^{T}P\right]=1\end{array}---\left(6\right)\right.$

In formula (6), X is input high dimensional data, and W, W' are respectively weight matrix corresponding to G and G'; D and D' is diagonal matrix, and its diagonal element is tried to achieve by formula (7):

$\left\{\begin{array}{c}{d}_{\mathrm{ii}}=\underset{j}{\mathrm{\Σ}}{w}_{\mathrm{ij}}\\ d_{\mathrm{ii}}^{\′}=\underset{j}{\mathrm{\Σ}}{w}_{\mathrm{ij}}^{\′}\end{array}\right.---\left(7\right)$

To formula (6) application lagrange's method of multipliers, draw shown in formula (8):

X(D′-W′)X ^TP＝λX(D-W)X ^TP (8)

Generalized eigenvalue decomposition is carried out to formula (8), draws the eigenvalue λ=[λ of its Eigenvalues Decomposition ₁, λ ₂..., λ _n] ^tand characteristic vector p=[p ₁, p ₂... _,p _n] ^t;

Step the May 4th, intrinsic dimension are estimated:

The characteristic value obtained according to step 5 three and characteristic vector thereof, estimate intrinsic dimension according to formula (9):

$\frac{\underset{i=1}{\overset{d}{\mathrm{\Σ}}}{\mathrm{\λ}}_i}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\λ}}_i}\≥{\mathrm{\η}}^{*}---\left(9\right)$

Wherein: η ^*be the threshold value that projector space retains information, usual value is greater than 80%, namely chooses front d eigenvalue of maximum sum and is not less than 80% with the ratio of All Eigenvalues summation, namely meets and embeds the good low-dimensional of primary data information (pdi);

Step 5 five, calculating embed result:

Estimate threshold value according to step the May 4th setting intrinsic dimension, the d chosen a characteristic value characteristic of correspondence vector forms change

Change matrix P=[p ₁, p ₂..., p _d], input high dimensional data point x is being calculated by formula (10) _idata Z after dimensionality reduction _ifor:

Z _i＝P ^Tx _i(10)

Drawn received signals fingerprint data and the eigentransformation matrix of low-dimensional by SDE algorithm, be designated as Radio Map respectively ^*and P.

6. the WLAN indoor orientation method of semi-supervised SDE algorithm according to claim 5, it is characterized in that described in step 7 to the every sub regions in K sub regions, utilize the low-dimensional Radio Map that step 5 is tried to achieve respectively ^*and eigentransformation matrix, employing k neighbor positions fingerprinting localization algorithm to the concrete grammar that test point positions is:

Test point is positioned in subregion by step July 1st, step 6, and the RSS signal that test point receives is higher-dimension live signal, is expressed as R _test=[r ₁, r ₂..., r _n]; Utilize formula (10) to be multiplied with the eigentransformation matrix P in this region, calculate the signal value after dimensionality reduction ${\tilde{R}}_{\mathrm{test}}=[{\tilde{r}}_1,{\tilde{r}}_2,...,{\tilde{r}}_d];$

The low dimensional feature vector of step 7 two, test point with this region low-dimensional Radio Map ^*in i-th reference point ${\tilde{R}}_i=[{\mathrm{rss}}_{i1},{\mathrm{rss}}_{i2},...,{\mathrm{rss}}_{\mathrm{id}}]$ Between distance tried to achieve by formula (11):

${\mathrm{Dis}}_i={\left(\underset{j=1}{\overset{d}{\mathrm{\Σ}}}{|{\tilde{r}}_j-{\mathrm{rss}}_{\mathrm{ij}}|}^2\right)}^{\frac{1}{2}}---\left(11\right)$

Step 7 three, from result, choose nearest with the test point characteristic vector reference point of k from small to large, by the location estimation coordinate of formula (12) calculating test point

$(\hat{x},\hat{y})=\frac{1}{k}\underset{i=1}{\overset{k}{\mathrm{\Σ}}}(x_{\mathrm{ix}},y_{\mathrm{iy}})---\left(12\right)$

Complete the location to test point.