CN101695152B - Method and system for indoor positioning - Google Patents

Abstract

Translated fromChinese

本发明涉及一种室内定位的方法及其系统，系统包括：步骤1，输入带位置标记的训练数据和无位置标记的训练数据，所述训练数据组成训练数据集；步骤2，根据无位置标记的训练数据和带位置标记的训练数据间的相似关系，由带位置标记的训练数据的位置标记得出无位置标记的训练数据对应的位置标记，使所述训练数据集中全部训练数据具有位置标记；步骤3，采用有监督学习方法由所述训练数据集定位待定目标。本发明能够降低室内无线定位技术训练数据采集代价。

The present invention relates to a method and system for indoor positioning. The system includes: step 1, input training data with position marks and training data without position marks, and the training data constitutes a training data set; step 2, according to the position mark without The similarity relationship between the training data of the training data and the training data with the position mark, obtain the corresponding position mark of the training data without the position mark from the position mark of the training data with the position mark, make all the training data in the training data set have the position mark ; Step 3, using a supervised learning method to locate the undetermined target from the training data set. The invention can reduce the training data acquisition cost of the indoor wireless positioning technology.

Description

The method of indoor positioning and system thereof

Technical field

The present invention relates to wireless communication technology field, particularly relate to method and the system thereof of indoor positioning.

Background technology

Along with developing rapidly with universal gradually of mobile computing device, the demand (Location-Based Service, LBS) of the various position-baseds services under the indoor environment is day by day urgent.Because existing global position system, such as the global positioning system (Global Positioning System, GPS) of the U.S. and the big-dipper satellite navigation system of China, at indoor environment or high-lager building dense city, satellite positioning signal is subject to the obstruct of building, is difficult to effective location.Indoor positioning generally adopts the transducing signals such as infrared ray, ultrasonic wave, radio frequency at present, wherein higher based on infrared ray, hyperacoustic location technology precision, but need to use special hardware facility, and the signal demand line-of-sight transmission, orientation range is relatively limited, is difficult to large scale deployment.

In recent years, along with the large scale deployment of wireless network, be subject to extensive concern based on the indoor positioning of WLAN (Wireless LAN, WLAN (wireless local area network)).Its main cause is based on the WLAN radiofrequency signal and locates not only long transmission distance, ignores apart from requiring, and need not to increase additional hardware, adds software simple, uses the location technology of particular device to compare with other, and cost advantage is fairly obvious.Become at present the study hotspot of indoor positioning technology based on the radio-frequency (RF) signal strength location.

The supervised learning method adopts the thought of pattern classification in the prior art based on the localization method of radio-frequency (RF) signal strength, orientation problem is converted to the pattern recognition problem of radio-frequency (RF) signal strength and position.These class methods mainly are divided into off-line training and online two stages of location, in off-line training step, at first the practical application scene is divided at a certain distance the grid of rule, then gather the radio-frequency (RF) signal strength information of some at each grid, construct radio frequency map (Radio Map) location model; At online positioning stage, according to the radio-frequency (RF) signal strength information that target real-time monitored to be positioned arrives, carry out position calculation by location model, thus the location that localizing objects is treated in realization.These class methods are regarded the signal strength signal intensity vector as the feature (Feature) of signal mode (Pattern) in signal strength space of correspondence position, actual position then can be regarded as the true mark (Label) of this pattern, signal strength signal intensity vector (Feature) and corresponding position coordinates (Label) thereof are formed training data, training data forms training dataset, and grader (Classifier) or regression function (Regression Function) that training obtains just can be as location models.In a word, this class localization method is by the inherent mapping principle between study radio-frequency (RF) signal strength and position, then based on the implementation of inference target localization.

As mentioned above, existing supervised learning method is a kind of method of Schema-based classification, only need to know the corresponding signal strength characteristics in each position, and not need to know the priori of AP position.But existing this class location algorithm need to be in the off-line training step collection in a large number with the data of position mark as training data, this is the extremely work of labor intensive and financial resources, gathers unmarked training data then relatively simple.

Summary of the invention

For addressing the above problem, the invention provides method and the system thereof of indoor positioning, can reduce indoor wireless location technology collecting training data cost.

The invention discloses a kind of method of indoor positioning, comprising:

Step 1, the training data of input tape position mark and without the training data of position mark, described training data forms training dataset;

Step 2, according to without the training data of position mark with the similarity relation between the training data of position mark, drawn without position mark corresponding to the training data of position mark by the position mark with the training data of position mark, make described training data concentrate whole training datas to have position mark;

Step 3 adopts the supervised learning method to be located by described training dataset and waits to set the goal.

Described step 2 further is,

Step 21, the adjacent map of the signal strength signal intensity vector similarity relation of all training datas of structure expression carries out Eigenvalues Decomposition to described in abutting connection with Laplacian matrix of graphs, characteristic vector composition characteristic vector space;

Step 22 makes up the grader on the described characteristic vector space, finds the solution the parameter of described grader according to the position mark of described training data with position mark, is drawn described without position mark corresponding to the training data of position mark by described grader.

Described step 21 further is,

Step 31 makes up described adjacent map;

Step 32, be calculated as follows described in abutting connection with Laplacian matrix of graphs,

L＝D-W，

Wherein, L is described in abutting connection with Laplacian matrix of graphs, and D is the weights degree diagonal matrix of the node of described adjacent map, and W is the weight matrix on described adjacent map limit;

Step 33 is carried out Eigenvalues Decomposition to described Laplacian Matrix, obtains the characteristic vector of described Laplacian Matrix, described characteristic vector composition characteristic vector space.

Also comprise between described step 32 and the described step 33,

Step 41 is carried out normalization to described Laplacian Matrix.

Described step 22 further is,

Step 51 makes up described grader and is,

$f_j\≈\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{a}_i{\mathrm{\φ}}_{\mathrm{ji}}(j=1,...l+u,p\≤l)$

A wherein_iBe the parameter of grader, φ_JiThe value that represents j element of i characteristic vector, f_jBe the position mark of training data, during j≤l, f_jBe the position mark with the training data of position mark, during j＞l, f_jBe the position mark without the training data of position mark, p is the quantity of the characteristic value used, and l is the quantity with the training data of position mark, and u is the quantity without the training data of position mark;

Step 52, the error of calculating the position mark of described training data with position mark is

$E\left(a\right)=\underset{j=1}{\overset{l}{\mathrm{\Σ}}}{(f_j-\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{a}_i{\mathrm{\φ}}_{\mathrm{ji}})}^2,$

By the send as an envoy to parameter of described grader of this error minimum of least square solution;

Step 53, the position mark that is drawn without the position mark training data by described grader is

$f_j=\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{a}_i{\mathrm{\φ}}_{\mathrm{ji}}(j=l+1,...l+u).$

Described step 31 further is,

Step 61, the training data of concentrating take described training data is as node, and the weights between computing node are

$w_{\mathrm{ij}}=\exp \{-\frac{d{({\mathrm{RSS}}_i,{\mathrm{RSS}}_j)}^2}{2{\mathrm{\σ}}^2}\}$

Wherein, RSS_iBe the signal strength signal intensity of training data i, RSS_jBe the signal strength signal intensity of training data j, d (RSS_i, RSS_j) expression training data the distance on signal strength space, σ is the window coefficient of gaussian kernel function;

Step 62 for each node, is arranged node by the weights order from big to small with described node, chooses a front k node as the neighbours of described node, and k is the integer greater than 0;

Step 63 with the connection of described node with described node neighbours, constructs described adjacent map.

Described step 31 further is,

Step 71, the training data of concentrating take described training data connects all nodes in twos as node, forms described adjacent map;

Step 72 determines that the weights on limit in the described adjacent map are

$w_{\mathrm{ij}}=\exp \{-\frac{d{({\mathrm{RSS}}_i,{\mathrm{RSS}}_j)}^2}{2{\mathrm{\σ}}^2}\}$

Wherein, RSS_iBe the signal strength signal intensity of training data i, RSS_jBe the signal strength signal intensity of training data j, d (RSS_i, RSS_j) expression training data the distance in signal strength space, σ is the window coefficient of Gaussian function.

Described training data in the distance of signal strength space is || RSS_j-RSS_i||, RSS_iBe the signal strength signal intensity of training data i, RSS_jSignal strength signal intensity for training data j.

The invention also discloses a kind of system of indoor positioning, comprising:

Training dataset forms module, is used for the training data of input tape position mark and without the training data of position mark, described training data forms training dataset;

Training data position mark module, be used for according to without the training data of position mark with the similarity relation between the training data of position mark, drawn without position mark corresponding to the training data of position mark by the position mark with the training data of position mark, make described training data concentrate whole training datas to have position mark;

The target localization module is used for adopting the supervised learning method to be located by described training dataset and waits to set the goal.

Described training data position mark module further comprises:

Characteristic vector space makes up module, is used for making up the adjacent map of the signal strength signal intensity vector similarity relation that represents all training datas, carries out Eigenvalues Decomposition to described in abutting connection with Laplacian matrix of graphs, characteristic vector composition characteristic vector space;

The position mark module, be used for making up the grader on the described characteristic vector space, position mark according to described training data with position mark is found the solution the parameter of described grader, is drawn described without position mark corresponding to the training data of position mark by described grader.

Described characteristic vector space makes up module and is further used for making up described adjacent map; By formula L=D-W calculating is described in abutting connection with Laplacian matrix of graphs, and wherein, L is described in abutting connection with Laplacian matrix of graphs, and D is the weights degree diagonal matrix of the node of described adjacent map, and W is the weight matrix on described adjacent map limit; Described Laplacian Matrix is carried out Eigenvalues Decomposition, obtain the characteristic vector of described Laplacian Matrix, described characteristic vector composition characteristic vector space.

Described characteristic vector space makes up module and also is used for described Laplacian Matrix is carried out normalization after having calculated Laplacian Matrix.

Described position mark module is further used for making up described grader

$f_j\≈\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{a}_i{\mathrm{\φ}}_{\mathrm{ji}}(j=1,...l+u,p\≤l)$

A wherein_iBe the parameter of grader, φ_JiThe value that represents j element of i characteristic vector, f_jBe the position mark of training data, during j≤l, f_jBe the position mark with the training data of position mark, during j＞l, f_jBe the position mark without the training data of position mark, p is the quantity of the characteristic value used, and l is the quantity with the training data of position mark, and u is the quantity without the training data of position mark; The error of calculating the position mark of described training data with position mark is

$E\left(a\right)=\underset{j=1}{\overset{l}{\mathrm{\Σ}}}{(f_j-\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{a}_i{\mathrm{\φ}}_{\mathrm{ji}})}^2,$

By the send as an envoy to parameter of described grader of this error minimum of least square solution; The position mark that is drawn without the position mark training data by described grader is

$f_j=\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{a}_i{\mathrm{\φ}}_{\mathrm{ji}}(j=l+1,...l+u).$

The training data that described position mark module is further used for concentrating take described training data when making up described adjacent map is as node, and the weights between computing node are

$w_{\mathrm{ij}}=\exp \{-\frac{d{({\mathrm{RSS}}_i,{\mathrm{RSS}}_j)}^2}{2{\mathrm{\σ}}^2}\}$

Wherein, RSS_iBe the signal strength signal intensity of training data i, RSS_jBe the signal strength signal intensity of training data j, d (RSS_i, RSS_j) expression training data the distance on signal strength space, σ is the window coefficient of gaussian kernel function; For each node, by the weights order from big to small with described node node is arranged, choose a front k node as the neighbours of described node, k is the integer greater than 0; With the connection of described node with described node neighbours, construct described adjacent map.

The training data that described position mark module is further used for concentrating take described training data when making up described adjacent map connects all nodes in twos as node, forms described adjacent map; The weights of determining limit in the described adjacent map are

$w_{\mathrm{ij}}=\exp \{-\frac{d{({\mathrm{RSS}}_i,{\mathrm{RSS}}_j)}^2}{2{\mathrm{\σ}}^2}\}$

Wherein, RSS_iBe the signal strength signal intensity of training data i, RSS_jBe the signal strength signal intensity of training data j, d (RSS_i, RSS_j) expression training data the distance in signal strength space, σ is the window coefficient of Gaussian function.

Described training data in the distance of signal strength space is || RSS_j-RSS_i||, RSS_iBe the signal strength signal intensity of training data i, RSS_jSignal strength signal intensity for training data j.

Beneficial effect of the present invention is, utilization is without the training data of position mark with the potential relation between the training data of position mark, by the position mark with the training data of position mark the training data without position mark is carried out mark, can under the prerequisite that guarantees the location model positioning accuracy, reduce the collection cost of training dataset.

Description of drawings

Fig. 1 is the flow chart of the method for indoor positioning of the present invention;

Fig. 2 is the chain figure with two connected components;

Fig. 3 is the syntople figure of node on Laplce's characteristic vector space of figure among Fig. 2;

Fig. 4 is the structure chart of the system of indoor positioning of the present invention;

Fig. 5 is when the concentrated training data with position mark of training data accounts for 17%, the training data without position mark is carried out the precision of mark with the graph of a relation of the characteristic vector quantity of using;

Fig. 6 is when the concentrated training data with position mark of training data accounts for 25%, the training data without position mark is carried out the precision of mark with the graph of a relation of the characteristic vector quantity of using;

Fig. 7 concentrates ratio with the accuracy relation figure that carries out mark without the training data of position mark with the training data of position mark at training data.

Embodiment

In order to make purpose of the present invention, technical scheme and advantage clearer, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, is not intended to limit the present invention.

The method of indoor positioning of the present invention comprises:

Step S100, the training data of input tape position mark and without the training data of position mark, described training data forms training dataset.

Step S200, according to without the training data of position mark with the similarity relation between the training data of position mark, drawn without position mark corresponding to the training data of position mark by the position mark with the training data of position mark, make described training data concentrate whole training datas to have position mark.

Step S300 adopts the supervised learning method to be located by described training dataset and waits to set the goal.

Better, described step S200 further is,

Step S210, the adjacent map of the signal strength signal intensity vector similarity relation of all training datas of structure expression carries out Eigenvalues Decomposition to described in abutting connection with Laplacian matrix of graphs, characteristic vector composition characteristic vector space;

Step S220 makes up the grader on the described characteristic vector space, finds the solution the parameter of grader according to the position mark with the training data of position mark, is drawn described without position mark corresponding to the training data of position mark by grader.

The embodiment of the inventive method is as described below.

The inventive method need to gather a small amount of training data with position mark, utilize simultaneously a large amount of relatively low nothings of cost that gather with the training data of position mark, utilize the relation of all training datas on the characteristic vector space of Laplacian Matrix, train the location model with certain generalization ability.By forming training dataset with the training data of position mark with without the training data of position mark; Carry out spectral factorization by the adjacent map that all training datas are consisted of, spectral factorization is for to carry out Eigenvalues Decomposition to the adjacency Laplacian matrix of graphs, obtain the expression of all training datasets on characteristic vector space, then according to the constant principle of the position mark of identical data node on different representation spaces, know the position mark of training data on characteristic vector space with position mark, according to the position mark with the training data of position mark the training data without position mark is carried out mark, thereby obtain one entirely with the training dataset of position mark.

The method may further comprise the steps:

Step S101, the training data of input tape position mark and without the training data of position mark, those training datas form training datasets.

Training dataset is S={ldata, udata}, wherein ldata={f_Lab, RSS} is the training data with position mark, f_LabBe position mark corresponding to this training data, RSS be this training data corresponding signal strength signal intensity vector, udata={f_Unlal, RSS} is the training data without position mark, RSS is signal strength signal intensity vector corresponding to this training data, f_UnlabBe estimated position mark corresponding to this training data.

Step S201, the adjacent map of the signal strength signal intensity vector similarity relation of all training datas of structure expression.

Adjacent map is expressed as G (V, E), and V is node, and E is the limit.Wherein, set of node is all training datas, comprises l with training data and u the training data without position mark of position mark, and the limit collection E between the node is the nonnegative value matrix W of (l+u) * (l+u), wherein w_IjRepresent the syntople between i training data and j the training data, this syntople is measured according to the similarity between the signal strength signal intensity vector of training data.

Make up the embodiment one of adjacent map

According to all training datas, comprise with the training data of position mark with without the training data of position mark, adopt the mode of k arest neighbors to make up adjacent map G (V, E).

It is described that the mode of employing k arest neighbors makes up being implemented as follows of adjacent map.

Be w with the weights of any two nodes_Ij＞0.

According to RSS_iWith RSS_jBetween distance on signal strength space, adopt the mode of gaussian kernel function to compose power.

Gaussian kernel function is,

$w_{\mathrm{ij}}=\exp \{-\frac{d{({\mathrm{RSS}}_i,{\mathrm{RSS}}_j)}^2}{2{\mathrm{\σ}}^2}\},$

Wherein, RSS_iBe the signal strength signal intensity of training data i, RSS_jBe the signal strength signal intensity of training data j, d (RSS_i, RSS_j) expression training data the distance on signal strength space, σ is the window coefficient of gaussian kernel function.The distance of training data on signal strength space be || RSS_j-RSS_i||.

For each node, according to the weights of this node, other nodes except this node are pressed from big to small arranged sequentially, choose a front k node as the neighbours of this node, k is the integer greater than 0; Node connects with its neighbours, constructs adjacent map.

Make up the embodiment two of adjacent map

Adopt full method of attachment to make up adjacent map, adjacency all between any two training datas.

The distance of training data on signal strength space be || RSS_j-RSS_i||.

According to RSS_iWith RSS_jBetween distance on signal strength space, adopt the mode of gaussian kernel function to compose power

$w_{\mathrm{ij}}=\exp \{-\frac{d{({\mathrm{RSS}}_i,{\mathrm{RSS}}_j)}^2}{2{\mathrm{\σ}}^2}\},$

Wherein, d (RSS_i, RSS_j) distance of expression training data on signal strength space, σ is the window coefficient of gaussian kernel function.

Step S202 calculates in abutting connection with Laplacian matrix of graphs.

Calculating is in abutting connection with the embodiment one of Laplacian matrix of graphs

On the basis of adjacent map G (V, E), the calculating Laplacian Matrix is L=D-W, and wherein D is the weights degree diagonal matrix of node, and W is the weight matrix on adjacent map limit.

Weights degree diagonal matrix is D={d_Ii=∑_jw_Ij, represent the diagonal matrix that all limit weights sums relevant with node consist of.

When k arest neighbors method, all limit weights sums that the element representation of weights diagonal matrix and node are adjacent; When adopting full method of attachment, degree of node in the element representation adjacent map of weights diagonal matrix.

Calculating is in abutting connection with the embodiment two of Laplacian matrix of graphs

Normalization Laplacian Matrix on the basis of embodiment one:

Wherein, I representation unit vector, L is Laplacian Matrix, and D is the weights degree diagonal matrix of node, and W is the weight matrix on adjacent map limit.

Step S203 carries out Eigenvalues Decomposition to Laplacian Matrix.

Obtain spectrum and the characteristic of correspondence vector of Laplacian Matrix by Eigenvalues Decomposition, thereby all training datas can be mapped on the orthogonal intersection space of being opened by p characteristic vector, p is the number of the characteristic value of the Laplacian Matrix of use.

After Laplacian Matrix carried out Eigenvalues Decomposition, characteristic value and the characteristic vector of Laplacian Matrix were respectively { λ_i, φ_i, λ_iThe representation feature value, φ_iRepresentation feature value λ_iCharacteristic of correspondence vector, and characteristic value arranges with the non-order that falls, then

$L=\underset{i=1}{\overset{l+u}{\mathrm{\Σ}}}{\mathrm{\λ}}_i{\mathrm{\φ}}_i{{\mathrm{\φ}}_i}^T---\left(1\right)$

The spectrum of Laplacian Matrix be the characteristic value collection of Laplacian Matrix, { λ_i.

The characteristic vector of Laplacian Matrix has embodied bunch information that original training data is concentrated.

For example, the chain figure with two connected components as shown in Figure 2, solid node represents the training data with position mark, and hollow node represents the training data without position mark, and the syntople of all nodes on the orthogonal intersection space that 2 characteristic vectors of this figure are opened as shown in Figure 3 among Fig. 2.Dotted line among Fig. 3 between two nodes has represented these two nodes adjacency on this orthogonal intersection space, from Fig. 2 and Fig. 3 as seen, the characteristic vector of Laplacian Matrix has implied bunch information of node in the original graph, has effectively characterized with the training data of position mark with without the annexation between the training data of position mark.

Step S204, the grader on the construction feature vector space is found the solution the parameter of grader according to the position mark with the training data of position mark, is drawn described without position mark corresponding to the training data of position mark by grader.

Grader is used for according to the expression of training data on characteristic vector space, determines the position mark of training data.

By minimizing the formula error function, make up a grader between the characteristic vector sky, obtain classifier parameters according to least square solution.

After all training datas are mapped to characteristic vector space, utilize this bunch information, because sample example in identical cluster (Cluster) has and larger may have identical position mark, and then realizes having the position mark of flag data to propagate in whole datagram.

Because all characteristic values of Laplacian Matrix satisfy 0=λ₁≤ λ₂λ_L+u, therefore, Laplacian Matrix is positive semidefinite (positive semi-definite), the characteristic vector of Laplacian Matrix forms Hilbert space L²(M) one group of orthogonal basis.For any function f (x) ∈ L²(M), can be expressed as the linear combination of orthogonal basis:

$f\left(x\right)=\underset{i=1}{\overset{\∞}{\mathrm{\Σ}}}{a}_i{\mathrm{\φ}}_i\left(x\right)$

Wherein, φ_iBe characteristic vector, expression orthogonal basis, a_iRepresent basic φ_iCorresponding linear coefficient.

Based on above-mentioned principle, step S204 embodiment is as follows.

The structure grader is

$f_j\≈\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{a}_i{\mathrm{\φ}}_{\mathrm{ji}}(j=1,...l+u,p\≤l)$

Wherein, a_iBe the parameter of grader, φ_JiThe value that represents j element of i characteristic vector, f_jBe the position mark of training data, during j≤l, f_jBe the training data with position mark, during j＞l, f_jBe the training data without position mark, p is the quantity of the characteristic value of use, and l is the quantity with the training data of position mark, and u is the quantity without the training data of position mark.

In the error with the training data of position mark be

$E\left(a\right)=\underset{j=1}{\overset{l}{\mathrm{\Σ}}}{(f_j-\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{a}_i{\mathrm{\φ}}_{\mathrm{ji}})}^2$

Optimum fitting parameter a=(a₁, a₂A_p)^T,

$\stackrel{\‾}{a}=\underset{a=(a_1...a_p)}{\arg \min }\underset{j=1}{\overset{l}{\mathrm{\Σ}}}{(f_j-\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{a}_i{\mathrm{\φ}}_{\mathrm{ji}})}^2$

Tried to achieve by least square solution, the parameter of grader is

$a={\left(E_{\mathrm{lab}}^T{E}_{\mathrm{lab}}\right)}^{-1}{E}_{\mathrm{lab}}^T{f}_{\mathrm{lab}}---\left(6\right)$

Wherein, f_Lab=(f₁, f₂... f_l)^TBe the position mark with the training data of position mark,

E_LabFor the training data with position mark projects to p dimension expression on the orthogonal intersection space that p characteristic vector generate.

By grader, the training data without position mark is carried out mark.Position mark without the training data of position mark is

$f_j=\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{a}_i{\mathrm{\φ}}_{\mathrm{ji}}$(j＝l+1，...l+u)

Step S301 according to complete all mark training dataset, adopts the localization method of supervised learning, such as maximum a posteriori (Maximum a Posteriori, MAP) method, treats localizing objects and positions.

The system of indoor positioning of the present invention as shown in Figure 4.

Trainingdataset forms module 100, is used for the training data of input tape position mark and without the training data of position mark, those training datas form training datasets.

Training dataposition mark module 200, be used for according to without the training data of position mark with the similarity relation between the training data of position mark, drawn without position mark corresponding to the training data of position mark by the position mark with the training data of position mark, make described training data concentrate whole training datas to have position mark;

Target localization module 300 is used for adopting the supervised learning method to be located by described training dataset and waits to set the goal.

Training dataposition mark module 200 further comprises:

Characteristic vector space makes upmodule 201, is used for making up the adjacent map of the signal strength signal intensity vector similarity relation that represents all training datas, carries out Eigenvalues Decomposition to described in abutting connection with Laplacian matrix of graphs, characteristic vector composition characteristic vector space.

Position mark module 202, be used for the grader on the construction feature vector space, position mark according to described training data with position mark is found the solution the parameter of described grader, is drawn described without position mark corresponding to the training data of position mark by described grader.

Better, characteristic vector space makes upmodule 201 and is further used for making up described adjacent map; By formula L=D-W calculating is described in abutting connection with Laplacian matrix of graphs,

Wherein, L is described in abutting connection with Laplacian matrix of graphs, and D is the weights degree diagonal matrix of the node of described adjacent map, and W is the weight matrix on described adjacent map limit;

Described Laplacian Matrix is carried out Eigenvalues Decomposition, obtain the characteristic vector of described Laplacian Matrix, described characteristic vector composition characteristic vector space.

Better, characteristic vector space makes upmodule 201 and also is used for described Laplacian Matrix is carried out normalization after having calculated Laplacian Matrix.

Better,position mark module 202 is further used for making up described grader and is

$f_j\≈\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{a}_i{\mathrm{\φ}}_{\mathrm{ji}}$(j＝1，...l+u，p≤l)

A wherein_iBe the parameter of grader, φ_JiThe value that represents j element of i characteristic vector, f_jBe the position mark of training data, during j≤l, f_jBe the position mark with the training data of position mark, during j＞l, f_jBe the position mark without the training data of position mark, p is the quantity of the characteristic value used, and l is the quantity with the training data of position mark, and u is the quantity without the training data of position mark;

The error of calculating the position mark of described training data with position mark is

$E\left(a\right)=\underset{j=1}{\overset{l}{\mathrm{\Σ}}}{(f_j-\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{a}_i{\mathrm{\φ}}_{\mathrm{ji}})}^2,$

By the send as an envoy to parameter of described grader of this error minimum of least square solution; The position mark that is drawn without the position mark training data by described grader is

$f_j=\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{a}_i{\mathrm{\φ}}_{\mathrm{ji}}$(j＝l+1，...l+u)。

Better, the training data that positionmark module 202 is further used for concentrating take described training data when making up described adjacent map is as node, and the weights between computing node are

$w_{\mathrm{ij}}=\exp \{-\frac{d{({\mathrm{RSS}}_i,{\mathrm{RSS}}_j)}^2}{{2\mathrm{\σ}}^2}\}$

Wherein, RSS_iBe the signal strength signal intensity of training data i, RSS_jBe the signal strength signal intensity of training data j, d (RSS_i, RSS_j) expression training data the distance on signal strength space, σ is the window coefficient of gaussian kernel function; For each node, by the weights order from big to small with described node node is arranged, choose a front k node as the neighbours of described node, k is the integer greater than 0; With the connection of described node with described node neighbours, construct described adjacent map.

Better, the training data that positionmark module 202 is further used for concentrating take described training data when making up described adjacent map connects all nodes in twos as node, forms described adjacent map; The weights of determining limit in the described adjacent map are

$w_{\mathrm{ij}}=\exp \{-\frac{d{({\mathrm{RSS}}_i,{\mathrm{RSS}}_j)}^2}{{2\mathrm{\σ}}^2}\}$

Wherein, RSS_iBe the signal strength signal intensity of training data i, RSS_jBe the signal strength signal intensity of training data j, d (RSS_i, RSS_j) expression training data the distance in signal strength space, σ is the window coefficient of Gaussian function.

Described training data in the distance of signal strength space is || RSS_j-RSS_i||, RSS_iBe the signal strength signal intensity of training data i, RSS_jSignal strength signal intensity for training data j.

Beneficial effect of the present invention is as follows.

When Fig. 5 is training data with position mark for concentrate 17% training data at training data, to carry out the precision of mark without the training data of position mark.As can be seen from Figure 1, along with the increase of used characteristic vector number, the namely increase of above-mentioned p, the trend that the position mark precision slowly reduces after presenting and improving rapidly first.This be because, when p hour, the number of the characteristic vector that adopts is less, causes occurring not foot phenomenon of match when the solution node classifier parameters, thereby cause to the Generalization Capability that carries out mark without the position mark training data a little less than, so the position mark precision is lower.And when p increases to a certain degree, as reach haveflag data quantity 50% the time, the telltale mark precision begins to descend, this is because too much characteristic vector causes overfitting when finding the solution classifier parameters, has caused the lower result of positioning accuracy.

When Fig. 6 is training data with position mark forconcentrate 25% training data at training data, the training data without position mark is carried out the precision of mark and the relation between the characteristic vector number of adopting.Comparison diagram 5 and Fig. 6 can find out, when the characteristic vector number that adopts accounted for the 20%-25% left and right sides of all characteristic vector numbers, the position mark precision reached peak.

Fig. 7 is under the training data condition with position mark of different proportion, to carry out the Accuracy of mark without the training data of position mark.As can be seen from Figure 7, along with the increasing of the training data ratio of position mark, the label information that provides with the training data of position mark increases, and the precision of therefore training data without position mark being carried out mark increases.Simultaneously, when the training data ratio with position mark rises to a certain degree, such as 15%, the trend that increases progressively of the training data without position mark being carried out the precision of mark becomes slow, this be because, when the parameter of application class device is carried out mark to the training data without position mark, can obtain preferably fitting coefficient when reaching certain degree with the quantity 1 of the training data of position mark, the quantity that further increases with the training data of position mark can not obtain equal repayment.

In sum, for with the higher problem of the training dataset cost of position mark, based on two training samples close on signal strength space, their position mark should be similar, this patent has adopted the method for figure Laplce matrix spectra, by making up on a small quantity with the training data of position mark and propagating relation without the mark between the training data of position mark in a large number, unmarked training data is carried out mark, thereby reduced the collection cost of training dataset.Experimental result shows, only needs a small amount of flag data that has, about 20%, just can with higher precision, near 80%, realize the mark without the position mark training data.

Those skilled in the art can also carry out various modifications to above content under the condition that does not break away from the definite the spirit and scope of the present invention of claims.Therefore scope of the present invention is not limited in above explanation, but determined by the scope of claims.

Claims (14)

Translated fromChinese

1.一种室内定位的方法，其特征在于，包括：1. A method for indoor positioning, comprising:步骤1，输入带位置标记的训练数据和无位置标记的训练数据，所述训练数据组成训练数据集；Step 1, input training data with position markers and training data without position markers, the training data constitutes a training data set;步骤2，构建表示所有训练数据的信号强度向量相似关系的邻接图，对所述邻接图的拉普拉斯矩阵进行特征值分解，特征向量组成特征向量空间；构建所述特征向量空间上的分类器，根据所述带位置标记的训练数据的位置标记求解所述分类器的参数，由所述分类器得出所述无位置标记的训练数据对应的位置标记；Step 2, constructing an adjacency graph representing the similarity relationship of signal strength vectors of all training data, performing eigenvalue decomposition on the Laplacian matrix of the adjacency graph, and eigenvectors forming an eigenvector space; constructing classification on the eigenvector space A device that solves the parameters of the classifier according to the position marks of the training data with position marks, and obtains the position marks corresponding to the training data without position marks by the classifier;步骤3，采用有监督学习方法由所述训练数据集定位待定目标。Step 3, using a supervised learning method to locate the undetermined target from the training data set.2.如权利要求1所述的室内定位的方法，其特征在于，所述步骤2进一步为，2. The indoor positioning method according to claim 1, characterized in that the step 2 further comprises,步骤31，构建所述邻接图；Step 31, constructing the adjacency graph;步骤32，按如下公式计算所述邻接图的拉普拉斯矩阵，Step 32, calculate the Laplacian matrix of the adjacency graph according to the following formula,L＝D-W，L=D-W,其中，L为所述邻接图的拉普拉斯矩阵，D为所述邻接图的节点的权值度对角矩阵，W为所述邻接图边的权值矩阵；Wherein, L is the Laplacian matrix of the adjacency graph, D is the weight degree diagonal matrix of the node of the adjacency graph, and W is the weight matrix of the edge of the adjacency graph;步骤33，对所述拉普拉斯矩阵进行特征值分解，得到所述拉普拉斯矩阵的特征向量，所述特征向量组成特征向量空间。Step 33, performing eigenvalue decomposition on the Laplacian matrix to obtain eigenvectors of the Laplacian matrix, and the eigenvectors form an eigenvector space.3.如权利要求2所述的室内定位的方法，其特征在于，所述步骤32和所述步骤33之间还包括，3. The indoor positioning method according to claim 2, characterized in that, between the step 32 and the step 33, further comprising:步骤41，对所述拉普拉斯矩阵进行归一化。Step 41, normalize the Laplacian matrix.4.如权利要求2所述的室内定位的方法，其特征在于，所述步骤2进一步为，4. The indoor positioning method according to claim 2, characterized in that the step 2 further comprises,步骤51，构建所述分类器为，Step 51, constructing the classifier as,$f_j\&ap;\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}_i{\mathrm{\&phi;}}_{\mathrm{ji}}$(j＝1，...l+u，p≤l)$f_j\&ap;\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}_i{\mathrm{\&phi;}}_{\mathrm{the\; ji}}$ (j=1,...l+u, p≤l)其中a_i为分类器的参数，φ_ji表示第i个特征向量的第j个元素的值，f_j为训练数据的位置标记，j≤l时，f_j为带位置标记的训练数据的位置标记，j＞l时，f_j为无位置标记的训练数据的位置标记，p为使用的特征值的数量，l为带位置标记的训练数据的数量，u为无位置标记的训练数据的数量；Where a_i is the parameter of the classifier, φ_ji represents the value of the jth element of the i-th feature vector, f_j is the position mark of the training data, when j≤l, f_j is the position of the training data with position mark mark, when j>l, f_j is the position mark of the training data without position marks, p is the number of feature values used, l is the number of training data with position marks, u is the number of training data without position marks ;步骤52，计算所述带位置标记的训练数据的位置标记的误差为Step 52, calculating the error of the position mark of the training data with position mark as$\mathrm{<span><span>E</span>E.</span>}<span><span>(</span>(</span>\mathrm{<span><span>a</span>a</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>l</span>l</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{<span><span>(</span>(</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>-</span>-</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>p</span>p</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>\&phi;</span>\&phi;</span>}}_{\mathrm{<span><span>ji</span>the\; ji</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>,</span>,</span>$由最小二乘解出使该误差最小的所述分类器的参数；Solving the parameters of the classifier that minimizes the error by least squares;步骤53，由所述分类器得出无位置标记训练数据的位置标记为Step 53, the position mark of the training data without position mark obtained by the classifier is$f_j=\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}_i{\mathrm{\&phi;}}_{\mathrm{ji}}$(j＝l+1，...l+u)$f_j=\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}_i{\mathrm{\&phi;}}_{\mathrm{the\; ji}}$ (j=l+1,...l+u)5.如权利要求2所述的室内定位的方法，其特征在于，5. The method for indoor positioning as claimed in claim 2, characterized in that,所述步骤31进一步为，The step 31 is further as follows,步骤61，以所述训练数据集中的训练数据为节点，计算节点间的权值为Step 61, take the training data in the training data set as nodes, and calculate the weights between nodes as${\mathrm{<span><span>w</span>w</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>=</span>=</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>\{</span>\{</span><span><span>-</span>-</span>\frac{\mathrm{<span><span>d</span>d</span>}{<span><span>(</span>(</span>{\mathrm{<span><span>RSS</span>RSS</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>RSS</span>RSS</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\}</span>\}</span>$其中，RSS_i为训练数据i的信号强度，RSS_j为训练数据j的信号强度，d(RSS_i，RSS_j)表示训练数据的在信号强度空间上的距离，σ为高斯核函数的窗口系数；Among them, RSS_i is the signal strength of training data i, RSS_j is the signal strength of training data j, d(RSS_i , RSS_j ) represents the distance of training data in signal strength space, σ is the window coefficient of Gaussian kernel function ;步骤62，对于每个节点，按同所述节点的权值从大到小的顺序将节点排列，选取前k个节点作为所述节点的邻居，k为大于0的整数；Step 62, for each node, arrange the nodes according to the order of the weight of the node from large to small, select the first k nodes as the neighbors of the node, and k is an integer greater than 0;步骤63，将所述节点同所述节点邻居的连接，构建出所述邻接图。Step 63, constructing the adjacency graph by connecting the node with the neighbors of the node.6.如权利要求2所述的室内定位的方法，其特征在于，6. The method for indoor positioning according to claim 2, characterized in that:所述步骤31进一步为，The step 31 is further as follows,步骤71，以所述训练数据集中的训练数据为节点，将所有节点两两连接，组成所述邻接图；Step 71, using the training data in the training data set as nodes, connecting all nodes in pairs to form the adjacency graph;步骤72，确定所述邻接图中边的权值为Step 72, determine the weight of the edge in the adjacency graph as${\mathrm{<span><span>w</span>w</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>=</span>=</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>\{</span>\{</span><span><span>-</span>-</span>\frac{\mathrm{<span><span>d</span>d</span>}{<span><span>(</span>(</span>{\mathrm{<span><span>RSS</span>RSS</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>RSS</span>RSS</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\}</span>\}</span>$其中，RSS_i为训练数据i的信号强度，RSS_j为训练数据j的信号强度，d(RSS_i，RSS_j)表示训练数据的在信号强度空间的距离，σ为高斯函数的窗口系数。Among them, RSS_i is the signal strength of training data i, RSS_j is the signal strength of training data j, d(RSS_i , RSS_j ) represents the distance of training data in signal strength space, and σ is the window coefficient of Gaussian function.7.如权利要求5或6所述的室内定位的方法，其特征在于，7. The indoor positioning method according to claim 5 or 6, characterized in that,所述训练数据在信号强度空间的距离为||RSSS_j-RSS_i||，RSS_j为训练数据i的信号强度，RSS_j为训练数据j的信号强度。The distance of the training data in the signal strength space is ||RSSS_j −RSS_i ||, RSS_j is the signal strength of the training data i, and RSS_j is the signal strength of the training data j.8.一种室内定位的系统，其特征在于，包括：8. A system for indoor positioning, characterized in that it comprises:训练数据集组成模块，用于输入带位置标记的训练数据和无位置标记的训练数据，所述训练数据组成训练数据集；The training data set forms a module, which is used to input training data with a position mark and training data without a position mark, and the training data forms a training data set;训练数据位置标记模块包括特征向量空间构建模块和位置标记模块，其中特征向量空间构建模块，用于构建表示所有训练数据的信号强度向量相似关系的邻接图，对所述邻接图的拉普拉斯矩阵进行特征值分解，特征向量组成特征向量空间；位置标记模块，用于构建所述特征向量空间上的分类器，根据所述带位置标记的训练数据的位置标记求解所述分类器的参数，由所述分类器得出所述无位置标记的训练数据对应的位置标记；The training data position labeling module includes a feature vector space building block and a position labeling module, wherein the feature vector space building block is used to build an adjacency graph representing the similarity relationship between signal strength vectors of all training data, and the Laplacian of the adjacency graph The matrix is subjected to eigenvalue decomposition, and the eigenvectors form the eigenvector space; the position marking module is used to construct the classifier on the eigenvector space, and solves the parameters of the classifier according to the position marks of the training data with position marks, Obtaining a position mark corresponding to the training data without a position mark by the classifier;目标定位模块，用于采用有监督学习方法由所述训练数据集定位待定目标。The target positioning module is used for locating the undetermined target from the training data set by adopting a supervised learning method.9.如权利要求8所述的室内定位的系统，其特征在于，所述特征向量空间构建模块进一步用于构建所述邻接图；按公式L＝D-W计算所述邻接图的拉普拉斯矩阵，其中，L为所述邻接图的拉普拉斯矩阵，D为所述邻接图的节点的权值度对角矩阵，W为所述邻接图边的权值矩阵；对所述拉普拉斯矩阵进行特征值分解，得到所述拉普拉斯矩阵的特征向量，所述特征向量组成特征向量空间。9. The system of indoor positioning as claimed in claim 8, is characterized in that, described eigenvector space construction module is further used in constructing described adjacency graph; Calculate the Laplacian matrix of described adjacency graph by formula L=D-W , wherein, L is the Laplacian matrix of the adjacency graph, D is the weight degree diagonal matrix of the nodes of the adjacency graph, and W is the weight matrix of the edge of the adjacency graph; for the Laplacian Eigenvalue decomposition is performed on the Laplacian matrix to obtain eigenvectors of the Laplacian matrix, and the eigenvectors form an eigenvector space.10.如权利要求9所述的室内定位的系统，其特征在于，所述特征向量空间构建模块在计算完拉普拉斯矩阵后还用于对所述拉普拉斯矩阵进行归一化。10. The indoor positioning system according to claim 9, wherein the eigenvector space construction module is further used to normalize the Laplacian matrix after calculating the Laplacian matrix.11.如权利要求9所述的室内定位的系统，其特征在于，所述位置标记模块进一步用于构建所述分类器为11. The system for indoor positioning according to claim 9, wherein the position marking module is further used to construct the classifier as$f_j\&ap;\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}_i{\mathrm{\&phi;}}_{\mathrm{ji}}$(j＝1，...l+u，p≤l)$f_j\&ap;\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}_i{\mathrm{\&phi;}}_{\mathrm{the\; ji}}$ (j=1,...l+u, p≤l)其中a_i为分类器的参数，φ_ji表示第i个特征向量的第j个元素的值，f_j为训练数据的位置标记，j≤l时，f_j为带位置标记的训练数据的位置标记，j＞l时，f_j为无位置标记的训练数据的位置标记，p为使用的特征值的数量，l为带位置标记的训练数据的数量，u为无位置标记的训练数据的数量；计算所述带位置标记的训练数据的位置标记的误差为Where a_i is the parameter of the classifier, φ_ji represents the value of the jth element of the i-th feature vector, f_j is the position mark of the training data, when j≤l, f_j is the position of the training data with position mark mark, when j>l, f_j is the position mark of the training data without position marks, p is the number of feature values used, l is the number of training data with position marks, u is the number of training data without position marks ; The error of calculating the position mark of the training data with position mark is$\mathrm{<span><span>E</span>E.</span>}<span><span>(</span>(</span>\mathrm{<span><span>a</span>a</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>l</span>l</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{<span><span>(</span>(</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>-</span>-</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>p</span>p</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>\&phi;</span>\&phi;</span>}}_{\mathrm{<span><span>ji</span>the\; ji</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>,</span>,</span>$由最小二乘解出使该误差最小的所述分类器的参数；由所述分类器得出无位置标记训练数据的位置标记为Solve the parameter of the described classifier that makes this error minimum by least squares; Draw the position mark that does not have position mark training data by described classifier as$f_j=\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}_i{\mathrm{\&phi;}}_{\mathrm{ji}}$(j＝l+1，...l+u)$f_j=\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}_i{\mathrm{\&phi;}}_{\mathrm{the\; ji}}$ (j=l+1,...l+u)12.如权利要求9所述的室内定位的系统，其特征在于，12. The indoor positioning system according to claim 9, characterized in that,所述位置标记模块在构建所述邻接图时进一步用于以所述训练数据集中的训练数据为节点，计算节点间的权值为The position marking module is further used to use the training data in the training data set as nodes when constructing the adjacency graph, and calculate the weight between nodes as${\mathrm{<span><span>w</span>w</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>=</span>=</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>\{</span>\{</span><span><span>-</span>-</span>\frac{\mathrm{<span><span>d</span>d</span>}{<span><span>(</span>(</span>{\mathrm{<span><span>RSS</span>RSS</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>RSS</span>RSS</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\}</span>\}</span>$其中，RSS_i为训练数据i的信号强度，RSS_j为训练数据j的信号强度，d(RSS_i，RSS_j)表示训练数据的在信号强度空间上的距离，σ为高斯核函数的窗口系数；对于每个节点，按同所述节点的权值从大到小的顺序将节点排列，选取前k个节点作为所述节点的邻居，k为大于0的整数；将所述节点同所述节点邻居的连接，构建出所述邻接图。Among them, RSS_i is the signal strength of training data i, RSS_j is the signal strength of training data j, d(RSS_i , RSS_j ) represents the distance of training data in signal strength space, σ is the window coefficient of Gaussian kernel function ; For each node, arrange the nodes according to the order of the weight of the same node from large to small, select the first k nodes as the neighbors of the node, and k is an integer greater than 0; The connection of node neighbors constructs the adjacency graph.13.如权利要求9所述的室内定位的系统，其特征在于，13. The indoor positioning system according to claim 9, characterized in that,所述位置标记模块在构建所述邻接图时进一步用于以所述训练数据集中的训练数据为节点，将所有节点两两连接，组成所述邻接图；确定所述邻接图中边的权值为The position marking module is further used to use the training data in the training data set as nodes when constructing the adjacency graph, and connect all nodes in pairs to form the adjacency graph; determine the weight of the edge in the adjacency graph for${\mathrm{<span><span>w</span>w</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>=</span>=</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>\{</span>\{</span><span><span>-</span>-</span>\frac{\mathrm{<span><span>d</span>d</span>}{<span><span>(</span>(</span>{\mathrm{<span><span>RSS</span>RSS</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>RSS</span>RSS</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\}</span>\}</span>$其中，RSS_i为训练数据i的信号强度，RSS_j为训练数据j的信号强度，d(RSS_i，RSS_j)表示训练数据的在信号强度空间的距离，σ为高斯函数的窗口系数。Among them, RSS_i is the signal strength of training data i, RSS_j is the signal strength of training data j, d(RSS_i , RSS_j ) represents the distance of training data in signal strength space, and σ is the window coefficient of Gaussian function.14.如权利要求12或13所述的室内定位的系统，其特征在于，14. The indoor positioning system according to claim 12 or 13, characterized in that,所述训练数据在信号强度空间的距离为||RSS_j-RSS_i‖，RSS_i为训练数据i的信号强度，RSS_j为训练数据j的信号强度。The distance of the training data in the signal strength space is ||RSS_j −RSS_i ∥, RSS_i is the signal strength of the training data i, and RSS_j is the signal strength of the training data j.

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