CN108627798B - WLAN indoor positioning algorithm based on linear discriminant analysis and gradient lifting tree - Google Patents

WLAN indoor positioning algorithm based on linear discriminant analysis and gradient lifting tree Download PDF

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CN108627798B
CN108627798B CN201810298929.5A CN201810298929A CN108627798B CN 108627798 B CN108627798 B CN 108627798B CN 201810298929 A CN201810298929 A CN 201810298929A CN 108627798 B CN108627798 B CN 108627798B
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张会清
牛铮
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Beijing University of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/0252—Radio frequency fingerprinting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/30—Services specially adapted for particular environments, situations or purposes
    • H04W4/33—Services specially adapted for particular environments, situations or purposes for indoor environments, e.g. buildings
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
    • H04W64/006—Locating users or terminals or network equipment for network management purposes, e.g. mobility management with additional information processing, e.g. for direction or speed determination

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Abstract

The invention relates to a WLAN indoor positioning algorithm based on linear discriminant analysis and a gradient lifting tree. In order to reduce the influence of the time-varying characteristic of a received signal strength value (RSSI) on positioning accuracy in an indoor WLAN environment, the method for predicting the position coordinates by extracting the positioning characteristics of an original RSSI signal by utilizing LDA and constructing a GBDT model is proposed. The method is mainly divided into 4 processes. 1) Collecting the RSSI signal value of the AP at a reference point, forming fingerprint data with the position coordinates of the reference point, and storing the fingerprint data into a fingerprint database; 2) solving an intra-class divergence matrix and an inter-class divergence matrix of the fingerprint data to obtain a projection matrix, and realizing the extraction of the RSSI signal positioning characteristics; 3) generating a GBDT positioning model in an iteration mode by utilizing a forward distribution algorithm and an addition model; 4) and in the online stage, the RSSI signal values of the APs around the test points are collected, LDA is used for feature extraction, and the GBDT positioning model is input to calculate the position coordinates.

Description

WLAN indoor positioning algorithm based on linear discriminant analysis and gradient lifting tree
The technical field is as follows:
the invention belongs to the field of WLAN indoor positioning. The method is an indoor positioning method for extracting positioning characteristics from fingerprint data by Linear Discriminant Analysis (LDA) in an off-line WLAN indoor positioning stage and constructing a positioning model by a gradient lifting tree (GBDT). The method can effectively improve the WLAN indoor positioning precision.
Background art:
in recent years, with breakthroughs in intelligent devices and internet technologies, more and more scenes needing location services are derived, and the demand of people for location services is also expanded from outdoor driving navigation to indoor positioning. However, a Global Positioning System (GPS), which is commonly used outdoors, cannot operate in an indoor environment because a building wall blocks a signal. In order to enable users to obtain accurate position information indoors, researchers at home and abroad develop various indoor positioning systems according to different working principles. Among them, systems based on WLAN technology are the most common. Since the WLAN is one of the infrastructures in the building, the WLAN-based positioning system does not need to build a hardware device dedicated to positioning, thereby reducing the cost and the implementation difficulty of the system. The WLAN indoor positioning is divided into an offline phase and an online phase.
And in the off-line stage, a received signal strength value (RSSI) of an Access Point (AP) is collected on a reference point, and the RSSI and the position coordinates of the reference point form a piece of fingerprint information which is stored in a fingerprint database. However, referring to fig. 1, the RSSI signal exhibits time varying characteristics due to multipath propagation, shadowing, and the like. The use of raw fingerprint data can severely degrade the prediction accuracy of the positioning algorithm. The prediction algorithm for the real-time location of the user can be classified into a nearest neighbor method (NN), a maximum likelihood method, and an artificial neural network method. The NN precision is too low, the real-time performance of the maximum likelihood method is poor, and the generalization capability of the artificial neural network method is insufficient. Therefore, the invention provides a WLAN indoor positioning algorithm based on linear discriminant analysis and gradient-boosted tree (LDA-GBDT).
The invention content is as follows:
aiming at the problem that the time-varying characteristic of the RSSI signal reduces the positioning accuracy, the invention provides that the positioning characteristic in the RSSI signal is extracted by LDA, and the prediction of the position coordinate is realized by constructing a GBDT positioning model.
In order to achieve the purpose, the invention adopts the following technical scheme: in the off-line stage, firstly, the RSSI signal value of the AP is collected at each reference point, and constitutes fingerprint data together with the corresponding position coordinates, and then the LDA is used to extract the positioning characteristics of the original RSSI signal, so as to eliminate the influence of time-varying characteristics, noise and the like of the RSSI signal. And finally, updating the original fingerprint database, and generating the GBDT positioning model through a forward distribution algorithm and an addition model iteration. And in the online stage, the RSSI signal values of the APs around the test points are collected, the LDA is used for carrying out positioning feature extraction on the signals, and then the signals are input into a GBDT positioning model to predict the position coordinates, and a schematic diagram of the positioning method is shown in figure 2.
An LDA-GBDT-based WLAN indoor positioning algorithm sequentially comprises the following steps:
(1) uniformly selecting reference points in an area to be positioned, collecting RSSI signal values of Access Points (AP) on the reference points, and forming an ordered vector with the coordinates of the reference points, wherein the vector is position fingerprint data of the reference points.
(2) The method adopts LDA to extract the positioning characteristics in the original RSSI signal, and comprises the following steps:
1) constructing an objective function;
2) dividing the position fingerprint data into k categories according to the coordinates of the reference point to obtain an inter-category divergence matrix S of various types of fingerprint databThe calculation formula is as follows:
Figure BDA0001619204190000021
wherein Z isjIndicates the number of the j (j ═ 1, 2.., k) th fingerprint data, μjDenotes a mean vector of the j-th (j ═ 1, 2., k-th class fingerprint data, and μ denotes a mean vector of all fingerprint data.
3) Calculating the intra-class divergence matrix S of various types of fingerprint data according to the following formulaω；
Figure BDA0001619204190000022
Wherein eta isjThe set of j (j) th class fingerprint data is 1, 2,., k), and γ denotes fingerprint data in the j (j) th class fingerprint data set.
4) Calculating a matrix S according to the calculation results of 2) and 3)ω -1SbAnd obtaining a projection matrix.
5) And 4) calculating a new fingerprint data set after the LDA extraction of the positioning characteristics by using the projection matrix obtained in the step 4).
(3) And (3) fitting a classification regression tree by using the new fingerprint data set obtained in the step (2) and taking the negative gradient value of the loss function as an approximate value of residual errors in the regression problem lifting tree algorithm according to a forward distribution algorithm.
(4) Linearly combining the classification regression trees generated in (3) using an additive model.
(5) And (4) repeating the steps (3) and (4) to establish a GBDT positioning model.
(6) And (3) acquiring RSSI signals of the AP at the test points, extracting the positioning characteristics of the signals by utilizing LDA, and inputting the signals into the GBDT positioning model established in the step (5) to calculate the coordinates of the test points.
The algorithm aims to extract the positioning characteristics in the original RSSI signal by utilizing LDA, reduce the influence of the time-varying characteristics on the positioning precision and predict the position coordinates by constructing a GBDT positioning model. Compared with the prior art, the invention has the following advantages:
(1) the positioning characteristics of the original RSSI signals are extracted, and redundant signals and noise contained in the original RSSI signals can be effectively filtered;
(2) the GBDT positioning model can reduce the influence of abnormal values on the positioning precision by constructing an accurate loss function;
(3) under the condition of the same positioning error, the algorithm provided by the invention uses less AP number.
Description of the drawings:
FIG. 1 is a graph of the source of time varying error in an RSSI signal;
FIG. 2 is a schematic diagram of the indoor positioning algorithm;
FIG. 3 is a flow chart of the algorithm of the present invention;
fig. 4 is an indoor positioning scene diagram.
The specific implementation mode is as follows:
the method of the invention is illustrated in flow diagram form in FIG. 3. The off-line stage is implemented by collecting the RSSI signal values of the APs on the reference point by the mobile device, and forming a set of ordered vectors with the coordinates of the location, where the vectors are the location fingerprint data of the reference point. And finally, linearly combining the generated classification regression trees by using an addition model to generate a GBDT positioning model. And in the online stage, the RSSI signal value of the AP on the test point is collected, the LDA is used for extracting the positioning characteristics, the positioning characteristics are input into the GBDT positioning model, and the coordinates of the test point are calculated. The specific implementation steps are as follows:
(1) referring to fig. 4, which is a plan view of an indoor scene to be positioned, the whole area is 221 square meters. The uniformly selected reference points in this area are indicated by light dots and the randomly selected test points are indicated by dark squares.
(2) And (3) specifying the origin of coordinates of the area to be positioned, and measuring the position coordinates of the reference point and the test point selected in the step (1).
(3) And (3) acquiring the RSSI signal value of the AP on a reference point, and forming an ordered vector together with the position coordinate of the reference point measured in the step (2), wherein the vector is position fingerprint data of the reference point and is stored in a fingerprint database. The LDA is then used to extract the location features of the original RSSI signal.
Wherein the fingerprint database is a database for storing reference point fingerprint data.
The specific operation steps of "LDA extracting the positioning characteristics of the original RSSI signal" are as follows:
1) inputting raw location fingerprint data set
Figure BDA0001619204190000041
Where N is the total number of reference points, γi＝(rss1，rss2，...，rssn) The RSSI values of n APs collected at the ith reference point are shown, and n represents the total number of APs. li denotes the coordinates of the ith reference point.
2) And constructing an objective function.
3) Dividing the fingerprint data into k classes according to the coordinates of the reference points, and calculating the inter-class divergence matrix sb(ii) a Wherein, the said "inter-class divergence matrix" is expressed as
Figure BDA0001619204190000042
k represents the total number of classes of fingerprint data, ZjIndicates the number of the j (j ═ 1, 2.., k) th fingerprint data, μjDenotes a mean vector of the j (j ═ 1, 2.. multidata, k) th class fingerprint data, and μ denotes a mean vector of all fingerprint data.
4) Calculating an intra-class divergence matrix Sω；
Wherein, the said 'intra-class divergence matrix' is expressed as
Figure BDA0001619204190000043
k represents the total number of classes, η, of the fingerprint datajIs a set of j (j ═ 1, 2.. multidot.k) type fingerprint data, gamma denotes fingerprint data, and mu denotesjA mean vector representing the j (j ═ 1, 2.., k) th class of fingerprint data.
5) Calculating a matrix S according to the results of 3) and 4)ω -1SbThe eigenvalues and eigenvectors.
6) Selecting matrix Sω -1SbExpanding the corresponding eigenvectors of the first theta eigenvalues into a projection matrix psi;
wherein, theta represents the dimension of the matrix psi, and the value range is [1, n ], namely the dimension of the fingerprint data after the positioning characteristics are extracted. n represents the total number of APs.
7) According to
Figure BDA0001619204190000044
Calculating a new fingerprint data set after the positioning features are extracted;
wherein the new fingerprint data set can be expressed as
Figure BDA0001619204190000045
N is the total number of reference points,
Figure BDA0001619204190000046
representing theta-dimensional position fingerprint data, r, at the ith reference point after extraction of the location featuresss′Represents the new RSSI signal value, gamma, after the extraction of the positioning featuresiRepresenting the original fingerprint data at the ith reference point, liIndicating the coordinates of the ith reference point.
8) And repeating the step 7, and performing LDA positioning feature extraction on the original RSSI signal according to another dimensional position coordinate.
(3) Initializing a first classification regression using the new fingerprint dataset D' obtained in (2)Tree (R)
Figure BDA0001619204190000051
Where N is the total number of reference points. L is a loss function, and the Huber loss function is adopted in the method, so that the influence of abnormal values in the fingerprint data set D' on the positioning result can be obviously reduced. liIndicating the coordinates of the ith reference point. τ represents the leaf node output value of the classification regression tree.
(4) When generating the M (M ═ 1, 2.., M) th classification regression tree, the negative gradient value α of the loss function is determinedmiFitting a classification regression tree as an approximate value of the residual error in the regression problem lifting tree algorithm.
Wherein alpha ismiThe negative gradient value of the loss function of the fingerprint data of the ith (i ═ 1, 2.., N) reference point when generating the mth (M ═ 1, 2.., M) classification regression tree is expressed. M is the total number of the generational regression trees.
The specific steps of fitting a classification regression tree are as follows:
1) is provided with
Figure BDA0001619204190000052
Is an input space;
where N is the total number of reference points.
2) Traversing the segmentation feature h (h ═ 1, 2.,. theta.), and scanning the fixed segmentation feature h for the segmentation point s (s ═ rss'1，rss′2，...，rss′θ) Recursively dividing the input space P into two regions;
3) when the mean square error of each set of the two subdomains in the step 2) is minimum, and the segmentation characteristic and characteristic value division point corresponding to the minimum sum of the mean square errors is the optimal segmentation variable and the optimal segmentation point;
4) dividing the input space P into two sub-regions by using the optimal segmentation variable and the segmentation point (h, s) selected in the step 3), and calculating the output value of each sub-region by adopting linear search;
5) repeating the operations of 2), 3) and 4), recursively partitioning the input space P into β1，β2，...，βRAnd the R sub-regions do not intersect each other. The output value of each sub-region of the mth classification regression tree is represented by τmrRepresents;
where R (R ═ 1, 2.., R) denotes the sequence number of the sub-region.
6) According to the output value tau of each sub-regionmrThe mth classification regression tree is expressed as
Figure BDA0001619204190000061
(5) And multiplying the classification regression tree by a regularization coefficient lambda in a value range of (0, 1) so as to avoid the condition of overfitting the training sample data.
(6) Linearly adding the classification regression trees normalized in (5) using an addition model. Wherein the addition model is Fm＝Fm-1+λmTm。λmThe regularization coefficients represent the M (M ═ 1, 2.., M) th classification regression tree.
(7) Repeating the steps (4) to (6) to generate a GBDT positioning model FM。
Wherein, the GBDT positioning model can be expressed as
Figure BDA0001619204190000062
M represents the total number of classification regression trees generated.
(8) And in the online stage, the RSSI signal value of the AP on the test point is collected, the LDA is used for extracting the positioning characteristics, and the positioning characteristics are input into the GBDT positioning model generated in the step (7) to obtain the specific test point coordinates.
And (3) comparing the coordinate of the test point obtained by the calculation in the step (8) with the real value of the coordinate of the test point measured in the step (2) to obtain the average positioning error of 1.51m, so that the algorithm can obtain higher positioning precision in the WLAN indoor environment.

Claims (1)

1. A proposed LDA-GBDT based WLAN indoor positioning algorithm, characterized by the following steps:
(1) uniformly selecting a reference point in a to-be-positioned area, collecting RSSI signal values of an access point AP on the reference point, and forming an ordered vector with the coordinates of the reference point, wherein the vector is position fingerprint data of the reference point;
(2) the method adopts LDA to extract the positioning characteristics in the original RSSI signal, and comprises the following steps:
1) constructing an objective function;
2) dividing the position fingerprint data into k categories according to the coordinates of the reference point to obtain an inter-category divergence matrix S of various types of fingerprint databThe calculation formula is as follows:
Figure FDA0001619204180000011
wherein Z isjIndicates the number of the j (j ═ 1, 2.., k) th fingerprint data, μjRepresents a mean vector of the j (j ═ 1, 2.. multidata, k) th class fingerprint data, and μ represents a mean vector of all fingerprint data;
3) calculating the intra-class divergence matrix S of various types of fingerprint data according to the following formulaω；
Figure FDA0001619204180000012
Wherein eta isjA set of j (j ═ 1, 2.. times, k) th class fingerprint data, γ denotes fingerprint data in the j (j ═ 1, 2.. times, k) th class fingerprint data set;
4) calculating a matrix S according to the calculation results of 2) and 3)ω -1SbObtaining a projection matrix according to the eigenvalue and the eigenvector;
5) calculating a new fingerprint data set after the LDA extraction positioning characteristics by using the projection matrix obtained in the step 4);
(3) fitting a classification regression tree by using the new fingerprint data set obtained in the step (2) and according to a forward distribution algorithm and by using the negative gradient value of the loss function as an approximate value of residual errors in a regression problem lifting tree algorithm;
(4) linearly combining the classification regression trees generated in (3) using an additive model;
(5) repeating the steps (3) and (4) to establish a GBDT positioning model;
(6) and (3) acquiring RSSI signals of the AP at the test points, extracting the positioning characteristics of the signals by utilizing LDA, and inputting the signals into the GBDT positioning model established in the step (5) to calculate the coordinates of the test points.
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