CN110519692B - Positioning and partitioning method based on Bayes-k mean clustering - Google Patents

Positioning and partitioning method based on Bayes-k mean clustering Download PDF

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CN110519692B
CN110519692B CN201910862734.3A CN201910862734A CN110519692B CN 110519692 B CN110519692 B CN 110519692B CN 201910862734 A CN201910862734 A CN 201910862734A CN 110519692 B CN110519692 B CN 110519692B
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CN110519692A (en
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龙军
钟思伟
李斌
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Central South University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • H04W4/021—Services related to particular areas, e.g. point of interest [POI] services, venue services or geofences
    • 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

Abstract

The invention discloses an indoor positioning partitioning method based on Bayesian-k mean clustering, which comprises an offline training stage and an online positioning stage, wherein the offline training stage divides a positioning area into a plurality of sub-areas by using a k mean clustering algorithm, and an initial clustering center adopts an initial clustering center selection algorithm of the nearest AP position; in the stage of online positioning, a plurality of subregions with the minimum distance are firstly obtained, and then the subregions with the maximum posterior probability are used as the positioning partition results by comparing the posterior probabilities of the subregions which are divided into each region. Compared with the prior art, the positioning and partitioning method provided by the invention solves the problem of local optimization caused by improper selection of the initial clustering center by combining the initial clustering center selection algorithm of the AP closest position; in addition, the problem that the Euclidean distance cannot be well fitted with a mapping relation is solved by combining a Bayesian algorithm partition prediction algorithm.

Description

Positioning and partitioning method based on Bayes-k mean clustering
Technical Field
The invention relates to the technical field of computers, in particular to an indoor positioning and partitioning method based on Bayesian-k mean clustering.
Background
The tremendous application and commercial potential that indoor location services can bring has prompted the development of location services related technologies and industries indoors to provide ubiquitous location-based services. As a new positioning technology, the WLAN positioning technology is completely based on the existing network infrastructure, can provide relatively accurate positioning information in real time, and most mobile end devices can detect WLAN signals with the development of mobile internet terminals, so that the WLAN-based positioning technology is very beneficial to large-scale popularization and application of the indoor positioning technology, and has strong applicability.
In a positioning scene of a large place, due to the fact that the area of a positioning area is large, the number of referenced APs is increased rapidly, the feature dimension of a position fingerprint database is extremely large, and dimension disaster is caused. At present, the method for solving the above problems is to divide a large-scale place into regions artificially in advance in an off-line stage, then to establish a region feature fingerprint library for each sub-region, and during on-line positioning, to divide a user into the preset sub-regions, and then to precisely position the sub-regions by matching the position fingerprint library of the region through a positioning algorithm, which can greatly reduce the dimension and data volume of the position fingerprint library. The k-means clustering algorithm is simple in calculation and low in time complexity, and is suitable for processing large data sets in large-scale indoor positioning problems, so that the invention researches the clustering partitioning algorithm based on the k-means algorithm.
When the K-means clustering algorithm is used for indoor positioning partition, the following problems exist: 1. since the mapping relationship between the RSS information and the physical position is a complex nonlinear relationship, the k-means algorithm cannot be well fitted with the mapping relationship measured by the Euclidean distance. 2. In addition, another significant defect of the k-means clustering algorithm is that the clustering result is seriously influenced by the initial clustering center, and if the initial clustering center is improperly selected, local optimization is caused, and global optimization cannot be guaranteed.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a positioning and partitioning method based on Bayesian-k mean clustering, which aims to solve the problems of complex mapping relation between RSS information and physical positions, and poor precision and result stability in the prior art.
The invention provides an indoor positioning partition method based on Bayesian-k mean clustering, which comprises an off-line training stage and an on-line positioning stage, wherein the off-line stage comprises the following steps,
s11, uniformly selecting a plurality of position reference points in the positioning area, collecting RSS vectors at each reference point, and forming a global fingerprint database by all the RSS vectors;
s12, a k-means clustering algorithm is adopted for the global fingerprint library, the positioning area is automatically divided into k sub-areas through unsupervised learning, k clustering centers which are in one-to-one correspondence with the k sub-areas are obtained, wherein the value of k is selected and set in advance, and the k initial clustering centers in the k-means clustering algorithm are adopted for the global fingerprint library, and the k initial clustering centers are obtained through the following steps:
obtaining an RSS vector nearest to each AP position from the global fingerprint library to form an approximate position RSS vector set;
obtaining k clustering centers of the position approximate RSS vector set by using a k mean value clustering algorithm;
taking k clustering centers of the obtained RSS vector set approximate in position as initial clustering centers of the global fingerprint database;
the on-line positioning stage comprises the following steps:
s21, calculating Euclidean distances between the real-time RSS vectors and k clustering centers of the global fingerprint library, and selecting sub-regions corresponding to the clustering centers of q global fingerprint libraries with the smallest distance, wherein the value of q is set by pre-selection;
s22, calculating the posterior probability of each sub-region of the q sub-regions of the real-time RSS vector by adopting a Bayesian algorithm, and then selecting the sub-region with the maximum posterior probability as a result of positioning the sub-region.
Further, step S11 specifically includes the following steps: uniformly selecting a plurality of reference points in the positioning area, collecting 5 RSS vectors at each reference point, and forming a global fingerprint database by all the RSS vectors.
Further, in step S12, a k-means clustering algorithm is applied to the global fingerprint library, the positioning region is automatically divided into k sub-regions through unsupervised learning, and k clustering centers corresponding to the k sub-regions one to one are obtained, which specifically includes the following steps:
s121, initializing K clustering centers of a global fingerprint library by the K clustering centers of the position approximate RSS vector set;
s122, calculating Euclidean distances from the RSS vector of each reference point to k clustering centers of the global fingerprint library;
s123, distributing the reference points to the sub-regions where the clustering centers of the nearest global fingerprint library are located, and recalculating the clustering centers corresponding to each sub-region;
and S124, repeating the steps S122 and S123 until each clustering center does not change any more or the change amplitude is smaller than a preset value, and obtaining k sub-regions and k clustering centers corresponding to the k sub-regions.
Further, the method for acquiring the RSS vector closest to each AP location from the global fingerprint library in step S12 is as follows: and for the jth AP, acquiring a reference point position corresponding to the jth AP with the strongest signal in all RSS vectors as the nearest position of the jth AP, wherein the RSS vector corresponding to the reference point is the RSS vector closest to the jth AP, and the RSS vector corresponding to the reference point is used as the approximate RSS vector of the jth AP.
Further, in step S12, the k clustering centers of the position-approximated RSS vector set are obtained by using a k-means clustering algorithm on all the obtained position-approximated RSS vectors, and the specific steps are as follows:
s125, randomly selecting k clustering centers of which the initialized positions approximate to the RSS vector set from the k clustering centers;
s126, calculating Euclidean distances from each position approximate RSS vector to k clustering centers of the position approximate RSS vector set;
s127, distributing the position approximate RSS vectors to the sub-regions where the clustering centers of the nearest position approximate RSS vector sets are located, and recalculating the clustering centers corresponding to each sub-region;
and S128, repeating the steps S126 and S127 until each clustering center does not change any more or the change amplitude is smaller than a preset value, and obtaining k clustering centers with the positions approximate to the RSS vector set.
Further, the posterior probability in step S22 is calculated by the formula
Figure BDA0002200296150000031
Wherein z isiRepresents the ith sub-region, rsstRepresenting the acquired real-time RSS vector, P (z)i|rsst) Representing real-time RSS vectors dividedPosterior probability to ith sub-region, P (rss)t|zi) Is that within the ith sub-region a certain RSS vector is RSStA priori of P (z)i) Is the probability of randomly dividing into the ith sub-region, p (rss)t) Is that a certain RSS vector is RSStProbability of (a), P (z)i) And p (rss)t) Are all constants.
Further, P (rss)t|zi) Is calculated in such a way that if the RSS signals of each AP are independent and do not interfere with each other, then
Figure BDA0002200296150000032
Further, the air conditioner is provided with a fan,
Figure BDA0002200296150000033
the calculation method of (1) is that the distribution of the wireless signals transmitted by the same AP in space can be approximately expressed by Gaussian distribution, the RSS signal distribution of the ith sub-area is fitted to the Gaussian distribution by counting the sample mean and variance of the RSS values of the single AP in the ith sub-area,
Figure BDA0002200296150000034
wherein u isiIs the average of the RSS values of the jth AP in the ith sub-area,iis the variance of the RSS value of the jth AP in the ith sub-region,
Figure BDA0002200296150000035
representing the real-time RSS value of the jth AP within the sub-region.
Advantageous effects
Compared with the prior art, the positioning and partitioning method provided by the invention has the advantages that firstly, the RSS vector closest to each AP position is selected to form a position approximate RSS vector set, and then k clustering centers of the position approximate RSS vector set are obtained by using a k-means clustering algorithm to serve as initial clustering centers of a global fingerprint library, so that the global optimum of the result is ensured, and the problem of local optimum caused by improper selection of the initial clustering centers is avoided; when the partition is positioned, firstly, q sub-regions with the smallest clustering are selected according to the Euclidean distance from the real-time RSS vector to the clustering center, primary screening is carried out, then the posterior probability that the real-time RSS vector is distributed to the q sub-regions is calculated by combining the Bayesian algorithm, and the sub-region with the largest posterior probability is selected as a result of positioning the partition.
Detailed Description
The present invention will be described in further detail with reference to specific embodiments.
The invention discloses an indoor positioning partition method based on Bayesian-k mean clustering, which comprises an off-line training stage and an on-line positioning stage, wherein the off-line stage comprises the following steps,
s11, uniformly selecting a plurality of position reference points in the positioning area, collecting RSS vectors at each reference point, and during specific implementation, collecting 5 RSS vectors at each reference point, wherein all RSS vectors form a global fingerprint database;
s12, a k-means clustering algorithm is adopted for the global fingerprint library, the positioning area is automatically divided into k sub-areas through unsupervised learning, k clustering centers which are in one-to-one correspondence with the k sub-areas are obtained, wherein the value of k is preset, for example, the value of k is artificially selected to be 6 in the embodiment, and the k initial clustering centers in the k-means clustering algorithm are obtained by adopting the following steps for the global fingerprint library:
obtaining an RSS vector nearest to each AP position from the global fingerprint library to form an approximate position RSS vector set; the specific method is that according to the principle that the closer to the AP, the RSS signal intensity is stronger, for the jth AP, the position of a reference point corresponding to the strongest jth AP signal in all RSS vectors is obtained to be used as the nearest position of the jth AP, the RSS vector corresponding to the reference point is the RSS vector closest to the jth AP, and the RSS vector corresponding to the reference point is used as the approximate RSS vector of the jth AP; j is greater than or equal to 1 and less than or equal to the total number of APs;
obtaining 6 clustering centers of the position approximate RSS vector set by using a k-means clustering algorithm;
taking 6 clustering centers of the obtained RSS vector set approximate positions as initial clustering centers of the global fingerprint database;
the on-line location phase comprises the following steps,
s21, calculating Euclidean distances between the real-time RSS vectors and 6 clustering centers of the global fingerprint library, and selecting sub-regions corresponding to the clustering centers of q global fingerprint libraries with the smallest distance, wherein the value of q is preset, and the value of q is 3 in the embodiment;
s22, calculating the posterior probability of each sub-region of the real-time RSS vector divided into 3 sub-regions by adopting a Bayesian algorithm, and then selecting the sub-region with the maximum posterior probability as a result of positioning the sub-region.
In this embodiment, in step S12, a k-means clustering algorithm is used for the global fingerprint library, the positioning region is automatically divided into k sub-regions through unsupervised learning, and k clustering centers corresponding to the k sub-regions one to one are obtained, which specifically includes the following steps:
s121, initializing K clustering centers of a global fingerprint library by the K clustering centers of the position approximate RSS vector set;
s122, calculating Euclidean distances from the RSS vector of each reference point to k clustering centers of the global fingerprint library;
s123, distributing the reference points to the sub-regions where the clustering centers of the nearest global fingerprint library are located, and recalculating the clustering centers corresponding to each sub-region; the method for recalculating the clustering center corresponding to each sub-region comprises the following steps: calculating the average value of all RSS vectors in each sub-region, and using the average value as the clustering center of the sub-region;
and S124, repeating the steps S122 and S123 until each clustering center does not change any more or the change amplitude is smaller than a preset value, and obtaining k sub-regions and k clustering centers corresponding to the k sub-regions.
In this embodiment, in step S12, k clustering centers of the position-approximated RSS vector set are obtained by using a k-means clustering algorithm for all the obtained position-approximated RSS vectors, and the specific steps are as follows:
s125, randomly selecting k clustering centers of which the initialized positions approximate to the RSS vector set from the k clustering centers;
s126, calculating Euclidean distances from each position approximate RSS vector to k clustering centers of the position approximate RSS vector set;
s127, distributing the position approximate RSS vectors to the sub-regions where the clustering centers of the nearest position approximate RSS vector sets are located, and recalculating the clustering centers corresponding to each sub-region; the method for recalculating the clustering center corresponding to each sub-region comprises the following steps: calculating the average value of the approximate RSS vectors of all the positions in each sub-region, and using the average value as the clustering center of the sub-region;
and S128, repeating the steps S126 and S127 until each clustering center does not change any more or the change amplitude is smaller than a preset value, and obtaining k clustering centers with the positions approximate to the RSS vector set.
In this embodiment, the formula for calculating the posterior probability in step S22 is
Figure BDA0002200296150000051
Wherein z isiRepresents the ith sub-region, rsstRepresenting the acquired real-time RSS vector, P (z)i|rsst) Representing the posterior probability, P (RSS), that the real-time RSS vector is divided into the ith sub-regiont|zi) Is that within the ith sub-region a certain RSS vector is RSStA priori of P (z)i) Is the probability of randomly dividing into the ith sub-region, p (rss)t) Is that a certain RSS vector is RSStProbability of (a), P (z)i) And p (rss)t) Are all constants. P (z)i) Has a value of 1/q, in this example 1/3, p (rss)t) The value of (1/m) is the total number of RSS vectors in the global fingerprint library.
Wherein, P (rss)t|zi) Is calculated in such a way that if the RSS signals of each AP are independent and do not interfere with each other, then
Figure BDA0002200296150000052
Wherein the content of the first and second substances,
Figure BDA0002200296150000053
meter (2)The wireless signal transmitted by the same AP can be approximately represented by Gaussian distribution in space, the RSS signal distribution of the ith sub-area is fitted to the Gaussian distribution by counting the mean and variance of samples of the RSS values of the single AP in the ith sub-area,
Figure BDA0002200296150000054
wherein u isiIs the average of the RSS values of the jth AP in the ith sub-area,iis the variance of the RSS value of the jth AP in the ith sub-region,
Figure BDA0002200296150000055
representing the real-time RSS value of the jth AP within the sub-region.
The specific implementation of the algorithm is as follows:
Figure BDA0002200296150000056
Figure BDA0002200296150000061
and (4) counting the partition accuracy, and comparing with a classical k-means algorithm.
The calculation of the evaluation index Dunn value of the clustering effect, the large index value of Dunn means that dense and well-separated clusters exist, because the distance between the clusters is large and the diameter of the clusters is small, the larger the Dunn index is, the more the calculation formula of the local optimum condition can not appear as follows:
Figure BDA0002200296150000062
wherein d (C)i,Cj) Is ═ CiAnd CjThe dissimilarity function between them is as follows:
Figure BDA0002200296150000063
diam (C) is the diameter of cluster C, as shown in the following equation:
Figure BDA0002200296150000064
by comparing the clustering partition rate with the Dunn value, the clustering effect of the method provided by the patent is based on the classical k-means algorithm.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (8)

1. An indoor positioning and partitioning method based on Bayesian-k mean clustering is characterized by comprising an offline training stage and an online positioning stage, wherein the offline stage comprises the following steps:
s11, uniformly selecting a plurality of position reference points in the positioning area, collecting RSS vectors at each reference point, and forming a global fingerprint database by all the RSS vectors;
s12, a k-means clustering algorithm is adopted for the global fingerprint library, the positioning area is automatically divided into k sub-areas through unsupervised learning, k clustering centers which are in one-to-one correspondence with the k sub-areas are obtained, wherein the value of k is selected and set in advance, and the k initial clustering centers in the k-means clustering algorithm are adopted for the global fingerprint library, and the k initial clustering centers are obtained through the following steps:
obtaining an RSS vector nearest to each AP position from the global fingerprint library to form an approximate position RSS vector set;
obtaining k clustering centers of the position approximate RSS vector set by using a k mean value clustering algorithm;
taking k clustering centers of the obtained RSS vector set approximate in position as initial clustering centers of the global fingerprint database;
the on-line positioning stage comprises the following steps:
s21, calculating Euclidean distances between the real-time RSS vectors and k clustering centers of the global fingerprint library, and selecting sub-regions corresponding to the clustering centers of q global fingerprint libraries with the smallest distance, wherein the value of q is set by pre-selection;
s22, calculating the posterior probability of each sub-region of the q sub-regions of the real-time RSS vector by adopting a Bayesian algorithm, and then selecting the sub-region with the maximum posterior probability as a result of positioning the sub-region.
2. The Bayesian-k-means clustering-based indoor positioning and partitioning method according to claim 1, wherein the step S11 specifically comprises the following steps: uniformly selecting a plurality of reference points in the positioning area, collecting 5 RSS vectors at each reference point, and forming a global fingerprint database by all the RSS vectors.
3. The Bayesian-k-means clustering-based indoor positioning and partitioning method according to claim 1, wherein a k-means clustering algorithm is applied to the global fingerprint database in step S12, the positioning region is automatically divided into k sub-regions through unsupervised learning, and k clustering centers corresponding to the k sub-regions one to one are obtained, and the method specifically comprises the following steps:
s121, initializing K clustering centers of a global fingerprint library by the K clustering centers of the position approximate RSS vector set;
s122, calculating Euclidean distances from the RSS vector of each reference point to k clustering centers of the global fingerprint library;
s123, distributing the reference points to the sub-regions where the clustering centers of the nearest global fingerprint library are located, and recalculating the clustering centers corresponding to each sub-region;
and S124, repeating the steps S122 and S123 until each clustering center does not change any more or the change amplitude is smaller than a preset value, and obtaining k sub-regions and k clustering centers corresponding to the k sub-regions.
4. The Bayesian-k-means clustering-based indoor positioning and partitioning method according to claim 1, wherein the method for obtaining the RSS vector nearest to each AP position from the global fingerprint database in step S12 is as follows: and for the jth AP, acquiring a reference point position corresponding to the jth AP with the strongest signal in all RSS vectors as the nearest position of the jth AP, wherein the RSS vector corresponding to the reference point is the RSS vector closest to the jth AP, and the RSS vector corresponding to the reference point is used as the approximate RSS vector of the jth AP.
5. The Bayesian-k-means clustering-based indoor positioning and partitioning method according to claim 4, wherein k clustering centers of the location-approximated RSS vector set are obtained by using a k-means clustering algorithm for all the obtained location-approximated RSS vectors in step S12, and the specific steps are as follows:
s125, randomly selecting k clustering centers of which the initialized positions approximate to the RSS vector set from the k clustering centers;
s126, calculating Euclidean distances from each position approximate RSS vector to k clustering centers of the position approximate RSS vector set;
s127, distributing the position approximate RSS vectors to the sub-regions where the clustering centers of the nearest position approximate RSS vector sets are located, and recalculating the clustering centers corresponding to each sub-region;
and S128, repeating the steps S126 and S127 until each clustering center does not change any more or the change amplitude is smaller than a preset value, and obtaining k clustering centers with the positions approximate to the RSS vector set.
6. The Bayesian-k-means clustering-based indoor positioning and partitioning method as recited in claim 1, wherein the posterior probability in step S22 is calculated according to the formula
Figure FDA0002610732320000021
Wherein z isiRepresents the ith sub-region, rsstRepresenting the acquired real-time RSS vector, P (z)i|rsst) Representing the posterior probability, P (RSS), that the real-time RSS vector is divided into the ith sub-regiont|zi) Is that within the ith sub-region a certain RSS vector is RSStA priori of P (z)i) Is the probability of randomly dividing into the ith sub-region, p (rss)t) Is a certain RSS directionIn an amount of rsstProbability of (a), P (z)i) And p (rss)t) Are all constants.
7. The Bayesian-k-means clustering-based indoor positioning and partitioning method according to claim 6, wherein P (rss)t|zi) The way of calculating (a) is as follows,
Figure FDA0002610732320000022
Figure FDA0002610732320000023
representing the real-time RSS value of the jth AP within the sub-region, and m representing the number of RSS values contained in the RSS vector.
8. The Bayesian-k-means clustering-based indoor positioning partitioning method according to claim 7,
Figure FDA0002610732320000024
the way of calculating (a) is as follows,
Figure FDA0002610732320000025
wherein u isiIs the average of the RSS values of the jth AP in the ith sub-area,iis the variance of the RSS value of the jth AP in the ith sub-region.
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