CN108919182B - Target positioning method based on support set and expectation maximization in WIFI environment - Google Patents

Target positioning method based on support set and expectation maximization in WIFI environment Download PDF

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CN108919182B
CN108919182B CN201810443983.4A CN201810443983A CN108919182B CN 108919182 B CN108919182 B CN 108919182B CN 201810443983 A CN201810443983 A CN 201810443983A CN 108919182 B CN108919182 B CN 108919182B
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CN108919182A (en
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郭贤生
李林
朱世林
李会勇
万群
殷光强
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University of Electronic Science and Technology of China
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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
    • G01S5/08—Position of single direction-finder fixed by determining direction of a plurality of spaced sources of known location
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • G01C21/206—Instruments for performing navigational calculations specially adapted for indoor navigation
    • 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
    • H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
    • 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

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Abstract

The invention discloses a target positioning method based on a support set and expectation maximization in a WiFi environment, which relates to the field of WiFi positioning and comprises the following steps: step 1: establishing an off-line fingerprint database; step 2: constructing a support set according to the target signal acquired on line and an off-line fingerprint library, and finding and estimating a correct position by carrying out true value on the support set to complete target positioning; the invention provides a method for overcoming the defect of the optimal matching criterion by utilizing the support set, and the accurate estimation of the target position is carried out from the support set by the expectation maximization algorithm, so that the problems of the RSS fluctuation caused by environmental change and heterogeneous equipment can be effectively solved, and the positioning precision and the positioning robustness are improved.

Description

Target positioning method based on support set and expectation maximization in WIFI environment
Technical Field
The invention relates to the field of WIFI positioning, in particular to a target positioning method based on a support set and expectation maximization in a WIFI environment.
Background
In recent years, indoor positioning technology shows wide development prospects and commercial values, such as tracking management of goods in a large supermarket, real-time monitoring of positions of patients by hospitals, navigation of museum contents and various applications of smart homes. The indoor positioning system needs to install transmitting equipment at a fixed position to send positioning signals, common transmitting equipment comprises WIFI, Bluetooth, RFID, UWB and the like, but a large amount of manpower and material resources are needed for installing a large amount of transmitting equipment, so that most positioning systems tend to use existing widely deployed wireless equipment to realize indoor positioning, and the WIFI is widely used in various large or small buildings such as homes, markets, airports and the like, so that the WIFI becomes a most attractive wireless technology in the positioning field.
Positioning methods based on WIFI include two categories: parametric estimation based methods and fingerprint based methods, which are receiving much attention due to the fact that no parameter estimation and good positioning performance are required. However, the existing fingerprint positioning method uses the optimal matching criterion to position the measured sample, which is easily affected by the fluctuation of the received Signal strength rss (received Signal strength), so that the positioning using the optimal matching criterion will usually match the wrong position, resulting in a large positioning error. One of the main causes of RSS fluctuation is the dynamic characteristics of the indoor environment, including people walking, opening and closing of doors and windows, variation in the transmission power of the AP, and temperature and humidity changes of the indoor environment. Another main reason is that different devices may be used by different users when the devices are located online, and different vendors have different hardware specifications, so that even if the devices are located at the same location, the RSS fluctuates greatly in the same environment. Currently, RSS fluctuation caused by environmental changes and heterogeneous devices is the biggest bottleneck restricting the performance of the fingerprint positioning method, and how to find a high-precision real-time positioning system capable of overcoming RSS fluctuation in a complex indoor environment has become a research focus in the industry.
In the prior art, a conventional fingerprint positioning method based on an optimal matching criterion includes the following steps: firstly, collecting RSS at divided lattice points to establish an offline fingerprint database; and secondly, in an online positioning stage, performing Euclidean distance matching by using the RSS of the measured data and an offline RSS fingerprint database, and selecting a lattice point corresponding to the offline fingerprint with the highest matching similarity as a final position estimation. Although this positioning method can achieve good positioning accuracy in a simple indoor environment, it still faces the challenges of the dynamic characteristics and heterogeneous devices of the indoor environment: when the indoor environment has strong multipath propagation effect and large environment change, the RSS fluctuation is obvious; for heterogeneous equipment, large RSS fluctuation can be generated in the same environment during online positioning; in the two cases, the traditional optimal matching method is mismatched, so that the positioning error is larger; therefore, a WIFI positioning method is needed that can achieve accurate and stable target position estimation in a complex indoor environment.
Disclosure of Invention
The invention aims to: the invention provides a target positioning method based on a support set and expectation maximization in a WIFI environment, and solves the technical problem that the dynamic characteristics of heterogeneous equipment and the environment cannot be solved by the conventional method for realizing position estimation through similarity calculation.
The technical scheme adopted by the invention is as follows:
a target positioning method based on a support set and expectation maximization in a WIFI environment comprises the following steps:
step 1: establishing an off-line fingerprint database;
step 2: and constructing a support set according to the target signal acquired on line and the off-line fingerprint library, and finding and estimating a correct position by carrying out truth value on the support set to complete target positioning.
Preferably, the truth finding comprises the expectation maximization, EM, algorithm.
Preferably, the step 1 comprises the steps of:
step 1.1: fixing the AP position in a positioning environment, and dividing the positioning environment into a plurality of grid points;
step 1.2: building a WIFI network, placing a signal source in each grid point and recording the position coordinates of the signal source at the moment;
step 1.3: and the placed signal source transmits a signal, and the RSS value of the signal source received by each AP is recorded and stored to complete the establishment of the off-line fingerprint database.
Preferably, the step 2 comprises the steps of:
step 2.1: acquiring a real-time positioning stage, namely an on-line target signal, and constructing a support set according to the similarity of the target signal and an off-line fingerprint library;
step 2.2: determining the size of a support set by using an optimal support set selection algorithm;
step 2.3: the target position is estimated from the support set using expectation maximization.
Preferably, said step 2.1 comprises the steps of:
and 2. step 2.1.1: acquiring a target signal
Figure GDA0003548763630000021
By Euclidean distance dknCalculating a target signal
Figure GDA0003548763630000022
And an off-line fingerprint library rkThe similarity of (n) obtains a distance vector d, and the calculation formula is as follows:
Figure GDA0003548763630000023
d＝[d11，d12，…，dGM]T
wherein G represents the number of grid points, M represents the number of RSS samples of each grid point in the off-line stage, and k represents the serial number of the grid point;
step 2.1.2: selecting the labels corresponding to the K distances with the minimum distance in the distance vector d to construct a support set x, wherein the calculation formula is as follows:
X＝[x1，x2，…，xK]T
wherein x isiIndicating the label corresponding to the sample below the line with the small distance from the ith.
Preferably, said step 2.2 comprises the steps of:
step 2.2.1: acquiring a target signal, and selecting an optimal support set through Bayesian information criterion BIC, wherein the calculation formula is as follows:
BIC(K)＝ln(K)-2lnL(θ(t))
wherein, theta(t)K is the size of the support set for the hypothesis estimation, in order to expect to maximize the estimated fingerprint quality after convergence;
step 2.2.2: selecting the K value corresponding to the minimum BIC as the size of the support set
Figure GDA0003548763630000031
The calculation formula is as follows:
Figure GDA0003548763630000032
preferably, said step 2.3 comprises the steps of:
step 2.3.1: by assuming that the fingerprint quality θ is defined, the calculation formula is as follows:
Figure GDA0003548763630000033
wherein N istIndicates the number of occurrences of the correct position in x, NfIndicating the number of occurrences of the error location in x, y indicating the number of labels, i.e. grid points, of the target location, ylRepresenting an estimate of the target location tag, xiA label corresponding to an offline sample with a small distance from the ith;
step 2.3.2: defining an objective function using the beta distribution and the likelihood function to estimate the fingerprint quality θ, the calculation formula is as follows:
L(θ)＝P(θ|β)P(x|θ)
wherein P (x | θ) is a likelihood function, and P (θ | β) is a probability density function of the beta distribution;
step 2.3.3: calculating the label x corresponding to the sample under the given ith small lineiAnd the posterior probability distribution of the label y of the target position under the fingerprint quality theta, and the calculation formula is as follows:
Figure GDA0003548763630000034
wherein t represents the tth iteration;
step 2.3.4: the new fingerprint quality is obtained by maximizing the objective function formula, and the calculation formula is as follows:
Figure GDA0003548763630000041
step 2.3.5: repeating the step 2.3.3 and the step 2.3.4 until convergence, wherein the convergence condition is L (theta)(t))-L(θ(t-1)) < ε, i.e. the t-th sumThe error between the t-1 th order objective functions is less than a given threshold epsilon, which is 10-6And after convergence, obtaining the final probability distribution of the label y of the target position, wherein the calculation formula is as follows:
Figure GDA0003548763630000042
wherein N is the number of different positions where x appears;
step 2.3.6: obtaining the subscript corresponding to the maximum probability based on the final probability distribution of the labels y of the target positions
Figure GDA0003548763630000043
The tag estimate of the target is obtained by the following formula:
Figure GDA0003548763630000044
estimating the label of the object by
Figure GDA0003548763630000045
And converting the function into two-dimensional coordinates of the target to complete the estimation of the target position.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
1. the invention provides a method for overcoming the defect of an optimal matching criterion by using a support set, and accurately estimating the target position from the support set by an expectation maximization algorithm, so that the problems of RSS fluctuation caused by environmental change and heterogeneous equipment can be effectively solved, and the positioning precision and robustness are improved;
2. according to the invention, truth value discovery is carried out by using expectation maximization, the size of a support set can be dynamically constructed according to on-line positioning data, and the method has strong adaptability; the truth finding is carried out on the support set by utilizing expectation maximization, and the target position can be accurately estimated on the basis of correctly evaluating the fingerprint quality of the support set.
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The invention will now be described, by way of example, with reference to the accompanying drawings, in which:
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a plot of the positioning error of the present invention under varying circumstances;
fig. 3 is a positioning error diagram in the case of heterogeneous devices according to the present invention.
Detailed Description
All of the features disclosed in this specification, or all of the steps in any method or process so disclosed, may be combined in any combination, except combinations of features and/or steps that are mutually exclusive.
The present invention is described in detail below with reference to fig. 1-3.
Example 1
Truth finds using expectation maximization:
step 1.1, fixing the position of an AP in a positioning environment and dividing the positioning environment into a plurality of grid points;
step 1.2, constructing a WIFI network, sequentially placing a signal source in each grid point in a positioning environment and recording the position coordinates of the signal source at the moment;
step 1.3, the placed signal source transmits signals, and RSS values of the signal source received by each AP are recorded and stored to complete the establishment of an off-line fingerprint database;
step 2.1, obtaining a target signal to be positioned;
2.2, selecting a proper support set size by using an optimal support set selection algorithm; constructing a support set according to the similarity of the target signal and the off-line fingerprint library;
step 2.3. estimate the correct position from the support set using expectation maximization.
Arrangement of experimental sites
The experimental environment is an office environment of 73m 20m, is located 21 th of innovative building of university of electronic technology, and the environment includes 10 offices and a corridor, and nine APs (access points) that are wireless network access points are evenly deployed in the whole environment, and the place is divided into 175 lattice points, and adjacent lattice point interval is 0.8 m.
Acquiring data and forming an offline fingerprint library
Step 1.2, a WIFI positioning environment is set up, a signal source, namely a mobile phone is placed at any lattice point in the environment, the lattice point serial number and the two-dimensional coordinate at the moment are recorded, then signals are transmitted, the signal strength of the mobile phone received by each AP is recorded, and the RSS measurement value of the mobile phone from the k lattice point received by the q-th AP at the n moment is set as
Figure GDA0003548763630000051
Assuming that L APs are provided, M RSS samples are collected to obtain a fingerprint library D at a lattice point kk：
Figure GDA0003548763630000052
Step 1.3, storing the fingerprint libraries of different lattice points obtained in step 1.2 to obtain a fingerprint library D of the whole environment:
D＝[D1,D2,…,DG] (2)
where G is the number of grid points of the environment.
Building supporting set
2.1.1. Receiving an inline RSS test sample
Figure GDA0003548763630000061
Reuse of Euclidean distance dknMeasurement test sample
Figure GDA0003548763630000062
And offline RSS samples rkSimilarity of (n):
Figure GDA0003548763630000063
obtaining distance vector d ═ d11，d12，…，dGM]T。
2.1.2. Constructing a support set x, namely selecting labels corresponding to K samples with the minimum distance in d:
X＝[x1，x2，…，xK]T (4)
wherein x isiIs the label corresponding to the sample under the line with the distance of ith smaller; for obtaining x sequentiallyiFirst, the minimum distance value and its index are obtained:
[value，index]＝min(d) (5)
wherein value is the minimum distance, index is the corresponding index, and the first label in the supporting set is obtained through the following formula:
x1＝ceil(index/M) (6)
wherein ceil () is used for rounding to positive infinity;
obtaining x1After that, the distance vector d is updated:
d＝d→value (7)
where → represents the deletion of an element from d, and thus, the support set x can be obtained by repeating the formulae (5) to (7).
Order to
Figure GDA0003548763630000064
Is the different positions appearing in x, where N is the number of different positions, and N ═ N1，n2，…，nN]TWherein n islIs ylThe number of occurrences in x;
optimal support set selection
2.2.1. For adaptive support set size selection, an optimal support set selection algorithm is employed that estimates K by using the bayesian information criterion BIC, which is defined as:
BIC(K)＝ln(K)-2lnL(θ(t)) (21)
wherein, theta(t)Is the fingerprint quality estimated after the expectation maximization convergence, K is the size of the support set of the hypothesis estimation;
2.2.2. given an in-line test specimen
Figure GDA0003548763630000071
Selecting the K value corresponding to the minimum BIC as the size of the support set
Figure GDA0003548763630000072
The calculation formula is as follows:
Figure GDA0003548763630000073
wherein, theta(t)Is expected to maximize the estimated fingerprint quality after convergence;
the selection of the optimal support set is implemented as follows: the method includes that an EM algorithm needs to be given a support set, the size of the support set, namely K, is determined by adopting an optimal support set selection algorithm, generally speaking, the possible value range of the size of K is 1 to the maximum sampling number M of each lattice point, firstly, if K is 1, the EM algorithm is carried out to obtain the fingerprint quality theta at the moment(t)Substituting equation (21) to calculate BIC (1), assuming K is 2 again, and calculating the fingerprint quality θ at the time of the expectation maximization(t)Substituting the value into a formula (21) to calculate BIC (2), and repeating the steps to obtain M BIC (K) values, and determining the size of the optimal support set by selecting the K value corresponding to the minimum BIC value.
Expectation maximization
2.3.1. Assuming the correct position in the support set x to be ylI.e. the estimation of the target location tag, let NtIndicates the number of occurrences of the correct position in x, NfRepresenting the number of occurrences of the error location in x, the fingerprint quality θ can be defined as:
Figure GDA0003548763630000074
wherein x isiA label corresponding to an offline sample with a small distance from the ith;
in practical cases, θ is unknown, so using the maximum likelihood estimate θ, the prior of θ is controlled using a beta distribution with two parameters β1And beta2And they represent the false counts of the correct and wrong positions in x, respectively, in the present invention, we set the initial value of the fingerprint quality θ as the value when the beta distribution probability takes the maximum:
Figure GDA0003548763630000075
let y have a probability distribution of p ═ p1，p2，…，pN]TWherein p isl＝P(y＝yl) (1, 2, …, N) indicates the correct position is ylThe probability of (d); the invention provides a strategy based on frequency and probability joint initialization, and the position which is closer to a geometric center is endowed with higher prior probability when the occurrence frequency is more, so that plThe prior probability of (a) can be defined as:
Figure GDA0003548763630000081
wherein, g (y)l) Tag y as target locationlG (-) is a function mapping the label of the target location to a two-dimensional coordinate;
2.3.2. defining the objective function as the product of the likelihood function and the beta distribution:
L(θ)＝P(θ|β)P(x|θ) (11)
where P (x | θ) is the likelihood function:
Figure GDA0003548763630000082
p (θ | β) is the probability density function of the beta distribution:
Figure GDA0003548763630000083
maximizing the objective function: the expectation maximization comprises two steps: a desired step (E step) and a maximum step (M step), where E step is calculated at a given xiAnd y posterior probability distribution under the fingerprint quality theta, and updating the fingerprint quality in the step M. The specific process is as follows:
step E: suppose now iterates to step t, given xiAnd fingerprint qualityQuantity theta(t-1)After, ylThe posterior probability of (d) can be expressed as:
Figure GDA0003548763630000084
wherein t represents the tth iteration;
wherein the second term in formula (14) results from a Bernoulli distribution:
Figure GDA0003548763630000085
where | xi＝ylL is in xi＝ylThe time is 1, otherwise, the time is 0;
the correct label is ylThe probability of (d) is updated as:
Figure GDA0003548763630000086
2.3.4.M step: maximizing the objective function (11) to obtain new fingerprint quality, i.e.
Figure GDA0003548763630000091
The solution is to derive L (θ) with respect to θ and make it 0 to get an estimate of θ:
Figure GDA0003548763630000092
where a is the pseudo-count of the number of correct tags in the support set x:
Figure GDA0003548763630000093
2.3.5-2.3.6. expectation maximization will repeat steps E and M until convergence, with the convergence condition:
L(θ(t))-L(θt-1))＜ε (20)
selecting L (theta)(t))-L(θ(t-1)) < ε, i.e. the error between the objective function at times t and t-1 is less than a given threshold ε, which is set to 10 as the convergence criterion-6；
Assuming that given a measured sample, based on the selected support set size, through the expectation maximization iteration, assuming that the expectation maximization converges in the t-th iteration, the final probability distribution of y can be expressed as
Figure GDA0003548763630000094
Wherein N is the number of different positions where x appears; p is a radical of(t)The subscript corresponding to the highest probability of being:
Figure GDA0003548763630000095
the tag estimate of the target may be obtained by the following formula:
Figure GDA0003548763630000096
estimating the label of the object by
Figure GDA0003548763630000097
And converting the function into two-dimensional coordinates of the target to complete the estimation of the target position.
At present, the test sample with the correct position as the lattice point 3 is subjected to actual measurement verification of the algorithm, and the optimal size is obtained by the selection algorithm of the optimal support set on the assumption that
Figure GDA0003548763630000098
And 10, constructing a support set according to the similarity of the test sample and the offline fingerprint library to obtain:
x＝[1，1，11，13，3，1，1，3，9，11]T
wherein y is [1, 3, 9, 11, 13 ]]TIt can be seen that if the root isAccording to the optimal matching criterion in the conventional fingerprint method, an error positioning result 1 can be obtained, the support set provided by the invention is a set containing correct positions, the defect of the optimal matching criterion under the condition of large RSS fluctuation can be effectively overcome, then the position estimation is carried out in the support set through expectation maximization, wherein the parameters of beta distribution are set as
Figure GDA0003548763630000101
The reason is that1And beta2Representing a pseudo-count of correct and incorrect positions in the support set, at which setting the initial value of the fingerprint quality θ(0)About 0.25, which represents that the position with a large number of occurrences in the support set may be wrong, which is reasonable in a complex indoor environment with obvious RSS fluctuation, and the initial value of the probability distribution of y can be obtained according to a strategy based on frequency and probability joint initialization:
p(0)＝[0.26，0.22，0.19，0.17，0.16]T
and E and M steps of iteration are carried out on the expectation maximization, and finally the probability distribution of y which is expected to be maximized after t rounds of convergence is obtained as follows:
p(t)＝[0.16，0.58，0.12，0.09，0.05]T
to obtain
Figure GDA0003548763630000102
Final position estimation
Figure GDA0003548763630000103
The present invention can estimate the correct location from a complex indoor environment, whereas the conventional method based on the optimal matching criterion matches to the wrong location due to RSS fluctuation.
The invention designs two groups of experiments to verify the superiority of the proposed algorithm, the first group of experiments is that 975 test samples are randomly collected for actual measurement positioning in a period of time after an off-line fingerprint database is established, the average positioning error is 2.51 meters, and FIG. 2 is a comparison graph of positioning error performance of a background technology method and the method of the invention under the condition of environmental change; the second group of experiments are that 975 test samples are randomly collected by using different receiving equipment to carry out actual measurement positioning after an offline fingerprint database is established, and fig. 3 is a comparison graph of positioning error performance of a background technology method and the method of the invention under the condition of heterogeneous equipment; the algorithm provided by the invention is obviously better than the traditional fingerprint positioning method no matter under the condition of environmental change or heterogeneous equipment, the invention provides the method for overcoming the defect of the optimal matching criterion by utilizing the support set, and the accurate estimation of the target position is carried out from the support set by the expectation maximization algorithm, so that the RSS fluctuation problem caused by environmental change and heterogeneous equipment can be effectively overcome, and the experimental result proves that the positioning precision and the positioning robustness are improved.
Example 2
The truth discovery may also employ a voting method.

Claims (4)

1. A target positioning method based on a support set and expectation maximization in a WiFi environment is characterized in that: the method comprises the following steps:
step 1: establishing an off-line fingerprint database;
step 2: constructing a support set according to the target signal acquired on line and an off-line fingerprint library, and finding and estimating a correct position by carrying out true value on the support set to complete target positioning;
the truth finding comprises an Expectation Maximization (EM) algorithm;
the step 2 comprises the following steps:
step 2.1: acquiring a real-time positioning stage, namely an on-line target signal, and constructing a support set according to the similarity of the target signal and an off-line fingerprint library;
step 2.2: determining the size of a support set by using an optimal support set selection algorithm;
step 2.3: estimating a target position from the support set using expectation maximization;
the step 2.3 comprises the following steps:
step 2.3.1: by assuming that the fingerprint quality θ is defined, the calculation formula is as follows:
Figure FDA0003548763620000011
wherein N istIndicates the number of occurrences of the correct position in x, NfIndicating the number of occurrences of the error location in x, y indicating the number of labels, i.e. grid points, of the target location, ylRepresenting an estimate of the target location tag, xiA label corresponding to an offline sample with a small distance from the ith;
step 2.3.2: defining an objective function using the beta distribution and the likelihood function to estimate the fingerprint quality θ, the calculation formula is as follows:
L(θ)＝P(θ|β)P(x|θ)
wherein P (x | θ) is a likelihood function, and P (θ | β) is a probability density function of the beta distribution;
step 2.3.3: calculating the label x corresponding to the sample under the given ith small lineiAnd the posterior probability distribution of the label y of the target position under the fingerprint quality theta, and the calculation formula is as follows:
Figure FDA0003548763620000012
wherein t represents the tth iteration;
step 2.3.4: the new fingerprint quality is obtained by maximizing the objective function formula, and the calculation formula is as follows:
Figure FDA0003548763620000013
step 2.3.5: repeating the step 2.3.3 and the step 2.3.4 until convergence, wherein the convergence condition is L (theta)(t))-L(θ(t-1)) < ε, i.e. the error between the objective function at times t and t-1 is less than a given threshold ε, ε is taken to be 10-6And after convergence, obtaining the final probability distribution of the label y of the target position, wherein the calculation formula is as follows:
Figure FDA0003548763620000014
wherein N is the number of different positions where x appears;
step 2.3.6: obtaining the subscript corresponding to the maximum probability based on the final probability distribution of the labels y of the target positions
Figure FDA0003548763620000015
The tag estimate of the target is obtained by the following formula:
Figure FDA0003548763620000016
estimating the label of the object by
Figure FDA0003548763620000021
And converting the function into two-dimensional coordinates of the target to complete the estimation of the target position.
2. The method of claim 1, wherein the method comprises: the step 1 comprises the following steps:
step 1.1: fixing the AP position in a positioning environment, and dividing the positioning environment into a plurality of grid points;
step 1.2: building a WIFI network, placing a signal source in each grid point and recording the position coordinates of the signal source at the moment;
step 1.3: and the placed signal source transmits a signal, and the RSS value of the signal source received by each AP is recorded and stored to complete the establishment of the off-line fingerprint database.
3. The method of claim 1, wherein the method comprises: the step 2.1 comprises the following steps:
step 2.1.1: acquiring a target signal
Figure FDA0003548763620000022
By Euclidean distance dknCalculating a target signal
Figure FDA0003548763620000023
And an off-line fingerprint library rkThe similarity of (n) obtains a distance vector d, and the calculation formula is as follows:
Figure FDA0003548763620000024
d＝[d11，d12，…，dGM]T
wherein G represents the number of grid points, M represents the number of RSS samples of each grid point in the off-line stage, and k represents the serial number of the grid point;
step 2.1.2: selecting the labels corresponding to the K distances with the minimum distance in the distance vector d to construct a support set x, wherein the calculation formula is as follows:
x＝[x1，x2，…，xK]T
wherein x isiIndicating the label corresponding to the sample below the line with the small distance from the ith.
4. The method of claim 1, wherein the method comprises: the step 2.2 comprises the following steps:
step 2.2.1: acquiring a target signal, and selecting an optimal support set through Bayesian information criterion BIC, wherein the calculation formula is as follows:
BIC(K)＝ln(K)-2lnL(θ(t))
wherein, theta(t)K is the size of the support set for the hypothesis estimation, in order to expect to maximize the estimated fingerprint quality after convergence;
step 2.2.2: selecting the K value corresponding to the minimum BIC as the size of the support set
Figure FDA0003548763620000025
The calculation formula is as follows:
Figure FDA0003548763620000026
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