CN104507050B - Probabilistic type finger print matching method in a kind of WiFi indoor positionings - Google Patents
Probabilistic type finger print matching method in a kind of WiFi indoor positionings Download PDFInfo
- Publication number
- CN104507050B CN104507050B CN201410680673.6A CN201410680673A CN104507050B CN 104507050 B CN104507050 B CN 104507050B CN 201410680673 A CN201410680673 A CN 201410680673A CN 104507050 B CN104507050 B CN 104507050B
- Authority
- CN
- China
- Prior art keywords
- mrow
- msub
- msup
- probability
- mover
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 66
- 230000008447 perception Effects 0.000 claims abstract description 27
- 238000007476 Maximum Likelihood Methods 0.000 claims abstract description 19
- 230000006870 function Effects 0.000 claims description 17
- 238000012549 training Methods 0.000 claims description 17
- 238000004364 calculation method Methods 0.000 claims description 15
- 238000012360 testing method Methods 0.000 claims description 12
- 238000005259 measurement Methods 0.000 claims description 10
- 238000005457 optimization Methods 0.000 claims description 6
- 238000005070 sampling Methods 0.000 claims description 4
- 230000001131 transforming effect Effects 0.000 claims description 2
- 238000005516 engineering process Methods 0.000 abstract description 12
- 238000012512 characterization method Methods 0.000 abstract 1
- 238000004422 calculation algorithm Methods 0.000 description 5
- 238000007619 statistical method Methods 0.000 description 4
- 230000005540 biological transmission Effects 0.000 description 1
- 230000001186 cumulative effect Effects 0.000 description 1
- 238000013480 data collection Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000005315 distribution function Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 230000004807 localization Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
Landscapes
- Position Fixing By Use Of Radio Waves (AREA)
- Mobile Radio Communication Systems (AREA)
Abstract
The present invention provides probabilistic type finger print matching method in a kind of WiFi indoor positionings, and it is a kind of probabilistic type indoor orientation method based on perception probability and Density Estimator, there is five big steps.Specifically a kind of method introducing perception probability and printenv Density Estimator technology in maximum likelihood probability.This method, so as to reduce position error, can obtain preferable positioning precision by the distribution characteristics of Density Estimator method more accurate characterization complexity radiofrequency signal.
Description
Technical Field
The invention provides a probability type fingerprint matching method in WiFi indoor positioning, in particular to a method for introducing a perception probability and a parameter-free kernel density estimation technology into a maximum likelihood probability. The method can accurately represent the distribution characteristics of the complex radio frequency signals through a kernel density estimation method, obtains better positioning precision, and belongs to the technical field of WiFi indoor positioning, wireless transmission and navigation.
Background
With the development of modern positioning and navigation technologies, various location-based services increasingly become important components in intelligent life, and a Global Navigation Satellite System (GNSS) provides people with high-precision and all-weather positioning services, but due to the characteristic that measurement signals of the GNSS cannot penetrate buildings, the positioning services cannot be effectively performed in high-density building groups and indoors, so that an indoor positioning system is rapidly developed to obtain effective positioning services indoors.
Indoor location technologies based on fingerprint matching typically work in two phases, an offline training phase and an online location phase. During the off-line training phase, the signal strength information from the available access points received by all reference points in the target area form a fingerprint database. In the on-line positioning stage, the Received Signal Strength (RSSI) acquired in real time is matched with the fingerprint in the fingerprint database, so that the position information of the positioning equipment is obtained.
The probability type algorithm considers the matching process of the actually measured RSSI and the fingerprints in the fingerprint database as a probability estimation problem, and establishes a probability distribution model of the radio frequency signals in the indoor environment based on the statistical characteristics of the RSSI signals, thereby solving the uncertainty of the RSSI values in the complex environment. A commonly used probability-based algorithm is a Maximum Likelihood (ML) algorithm, the posterior probability is converted into a likelihood probability problem based on a Bayesian framework theory, and the maximum likelihood probability is matched to obtain estimated position information.
The nuclear density estimation method does not utilize prior knowledge about data distribution, does not add any hypothesis to the data distribution, is a method for researching data distribution characteristics from a data sample, and can more accurately represent the distribution of complex signals, thereby improving the positioning accuracy. The kernel-wide parameter of the kernel function reflects the extent of influence that a single sample "contributes" to the overall density distribution. The sample variation range sampled over time is limited and each value has the potential to participate in the calculation. The larger the variation range of the sample value is, the larger the contribution range of each sample to the overall density distribution is, and at the moment, the kernel function has larger kernel width; conversely, a smaller range of variation in the sample values indicates that the contribution of each sample to the overall density distribution is relatively concentrated, and the kernel function should have a smaller kernel width. Therefore, when updating with the kernel density estimation algorithm, it is very important to select the appropriate kernel width parameter.
The invention provides a probability type indoor positioning method based on perception probability and kernel density estimation through research on a WiFi positioning technology and a kernel density estimation technology.
Disclosure of Invention
The invention aims to: the probability type indoor positioning method based on the fingerprint matching is a modified probability type indoor positioning method based on the fingerprint matching, the likelihood probability is calculated by using a parameter-free kernel density estimation technology and is fused with the perception probability of a reference point, so that the discontinuity calculated by the traditional histogram statistical method is eliminated, and the positioning accuracy of the system is improved.
The technical scheme of the invention is as follows:
the invention provides a probability type fingerprint matching method in WiFi indoor positioning. The probability type indoor positioning method mainly considers the matching of a measured signal and position fingerprint database information as a probability estimation problem based on a probability positioning model. The posterior probability problem is converted into a likelihood probability problem, the prior RSSI statistical characteristic information of each position is utilized, and the historical state information and the environment layout information of a positioning target can be utilized under certain conditions, so that higher positioning precision is obtained compared with the positioning precision based on a decision-making positioning technology at the cost of higher calculation complexity.
The probability type fingerprint matching method in WiFi indoor positioning provided by the invention is mainly characterized in that: the method is characterized in that a perception probability and kernel density estimation technology are integrated into a probability type indoor positioning algorithm, the perception probability reflects the distribution characteristics of signals to a certain extent, a non-parameter kernel density estimation technology is adopted to calculate the likelihood probability, and the perception likelihood probability is used as a positioning standard to improve the positioning accuracy by combining the perception probability.
The kernel density estimation method based on the nonparametric model can be used for modeling a system without giving a specific distribution model in advance and performing parameter estimation. Since the traditional histogram model calculates the likelihood probability value by counting the number of samples of different grouping intervals, the setting of the grouping intervals will cause the calculated likelihood probability value to be discontinuous, so the kernel density estimation is adopted to calculate the likelihood function value. Due to the non-parameter characteristic of the kernel density estimation method and the continuity of the kernel function, the method is more suitable for the radio frequency signal distribution in a complex indoor environment.
The invention discloses a probability type fingerprint matching method in WiFi indoor positioning, which comprises the following steps:
the method comprises the following steps: and in the off-line stage, data are collected in a test area, and a fingerprint database is established for matching calculation in the on-line stage. Before data collection, survey is firstly carried out on a test area, the positions of reference points are determined, then a certain number of pieces of sample information are collected at each reference point, and a fingerprint database is constructed.
Step two: and obtaining the perception probability of each reference point RP relative to the access point according to the reference point training sample information. Wherein if the AP signal strength at the test location is less than the minimum signal strength that the sampling device can sense, indicating that the device cannot sense the AP signal, replacing the non-sensing signal strength information with a fixed signal strength. Thus, AP signal acquisition can be viewed as a bernoulli process, where for a particular RP, a binary sequence B ═ is obtained for each sample (B)1,b2,…bj,…,bn) Wherein b isjE (0, 1). The perceptual probability is defined as: the ratio of the number of APs perceived by the reference point to the total number of training samples. The perception probability of the ith RP to the jth AP is calculated as follows:
wherein, ω isiAs a reference pointThe position of the mobile phone is determined,the number of times that the ith RP can sense the jth AP, N (1| ω)i) Is the total number of training samples.
Step three: matching the measured RSSI with the fingerprints in the fingerprint database, and obtaining the matching likelihood probability P (RSS) of the ith RP to the jth AP by adopting a kernel density estimation methodj|ωi)。
Firstly, converting the maximum posterior probability problem into a maximum likelihood probability problem according to Bayes theorem, wherein the expression of the Bayes theorem is as follows:
wherein, P (ω)i) For the probability of corresponding to the position of the reference point, P (ω) without considering the positioning history informationi) Is constant, P (RSS) is constant. P (RSS | ω)i) As a reference point omegaiThus transforming the maximum a posteriori probability problem into a maximum likelihood probability problem, i.e.:
P(RSS|ωi)＞P(RSS|ωj)i,j＝1,2,…,m,j≠i
the APs are independent of each other, so that the likelihood probability expression can be obtained:
wherein, P (RSS)j|ωi) The matching likelihood probability for the ith RP to the jth AP. The calculation steps for solving the matching likelihood probability are as follows:
1) the kernel density estimation equation is:
wherein,for the likelihood probability of the j-th AP with the real-time received signal strength of X, K (-) is the kernel equation, h is the kernel width parameter, Xk(k is more than or equal to 1 and less than or equal to N) is the kth value in the training database.
2) The kernel function K (-) is selected as a Gaussian kernel function
3) And optimizing the kernel width parameter h.
4)SkThe real-time signal strength of the kth AP received by the device. The likelihood of a match can be found to be
In the kernel density estimation method, the value of the kernel width parameter h has a large influence on the smoothness of a kernel density estimation curve based on training samples, the kernel density estimation curve may not be smooth when h is smaller, and although the information contained in each training sample can be better reflected, the density estimation is biased to distribute probability density to be too close to observation data, so that the estimated density function has many wrong peak values; conversely, if h is larger, the kernel density estimation curve is smoother, but the density estimation disperses the probability density contribution too much, which also results in the loss of some important features contained in the sample data, so h needs to be optimally selected, and the optimization step of h by minimizing the mean square error is as follows:
1) assuming the true kernel equation is f, then the kernel density estimation equationThe integral mean square error with the true kernel equation is:
2) since the integrand is non-negative, the MISE equation is rewritten as:
3) assuming that the kernel equation K (u) is continuous, the true kernel density equation f is bounded, and the second derivative is continuous, two constants α and β are defined, whereAccording to the Taylor expansion, the MISE can be expanded as follows:
4) thus, minimizing the mean square error MISE, an optimized solution of the kernel-width parameter can be obtained as:
5) when the kernel function is a gaussian equation, the optimal solution of the kernel width parameter is:
wherein n is the number of APs,mean of variance of all APs.
Step four: calculating a perceptual likelihood probability P' (RSS | ω) based on the perceptual probability and the match likelihood probabilityi)。
First, use a special characterThe constant value C is used for replacing the strength of the signal which can not be sensed to obtain the sensing likelihood probability P' (RSS) of the ith RP to the jth APj|ωi). The calculation equation is as follows:
secondly, the perceptual likelihood probability can be found as:
step five: the coordinates of the measurement position are found by a maximum likelihood probability (ML) method.
The calculation of the coordinates of the measurement locations is as follows:
1) by the ML method, the sequence number of the reference point with the maximum perception likelihood probability is obtained as follows:
2) let the coordinate with reference point number t be (x)t,yt) The estimated coordinates of the measurement location can be found as:
the invention has the advantages that:
the method integrates the perception probability and the kernel density estimation method into a maximum likelihood probability method, is a modified probability type indoor positioning method, and can improve the indoor positioning precision.
And secondly, the discontinuity of the histogram statistical method on the likelihood probability calculation is overcome by adopting a kernel density estimation method.
And thirdly, the kernel density estimation method does not utilize prior knowledge about data distribution, does not add any hypothesis to the data distribution, is a method for researching data distribution characteristics from a data sample, and can more accurately represent the distribution of complex signals.
Drawings
Fig. 1WiFi indoor positioning scene diagram.
FIG. 2 is a flow chart of the method of the present invention.
FIG. 3 is a flow chart of a kernel width parameter optimization process in a kernel density estimation method.
Fig. 4 is a positioning error map according to the present invention.
FIG. 5 is a map of the localization error based on the kernel-wide parameter optimization of the present invention.
The symbols and codes in the figure are explained as follows:
AP Access Point wireless Access Point
KDE kernel density estimation
Maximum likelihood of ML maximum likelihood
MISE mean integrated square error
CDF cumulative distribution function
Detailed Description
The following describes a probabilistic indoor positioning method based on perceptual probability and kernel density estimation, which is proposed by the present invention, in detail by taking a specific indoor test environment as an example, with reference to fig. 1, 2, 3, and 4.
Referring to fig. 1, a plan view of a specific indoor test area is shown, where there are 5 AP in the test area and the room area is divided into 1.1m × 1.1m grids; the corridor area is divided into 1.2m by 1.2m grids. The whole test area is divided into 195 grids, and the center of each grid is the position of the reference point RP.
Referring to fig. 2, a flow chart of the method of the present invention is shown. Taking a specific indoor test environment as an example, the invention relates to a probability type fingerprint matching method in WiFi indoor positioning, which comprises the following steps:
the method comprises the following steps: and acquiring training sample information for 195 RPs in the test area, wherein the sampling frequency of each reference point is 80 times, and establishing a fingerprint database by taking the signal intensity mean value in the acquired training sample information as a fingerprint for online stage matching calculation.
Step two: according to the reference point training sample information, obtaining the perception probability of 195 reference points RP relative to 5 access points APThe specific formula is as follows:
step three: the position (10.95, 1.65) is tested, and the obtained mean vector of the actually measured RSSI values isMeasuring the measured RSSI vectorMatching with fingerprints in a fingerprint library, and sequentially obtaining the matching likelihood probability P (RSS) of the ith RP to the jth AP by adopting a kernel density estimation methodj|ωi)。
Step four: calculating the perception likelihood probability of the ith RP to the jth AP according to the perception probability and the matching likelihood probability to obtain a perception likelihood probability P' (RSS | omega)i). The calculation formula is as follows:
and calculating the perception likelihood probability of the ith RP to the jth AP according to the formula (1), wherein a constant C is set to-100 dbm, and calculating the perception likelihood probability according to the formula (2).
Step five: and (4) solving the coordinates of the measuring position by a maximum likelihood probability method.
The calculation of the coordinates of the measurement locations is as follows:
by the ML method, the number t of the reference point with the maximum perception likelihood probability is found to be 37, and the calculation formula is as follows:
since the coordinates of the reference point number 37 are (10.95, 1.65), the estimated coordinates of the obtained measurement position are (10.58, 1.65).
The positioning is completed once through the five steps, the measurement is carried out at the point with the coordinate value of (10.95, 1.65), the probability type likelihood probability method is obtained through estimation based on the perception probability and the kernel density, the obtained estimated coordinate value is (10.58, 1.65), and the positioning error is 0.37 m.
Referring to fig. 3, in the kernel width parameter optimization process in the kernel density estimation method of the present invention, the kernel width parameter is the largest factor affecting the kernel density estimation, the integral mean square error between the kernel density estimation equation and the true kernel equation is calculated, the integral expression is simplified by taylor expansion, and the integral mean square error is minimized, so that the optimal solution of the kernel width parameter is obtained, where h is 6.87.
As shown in fig. 4, the actual experiment in the scenario shown in fig. 1 according to the method of the present invention obtains a CDF graph of the error between the positioning result and the actual position, in which the dashed line represents the positioning result obtained by using histogram statistics, and the solid line represents the positioning result obtained by using the method of the present invention, and it can be seen from the statistical results in the following table one that the average positioning error obtained by using the method of the present invention is 2.0941 meters, which is an improvement of the positioning accuracy by 34.2% compared to the histogram statistics.
TABLE 1
| Nuclear density estimation method | Histogram statistical method | |
| Mean error distance (m) | 2.0941 | 3.1846 |
As shown in fig. 5, the dashed line in the positioning error CDF graph obtained after the optimal solution of the kernel width parameter obtained by the method of the present invention indicates the positioning error when h is 2, and the solid line indicates the positioning error when h is 6.87. Therefore, the optimization of the kernel width parameter in the invention can obtain better positioning precision.
In summary, the probability type fingerprint matching method in WiFi indoor positioning provided by the present invention is based on WiFi fingerprint matching indoor positioning technology, and adopts kernel density estimation technology to calculate likelihood probability. The method is characterized in that the method for researching data distribution characteristics by the aid of the nuclear density estimation starting from the data samples, prior knowledge about data distribution is not used, no assumption is added to the data distribution, and the distribution of signals in a complex indoor environment can be more accurate. In addition, due to the continuity of the kernel density estimation function, the discreteness of likelihood probability calculated by the traditional histogram statistical method is overcome, the perception probability is combined, the perception likelihood probability is adopted as a measurement factor, and the positioning precision is improved.
Claims (1)
1. A probability type fingerprint matching method in WiFi indoor positioning is characterized in that: it comprises the following steps:
the method comprises the following steps: acquiring data in a test area in an off-line stage, and establishing a fingerprint database for matching calculation in an on-line stage; before data acquisition, surveying a test area to determine the position of a reference point RP, acquiring a certain number of sample information at each reference point, and constructing a fingerprint database;
step two: according to the reference point training sample information, obtaining the relative access of each reference point RPThe perception probability of the point AP; wherein if the AP signal strength at the test location is less than the minimum signal strength perceived by the sampling device, indicating that the device is not able to perceive the AP signal, replacing the signal strength information that is not able to be perceived with a fixed signal strength, thus regarding AP signal acquisition as a bernoulli process, for a particular RP, each sampling obtains a binary sequence B ═ B (B ═ B)1,b2,…bj,…,bn) Wherein b isjE (0, 1); n is the number of RP; the perceptual probability is defined as: the ratio of the number of AP times perceived by the reference point to the total number of training samples; the perception probability of the ith RP to the jth AP is calculated as follows:
<mrow> <msub> <mi>P</mi> <mrow> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>|</mo> <mi>&omega;</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>|</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>n</mi> <mrow> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>|</mo> <mi>&omega;</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>|</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>/</mo> <mi>N</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>|</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow>
wherein, ω isiAs a position of the reference point, the position of the reference point,the number of times that the ith RP can sense the jth AP, N (1| ω)i) The total number of training samples;
step three: the measured RSSI and finger are comparedMatching fingerprints in the fingerprint library, and obtaining the matching likelihood probability P (RSS) of the ith RP to the jth AP by adopting a kernel density estimation methodj|ωi)；
Firstly, converting the maximum posterior probability problem into a maximum likelihood probability ML problem according to Bayes theorem, wherein the expression of the Bayes theorem is as follows:
<mrow> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>|</mo> <mi>R</mi> <mi>S</mi> <mi>S</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>R</mi> <mi>S</mi> <mi>S</mi> <mo>|</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>R</mi> <mi>S</mi> <mi>S</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>
wherein, P (ω)i) For the probability of corresponding to the position of the reference point, P (ω) without considering the positioning history informationi) Is constant, P (RSS) is constant; p (RSS | ω)i) As a reference point omegaiThus transforming the maximum a posteriori probability problem into a maximum likelihood probability ML problem, i.e.:
P(RSS|ωi)＞P(RSS|ωj)i,j＝1,2,…,m,j≠i
the APs are independent of each other, so that the likelihood probability expression is obtained:
<mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>R</mi> <mi>S</mi> <mi>S</mi> <mo>|</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Pi;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mi>P</mi> <mrow> <mo>(</mo> <msup> <mi>RSS</mi> <mi>j</mi> </msup> <mo>|</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow>
wherein, P (RSS)j|ωi) The calculation steps for solving the matching likelihood probability of the ith RP to the jth AP are as follows:
1) the kernel density estimation equation is:
wherein,for the likelihood probability of the j-th AP having a real-time received signal strength of X, K (-) is the kernel function, h is the kernel width parameter, Xk(k is more than or equal to 1 and less than or equal to N) is the kth value in the training database;
2) the kernel function K (-) is selected as a Gaussian kernel function
3) Optimizing a kernel width parameter h;
4)Skfor the real-time signal strength of the kth AP received by the device, the matching likelihood probability is obtained
<mrow> <mi>P</mi> <mrow> <mo>(</mo> <msup> <mi>RSS</mi> <mi>j</mi> </msup> <mo>|</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <msub> <mi>s</mi> <mi>k</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>|</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow>
In the kernel density estimation method, the value of the kernel width parameter h has a large influence on the smoothness of a kernel density estimation curve based on training samples, the smaller h is, the unsmooth kernel density estimation curve is not smooth, and although the information contained in each training sample can be better reflected, the density estimation is biased to distribute probability density to be too close to observation data, so that the estimated density function has a plurality of wrong peak values; conversely, if h is larger, the kernel density estimation curve is smoother, but the density estimation disperses the probability density contribution too much, which also results in the loss of some important features contained in the sample data, so h needs to be optimally selected, and the optimization step of h by minimizing the mean square error is as follows:
1) assuming the true kernel function is f, then the kernel density estimation equationThe integrated mean square error from the true kernel is:
2) since the integrand is non-negative, the MISE equation is rewritten as:
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>M</mi> <mi>I</mi> <mi>S</mi> <mi>E</mi> <mrow> <mo>(</mo> <mover> <mi>f</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <mo>&Integral;</mo> <mi>E</mi> <msup> <mrow> <mo>&lsqb;</mo> <mover> <mi>f</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> <mn>2</mn> </msup> <mi>d</mi> <mi>x</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mo>&Integral;</mo> <msup> <mrow> <mo>&lsqb;</mo> <mi>E</mi> <mover> <mi>f</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> <mn>2</mn> </msup> <mi>d</mi> <mi>x</mi> <mo>+</mo> <mo>&Integral;</mo> <mi>var</mi> <mover> <mi>f</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>x</mi> </mrow> </mtd> </mtr> </mtable> </mfenced>
3) assuming that the kernel function K (u) is continuous, the true kernel density equation f is bounded, and the second derivative is continuous, two constants α and β are defined, whereβ＝∫{K(t)}2dt, according to taylor expansion, MISE expands as follows:
<mrow> <mi>M</mi> <mi>I</mi> <mi>S</mi> <mi>E</mi> <mrow> <mo>(</mo> <mover> <mi>f</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>&ap;</mo> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <msup> <mi>h</mi> <mn>4</mn> </msup> <msup> <mi>&alpha;</mi> <mn>2</mn> </msup> <mo>&Integral;</mo> <msup> <mrow> <mo>{</mo> <msup> <mo>&dtri;</mo> <mn>2</mn> </msup> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>}</mo> </mrow> <mn>2</mn> </msup> <mi>d</mi> <mi>x</mi> <mo>+</mo> <msup> <mi>N</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>h</mi> <mrow> <mo>-</mo> <mi>n</mi> </mrow> </msup> <mi>&beta;</mi> </mrow>
4) therefore, the mean square error MISE is minimized, resulting in an optimized solution for the kernel-width parameter as:
<mrow> <msubsup> <mi>h</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>4</mn> </mrow> </msubsup> <mo>=</mo> <msup> <mi>d&beta;&alpha;</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> <msup> <mrow> <mo>{</mo> <mo>&Integral;</mo> <msup> <mrow> <mo>(</mo> <msup> <mo>&dtri;</mo> <mn>2</mn> </msup> <mi>f</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>}</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>N</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow>
5) when the kernel function is a gaussian equation, the optimal solution of the kernel width parameter is:
<mrow> <msub> <mi>h</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mn>4</mn> <mi>N</mi> </mrow> <mrow> <mi>d</mi> <mo>+</mo> <mn>2</mn> </mrow> </mfrac> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </msup> <mover> <mi>&sigma;</mi> <mo>^</mo> </mover> </mrow>
wherein n is the number of APs,mean of variance for all APs;
step four: calculating a perceptual likelihood probability P' (RSS | ω) based on the perceptual probability and the match likelihood probabilityi)；
First, a specific value C is used to replace the strength of the signal which can not be sensed, and the matching likelihood probability P' (RSS) of the ith RP to the jth AP is obtainedj|ωi) The calculation equation is as follows:
<mrow> <msup> <mi>P</mi> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>RSS</mi> <mi>j</mi> </msup> <mo>|</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mo>{</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>|</mo> <mi>&omega;</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>|</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <msub> <mi>s</mi> <mi>k</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>|</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>}</mo> </mrow> <msub> <mi>b</mi> <mi>j</mi> </msub> </msup> <mo>&times;</mo> <msup> <mrow> <mo>{</mo> <mo>&lsqb;</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>|</mo> <mi>&omega;</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>|</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <msub> <mi>s</mi> <mi>k</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>C</mi> <mo>|</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>}</mo> </mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </msup> </mrow>
secondly, the perception likelihood probability is obtained as follows:
step five: obtaining the coordinate of the measuring position by a maximum likelihood probability ML method;
the calculation of the coordinates of the measurement locations is as follows:
1) by the ML method, the sequence number of the reference point with the maximum perception likelihood probability is obtained as follows:
<mrow> <mi>t</mi> <mo>=</mo> <munder> <mrow> <mi>arg</mi> <mi>max</mi> </mrow> <mrow> <mi>i</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>1</mn> <mo>,</mo> <mi>m</mi> <mo>&rsqb;</mo> </mrow> </munder> <mo>&lsqb;</mo> <munder> <mi>&Pi;</mi> <mrow> <mn>1</mn> <mo>&le;</mo> <mi>j</mi> <mo>&le;</mo> <mi>n</mi> </mrow> </munder> <msup> <mi>P</mi> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>RSS</mi> <mi>j</mi> </msup> <mo>|</mo> <msub> <mi>&omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow>
2) let the coordinate with reference point number t be (x)t,yt) The estimated coordinates of the measurement location can be found as:
<mrow> <mo>(</mo> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>,</mo> <mover> <mi>y</mi> <mo>^</mo> </mover> <mo>)</mo> <mo>=</mo> <mo>(</mo> <msub> <mi>x</mi> <mi>t</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>)</mo> <mo>.</mo> </mrow>
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410680673.6A CN104507050B (en) | 2014-11-24 | 2014-11-24 | Probabilistic type finger print matching method in a kind of WiFi indoor positionings |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410680673.6A CN104507050B (en) | 2014-11-24 | 2014-11-24 | Probabilistic type finger print matching method in a kind of WiFi indoor positionings |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN104507050A CN104507050A (en) | 2015-04-08 |
| CN104507050B true CN104507050B (en) | 2018-04-10 |
Family
ID=52948752
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201410680673.6A Active CN104507050B (en) | 2014-11-24 | 2014-11-24 | Probabilistic type finger print matching method in a kind of WiFi indoor positionings |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN104507050B (en) |
Families Citing this family (14)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106162559A (en) * | 2015-05-12 | 2016-11-23 | 三星电子株式会社 | For estimating equipment and the method for position in a wireless communication system |
| CN104853435B (en) * | 2015-05-26 | 2018-08-14 | 北京京东尚科信息技术有限公司 | A kind of indoor orientation method based on probability and device |
| CN106714097B (en) * | 2015-07-31 | 2020-07-03 | 阿里巴巴集团控股有限公司 | Method for determining wireless local area network deployment information, method for positioning terminal and related device |
| CN105764137A (en) * | 2016-02-02 | 2016-07-13 | 北京邮电大学 | Indoor location method and system |
| CN105636102B (en) * | 2016-02-04 | 2019-05-10 | 林华珍 | A kind of localization method and device based on Bayes posterior probability |
| CN105768480A (en) * | 2016-02-25 | 2016-07-20 | 北京石油化工学院 | Positioning method, device and system for suitcase |
| CN108235429A (en) * | 2016-12-14 | 2018-06-29 | 中国电信股份有限公司 | Indoor orientation method, device and system |
| CN108680175A (en) * | 2017-12-12 | 2018-10-19 | 安徽工程大学 | Synchronous superposition method and device based on rodent models |
| CN108769910A (en) * | 2018-06-15 | 2018-11-06 | 闽南师范大学 | A kind of method of WiFi positioning |
| CN110361693A (en) * | 2019-07-15 | 2019-10-22 | 黑龙江大学 | A kind of indoor orientation method based on probability fingerprint |
| CN110543896B (en) * | 2019-08-16 | 2023-04-07 | 成都电科慧安科技有限公司 | Heterogeneous crowdsourcing fingerprint labeling method based on semi-supervised naive Bayes |
| CN111741429B (en) * | 2020-06-23 | 2022-05-03 | 重庆邮电大学 | Wi-Fi indoor positioning method based on signal distribution Wasserstein distance measurement |
| CN112566055B (en) * | 2020-11-27 | 2022-06-10 | 巢湖学院 | Indoor positioning algorithm based on radio frequency fingerprint matching |
| CN114646917A (en) * | 2022-03-07 | 2022-06-21 | 北京华信傲天网络技术有限公司 | Indoor positioning method based on RSSI fingerprint |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103096466A (en) * | 2013-01-17 | 2013-05-08 | 哈尔滨工业大学 | Wireless fidelity (Wi-Fi) indoor positioning method |
| CN103634901A (en) * | 2013-11-05 | 2014-03-12 | 上海交通大学 | Novel positioning fingerprint collection extraction method based on kernel density estimate |
| CN104076327A (en) * | 2014-07-15 | 2014-10-01 | 福建师范大学 | Continuous positioning method based on search space reduction |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8463291B2 (en) * | 2011-09-13 | 2013-06-11 | Alcatel Lucent | KL-divergence kernel regression for non-gaussian fingerprint based localization |
-
2014
- 2014-11-24 CN CN201410680673.6A patent/CN104507050B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103096466A (en) * | 2013-01-17 | 2013-05-08 | 哈尔滨工业大学 | Wireless fidelity (Wi-Fi) indoor positioning method |
| CN103634901A (en) * | 2013-11-05 | 2014-03-12 | 上海交通大学 | Novel positioning fingerprint collection extraction method based on kernel density estimate |
| CN104076327A (en) * | 2014-07-15 | 2014-10-01 | 福建师范大学 | Continuous positioning method based on search space reduction |
Non-Patent Citations (2)
| Title |
|---|
| 基于感知概率的室内定位算法;邹坤等;《全球定位系统》;20131215;第7-11页 * |
| 基于核函数法及马尔可夫链的节点定位算法;赵方等;《通信学报》;20101125;第195-203页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN104507050A (en) | 2015-04-08 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN104507050B (en) | Probabilistic type finger print matching method in a kind of WiFi indoor positionings | |
| CN104469942B (en) | A kind of indoor orientation method based on HMM | |
| KR102116824B1 (en) | Positioning system based on deep learnin and construction method thereof | |
| CN103476116B (en) | The anti-NLoS error location method merged based on positioning unit quality and many algorithm data | |
| CN108307301B (en) | Indoor positioning method based on RSSI ranging and track similarity | |
| CN109511085B (en) | UWB fingerprint positioning method based on MeanShift and weighted k nearest neighbor algorithm | |
| CN107621263B (en) | Geomagnetic positioning method based on road magnetic field characteristics | |
| CN105636201B (en) | Indoor orientation method based on sparse signal fingerprint database | |
| CN105792356A (en) | Wifi-based location fingerprint positioning method | |
| CN104853434A (en) | Indoor positioning method based on SVM and K mean value clustering algorithm | |
| CN103220777A (en) | Mobile device positioning system | |
| CN104038901A (en) | Indoor positioning method for reducing fingerprint data acquisition workload | |
| CN105120433A (en) | WLAN indoor positioning method based on continuous sampling and fuzzy clustering | |
| CN105491661A (en) | Improved Kalman filtering algorithm-based indoor positioning system and method | |
| AU2020203007B2 (en) | A method of setting-up a range-based tracking system utilising a tracking coordinate system | |
| CN106199500A (en) | Fingerprint characteristic localization method and device | |
| CN104507097A (en) | Semi-supervised training method based on WiFi (wireless fidelity) position fingerprints | |
| CN107979817A (en) | A kind of mobile terminal two dimension fingerprint positioning method | |
| CN105652235A (en) | Linear regression algorithm-based WLAN indoor positioning multi-user RSS (Received Signal Strength) fusion method | |
| CN110856100B (en) | Method and device for terminal positioning and positioning model construction based on 5G signal | |
| CN103888979A (en) | Indoor positioning method based on wireless local area network | |
| CN113449254B (en) | Method for analyzing monitoring stability of any net-type deformation and method for determining position of monitoring point | |
| CN104050254A (en) | Method for building 3D (three dimensional) indoor feature library by using indoor data | |
| Arai et al. | Color radiomap interpolation for efficient fingerprint wifi-based indoor location estimation | |
| CN107566981B (en) | Indoor high-precision positioning method, device and system based on optimal path |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |