CN102932738A - Improved positioning method of indoor fingerprint based on clustering neural network - Google Patents

Improved positioning method of indoor fingerprint based on clustering neural network Download PDF

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CN102932738A
CN102932738A CN2012104297840A CN201210429784A CN102932738A CN 102932738 A CN102932738 A CN 102932738A CN 2012104297840 A CN2012104297840 A CN 2012104297840A CN 201210429784 A CN201210429784 A CN 201210429784A CN 102932738 A CN102932738 A CN 102932738A
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丁根明
谈振辉
张金宝
张令文
陈铭珅
白嗣东
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Beijing Jiaotong University
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Abstract

The invention discloses the technical field of wireless communication and wireless network positioning, and in particular relates to an improved positioning method of an indoor fingerprint based on a clustering neural network. According to the technical scheme, the positioning method is characterized by comprising the following steps of: an offline phase: constructing a fingerprint database by fingerprint information collected from a reference point, sorting fingerprints in the fingerprint database by utilizing a clustering algorithm, and training the fingerprint and position information of each reference point by utilizing a artificial neural network model to obtain an optimized network model; and an online phase: carrying out cluster matching on the collected real-time fingerprint information and a cluster center in the fingerprint database to determine a primary positioning area, and taking the real-time fingerprint information in the primary positioning area as an input end of the neural network model of the reference point to acquire final accurate position estimation. The method has the advantages that low calculation and storage cost for the clustering artificial neural network fingerprint positioning method can be guaranteed, the positioning accuracy of the clustering artificial neural network fingerprint positioning method can be improved, and accurate positioning information is provided for users.

Description

A kind of improved indoor fingerprint positioning method based on the sub-clustering neural net
Technical field
The invention belongs to radio communication and wireless network field of locating technology, particularly a kind of improved indoor fingerprint positioning method based on the sub-clustering neural net.
Background technology
In recent years, along with society and economic development, and the continuous progress of information and communication technology (ICT), position-based information service (location based service, LBS) constantly increase in aspect demands such as Emergency Assistance, navigation, tracking and local searchs, present wide commercial promise and market value.At present, the position application overwhelming majority who develops based on intelligent terminal is confined to the outdoor positioning environment, yet people also grow with each passing day for the demand of indoor positioning technology, the services such as location navigation need to be provided for particular client such as airport hall, shopping center, office building, hospital etc., thereby more convenient people's life, provide better user to experience, improve businessman's service quality.
Indoor positioning algorithm commonly used mainly comprises three kinds of geometric measurement method, approximation method, fingerprint location method.Because the layout of each Indoor environment variation, the indoor environment complexity is changeful, the large grade of mobility of people is measured such as received signal strength (receive signal strength indoor radio signal, RSS), the time of advent (time ofarrival, TOA), the time of advent poor (time difference of arrival, TDOA) etc. have a huge impact, very difficult by the signal characteristics such as RSS are described accurate positional information.Thereby be difficult to obtain higher indoor position accuracy based on front two kinds of indoor positioning algorithms of radio waves propagation model.Thereby mate the location estimation that the mapping of carrying out again the locus realizes terminal for the fingerprint location algorithm by the fingerprint that the indoor signal characteristic value that gathers is consisted of, algorithm is simple and precision is high, and can adapt to by the real-time update of fingerprint base the variation of indoor environment, thereby be applied in the indoor locating system by wide model.
The fingerprint location algorithm is divided into off-line phase and on-line stage.Off-line phase utilizes terminal to gather wireless signal characteristic information such as RSS, the TOA etc. at indoor each reference point place, and the finger print information of being collected by each reference point place consists of the off-line fingerprint database of whole indoor arrangement.On-line stage consists of real-time finger print information by the wireless signal characteristic information at a certain the unknown blind spot place to be positioned is sampled, and obtains the location estimation of terminal by fingerprint matching algorithm again.Fingerprint matching algorithm commonly used comprises the nearest-neighbors method, KERNEL FUNCTION METHOD, SVMs method and neural network (artificial neural networks, ANN).Wherein, the neural net fingerprint matching algorithm can provide higher positioning accuracy and positioning stablity degree, but calculating and the storage overhead of this algorithm are large, have limited the exploitativeness of this algorithm for large-scale indoor place and terminal computing capability and the limited situation of storage capacity.Sub-clustering neural net fingerprint location method is divided into different zonules with indoor whole locating area and then carries out the training of ANN model and final location estimation by database fingerprint being carried out sub-clustering, and can reduce and calculate and storage overhead, improve the real-time of terminal positioning.Yet the suboptimum global convergence problem of sub-clustering neural network algorithm becomes the important factor in order of this location algorithm positioning accuracy, has reduced the positioning accuracy performance.For this problem, the present invention adopts RBF (Radio Basis Function, RBF) neural network model, a kind of fingerprint positioning method of improved sub-clustering neural net has been proposed, by weighted factor being retrained associating optimization neural network model, thereby when reducing computation complexity and memory requirements, improve the positioning accuracy of sub-clustering neural net fingerprint location algorithm, for the user provides more excellent location information service.
Summary of the invention
Problem for the suboptimum global convergence that solves model training in the sub-clustering neural net fingerprint location algorithm causes positioning accuracy to reduce the invention provides a kind of improved indoor fingerprint positioning method based on the sub-clustering neural net.
A kind of improved indoor fingerprint positioning method based on the sub-clustering neural net is characterized in that described method specifically may further comprise the steps:
Step 1: off-line phase gathers finger print information at indoor equally distributed reference point place and makes up fingerprint database;
Step 2: off-line phase, adopt clustering algorithm that the finger print information in the fingerprint database is classified, produce different classes and class center;
Step 3: off-line phase, utilize improved constraint Weighted Neural Network model that fingerprint and the positional information of each reference point are carried out the artificial neural net training, draw optimum network model, and the model parameter at the reference point place that optimization is obtained is input in the fingerprint database.
Step 4: on-line stage gathers indoor real-time finger print information;
Step 5: on-line stage, the class coupling is carried out at the real-time finger print information and the class center in the database that collect, select 2 ~ 3 classes of optimum Match as the Primary Location zone;
Step 6: on-line stage, according to the class matching result, with the real-time finger print information that comprises in the Primary Location zone input as the neural network model of each reference point in the selected class, M of selection has the minimum actual output location estimation corresponding with the model of desired output deviation and is weighted, thereby obtains final exact position estimation.
In the step 1, the foundation of the indoor fingerprint database of off-line phase specifically may further comprise the steps:
Step 101: equally distributed reference point RP is set according to indoor arrangement i, position coordinates l i=(x i, y i), i=1,2 ..., L.Wherein, L is the number of indoor reference point.
Step 102: at the channel parameter information v of each reference point place collection from the indoor n that a detects WAP (wireless access point) i(τ)=[v I, 1(τ) .., v I, n(τ)] T, τ=1 ..., m, m〉1, wherein, v I, j(τ) be reference point RP iReceive the channel parameter information from j access point when being in moment τ, m is the sampling period.
Step 103:v i(τ) be reference point RP iFinger print information, the finger print information of all reference point collections is stored in the database.Simultaneously, the sampling average with each each access point of reference point place is set to indoor wireless collection of illustrative plates V:
V = [ u 1 , u 2 , . . . , u L ]
= v 1,1 v 2,1 · · · v L , 1 v 1,2 v 2,2 · · · v L , 2 · · · · · · · · · · · · v 1 , n v 2 , n · · · V L , n - - - ( 1 )
Wherein,
Figure BDA00002339928300043
M is the sampling period; v I, j(τ) be reference point RP iReceive the channel parameter information from j access point when being in moment τ;
In the step 2, off-line phase fingerprint clustering algorithm adopts K-means clustering algorithm or affine propagation clustering algorithm, and the finger print information of L reference point among the wireless collection of illustrative plates V is carried out cluster, produces the individual different class of K
Figure BDA00002339928300044
K=1,2 ..., K all kinds ofly produces respectively a cluster centre c k
In the step 3, utilize improved constraint Weighted Neural Network model that fingerprint and the positional information of each reference point are carried out the artificial neural net training, draw optimum network model, comprise following step:
Step 301: the setting of improved constraint Weighted Neural Network model
1. neural net input; When the fan-in certificate is moment τ, at reference point RP iFrom the channel information parameter of an indoor n WAP (wireless access point), this n parameter value consists of sampling finger print information v i(τ)=[v I, 1(τ) ..., v I, n(τ)] T
2. neural net hidden layer end.According to cluster result in the step 2, determine the neuron number N that the hidden layer end comprises k, N kBe class
Figure BDA00002339928300051
Middle member's number, model hidden neuron excitation function are normalization gaussian kernel function h i(v):
Figure BDA00002339928300052
Wherein, u iAnd u jBe kernel function center, σ iAnd σ jBe the width of kernel function, width value is set to
Figure BDA00002339928300053
Nk is
Figure BDA00002339928300054
Class members's number, d Max=max||u i-u j||,
Figure BDA00002339928300055
3. the output desired value is reference point RP iActual position coordinate l i=(x i, y i);
Step 302: the training process of neural net is:
By optimization weighted factor W=[w iW j] TActual output and the desired output of neural net are minimized.Constraint function is:
Figure BDA00002339928300056
Wherein, Ψ (v)=Ψ (‖ v-u iBe about Euclidean distance ‖) || v-u iThe linearity of ‖ or Nonlinear Monotone decreasing function, w j=[w J1w J2] be the optimum target parameter, then utilize optimization algorithm to the Mathematical Modeling of artificial nerve network model training for minimizing such as minor function:
Figure BDA00002339928300058
Wherein, W=[w i..., w j], Be the optimization weighted factor.Thereby the Mathematical Modeling of obtaining of the optimal weighted factor of whole model is converted under the constraints of formula (3), minimizes target function formula (4).
Step 303: after model training finishes the model parameter at each reference point place is comprised nuclear center, the nuclear width of kernel function and optimize after weighted factor store in the database.
Described optimization algorithm comprises Newton method, conjugate gradient method or Levenberg-Marquardt least square method.
In the described step 5, definite process of the locating area of described Primary Location is:
Described on-line stage matching algorithm comprises minimum l 1General several method or minimum Eustachian distance method are chosen 2 ~ 3 classes of optimum Match; Calculate l 1General several distance
Figure BDA00002339928300061
Or Euclidean distance
Figure BDA00002339928300062
K=1,2 ..., K,
Figure BDA00002339928300063
Be real-time finger print information; The class of 2 ~ 3 correspondences of selected distance minimum is the class of optimum Match.
In the described step 6, according to the class matching result, with the real-time finger print information that comprises in the Primary Location zone input as the artificial neural net of each reference point in the selected class, M reference node positional information then therefrom choosing actual output and desired output deviation minimum is weighted obtains final location estimation:
l ~ = 1 Σ j = 1 M w j Σ j = 1 M w j l i ^ - - - ( 5 )
Wherein,
Figure BDA00002339928300065
Be the weighted factor of location estimation,
Figure BDA00002339928300066
Be class
Figure BDA00002339928300067
In the desired output l of i neural net iExport with reality
Figure BDA00002339928300068
The Euclidean squared distance value, For with real-time finger print information
Figure BDA000023399283000610
As the input of i neural net and the real output value of the neural net that obtains.
The invention has the beneficial effects as follows, use method of the present invention, can be in the lower calculating that ensures sub-clustering artificial neural net ANN fingerprint location method and storage overhead and higher location real-time, further improve the positioning accuracy of sub-clustering artificial neural net ANN fingerprint location method, thereby provide better location information service for the user.
Description of drawings
Fig. 1 is a kind of improved indoor fingerprint positioning method frame diagram based on the sub-clustering neural net provided by the invention;
Fig. 2 is improved constrained optimization RBF neural network model provided by the invention;
Fig. 3 is the experimental result of the positioning accuracy performance of a kind of improved indoor fingerprint positioning method based on the sub-clustering neural net provided by the invention.
Embodiment
Below in conjunction with accompanying drawing, preferred embodiment is elaborated.Should be emphasized that following explanation only is exemplary, rather than in order to limit the scope of the invention and to use.
Fig. 1 is a kind of improved indoor fingerprint positioning method frame diagram based on the sub-clustering neural net provided by the invention.Among Fig. 1, specifically comprise following steps:
Step 101: the foundation of the indoor fingerprint database of off-line phase.At first according to indoor arrangement equally distributed reference point RP is set i, position coordinates l i=(x i, y i), i=1,2 ..., L.Wherein, L is the number of indoor all reference points.At the channel parameter information v of each reference point place collection from the indoor n that a detects WAP (wireless access point) i(τ)=[v I, 1(τ) ..., v I, n(τ)] T, τ=1 ..., m, m＞1, wherein, v I, j(τ) be reference point RP iReceive the channel parameter information from j access point when being in moment τ, m is the sampling period.v i(τ) be reference point RP iFinger print information, then the finger print information with all reference point collections is stored in the database.Simultaneously, the sampling average with each each access point of reference point place is set to indoor wireless collection of illustrative plates V:
V = [ u 1 , u 2 , . . . , u L ]
= v 1,1 v 2,1 · · · v L , 1 v 1,2 v 2,2 · · · v L , 2 · · · · · · · · · · · · v 1 , n v 2 , n · · · V L , n - - - ( 1 )
Wherein, v i , j = 1 m Σ j = 1 m v i , j ( τ ) .
Step 102: off-line phase fingerprint cluster.Adopt K-means clustering algorithm, affine propagation clustering algorithm etc. that the finger print information of L reference point among the wireless collection of illustrative plates V is carried out cluster, produce K different class
Figure BDA00002339928300084
K=1,2 ..., K all kinds ofly produces respectively a cluster centre c k
Step 103: off-line phase sub-clustering artificial neural net ANN model training.Adopt the RBF nerve network model to train the optimal weighted factor that draws each reference point according to class, the mode input end is reference point RP iThe finger print information v that the place gathers, model hidden neuron excitation function is normalization gaussian kernel function h i(v):
Figure BDA00002339928300085
Wherein, u iAnd u jBe kernel function center, σ iAnd σ jBe the width of kernel function, width value is set to
Figure BDA00002339928300086
Nk is
Figure BDA00002339928300087
Class members's number, d Max=max||u i-u j‖,
Figure BDA00002339928300088
The output desired value is reference point RP iActual position coordinate l i=(x i, y i).Simultaneously weighted factor is retrained, constraint function is:
Figure BDA00002339928300089
Wherein, Ψ (v)=Ψ (|| v-u i||) be about Euclidean distance || v-u iThe linearity of ‖ or Nonlinear Monotone decreasing function, w j=[w J1w J2] be the optimum target parameter, then the Mathematical Modeling of ANN model training is for minimizing such as minor function:
Figure BDA00002339928300092
Wherein, W=[w i.., w j],
Figure BDA00002339928300093
Thereby the Mathematical Modeling of obtaining of the optimal weighted factor of whole model is converted under the constraints of formula (3), minimizes target function formula (4).The optimization algorithm that adopts comprises the least square methods such as Newton method, conjugate gradient method, Levenberg-Marquardt.After model training finishes the model parameter at each reference point place is comprised nuclear center, the nuclear width of kernel function and optimize after weighted factor store in the database.
Step 104: on-line stage class coupling.At first, carry out the measurement sampling of indoor radio signal channel parameter, then consist of new real-time finger print information
Figure BDA00002339928300094
Again with database in all kinds of class center of storing carry out l 1General several distance
Figure BDA00002339928300095
Or Euclidean distance
Figure BDA00002339928300096
K=1,2 ..., K calculates, and 2 ~ 3 classes of selected distance minimum are as the locating area of portable terminal Primary Location.
Step 105: on-line stage ANN accurately estimates the position.According to the class matching result, with the real-time finger print information that the gathers input as the ANN model of each reference point in the selected class, M reference node positional information then therefrom choosing actual output and desired output deviation minimum is weighted obtains the final location estimation of portable terminal:
l ~ = 1 Σ j = 1 M w i j Σ j = 1 M w i j l ^ i j - - - ( 5 )
Wherein, w i j = 1 ϵ + d ( l i j , l ^ i j ) , d ( l i j , l ^ i j ) = | | l i j - l ^ i j | | 2 ,
Figure BDA000023399283000910
M value 3 ~ 5.
Fig. 2 is improved constrained optimization RBF neural network model provided by the invention.Specifically comprise such as lower module.
Module 1, the neural net input.Fan-in according to be the moment during τ at reference point RP iFrom the channel information parameter of an indoor n WAP (wireless access point), such as RSS or TOA etc., this n parameter value consists of sampling finger print information v i(τ)=[v I, 1(τ) ..., v I, n(τ)] T Module 2, neural net hidden layer end.According to cluster result, the hidden layer end comprises N k(class
Figure BDA00002339928300101
Middle member's number) individual neuron, each neuron excitation function are the normalization gaussian kernel function shown in the formula (2), and kernel function center and nuclear width are according to the described value of the step 3 among Fig. 1.
Module 3, the neural net output.Output output desired value is true coordinate value corresponding to this RPi, by optimization weighted factor W=[w iW j] TActual output and the desired output of neural net are minimized.Therefore, can minimize target function formula (4) at the prerequisite of weighted factor constraints formula (3) optimum that gets off, obtain optimum neural metwork training model, thereby improve the positioning accuracy of sub-clustering neural net fingerprint location algorithm.
Fig. 3 shows the inventive method experimental result positioning accuracy performance, and performance map is the authentic testing experimental result of carrying out at Beijing Jiaotong University's Si Yuan building 8 floor.In the experimentation Si Yuan building 8 floor are evenly arranged 126 reference points, thereby each consists of indoor fingerprint database with reference to pointing out the received signal strength information of collection from the wireless channel of all indoor wireless WiFi access points.Adopt affine propagation fingerprint clustering method that all indoor reference points are divided into 11 classes, then classify each reference is trained according to original RBF neural network model and improved RBF neural network model one by one, and carried out the exact position estimation of portable terminal by final training pattern.Show in the experimental result picture, (improved affinity propagation clustering artificial neural networks, IAPCANN) is better than sub-clustering neural net fingerprint positioning method (APCANN) positioning performance of original affine propagation clustering for improved sub-clustering neural net fingerprint positioning method based on affine propagation clustering.The APCANN positioning accuracy is 43.6% less than the probability of 2m, and IAPCANN method positioning accuracy is 57.2% less than the probability of 2m, and performance has improved 31.2%.
The above; only for the better embodiment of the present invention, but protection scope of the present invention is not limited to this, anyly is familiar with those skilled in the art in the technical scope that the present invention discloses; the variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection range of claim.

Claims (7)

1. improved indoor fingerprint positioning method based on the sub-clustering neural net is characterized in that described method specifically may further comprise the steps:
Step 1: off-line phase gathers finger print information at indoor equally distributed reference point place and makes up fingerprint database;
Step 2: off-line phase, adopt clustering algorithm that the finger print information in the fingerprint database is classified, produce different classes and class center;
Step 3: off-line phase, utilize improved constraint Weighted Neural Network model that fingerprint and the positional information of each reference point are carried out the artificial neural net training, draw optimum network model, and the model parameter at the reference point place that optimization is obtained is input in the fingerprint database;
Step 4: on-line stage gathers indoor real-time finger print information;
Step 5: on-line stage, the class coupling is carried out at the real-time finger print information and the class center in the database that collect, select 2 ~ 3 classes of optimum Match as the locating area of Primary Location;
Step 6: on-line stage, according to the class matching result, with the real-time finger print information that comprises in the Primary Location zone input as the neural network model of each reference point in the selected class, M of selection has the minimum actual output location estimation corresponding with the model of desired output deviation and is weighted, thereby obtains final exact position estimation.
2. a kind of improved indoor fingerprint positioning method based on the sub-clustering neural net according to claim 1 is characterized in that in the described step 1, the foundation of the indoor fingerprint database of off-line phase specifically may further comprise the steps:
Step 101: equally distributed reference point RP is set according to indoor arrangement i, position coordinates l i=(x i, y i), i=1,2 ..., L; Wherein, L is the number of indoor reference point;
Step 102: at the channel parameter information v of each reference point place collection from the indoor n that a detects WAP (wireless access point) i(τ)=[v I, 1(τ) .., v I, n(τ)] T, τ=1 ..., m, m〉1, wherein, v I, j(τ) be reference point RP iReceive the channel parameter information from j access point when being in moment τ, m is the sampling period;
Step 103: with channel parameter information v i(τ) RP as a reference point iFinger print information be stored in the database, simultaneously, the sampling average of each each access point of reference point place is set to indoor wireless collection of illustrative plates V:
V = [ u 1 , u 2 , . . . , u L ]
= v 1,1 v 2,1 · · · v L , 1 v 1,2 v 2,2 · · · v L , 2 · · · · · · · · · · · · v 1 , n v 2 , n · · · V L , n - - - ( 1 )
Wherein,
Figure FDA00002339928200023
M is the sampling period; v I, j(τ) be reference point RP iReceive the channel parameter information from j access point when being in moment τ.
3. a kind of improved indoor fingerprint positioning method based on the sub-clustering neural net according to claim 1, it is characterized in that, in the described step 2, off-line phase fingerprint clustering algorithm adopts K-means clustering algorithm or affine propagation clustering algorithm, the finger print information of L reference point among the wireless collection of illustrative plates V is carried out cluster, produce K different class K=1,2 ..., K all kinds ofly produces respectively a cluster centre c k
4. a kind of improved indoor fingerprint positioning method based on the sub-clustering neural net according to claim 1, it is characterized in that, in the described step 3, utilize improved constraint Weighted Neural Network model that fingerprint and the positional information of each reference point are carried out the artificial neural net training, draw optimum network model, comprise following step:
Step 301: the setting of improved constraint Weighted Neural Network model
A. neural net input; When the fan-in certificate is moment τ, at reference point RP iFrom the channel information parameter of an indoor n WAP (wireless access point), this n parameter value consists of finger print information v i(τ)=[v I, 1(τ) ..., v I, n(τ)] T
B. neural net hidden layer end; According to cluster result in the step 2, determine the neuron number N that the hidden layer end comprises k, N kBe class
Figure FDA00002339928200031
Middle member's number, model hidden neuron excitation function are normalization gaussian kernel function h i(v):
Figure FDA00002339928200032
Wherein, u iAnd u jBe kernel function center, σ iAnd σ jBe the width of kernel function, width value is set to
Figure FDA00002339928200033
Nk is
Figure FDA00002339928200034
Class members's number, d Max=max||u i-u j||,
Figure FDA00002339928200035
C. neural net output desired value is reference point RP iActual position coordinate l i=(x i, y i);
Step 302: the training process of neural net is:
By optimization weighted factor W=[w iW j] TActual output and the desired output of neural net are minimized; Constraint function is:
Wherein, Ψ (v)=Ψ (|| v-u iBe about Euclidean distance ‖) || v-u iThe linearity of ‖ or Nonlinear Monotone decreasing function, w j=[w J1w J2] be the optimum target parameter, then utilize optimization algorithm to the Mathematical Modeling of artificial nerve network model training for minimizing such as minor function:
Figure FDA00002339928200037
Figure FDA00002339928200038
Wherein, W=[w i..., w j],
Figure FDA00002339928200041
Be the optimization weighted factor; Thereby the Mathematical Modeling of obtaining of the optimal weighted factor of whole model is converted under the constraints of formula (3), minimizes target function formula (4);
Step 303: after model training finishes the model parameter at each reference point place is comprised nuclear center, the nuclear width of kernel function and optimize after weighted factor store in the database.
5. a kind of improved indoor fingerprint positioning method based on the sub-clustering neural net according to claim 4 is characterized in that described optimization algorithm comprises Newton method, conjugate gradient method or Levenberg-Marquardt least square method.
6. a kind of improved indoor fingerprint positioning method based on the sub-clustering neural net according to claim 1 is characterized in that in the described step 5, the on-line stage matching algorithm comprises minimum l 1General several method or minimum Eustachian distance method are chosen 2 ~ 3 classes of optimum Match; Calculate l 1General several distance
Figure FDA00002339928200042
Or Euclidean distance
Figure FDA00002339928200043
K=1,2 ..., K,
Figure FDA00002339928200044
Be real-time finger print information; The class of 2 ~ 3 correspondences of selected distance minimum is the class of optimum Match.
7. a kind of improved indoor fingerprint positioning method based on the sub-clustering neural net according to claim 1, it is characterized in that, in the described step 6, according to the class matching result, with the real-time finger print information that comprises in the Primary Location zone input as the artificial neural net of each reference point in the selected class, M reference node positional information then therefrom choosing actual output and desired output deviation minimum is weighted obtains final location estimation:
l ~ = 1 Σ j = 1 M w j Σ j = 1 M w j l i ^ - - - ( 5 )
Wherein,
Figure FDA00002339928200046
Be the weighted factor of location estimation,
Figure FDA00002339928200047
Be class
Figure FDA00002339928200048
In the desired output l of i neural net iExport with reality The Euclidean squared distance value,
Figure FDA00002339928200051
For with real-time finger print information
Figure FDA00002339928200052
As the input of i neural net and the real output value of the neural net that obtains.
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