CN104869635A - Positioning matching method and system based on TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) - Google Patents

Abstract

The invention provides a positioning matching method based on TOPSIS (Technique for Order Preference by Similarity to Ideal Solution). The method comprises the following steps: performing measurement at a point to be positioned to obtain the signal intensity values of the point to be positioned; acquiring the signal intensity values of a plurality of reference points according to a preset fingerprint database; acquiring the differences between the signal intensities of the point to be positioned and the plurality of reference points from each AP (Access Point) with a method which combines relative entropy with TOPSIS according to the signal intensity values of the point to be positioned and the signal intensity values of the plurality of reference points; and selecting a reference point corresponding to a minimum difference, and using the position of the reference point as the position of the point to be positioned. The invention also provides a positioning matching system based on TOPSIS. The positioning matching system comprises a measuring unit, an acquisition unit, a calculation unit and a positioning unit. The method and system are small in positioning errors, and the point to be positioned can be positioned more accurately.

Description

A kind of position matching method and system based on TOPSIS

Technical field

The present invention relates to areas of information technology, particularly relate to a kind of position matching method and system based on TOPSIS.

Background technology

WLAN location fingerprint method position fixing process is divided into off-line training and two stages of tuning on-line, off-line training step be in area to be targeted according to certain spacing distance with the some sampled points of latticed setting, and the signal strength values recorded at each sampled point to be together saved in fingerprint database together with its positional information.In the tuning on-line stage, by being contrasted by the finger print information in the signal strength information measured in real time and fingerprint database, in conjunction with suitable matching algorithm, determine the position of equipment to be positioned.

Orientation and Matching Algorithm relatively more conventional at present has signal space nearest neighbor method (NearestNeighbor in Signal Space, be called for short NNSS) and signal space k nearest neighbor method (k-NNSS), immediate one or more finger print data with real-time signal strength sample is found out, average as customer location to be positioned using the sampling point position of their correspondences or multiple sampling point position in the fingerprint database of position.Also has the position matching method based on table look-up (Table-based).The similarity that they utilize manhatton distance to come between metric signal intensity sample, the position of the finger print data then mated most in table is as customer location to be positioned.

But arest neighbors matching algorithm calculates the absolute deviation sum in target fingerprint to be positioned and database between fingerprint, different radio access points (Wireless AccessPoint can not be reflected well, be called for short AP) otherness between deviation, in easy generation deviation and benefit, make indivedual AP deviation of signal very large, but the fingerprint deviation calculated is little, thus causes position error bigger than normal.

Summary of the invention

For the defect of prior art, the invention provides a kind of position matching method and system based on TOPSIS, can reflect the deviation of different radio access access AP signal well, position error is little, can more accurately treat anchor point and position.

First aspect, the invention provides a kind of position matching method based on TOPSIS, described method comprises:

Measure in site undetermined, obtain the signal strength values in site undetermined;

According to the fingerprint database preset, obtain the signal strength values of multiple reference point;

According to the signal strength values in described site undetermined and the signal strength values of described multiple reference point, the method adopting relative entropy and TOPSIS to combine, obtains the gap of the signal strength signal intensity from each AP of site undetermined and multiple reference point respectively;

Choose lowest difference apart from corresponding reference point, using the position of the position of described reference point as site undetermined.

Preferably, describedly to measure in site undetermined, before obtaining the step of the signal strength values in site undetermined, described method also comprises:

In region to be positioned, according to certain spacing distance, multiple sampled point is set with latticed;

Measure the signal strength signal intensity of m wireless access point AP at each sampled point, using the signal strength values of a described m signal strength signal intensity as this sampled point; Wherein, m is positive integer, and m is more than or equal to 1;

The signal strength values of each sampled point and positional information are saved in fingerprint database.

Preferably, describedly to measure in site undetermined, obtain the signal strength values in site undetermined, comprising:

Measure the signal strength signal intensity of m AP in described site undetermined, using the signal strength values of a described m signal strength signal intensity as site undetermined.

Preferably, the fingerprint database that described basis is preset, obtains the signal strength values of multiple reference point, comprising:

According to the fingerprint database preset, obtain the set X={x of the finger print data of multiple sampled point ₁, x ₂..., x _n;

According to described finger print data, obtain the signal strength values of each sampled point, as the signal strength values of each reference point;

According to the signal strength values of multiple reference point, structure decision matrix P:

Wherein, N is total number of sampled point, and the signal strength set of m AP in fingerprint is combined into F={f ₁, f ₂..., f _m, then x _i(f _j) (i=1,2 ..., N; J=1,2 ..., m) be the jth signal strength values of i-th finger print data.

Preferably, the fingerprint database that described basis is preset, after obtaining the step of the signal strength values of multiple reference point, described method also comprises:

Planningization process is done to described decision matrix:

$t_{\mathrm{ij}}=x_i\left(f_j\right)/\sqrt{\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{x}_n{\left(f_j\right)}^2},(1\≤i\≤N;1\≤j\≤m)$

Wherein t _ijrepresent a jth signal strength values of i-th reference point after standardization.

Preferably, the signal strength values of the described signal strength values according to described site undetermined and described multiple reference point, the method adopting relative entropy and TOPSIS to combine, obtains the gap of the signal strength signal intensity from each AP of site undetermined and multiple reference point respectively, comprising:

Relative entropy and TOPSIS method are combined, calculates the gap of the signal strength signal intensity of site undetermined and multiple reference point according to following formula

$S_i^{*}={\left\{\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\right[t_j^{*}\log \frac{t_j^{*}}{t_{\mathrm{ij}}}+(1-t_j^{*})\log \frac{1-t_j^{*}}{1-t_{\mathrm{ij}}}\left]\right\}}^{1/2},(1\≤i\≤N;1\≤j\≤m)$

Wherein, the signal strength values in site undetermined is $T^{*}=\left[\begin{array}{cccc}{t}_1^{*}& t_2^{*}& ...& t_m^{*}\end{array}\right],$ represent a site undetermined jth signal strength values.

Second aspect, the invention provides a kind of position matching system based on TOPSIS, described system comprises:

Measuring unit, for measuring in site undetermined, obtains the signal strength values in site undetermined;

Acquiring unit, for according to the fingerprint database preset, obtains the signal strength values of multiple reference point;

Computing unit, for according to the signal strength values in described site undetermined and the signal strength values of described multiple reference point, the method adopting relative entropy and TOPSIS to combine, obtains the gap of the signal strength signal intensity from each AP of site undetermined and multiple reference point respectively;

Positioning unit, for choosing lowest difference apart from corresponding reference point, using the position of the position of described reference point as site undetermined.

Preferably, described system also comprises training unit, specifically for:

In region to be positioned, according to certain spacing distance with the multiple sampled point of latticed setting;

Measure the signal strength signal intensity of m wireless access point AP at each sampled point, using the signal strength values of a described m signal strength signal intensity as this sampled point; Wherein, m is positive integer, and m is more than or equal to 1;

The signal strength values of each sampled point and positional information are saved in fingerprint database.

Preferably, described measuring unit, specifically for:

Measure the signal strength signal intensity of m AP in described site undetermined, using the signal strength values of a described m signal strength signal intensity as site undetermined.

Preferably, described acquiring unit, specifically for:

According to the fingerprint database preset, obtain the set X={x of the finger print data of multiple sampled point ₁, x ₂..., x _n;

According to described finger print data, obtain the signal strength values of each sampled point, as the signal strength values of each reference point;

According to the signal strength values of multiple reference point, structure decision matrix P:

Wherein, N is total number of sampled point, and the signal strength set of m AP in fingerprint is combined into F={f ₁, f ₂..., f _m, then x _i(f _j) (i=1,2 ..., N; J=1,2 ..., m) be the jth signal strength values of i-th finger print data.

As shown from the above technical solution, a kind of position matching method and system based on TOPSIS provided by the invention, by relative entropy and TOPSIS method are combined, obtain the gap of the signal strength signal intensity from each AP between site undetermined and reference point, the deviation of different radio access points AP signal can be reflected well, position error is little, can more accurately treat anchor point and position.

Accompanying drawing explanation

In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, be briefly described to the accompanying drawing used required in embodiment or description of the prior art below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, under the prerequisite not paying creative work, other accompanying drawing can also be obtained according to these figure.

Fig. 1 is WLAN location fingerprint legal position principle schematic;

Fig. 2 is the schematic flow sheet of the position matching method based on TOPSIS that one embodiment of the invention provides;

Fig. 3 is the structural representation of the position matching system based on TOPSIS that another embodiment of the present invention provides;

Fig. 4 is the experimental site schematic diagram that another embodiment of the present invention provides;

Fig. 5 (a) is that 5 positions of selecting at random that another embodiment of the present invention provides position the result of test;

Fig. 5 (b) is that 30 positions of selecting at random that another embodiment of the present invention provides position the result of test;

Fig. 5 (c) is that 50 positions of selecting at random that another embodiment of the present invention provides position the result of test.

Embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, be clearly and completely described the technical scheme in the embodiment of the present invention, obviously, described embodiment is only the present invention's part embodiment, instead of whole embodiments.Based on the embodiment in the present invention, those of ordinary skill in the art, not making the every other embodiment obtained under creative work prerequisite, belong to the scope of protection of the invention.

As shown in Figure 2, one embodiment of the invention provides a kind of position matching method based on TOPSIS, and the method comprises the steps:

S1: measure in site undetermined, obtains the signal strength values in site undetermined;

S2: according to the fingerprint database preset, obtain the signal strength values of multiple reference point;

S3: according to the signal strength values in described site undetermined and the signal strength values of described multiple reference point, adopt relative entropy and good and bad solution Furthest Neighbor (Technique for Order Preference bySimilarity to an Ideal Solution, TOPSIS) method combined, obtain the gap of the signal strength signal intensity from each WAP (wireless access point) (Access Point, AP) of site undetermined and multiple reference point respectively;

Wherein, TOPSIS method mainly carries out the method sorted according to the degree of closeness of limited evaluation object and idealized target, be the evaluation carrying out relative superior or inferior in existing object.Wherein, site undetermined signal strength information will as idealized target, and multiple reference point is as evaluation object.

S4: choose lowest difference apart from corresponding reference point, using the position of the position of described reference point as site undetermined.

In the present embodiment, before step S1, the method also comprises the steps:

A01, in region to be positioned, according to certain spacing distance, multiple sampled point is set with latticed;

A02, measure m AP signal strength signal intensity at each sampled point, using the signal strength values of a described m signal strength signal intensity as this sampled point; Wherein, m is positive integer, and m is more than or equal to 1;

A03, the signal strength values of each sampled point and positional information to be saved in fingerprint database.

Steps A 01 to A03 mainly off-line training step, for setting up fingerprint database.As shown in Figure 1, part above dotted line represents the off-line training step shown in steps A 01 to A03 in the present embodiment, AP1, AP2 and AP3 3 WAP (wireless access point) altogether in Fig. 1, then at the measurable signal strength values to three AP of each sampled point, as (rss11, rss12, rss13) represents the signal strength values of first sampled point, and L1 is the positional information that this sampled point is corresponding, as coordinate etc.So, by the signal strength values of multiple sampled point and positional information stored in fingerprint database.

And the part below dotted line in Fig. 1 represents the tuning on-line step of step S1 to S4 in the present embodiment, as obtained the positional information in a certain site undetermined, then obtains 3 AP signal strength values (rss herein at this point measurement to be positioned ₁, rss ₂, rss ₃), according to this technology matching algorithm, obtain the positional information in this site undetermined.

Specifically, obtain the signal strength values in site undetermined in step S1, specifically comprise:

Measure the signal strength signal intensity of m AP in described site undetermined, using the signal strength values of a described m signal strength signal intensity as site undetermined.

In the present embodiment, step S2 specifically comprises unshowned following sub-step in Fig. 1:

S21: according to the fingerprint database preset, obtain the set X={x of the finger print data of multiple sampled point ₁, x ₂..., x _n;

S22: according to described finger print data, obtains the signal strength values of each sampled point, as the signal strength values of each reference point;

S23: according to the signal strength values of multiple reference point, structure decision matrix P:

Wherein, N is total number of sampled point, and the signal strength set of m AP in fingerprint is combined into F={f ₁, f ₂..., f _m, then x _i(f _j) (i=1,2 ..., N; J=1,2 ..., m) be the jth signal strength values of i-th finger print data.

Further, when the signal strength values in each finger print data is more, after step S23, described method also comprises the steps:

Standardization processing is done to the decision matrix in above-mentioned formula (1):

$t_{\mathrm{ij}}=x_i\left(f_j\right)/\sqrt{\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{x}_n{\left(f_j\right)}^2},(1\≤i\≤N;1\≤j\≤m)---\left(2\right)$

Wherein t _ijrepresent a jth signal strength values of i-th reference point after standardization.

In the present embodiment, step S23 specifically comprises:

Relative entropy and TOPSIS method are combined, calculates the gap of the signal strength signal intensity from each AP of site undetermined and multiple reference point according to following formula (3)

$S_i^{*}={\left\{\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\right[t_j^{*}\log \frac{t_j^{*}}{t_{\mathrm{ij}}}+(1-t_j^{*})\log \frac{1-t_j^{*}}{1-t_{\mathrm{ij}}}\left]\right\}}^{1/2},(1\≤i\≤N;1\≤j\≤m)---\left(3\right)$

Wherein, the signal strength values in site undetermined is $T^{*}=\left[\begin{array}{cccc}{t}_1^{*}& t_2^{*}& ...& t_m^{*}\end{array}\right],$ represent a site undetermined jth signal strength values.

Obtain the gap of the signal strength signal intensity from each AP of site undetermined and each reference point according to formula (3), select the reference point that wherein lowest difference distance is corresponding, using the position of the position of this reference point as site undetermined, as positioning result.

Present embodiments provide a kind of position matching method and system based on TOPSIS, by relative entropy and TOPSIS method are combined, obtain the gap of the signal strength signal intensity from each AP between site undetermined and reference point, the deviation of different radio access access AP signal can be reflected well, position error is little, can more accurately treat anchor point and position.

As shown in Figure 3, another embodiment of the present invention provides a kind of position matching system based on TOPSIS, and this system comprises measuring unit 301, acquiring unit 302, computing unit 303 and positioning unit 304.Wherein:

Measuring unit 301, for measuring in site undetermined, obtains the signal strength values in site undetermined.

Acquiring unit 302, for according to the fingerprint database preset, obtains the signal strength values of multiple reference point.

Computing unit 303, for according to the signal strength values in described site undetermined and the signal strength values of described multiple reference point, the method adopting relative entropy and TOPSIS to combine, obtains the gap of the signal strength signal intensity from each AP of site undetermined and multiple reference point respectively.

Positioning unit 304, for choosing lowest difference apart from corresponding reference point, using the position of the position of described reference point as site undetermined.

In the present embodiment, described system also comprises training unit, specifically for:

In region to be positioned, according to certain spacing distance with the multiple sampled point of latticed setting;

Measure the signal strength signal intensity of m wireless access point AP at each sampled point, using the signal strength values of a described m signal strength signal intensity as this sampled point; Wherein, m is positive integer, and m is more than or equal to 1;

The signal strength values of each sampled point and positional information are saved in fingerprint database.

In the present embodiment, described measuring unit 301, specifically for:

Measure the signal strength signal intensity of m AP in described site undetermined, using the signal strength values of a described m signal strength signal intensity as site undetermined.

In the present embodiment, described acquiring unit 302, specifically for:

According to the fingerprint database preset, obtain the set X={x of the finger print data of multiple sampled point ₁, x ₂..., x _n;

According to described finger print data, obtain the signal strength values of each sampled point, as the signal strength values of each reference point;

According to the signal strength values of multiple reference point, structure decision matrix P:

Wherein, N is total number of sampled point, and the signal strength set of m AP in fingerprint is combined into F={f ₁, f ₂..., f _m, then x _i(f _j) (i=1,2 ..., N; J=1,2 ..., m) be the jth signal strength values of i-th finger print data.

In the present embodiment, described system also comprises normalization unit, specifically for:

Standardization processing is done to described decision matrix:

$t_{\mathrm{ij}}=x_i\left(f_j\right)/\sqrt{\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{x}_n{\left(f_j\right)}^2},(1\≤i\≤N;1\≤j\≤m)$

Wherein t _ijrepresent a jth signal strength values of i-th reference point after standardization.

In the present embodiment, described computing unit 303, specifically for:

Relative entropy and TOPSIS method are combined, calculates the gap of the signal strength signal intensity from each AP of site undetermined and multiple reference point according to following formula

$S_i^{*}={\left\{\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\right[t_j^{*}\log \frac{t_j^{*}}{t_{\mathrm{ij}}}+(1-t_j^{*})\log \frac{1-t_j^{*}}{1-t_{\mathrm{ij}}}\left]\right\}}^{1/2},(1\≤i\≤N;1\≤j\≤m)$

Wherein, represent the gap of the signal strength signal intensity from each AP of site undetermined and i-th reference point, the signal strength values in site undetermined is $T^{*}=\left[\begin{array}{cccc}{t}_1^{*}& t_2^{*}& ...& t_m^{*}\end{array}\right],$ represent a site undetermined jth signal strength values.

In order to be illustrated more clearly in the effect of technical solution of the present invention, another embodiment of the present invention compares the positioning result of position matching method based on TOPSIS and existing nearest neighbor method by experiment.

As shown in Figure 4, be experimental site schematic diagram.This room-size is 22 × 18m ², this experiment use 3 AP are used for location, and wherein 2 AP are positioned at this room, and another AP is not or not this room.Receiving terminal is for being equipped with the notebook computer of Intel (R) Centrino (R) Wireless-N 2200 wireless network card.Use inSSIDer software scans received signal strength (Received SignalStrength, RSS), every 0.5s run-down.Room is divided into the grid of 80 length of side 2m, 99 grid summits is set to reference point, sample 50 times at each AP of each reference point, using the mean value of 50 times together with the positional information of this reference point as finger print data stored in fingerprint database.

The tuning on-line stage, as shown in Fig. 5 (a), 5 (b) and 5 (c), random selecting 5,30,50 positions position test, carry out 20 times respectively, use of the present invention based on the matching algorithm of TOPSIS and the matching algorithm of arest neighbors, compare the average localization error that use two kinds of methods obtain.

According to Fig. 5 (a), 5 (b) and 5 (c), use two kinds of matching algorithms, carry out the average localization error of 20 experiments respectively as following table 1:

The average localization error of table 1 two kinds of matching algorithms

From experimental result: (1) is in every 1 experiment, adopt the average localization error obtained based on TOPSIS matching algorithm to be all less than arest neighbors matching algorithm, illustrate that the method for the position matching based on TOPSIS provided by the invention is better than arest neighbors matching algorithm; (2) repeat in experiment at 20 times, method position error fluctuation ratio nearest neighbor algorithm of the present invention is little, describes method of the present invention and has good stability, have stronger robustness in actual applications.

Above embodiment only in order to technical scheme of the present invention to be described, is not intended to limit; Although with reference to previous embodiment to invention has been detailed description, those of ordinary skill in the art is to be understood that; It still can be modified to the technical scheme described in foregoing embodiments, or carries out equivalent replacement to wherein portion of techniques feature; And these amendments or replacement, do not make the essence of appropriate technical solution depart from the spirit and scope of various embodiments of the present invention technical scheme.

Claims (10)

1. based on a position matching method of TOPSIS, it is characterized in that, described method comprises:

Measure in site undetermined, obtain the signal strength values in site undetermined;

According to the fingerprint database preset, obtain the signal strength values of multiple reference point;

According to the signal strength values in described site undetermined and the signal strength values of described multiple reference point, adopt relative entropy and the good and bad method of separating Furthest Neighbor TOPSIS and combining, obtain the gap of the signal strength signal intensity from each wireless access point AP of site undetermined and multiple reference point respectively;

Choose lowest difference apart from corresponding reference point, using the position of the position of described reference point as site undetermined.

2. method according to claim 1, is characterized in that, describedly measures in site undetermined, and before obtaining the step of the signal strength values in site undetermined, described method also comprises:

In region to be positioned, according to certain spacing distance, multiple sampled point is set with latticed;

Measure the signal strength signal intensity of m AP at each sampled point, using the signal strength values of a described m signal strength signal intensity as this sampled point; Wherein, m is positive integer, and m is more than or equal to 1;

The signal strength values of each sampled point and positional information are saved in fingerprint database.

3. method according to claim 1, is characterized in that, describedly measures in site undetermined, obtains the signal strength values in site undetermined, comprising:

Measure the signal strength signal intensity of m AP in described site undetermined, using the signal strength values of a described m signal strength signal intensity as site undetermined.

4. method according to claim 2, is characterized in that, the fingerprint database that described basis is preset, and obtains the signal strength values of multiple reference point, comprising:

According to the fingerprint database preset, obtain the set X={x of the finger print data of multiple sampled point ₁, x ₂..., x _n;

According to described finger print data, obtain the signal strength values of each sampled point, as the signal strength values of each reference point;

According to the signal strength values of multiple reference point, structure decision matrix P:

Wherein, N is total number of sampled point, and the signal strength set of m AP in fingerprint is combined into F={f ₁, f ₂..., f _m, then x _i(f _j) (i=1,2 ..., N; J=1,2 ..., m) be the jth signal strength values of i-th finger print data.

5. method according to claim 4, is characterized in that, the fingerprint database that described basis is preset, and after obtaining the step of the signal strength values of multiple reference point, described method also comprises:

Standardization processing is done to described decision matrix:

$t_{\mathrm{ij}}=x_i\left(f_j\right)/\sqrt{\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{x}_n{\left(f_j\right)}^2},(1\≤i\≤N;1\≤j\≤m)$

Wherein t _ijrepresent a jth signal strength values of i-th reference point after standardization.

6. method according to claim 5, it is characterized in that, the signal strength values of the described signal strength values according to described site undetermined and described multiple reference point, adopt the method that relative entropy and TOPSIS combine, obtain the gap of the signal strength signal intensity from each AP of site undetermined and multiple reference point respectively, comprising:

Relative entropy and TOPSIS method are combined, calculates the gap of the signal strength signal intensity of site undetermined and multiple reference point according to following formula

$S_i^{*}={\left\{\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\right[t_j^{*}\log \frac{t_j^{*}}{t_{\mathrm{ij}}}+(1-t_j^{*})\log \frac{1-t_j^{*}}{1-t_{\mathrm{ij}}}\left]\right\}}^{1/2},(1\≤i\≤N;1\≤j\≤m)$

Wherein, the signal strength values in site undetermined is represent a site undetermined jth signal strength values.

7. based on a position matching system of TOPSIS, it is characterized in that, described system comprises:

Measuring unit, for measuring in site undetermined, obtains the signal strength values in site undetermined;

Acquiring unit, for according to the fingerprint database preset, obtains the signal strength values of multiple reference point;

Computing unit, for according to the signal strength values in described site undetermined and the signal strength values of described multiple reference point, the method adopting relative entropy and TOPSIS to combine, obtains the gap of the signal strength signal intensity from each wireless access point AP of site undetermined and multiple reference point respectively;

Positioning unit, for choosing lowest difference apart from corresponding reference point, using the position of the position of described reference point as site undetermined.

8. system according to claim 7, is characterized in that, described system also comprises training unit, specifically for:

In region to be positioned, according to certain spacing distance with the multiple sampled point of latticed setting;

Measure the signal strength signal intensity of m wireless access point AP at each sampled point, using the signal strength values of a described m signal strength signal intensity as this sampled point; Wherein, m is positive integer, and m is more than or equal to 1;

The signal strength values of each sampled point and positional information are saved in fingerprint database.

9. system according to claim 7, is characterized in that, described measuring unit, specifically for:

Measure the signal strength signal intensity of m AP in described site undetermined, using the signal strength values of a described m signal strength signal intensity as site undetermined.

10. system according to claim 8, is characterized in that, described acquiring unit, specifically for:

According to the fingerprint database preset, obtain the set X={x of the finger print data of multiple sampled point ₁, x ₂..., x _n;

According to described finger print data, obtain the signal strength values of each sampled point, as the signal strength values of each reference point;

According to the signal strength values of multiple reference point, structure decision matrix P:

Wherein, N is total number of sampled point, and the signal strength set of m AP in fingerprint is combined into F={f ₁, f ₂..., f _m, then x _i(f _j) (i=1,2 ..., N; J=1,2 ..., m) be the jth signal strength values of i-th finger print data.