Fingerprinting Localization Method Based on TOA and Particle …downloads.hindawi.com/journals/mpe/2017/3215978.pdf · 2019. 7. 30. · of a UWB-based fingerprinting localization

Research ArticleFingerprinting Localization Method Based on TOA andParticle Filtering for Mines

Boming Song12 Shen Zhang12 Jia Long12 and Qingsong Hu12

1 Internet of Things (Perception Mine) Research Center China University of Mining amp Technology Xuzhou 221008 China2School of Information and Control Engineering China University of Mining amp Technology Xuzhou 221008 China

Correspondence should be addressed to Qingsong Hu hqsong722163com

Received 13 January 2017 Accepted 30 August 2017 Published 9 October 2017

Academic Editor Paolo Addesso

Copyright copy 2017 Boming Song et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Accurate target localization technology plays a very important role in ensuring mine safety production and higher productionefficiency The localization accuracy of a mine localization system is influenced by many factors The most significant factor is thenon-line of sight (NLOS) propagation error of the localization signal between the access point (AP) and the target node (Tag) Inorder to improve positioning accuracy the NLOS error must be suppressed by an optimization algorithm However the traditionaloptimization algorithms are complex and exhibit poor optimization performance To solve this problem this paper proposes a newmethod formine time of arrival (TOA) localization based on the idea of comprehensive optimizationThe proposedmethod utilizesparticle filtering to reduce the TOA data error and the positioning results are further optimized with fingerprinting based on theManhattan distanceThis proposed method combines the advantages of particle filtering and fingerprinting localization It reducesalgorithm complexity and has better error suppression performanceThe experimental results demonstrate that as compared to thesymmetric double-sided two-way ranging (SDS-TWR) method or received signal strength indication (RSSI) based fingerprintingmethod the proposedmethodhas a significantly improved localization performance and the environment adaptability is enhanced

1 Introduction

The Internet of Things and pervasive computing technologyhave continually progressed since their inception [1 2]At present the Internet of Things technology has becomeincreasingly used in a variety of fields For example Internetof Things technology for the mining industry was developedin order to obtain the status of coal mining and controlmine production safety It is crucial to know and managethe dynamic distribution of underground personnel for bothmine enterprise management and emergency rescue in caseof accidents [3] Therefore determining how to achieve anaccurate localization of mine underground personnel hasbecome a popular research topic

Mine target localization usually utilizes the range-basedmethod that is the location estimation is based on thedistance measurement In mine localization the most usedparameters are the RSSI of a wireless signal the angle ofarrival (AOA) the time of arrival (TOA) and the timedifference of arrival (TDOA) In addition some researchers

used range-free methods to solve the problem of target local-ization For example problems such as node connectivity[4 5] and beacon drift [6] are new research fields in thelocalization algorithm

Because the underground environments of coal minesare complex and personnel mobility is relatively high it isvery difficult to achieve accurate positioning of undergroundpersonnel The effect of NLOS propagation is the mainsource of wireless localization error in the undergroundenvironment At present the methods for reducing NLOSerror can be divided into direct methods and indirect meth-ods The direct methods directly process the measurementresults to reduce NLOS propagation error Commonly useddirect methods include the Wylie and Holtzman method [7]Kalman filtering [8] particle filtering [9] and mean filteringIndirect methods avoid the direct processing of wirelesssignals or measurement results instead they utilize differ-ent localization methods to improve the robustness of themeasurement results Fingerprinting localization technology

HindawiMathematical Problems in EngineeringVolume 2017 Article ID 3215978 10 pageshttpsdoiorg10115520173215978

2 Mathematical Problems in Engineering

is an indirect method This technology is also one of themost commonly used mine localization technologies and itis usually divided into two phases the offline Training phaseand Online Matching phase The task of the offline Trainingphase is to collect the signal characteristic parameter whichis usually the RSSI from different APs at the referencepointsThese collected parameters are then used to constructthe fingerprinting database In the Online Matching phasethe similarity matching between the current collected datawith fingerprinting database is conducted to obtain the bestestimation

Because fingerprinting localization methods have lowcomputational complexity and good performance for sup-pressing NLOS error there has been a lot of researchpublished on fingerprinting localization methods in the pastfew years Lin et al [10] proposed a method to construct afingerprint database by using the correlated RSSI of adjacentnodesTheMarkov chain predictionmodel was used to assistthe localization Guzman-Quiros et al [11] applied direc-tional antennas to the RSSI-based fingerprinting localizationmethod which reduced the required number of sensorsand improved the localization success rate To reduce theworkload of collecting fingerprint data in the offline phaseGu et al used compressed sensing to reduce the amount ofcollected fingerprint data [12]

Although the TOA-based ranging method can overcomesome shortcomings associated with RSSI NLOS propagationstill seriously impacts the localization accuracy In thispaper a TOA fingerprinting localization method based onparticle filtering is proposed according to the characteristicsof the fingerprinting localization method and TOA rangingtechnology The TOA ranging result vectors are stored ina fingerprint database and the 119896-nearest neighbour (KNN)algorithm is used to estimate the positions The proposedmethod uses both direct and indirect methods to suppressthe NLOS error When NLOS interference exists the TOAlocalization result can be greatly optimized The structure ofthe paper is as follows Section 2 summarizes the work relatedto the field of particle filtering and fingerprinting localizationSection 3 details the proposed method for constructing aTOA fingerprint database based on particle filtering and theposition estimation is performed by theKNNmatching local-ization method In Section 4 the localization performanceof the proposed method is experimentally tested Section 5concludes the paper

2 Related Works

Because indoor positioning technology offers wide appli-cation prospects many researchers have proposed differentindoor wireless positioning technologies in the past fewyears and consequently a large number of research resultshave been published on the topic One such example is thefirst developed RADAR system [13] which utilizes empiricaldata and the attenuation factor model The localization of amoving target is achieved using a pattern recognitionmethodafter the completion of data acquisition The MoteTracksystem [14] andHorus system [15] are also indoor positioningsystem based on RSSI These works laid a good foundation

for further improving the accuracy and robustness of indoorpositioning

The NLOS propagation phenomenon caused by obsta-cles is an important factor affecting wireless positioningaccuracy for coal mines For this reason direct or indirectoptimization can be used to eliminate or reduce the influenceof NLOS Direct optimization methods primarily includeKalman filtering particle filtering convex relaxation [1617] and iterative minimum residual method [18] Indirectoptimization methods mainly include the fingerprintingpositioning method Chan algorithm [19] and geometricprojection method [20] However the system performanceof a single optimization method has certain limitationsTherefore to suppress theNLOSpropagation error this paperutilizes both the particle filtering and fingerprinting methodto combine the advantages of direct optimization and indirectoptimization

Particle filtering combines the Bayesian filtering methodwith the Monte Carlo method It approximates the posteriorprobability distribution of random variables in a system bya series of weighted discrete random sampling points Thereare many kinds of particle filtering The most commonlyused are auxiliary particle filtering [21] regularized particlefiltering [22] adaptive particle filtering and so forth Particlefiltering has a wide range of application in the field of minepositioning and indoor positioning Jiang et al [23] combinedparticle filtering with Wi-Fi-based positioning informationand motion sensor information to obtain a more accurateand smooth target moving trajectory Based on the ideaof gradient fingerprinting positioning technology Shu etal [24] combined multiple dynamic detection results withextended particle filtering to obtain positioning for users andequipment Moreno-Cano et al [25] used particle filteringto track and predict the position and trajectory of movingtargets in positioning systems based on RFID and thermalinfrared Ma and Li [26] improved the positioning accuracyof mine rescue robots using modified particle filtering ZhuandYi [27] proposed amine undergroundpositioning systembased on UWB and the NLOS interference in the mineunderground is suppressed by using particle filtering

Fingerprinting localization includes an offline phase andan online phase The key to the Online Matching phaseis the design and selection of the pattern-matching algo-rithm which directly determines the positioning accuracyPresently the KNN algorithm and the weighted 119896-nearestneighbour (WKNN) algorithm [13] are the most commonlyused matching algorithms In [28] Li et al proposed a KNNalgorithm based on feature scaling Although their algorithmdoes consider the fact that the distance between RSSI vectorsin the fingerprint database and the actual distance are notperfectly matched their algorithm does not completely over-come the disadvantage that the RSSI can easily attenuate Atpresent most of the fingerprinting localization methods arebased on RSSI however in practical applications the com-plex mine environment will affect the way the RSSI changesusually resulting in low positioning accuracy for RSSI-basedmethods In order to overcome the shortcomings of RSSI-based localization technology Taok et al proposed an UWBfingerprinting localization method based on neural network

Mathematical Problems in Engineering 3

Node 1

Node 2

T1

T2 T3

T4

T5

T6 T7

T8

TＬＩＯＨ＞ 1

TＬＩＯＨ＞ 2

TＬＪＦＳ 1

TＬＪＦＳ 2

Figure 1 Frame of SDS-TWR

for coal mine underground [29]Their method obtains betterlocalization accuracy using the channel impulse response(CIR) instead of RSSI to construct the fingerprint databaseSun and Li [30] proposed a mine TOA localization methodbased on Kalman filtering and fingerprinting However theirresults lack validation experiments in different environmentsto compare the suppression performance for NLOS errorsIn [31] Kabir and Kohno also discussed the applicationsof a UWB-based fingerprinting localization method in anNLOS environment However the vast majority of currentlyused mine intelligent terminals cannot support the use ofUWB Instead Wi-Fi ZigBee and other technologies aremore popular

3 TOA for Fingerprints

This paper proposes a TOA fingerprinting localizationmethod based on particle filtering The distance measure-ments based on TOA are first carried out using a SDS-TWR algorithm to suppress errors such as synchronizationdelay in the process of ranging Then the excess delay errorscaused by the NLOS propagation in the mine undergroundare suppressed by particle filtering Finally the fingerprintdatabase is constructed according to the obtained accurateTOA ranging information The target position estimation isthen completed

31 Distance Measurements Based on SDS-TWR The TOAdata serves as the basis for constructing the fingerprintdatabase and positioning After the ranging system finishesthe ranging work the ranging result vectors are stored inthe fingerprint database formatching positioning At presentthe most commonly used TOA ranging algorithms mainlyinclude one-way ranging (OWR) [32] two-way ranging(TWR) [33] and SDS-TWR [34] In this paper the SDS-TWR algorithm is used The errors caused by the clocksynchronization error can be eliminated as far as the wirelesssignal undergoes on a round trip between the two nodesTherefore the system robustness is improved

As shown in Figure 1 the SDS-TWR algorithm calculatesthe distance between two nodes by accurately measuring thetwo-way arrival time and the internal reaction time In thealgorithm 119879round1 is the time difference between the timewhen node 1 transmits the signal to node 2 and the timewhenthe response signal is received from node 2 119879reply2 is the timedifference between the time when node 2 receives the signal

from node 1 and the time when the response signal is sent tonode 1 Similarly 119879round2 is the time difference between thetime when node 2 transmits the signal to node 1 and the timewhen the response signal is received from node 1 119879reply1 isthe time difference between the time when node 1 receivesthe signal from node 2 and the time when the response signalis sent to node 2 Assuming that the propagation velocity ofthe signal is V the distance between node 1 and node 2 is

V4 [(119879round1 minus 119879reply2) + (119879round2 minus 119879reply1)] (1)

32 NLOS Error Optimization Based on Particle FilteringNLOS propagation is a widespread phenomenon in themine environment The excess delay caused by the NLOSpropagation greatly affects the ranging process and resultsin large ranging errors which seriously decrease positioningaccuracy There are two main sources for excess delay in themine environment One is the stable excess delay caused bythe special structure fixed facilities equipment and pipelinesin the mine The other is the random excess delay causedby passing personnel and vehicles The stable excess delayhas certain regularity and can be analysed by the excessdelay model In contrast the random excess delay has a largeirregularity which is difficult to analyse and predict Further-more the random excess delay greatly impacts positioningaccuracy Therefore corresponding algorithms are requiredto suppress these effects This paper proposes a new methodbased on particle filtering to suppress the excess delay in orderto reduce NLOS error and improve positioning accuracy

The target node that needs to be located carries the Tagand moves in the mine tunnel The AP deployed in thetunnel measures the distance between the AP and the Tagusing the method described in Section 31Themoving of thepositioning target can be regarded as uniform linear motionin a short sampling interval 1198790 Assume that the state vectoris X119896 = [119904119896 V119896]119879 isin 119877119899 where 119904119896 and V119896 are the position com-ponent and the velocity component respectively Assumingthat the observed value is 119884119896 then the state equation and theobservation equation are as follows

X119896+1 = 120593X119896 + 120574120596119896 (2)

119884119896 = H (X119896) + 120579119896 (3)

where120593 = [ 1 11987900 1

] 120574 = [ 0511987920 00 1198790

] Both120596119896 and 120579119896 areGaussianwhite noise and H(X119896) is the distance relationship betweenthe AP and Tag

The above state transition equation only describes themotion state information of the Tag and the distance betweenthe AP and the target node (ie observation value 119884119896)Assuming that the coordinate of the AP is (119909119904 119910119904) and thecoordinate of the Tag is (120572 120573) then the function H(X119896) canbe expressed as follows

H (X119896) = radic(120572119896 minus 119909119904)2 + (120573119896 minus 119910119904)2 (4)

The shape and structure of the mine tunnel make minepositioning a one-dimensional problem Assuming that the


0 100 200 300 400 500 600 700 800 9000

20

40

60

80

100

120

Rang

ing

resu

lts (m

)1-dimension TOA curve in NLOS propagation

Sampling times (sampling period = 01 Ｍ)

(a)

0 100 200 300 400 500 600 700 800 9000

5

10

15

20

25

30

35

Rang

ing

erro

rs (m

)

Comparison of ranging errors


(b)

Figure 2 Comparison of ranging results before and after the particle filtering (a) Comparison of positioning results under one-dimensionalNLOS propagation conditions (b) Comparison of positioning error between the original TOA and after particle filtering

position of the AP is 119904 and the position of the Tag is 119904119896 then(4) can be simplified as

H (X119896) = 1003816100381610038161003816119904 minus 1199041198961003816100381610038161003816 (5)

It is further assumed that the Tag moves linearly fromthe origin From (2) it can be seen that the actual distancecan be approximated by a straight line However as shownin Figure 2 the equipment error and the excess delay causedby NLOS propagation cause a large irregular fluctuation inthe measured data However the fluctuation amplitude of theranging curve is greatly reduced after the particle filteringwhich demonstrates that the ranging accuracy is greatlyimproved and the NLOS error suppression performance isgood

33 The Construction of the Localization FingerprintingDatabase Based on the Optimized Ranging Data This sectionuses the optimized TOA data to construct the fingerprintdatabase required for positioning As mentioned above thefingerprinting localization method includes an offline phaseand an online phase The fingerprint database is constructedin the offline training phase For this purpose the AP is firstdeployed according to the target area environment and theposition of the reference point is selected The Tag is usedto obtain the optimum distance (see Sections 31 and 32)at each reference point which is used as the training vectorDis119894119895 After the acquisition of all reference points a RadioMap matrix is obtained as shown in

[[[[[[[[[

Dis11 Dis1119895 Dis1119869sdot sdot sdotDis1198941 Dis119894119895 Dis119894119869sdot sdot sdotDis1198681 Dis119868119895 Dis119868119869

]]]]]]]]] (6)

where 119868 and 119869 denote the total number of reference points(RP) and AP respectively Disij is collected at the 119894threference point and it represents the distance informationbetween the 119894th reference point and the 119895th AP Furthermore1 ⩽ 119894 ⩽ 119868 1 ⩽ 119895 ⩽ 119869 The 119894th row of vectors in the matrixrepresents the training vectors collected at the 119894th referencepoint and (Dis1 sdot sdot sdot Dis119895 sdot sdot sdot Dis119869) represents the trainingvector collected by the Tag at the reference point

In the KNN algorithm the similarity between the posi-tioning vector p in the online phase and the training vectorin the offline phase is usually used to estimate the targetposition Numerous methods can be used to calculate sim-ilarity such as the Euclidean distance Manhattan distanceChebyshev distance and Spearman correlation The similar-ity calculation method based on the Euclidean distance is thesimplest which is shown in

119889119894 = radic 119869sum119895=1

(Dis119894119895 minus 119901119895)2 (7)

The results of Chen et al [35] Farshad et al [36] andNiu et al [37] reveal that results of the Manhattan distancemethod are superior to those of other similarity calculationmethodsTheManhattan distance is also called theCity Blockdistance which represents the sum of the distances projectedon two axes for a line between two points in Euclidean spaceThe Manhattan distance is shown in

119889119894 = 119869sum119895=1

10038161003816100381610038161003816Dis119894119895 minus 11990111989510038161003816100381610038161003816 (8)

Because the experimental conditions in this paper arevery similar to those in the above works the Manhattandistance is also selected to calculate the similarity


Staircase

AP in LOS conditionReference pointsAP in NLOS condition

Corridor 60Ｇ

Figure 3 Schematic diagram of the line corridor environment and experimental deployment

4 Experimental Results

This section evaluates the performance of the proposed TOAfingerprinting localization method based on particle filteringthrough experiments under various conditions This pro-posed method is compared to the RSSI-based fingerprintinglocalization method and the traditional TOA localizationmethod In these experiments all of the background controland data processing were completed by a PC with an IntelCore i7-3630QM and 8GB RAM The TOA ranging wascompleted using a NanoPAN 5375 wireless module

41 The Experimental Setup Here the focus is on localiza-tion performance tests in long-distance corridor and tunnelenvironments because these environmental characteristicsare more similar to mine tunnels The APs are deployed atthe two ends of the corridor or tunnel When a line of sight(LOS) propagation path exists between APs it is referred toas the LOS propagation condition When there is no LOSpropagation path between APs it is referred to as the NLOSpropagation condition Taking into account the existence ofa variety of practical scenes in mine tunnels experiments inline corridors and curve corridors were carried out

The line corridor structure is shown in Figure 3 Thiscorridor is located in building A of the Internet of ThingsResearch Center at China University of Mining and Tech-nology Xuzhou China The dimension of the corridor is23m by 60m A positioning AP is deployed at each endof the corridor The distance between two APs is 576mA reference point is selected every 24m between the twoAPs and 23 reference points are selected in total to coverthe entire corridor During the experiment the localizationexperiments were carried out at random positions in thecorridor The performance of the localization method wasevaluated by the error between the localized results and theactual positions

The curve corridor structure is shown in Figure 4 Thiscorridor is located on the fourth floor of the School ofEnvironment Science and Spatial Informatics China Uni-versity of Mining and Technology Xuzhou China Thewidth of the corridor is three meters and the corner angleis approximately 121 degrees The corridor corner is usedas the midpoint and the positioning APs are deployed

symmetrically on both sides of the corridor After multipletests it was determined that stable communications cannotbe established when the distance between the AP and thecorridor corner is greater than 12 meters Therefore the APsare deployed 12meters away from the corridor corner that isthe distance between the two APs is 24m Reference pointsare selected every 24m between the two APs There are ninereference points in total Similar to the long straight corridorthe positions in the corridor are randomly selected for thepositioning experiments In order to accurately evaluate theparticle filteringrsquos ability to improve positioning accuracythree lab assistants randomly walked in the test environmentsof both corridors to simulate the random excess delay in realpositioning environments

42 Experiments in LOS Propagation Under the conditionof LOS propagation this paper compares the TOA-basedlocalization method RSSI-based fingerprinting localizationmethod TOA fingerprinting localization method with-out particle filtering and TOA fingerprinting localizationmethod based on particle filtering

First a localization experiment was carried out using thelocalization method based on TOA ranging Two APs weredeployed at both ends of the corridor and their deploymentlocations are shown in Figure 2 During the experiments alab assistant walked from one AP to the other AP holding aTag with constant speed The localized results are comparedto the real-time recorded actual positions

Then a localization experiment was carried out usingthe RSSI-based fingerprinting localization method under thesame experimental environment In this experiment theAP is deployed in the same manner as in the previousexperiment The positions of the selected 23 reference pointsare shown in Figure 2 In the offline phase the fingerprintdatabase is constructed according to the fingerprint informa-tion collected at the reference points The database is usedfor the matching positioning in the online phase The KNNalgorithm was used as the matching algorithm in the onlinephase and the 119896 value is set as 3 according to the experimentalstatistical data

In the third experiment a TOA fingerprinting localiza-tion method without particle filtering was used Finally the


Staircase

APReference points

Corridor 12Ｇ

Corridor 12

Ｇ

Figure 4 Schematic diagram of the curve corridor environment and experimental deployment

LOS inline corridor

Traditional TOARSSI for FP

TOA for FPTOA-based PF for FP

NLOS inline corridor

NLOS incurve corridor

0

1

2

3

4

5

Mea

n er

ror

05

15

25

35

45

(a)

LOS inline corridor



0

05

1

15

2

25

3

35

4

45

RSM

E



(b)

Figure 5 Performances of the four localization methods under different experimental conditions (a) The mean error under differentexperimental conditions (b) The root mean square error under different experimental conditions

proposed TOA fingerprinting localization method based onparticle filtering was used for the localization experiment Allexperimental parameters and 119896 values are the same as thoseof the second experiment

From the experiments it was determined that the RSSI-based fingerprinting localization method has the highestpositioning error (2974m) by comparing the positioningresults of the four experiments (see Figure 5) In contrast

the positioning accuracy of the TOA-based positioningmethod is much better (0932m) however the localizationaccuracy is further improved using the TOA fingerprintinglocalization method without particle filtering which pro-duced an average positioning error of 0696m Finally thepositioning accuracy is only 0574m for the proposed TOAfingerprinting localizationmethod based on particle filteringAs compared to the traditional TOA localizationmethod and


theTOAfingerprinting localizationmethodwithout filteringthe proposed method results in 384 and 175 increasesin positioning accuracy respectively The root mean squareerror of the traditional TOA localization method is 1131 therootmean square error of theTOAfingerprinting localizationmethodwithout particle filtering is 0693 and that of theTOAfingerprinting localization method based on particle filteringis 0563

43 Experiments in NLOS Propagation In order to test thelocalization performance under NLOS propagation condi-tions the localization experiments were carried out in bothcorridors with different structures as shown in Figures 3 and4

431 Line Corridor In Figure 3 the deployment location ofthe left AP is changed to the red five-star location so thatthere is no LOS propagation path between the left and rightAPs Under this NLOS propagation condition the above fourexperiments were repeated

As shown in Figure 5 in the NLOS propagation envi-ronment the obtained positioning error of the RSSI-basedfingerprinting localizationmethod is relatively large (431m)The localization error obtained by the TOA-based local-ization method also increased as compared to that of theprevious experiment due to the NLOS interference andthe localization error is 2054m The positioning error ofthe TOA-based fingerprinting localization method is 1134mwhen the particle filtering is not used With the proposedTOA fingerprinting localization method based on particlefiltering the NLOS interference is effectively suppressed andthe localization error is only 0767m As compared to thetraditional TOA localizationmethod andTOAfingerprintinglocalization method without filtering the proposed methodresults in 627 and 324 increases in positioning accuracyrespectively In this case the root mean square error of thetraditional TOA localization method is 241 whereas it is0801 for the TOA fingerprinting localization method basedon the particle filtering It is evident from the results thatthe proposed TOA fingerprinting localization method basedon particle filtering greatly improves both the positioningaccuracy and the root mean square error in the line corridorNLOS propagation condition

432 Curve Corridor For the curve corridor the deployedpositions of the APs and the selected nine reference points areshown in Figure 3There is no LOS propagation path betweenthe two APs which is consistent with the NLOS propagationcondition established in this paper The above four experi-ments are repeated under this condition Additionally thedeployed positions of the APs and the selected referencepoints are fixed in all four experiments As mentioned abovethe maximum distance between the APs for establishingstable communication is 24m under this condition Thisdistance is much shorter than that in the line corridor

In the curve corridor the obtained positioning error ofthe RSSI-based fingerprinting localization method is stilllarge (4563m) The obtained positioning error of the TOA-based positioning method is 0964m which is roughly

equivalent to the positioning error under the LOS prop-agation condition and the positioning error of the TOA-based fingerprinting localization method is 0719m Thepositioning error of the proposed TOA fingerprinting local-ization method based on particle filtering is only 0637m Ascompared to the traditional TOA localization method andTOA fingerprinting localization method without filteringthe proposed method results in 339 and 114 increasesin positioning accuracy respectively The root mean squareerror of the traditional TOA localization method is 0832and that of the TOAfingerprinting localizationmethod basedon particle filtering is 0499 The mean error and root meansquare error under the four experimental conditions areshown in Figure 5

44 Results Analysis Figure 6 shows the cumulative dis-tribution function of errors of the four above-mentionedlocalization methods It can be seen from Figure 6(a) thatunder the LOS condition the probability for errors less than50 cm is 40 for the traditional TOA localization methodIn contrast the probability for the TOA fingerprinting local-ization method based on particle filtering is less than 20However the positioning error for the TOA fingerprintinglocalization method based on particle filtering is always lessthan 1m whereas the probability for errors less than 1m forthe traditional TOAmethod is 64These have been reflectedby the crossover points in Figure 6(a) which means thelocalization accuracy of traditional TOA method decreasedmore significantly with distance The positioning accuracyfluctuates greatly that leads to instability of the systemFor the RSSI-based fingerprinting localization method theprobability for positioning errors that are less than 2m is444

It can be seen from Figure 6(b) that under the line cor-ridor NLOS condition the probability for positioning errorsless than 1m for the TOA fingerprinting localization methodbased on particle filtering is 444 and its probability forerrors less than 14m is 9778The probability for errors lessthan 1m for the traditional TOA localizationmethod is 111The positioning error is always larger than 3m for the RSSI-based fingerprinting localization method and its probabilityfor positioning errors less than 4m is 311

Figure 6(c) demonstrates that the error of the RSSI-basedfingerprinting localizationmethod is still large and the prob-ability for errors less than 4m is 294 For the traditionalTOA localization method the probability for errors lessthan 1m is 7059 The error for the TOA fingerprintinglocalization method based on particle filtering is always lessthan 08m and its probability for errors less than 06m is8235

By comparing the four experiments it is apparent thatusing the SDS-TWR method to directly measure raw data issuperior to using the RSSI-based localization method how-ever the data still has a certain error and most of the errorsare within 2m When the excess delay is not suppressed bythe particle filtering the positioning accuracy is improved bycombining the TOA and fingerprinting localization methodThe average positioning error in such a case is 085m How-ever after using the particle filtering to suppress the excess


0 1 15 2 25 3 35 40

01

02

03

04

05

05

06

07

08

09

1

Distance error (m)

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF

In the line corridor LOS case

(a)

Distance error (m)

0010203040506070809

1

func

tion

CD

FCu

mul

ativ

e dist

ribut

ion

0 1 2 3 4 5 6

In the line corridor NLOS case

(b)

Distance error (m)

0010203040506070809

1

func

tion

CD

FCu

mul

ativ

e dist

ribut

ion

0 1 2 3 4 5 6

In the curve corridor NLOS case

(c)

Figure 6 Cumulative distribution functions of errors of the four algorithms under different conditions (a) Cumulative error distribution offour algorithms under line corridor LOS condition (b) Cumulative distribution functions of errors of four algorithms under line corridorNLOS condition (c) Cumulative distribution functions of errors of four algorithms under curve corridor NLOS condition

delay the average positioning error becomes 066m Thelocalization performance is more stable and it shows higherpositioning accuracy and system robustness Therefore theproposed TOA fingerprinting localization method based onparticle filtering can effectively eliminate the influence ofexcess delay It provides more stable higher positioningaccuracy and it has potential for greater application

5 Conclusions

NLOS interference is the most common problem for wirelesscommunication in the mine environment and it is also themain factor that affects mine positioning accuracy In thispaper a TOA fingerprinting localization method based onparticle filtering is proposed for NLOS propagation in amine environment To further optimize the fingerprintingmatching results the proposed method uses TOA rangingdata to construct a fingerprint database in the offline phaseand it uses the particle filtering to suppress the NLOS errorthat is caused by the excess delay in the online phase Basedon the original TOA ranging technique the proposedmethodoptimizes the localization results by direct and indirect

optimization The experimental results demonstrate that theproposed method can significantly improve the performanceof NLOS interference suppression in a mine environment Itobtains a higher positioning accuracy and stronger systemrobustness with lower complexity It has strong adaptability todifferent environments and it is easily transplanted to otherInternet of Things applications that cannot receive satellite-positioning signals

Conflicts of Interest

The authors declare that there are no conflicts of interest withthe publication of this paper

Acknowledgments

The presented work was supported by the fundamentalresearch funds for the central universities (2015XKMS097)

References

[1] J Hopkins and J Turner Go mobile Location-Based MarketingApps Mobile Optimized Ad Campaigns 2D Codes and Other


Mobile Strategies to Grow Your Business John Wiley amp Sons2012

[2] J Shang X Hu F Gu D Wang and S Yu ldquoImprovementschemes for indoor mobile location estimation a surveyrdquoMathematical Problems in Engineering vol 2015 Article ID397298 32 pages 2015

[3] A Chehri P Fortier and P M Tardif ldquoUWB-based sensornetworks for localization in mining environmentsrdquo Ad HocNetworks vol 7 no 5 pp 987ndash1000 2009

[4] Q Hu L Wu F Geng and C Cao ldquoA data transmission algo-rithm based on dynamic grid division for coal goaf temperaturemonitoringrdquo Mathematical Problems in Engineering vol 2014Article ID 652621 8 pages 2014

[5] J M Cabero I Olabarrieta S Gil-Lopez J Del Ser and J LMartın ldquoRange-free localization algorithm based on connectiv-ity andmotionrdquoWireless Networks vol 20 no 8 pp 2287ndash23052014

[6] Q Hu L Wu C Cao and S Zhang ldquoAn event-driven objectlocalizationmethod assisted by beaconmobility and directionalantennasrdquo International Journal of Distributed Sensor Networksvol 2015 Article ID 134964 12 pages 2015

[7] M P Wylie and J Holtzman ldquoNon-line of sight problem inmobile location estimationrdquo in Proceedings of the 1996 5th IEEEInternational Conference on Universal Personal Communica-tions ICUPCrsquo96 Part 1 (of 2) pp 827ndash831 October 1996

[8] B L Le K Ahmed and H Tsuji ldquoMobile location estimatorwith NLOS mitigation using Kalman filteringrdquo in Proceedingsof the 2003 IEEE Wireless Communications and NetworkingConference The Dawn of Pervasive Communication WCNC2003 pp 1969ndash1973 March 2003

[9] ZWu E Jedari R Muscedere and R Rashidzadeh ldquoImprovedparticle filter based on WLAN RSSI fingerprinting and smartsensors for indoor localizationrdquo Computer Communicationsvol 83 pp 64ndash71 2016

[10] K Lin M Chen J Deng M M Hassan and G FortinoldquoEnhanced fingerprinting and trajectory prediction for IoTlocalization in smart buildingsrdquo IEEE Transactions on Automa-tion Science and Engineering no 99 pp 1ndash14 2016

[11] R Guzman-Quiros AMartınez-Sala J L Gomez-Tornero andJ Garcıa-Haro ldquoIntegration of directional antennas in an RSSfingerprinting-based indoor localization systemrdquo Sensors vol16 no 1 article 4 2015

[12] Z Gu Z Chen and Y Zhang ldquoReducing fingerprint collectionfor indoor localizationrdquo Computer Communications vol 83 pp56ndash63 2016

[13] P Bahl and V N Padmanabhan ldquoRADAR An in-building RF-based user location and tracking systemrdquo in Proceedings of theNineteenth Annual Joint Conference of the IEEE Computer andCommunications Societies INFOCOM2000 vol 2 pp 775ndash784IEEE 2000

[14] K Lorincz and W M Motetrack ldquoA robust decentralizedapproach to RF-based location trackingrdquo in InternationalSymposium on Location-and Context-Awareness pp 63ndash82Springer Berlin Germany 2005

[15] M Youssef andAAgrawala ldquoTheHorusWLAN location deter-mination systemrdquo in Proceedings of the 3rd International Confer-ence onMobile Systems Applications and Services (MobiSys rsquo05)pp 205ndash218 ACM June 2005

[16] GWang H Chen Y Li andN Ansari ldquoNLOS errormitigationfor TOA-based localization via convex relaxationrdquo IEEE Trans-actions onWireless Communications vol 13 no 8 pp 4119ndash41312014

[17] S Zhang S Gao G Wang and Y Li ldquoRobust NLOS errormitigation method for TOA-based localization via second-order cone relaxationrdquo IEEE Communications Letters vol 19no 12 pp 2210ndash2213 2015

[18] M Horiba E Okamoto T Shinohara and K MatsumuraldquoAn accurate indoor-localization scheme with NLOS detectionand elimination exploiting stochastic characteristicsrdquo IEICETransactions on Communications vol E98B no 9 pp 1758ndash1767 2015

[19] Y T Chan W Y Tsui H C So and P C Ching ldquoTime-of-arrival based localization under NLOS conditionsrdquo IEEE Trans-actions on Vehicular Technology vol 55 no 1 pp 17ndash24 2006

[20] J Schroeder S Galler K Kyamakya and T Kaiser ldquoThree-dimensional indoor localization in Non Line of Sight UWBchannelsrdquo in Proceedings of the 2007 IEEE International Confer-ence on Ultra-Wideband ICUWB pp 89ndash93 September 2007

[21] S J McKenna and H Nait-Charif ldquoTracking human motionusing auxiliary particle filters and iterated likelihood weight-ingrdquo Image and Vision Computing vol 25 no 6 pp 852ndash8622007

[22] A Giremus J-Y Tourneret and P M Djuric ldquoAn improvedregularized particle filter for GPSINS integrationrdquo in Proceed-ings of the IEEE 6th Workshop on Signal Processing Advancesin Wireless Communications (SPAWC rsquo05) pp 1013ndash1017 NewYork NY USA June 2005

[23] X Jiang Y Chen J Liu D Liu Y Gu and Z Chen ldquoReal-timeand accurate indoor localization with fusion model of Wi-Fifingerprint and motion particle filterrdquo Mathematical Problemsin Engineering vol 2015 Article ID 545792 13 pages 2015

[24] Y Shu Y Huang J Zhang et al ldquoGradient-based fingerprintingfor indoor localization and trackingrdquo IEEE Transactions onIndustrial Electronics vol 63 no 4 pp 2424ndash2433 2016

[25] M V Moreno-Cano M A Zamora-Izquierdo J Santa and AF Skarmeta ldquoAn indoor localization system based on artificialneural networks and particle filters applied to intelligent build-ingsrdquo Neurocomputing vol 122 pp 116ndash125 2013

[26] H-WMa and X-P Li ldquoThe theoretical research on localizationusing improved particle filter formine rescue robot in unknownunderground spacerdquo Journal of Coal Science and Engineeringvol 14 no 3 pp 497ndash500 2008

[27] D Zhu and K Yi ldquoParticle filter localization in undergroundmines using UWB rangingrdquo in Proceedings of the 2011 4thInternational Conference on Intelligent Computation Technologyand Automation ICICTA 2011 pp 645ndash648 March 2011

[28] D Li B Zhang Z Yao and C Li ldquoA feature scaling basedk-nearest neighbor algorithm for indoor positioning systemrdquoin Proceedings of the IEEE Global Communications Conference(GLOBECOM rsquo14) pp 436ndash441 IEEE Austin Tex USADecember 2014

[29] A Taok N Kandil S Affes and S Georges ldquoFingerprintinglocalization using ultra-wideband and neural networksrdquo inProceedings of the International Symposium on Signals Systemsand Electronics (ISSSE rsquo07) pp 529ndash532 Montreal CanadaAugust 2007

[30] J Sun and C Li ldquoTunnel personnel positioning methodbased on TOA and modified location-fingerprint positioningrdquoInternational Journal of Mining Science and Technology vol 26no 3 pp 429ndash436 2016

[31] MH Kabir and R Kohno ldquoA hybrid TOA-fingerprinting basedlocalization of mobile nodes using UWB signaling for non line-of-sight conditionsrdquo Sensors vol 12 no 8 pp 11187ndash11204 2012


[32] H-S Ahn H Hwan and W-S Choi ldquoOne-way rangingtechnique for css-based indoor localizationrdquo in Proceedings ofthe IEEE INDIN 2008 6th IEEE International Conference onIndustrial Informatics pp 1513ndash1518 July 2008

[33] H Kim ldquoDouble-sided two-way ranging algorithm to reduceranging timerdquo IEEE Communications Letters vol 13 no 7 pp486ndash488 2009

[34] L J Xing L Zhiwei and F C P Shin ldquoSymmetric double sidetwo way ranging with unequal reply timerdquo in Proceedings of theIEEE 66thVehicular TechnologyConference (VTC rsquo07) pp 1980ndash1983 October 2007

[35] Y Chen D Lymberopoulos J Liu and B Priyantha ldquoIndoorlocalization using FM signalsrdquo IEEE Transactions on MobileComputing vol 12 no 8 pp 1502ndash1517 2013

[36] A Farshad J Li M K Marina and F J Garcia ldquoA microscopiclook at WiFi fingerprinting for indoor mobile phone localiza-tion in diverse environmentsrdquo inProceedings of the InternationalConference on Indoor Positioning and Indoor Navigation (IPINrsquo13) pp 1ndash10 IEEE October 2013

[37] J Niu B Lu L Cheng Y Gu and L Shu ldquoZiLoc energyefficient WiFi fingerprint-based localization with low-powerradiordquo in Proceedings of the Proceeding of the IEEE WirelessCommunications and Networking Conference (WCNC rsquo13) pp4558ndash4563 Shanghai China April 2013

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


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Differential EquationsInternational Journal of

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Applied MathematicsJournal of


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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


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Algebra

Discrete Dynamics in Nature and Society



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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


is an indirect method This technology is also one of themost commonly used mine localization technologies and itis usually divided into two phases the offline Training phaseand Online Matching phase The task of the offline Trainingphase is to collect the signal characteristic parameter whichis usually the RSSI from different APs at the referencepointsThese collected parameters are then used to constructthe fingerprinting database In the Online Matching phasethe similarity matching between the current collected datawith fingerprinting database is conducted to obtain the bestestimation

Because fingerprinting localization methods have lowcomputational complexity and good performance for sup-pressing NLOS error there has been a lot of researchpublished on fingerprinting localization methods in the pastfew years Lin et al [10] proposed a method to construct afingerprint database by using the correlated RSSI of adjacentnodesTheMarkov chain predictionmodel was used to assistthe localization Guzman-Quiros et al [11] applied direc-tional antennas to the RSSI-based fingerprinting localizationmethod which reduced the required number of sensorsand improved the localization success rate To reduce theworkload of collecting fingerprint data in the offline phaseGu et al used compressed sensing to reduce the amount ofcollected fingerprint data [12]

Although the TOA-based ranging method can overcomesome shortcomings associated with RSSI NLOS propagationstill seriously impacts the localization accuracy In thispaper a TOA fingerprinting localization method based onparticle filtering is proposed according to the characteristicsof the fingerprinting localization method and TOA rangingtechnology The TOA ranging result vectors are stored ina fingerprint database and the 119896-nearest neighbour (KNN)algorithm is used to estimate the positions The proposedmethod uses both direct and indirect methods to suppressthe NLOS error When NLOS interference exists the TOAlocalization result can be greatly optimized The structure ofthe paper is as follows Section 2 summarizes the work relatedto the field of particle filtering and fingerprinting localizationSection 3 details the proposed method for constructing aTOA fingerprint database based on particle filtering and theposition estimation is performed by theKNNmatching local-ization method In Section 4 the localization performanceof the proposed method is experimentally tested Section 5concludes the paper

2 Related Works

Because indoor positioning technology offers wide appli-cation prospects many researchers have proposed differentindoor wireless positioning technologies in the past fewyears and consequently a large number of research resultshave been published on the topic One such example is thefirst developed RADAR system [13] which utilizes empiricaldata and the attenuation factor model The localization of amoving target is achieved using a pattern recognitionmethodafter the completion of data acquisition The MoteTracksystem [14] andHorus system [15] are also indoor positioningsystem based on RSSI These works laid a good foundation

for further improving the accuracy and robustness of indoorpositioning

The NLOS propagation phenomenon caused by obsta-cles is an important factor affecting wireless positioningaccuracy for coal mines For this reason direct or indirectoptimization can be used to eliminate or reduce the influenceof NLOS Direct optimization methods primarily includeKalman filtering particle filtering convex relaxation [1617] and iterative minimum residual method [18] Indirectoptimization methods mainly include the fingerprintingpositioning method Chan algorithm [19] and geometricprojection method [20] However the system performanceof a single optimization method has certain limitationsTherefore to suppress theNLOSpropagation error this paperutilizes both the particle filtering and fingerprinting methodto combine the advantages of direct optimization and indirectoptimization

Particle filtering combines the Bayesian filtering methodwith the Monte Carlo method It approximates the posteriorprobability distribution of random variables in a system bya series of weighted discrete random sampling points Thereare many kinds of particle filtering The most commonlyused are auxiliary particle filtering [21] regularized particlefiltering [22] adaptive particle filtering and so forth Particlefiltering has a wide range of application in the field of minepositioning and indoor positioning Jiang et al [23] combinedparticle filtering with Wi-Fi-based positioning informationand motion sensor information to obtain a more accurateand smooth target moving trajectory Based on the ideaof gradient fingerprinting positioning technology Shu etal [24] combined multiple dynamic detection results withextended particle filtering to obtain positioning for users andequipment Moreno-Cano et al [25] used particle filteringto track and predict the position and trajectory of movingtargets in positioning systems based on RFID and thermalinfrared Ma and Li [26] improved the positioning accuracyof mine rescue robots using modified particle filtering ZhuandYi [27] proposed amine undergroundpositioning systembased on UWB and the NLOS interference in the mineunderground is suppressed by using particle filtering

Fingerprinting localization includes an offline phase andan online phase The key to the Online Matching phaseis the design and selection of the pattern-matching algo-rithm which directly determines the positioning accuracyPresently the KNN algorithm and the weighted 119896-nearestneighbour (WKNN) algorithm [13] are the most commonlyused matching algorithms In [28] Li et al proposed a KNNalgorithm based on feature scaling Although their algorithmdoes consider the fact that the distance between RSSI vectorsin the fingerprint database and the actual distance are notperfectly matched their algorithm does not completely over-come the disadvantage that the RSSI can easily attenuate Atpresent most of the fingerprinting localization methods arebased on RSSI however in practical applications the com-plex mine environment will affect the way the RSSI changesusually resulting in low positioning accuracy for RSSI-basedmethods In order to overcome the shortcomings of RSSI-based localization technology Taok et al proposed an UWBfingerprinting localization method based on neural network


Node 1

Node 2

T1

T2 T3

T4

T5

T6 T7

T8

TＬＩＯＨ＞ 1

TＬＩＯＨ＞ 2

TＬＪＦＳ 1

TＬＪＦＳ 2











X119896+1 = 120593X119896 + 120574120596119896 (2)

119884119896 = H (X119896) + 120579119896 (3)

where120593 = [ 1 11987900 1

] 120574 = [ 0511987920 00 1198790






0 100 200 300 400 500 600 700 800 9000

20

40

60

80

100

120

Rang

ing

resu

lts (m



(a)

0 100 200 300 400 500 600 700 800 9000

5

10

15

20

25

30

35

Rang

ing

erro

rs (m

)



(b)



H (X119896) = 1003816100381610038161003816119904 minus 1199041198961003816100381610038161003816 (5)



[[[[[[[[[


]]]]]]]]] (6)



119889119894 = radic 119869sum119895=1

(Dis119894119895 minus 119901119895)2 (7)


119889119894 = 119869sum119895=1

10038161003816100381610038161003816Dis119894119895 minus 11990111989510038161003816100381610038161003816 (8)



Staircase


Corridor 60Ｇ













Staircase

APReference points

Corridor 12Ｇ

Corridor 12

Ｇ


LOS inline corridor





0

1

2

3

4

5

Mea

n er

ror

05

15

25

35

45

(a)

LOS inline corridor



0

05

1

15

2

25

3

35

4

45

RSM

E



(b)


















0 1 15 2 25 3 35 40

01

02

03

04

05

05

06

07

08

09

1

Distance error (m)

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF


(a)

Distance error (m)

0010203040506070809

1

func

tion

CD

FCu

mul

ativ

e dist

ribut

ion

0 1 2 3 4 5 6


(b)

Distance error (m)

0010203040506070809

1

func

tion

CD

FCu

mul

ativ

e dist

ribut

ion

0 1 2 3 4 5 6


(c)



5 Conclusions





Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





Node 1

Node 2

T1

T2 T3

T4

T5

T6 T7

T8

TＬＩＯＨ＞ 1

TＬＩＯＨ＞ 2

TＬＪＦＳ 1

TＬＪＦＳ 2











X119896+1 = 120593X119896 + 120574120596119896 (2)

119884119896 = H (X119896) + 120579119896 (3)

where120593 = [ 1 11987900 1

] 120574 = [ 0511987920 00 1198790






0 100 200 300 400 500 600 700 800 9000

20

40

60

80

100

120

Rang

ing

resu

lts (m



(a)

0 100 200 300 400 500 600 700 800 9000

5

10

15

20

25

30

35

Rang

ing

erro

rs (m

)



(b)



H (X119896) = 1003816100381610038161003816119904 minus 1199041198961003816100381610038161003816 (5)



[[[[[[[[[


]]]]]]]]] (6)



119889119894 = radic 119869sum119895=1

(Dis119894119895 minus 119901119895)2 (7)


119889119894 = 119869sum119895=1

10038161003816100381610038161003816Dis119894119895 minus 11990111989510038161003816100381610038161003816 (8)



Staircase


Corridor 60Ｇ













Staircase

APReference points

Corridor 12Ｇ

Corridor 12

Ｇ


LOS inline corridor





0

1

2

3

4

5

Mea

n er

ror

05

15

25

35

45

(a)

LOS inline corridor



0

05

1

15

2

25

3

35

4

45

RSM

E



(b)


















0 1 15 2 25 3 35 40

01

02

03

04

05

05

06

07

08

09

1

Distance error (m)

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF


(a)

Distance error (m)

0010203040506070809

1

func

tion

CD

FCu

mul

ativ

e dist

ribut

ion

0 1 2 3 4 5 6


(b)

Distance error (m)

0010203040506070809

1

func

tion

CD

FCu

mul

ativ

e dist

ribut

ion

0 1 2 3 4 5 6


(c)



5 Conclusions





Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





0 100 200 300 400 500 600 700 800 9000

20

40

60

80

100

120

Rang

ing

resu

lts (m



(a)

0 100 200 300 400 500 600 700 800 9000

5

10

15

20

25

30

35

Rang

ing

erro

rs (m

)



(b)



H (X119896) = 1003816100381610038161003816119904 minus 1199041198961003816100381610038161003816 (5)



[[[[[[[[[


]]]]]]]]] (6)



119889119894 = radic 119869sum119895=1

(Dis119894119895 minus 119901119895)2 (7)


119889119894 = 119869sum119895=1

10038161003816100381610038161003816Dis119894119895 minus 11990111989510038161003816100381610038161003816 (8)



Staircase


Corridor 60Ｇ













Staircase

APReference points

Corridor 12Ｇ

Corridor 12

Ｇ


LOS inline corridor





0

1

2

3

4

5

Mea

n er

ror

05

15

25

35

45

(a)

LOS inline corridor



0

05

1

15

2

25

3

35

4

45

RSM

E



(b)


















0 1 15 2 25 3 35 40

01

02

03

04

05

05

06

07

08

09

1

Distance error (m)

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF


(a)

Distance error (m)

0010203040506070809

1

func

tion

CD

FCu

mul

ativ

e dist

ribut

ion

0 1 2 3 4 5 6


(b)

Distance error (m)

0010203040506070809

1

func

tion

CD

FCu

mul

ativ

e dist

ribut

ion

0 1 2 3 4 5 6


(c)



5 Conclusions





Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





Staircase


Corridor 60Ｇ













Staircase

APReference points

Corridor 12Ｇ

Corridor 12

Ｇ


LOS inline corridor





0

1

2

3

4

5

Mea

n er

ror

05

15

25

35

45

(a)

LOS inline corridor



0

05

1

15

2

25

3

35

4

45

RSM

E



(b)


















0 1 15 2 25 3 35 40

01

02

03

04

05

05

06

07

08

09

1

Distance error (m)

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF


(a)

Distance error (m)

0010203040506070809

1

func

tion

CD

FCu

mul

ativ

e dist

ribut

ion

0 1 2 3 4 5 6


(b)

Distance error (m)

0010203040506070809

1

func

tion

CD

FCu

mul

ativ

e dist

ribut

ion

0 1 2 3 4 5 6


(c)



5 Conclusions





Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





Staircase

APReference points

Corridor 12Ｇ

Corridor 12

Ｇ


LOS inline corridor





0

1

2

3

4

5

Mea

n er

ror

05

15

25

35

45

(a)

LOS inline corridor



0

05

1

15

2

25

3

35

4

45

RSM

E



(b)


















0 1 15 2 25 3 35 40

01

02

03

04

05

05

06

07

08

09

1

Distance error (m)

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF


(a)

Distance error (m)

0010203040506070809

1

func

tion

CD

FCu

mul

ativ

e dist

ribut

ion

0 1 2 3 4 5 6


(b)

Distance error (m)

0010203040506070809

1

func

tion

CD

FCu

mul

ativ

e dist

ribut

ion

0 1 2 3 4 5 6


(c)



5 Conclusions





Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of

















0 1 15 2 25 3 35 40

01

02

03

04

05

05

06

07

08

09

1

Distance error (m)

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF


(a)

Distance error (m)

0010203040506070809

1

func

tion

CD

FCu

mul

ativ

e dist

ribut

ion

0 1 2 3 4 5 6


(b)

Distance error (m)

0010203040506070809

1

func

tion

CD

FCu

mul

ativ

e dist

ribut

ion

0 1 2 3 4 5 6


(c)



5 Conclusions





Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





0 1 15 2 25 3 35 40

01

02

03

04

05

05

06

07

08

09

1

Distance error (m)

Cum

ulat

ive d

istrib

utio

n fu

nctio

n C

DF


(a)

Distance error (m)

0010203040506070809

1

func

tion

CD

FCu

mul

ativ

e dist

ribut

ion

0 1 2 3 4 5 6


(b)

Distance error (m)

0010203040506070809

1

func

tion

CD

FCu

mul

ativ

e dist

ribut

ion

0 1 2 3 4 5 6


(c)



5 Conclusions





Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of


















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of


















Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of











Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Documents

Fingerprinting Localization Method Based on TOA and Particle …downloads.hindawi.com/journals/mpe/2017/3215978.pdf · 2019. 7. 30. · of a UWB-based fingerprinting localization