A Mobile Positioning Method Based on Deep Learning Techniques

Transcription

1 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v Artcle A Moble Postonng Method Based on Deep Learnng Technques Lng Wu Ch-Hua Chen * and Qshan Zhang School of Economcs and Management Fuhou Unversty Fuhou 3506 Chna; wulng985@fu.edu.cn; hangqs@fu.edu.cn College of Mathematcs and Computer Scence Fuhou Unversty Fuhou 3506 Chna; wulng985@fu.edu.cn; chhua086@ fu.edu.cn * Correspondence: chhua086@fu.edu.cn; Tel.: Abstract: Ths study proposes a moble postonng method whch adopts recurrent neural network algorthms to analye the receved sgnal strength ndcatons from heterogeneous networks (e.g. cellular networks and W-F networks) for estmatng the locatons of moble statons. The recurrent neural networks wth multple consecutve tmestamps can be appled to extract the features of tme seres data for the mprovement of locaton estmaton. In practcal expermental envronments there are 455 records 59 dfferent base statons and 58 dfferent W-F access ponts detected n Fuhou Unversty n Chna. The lower locaton errors can be obtaned by the recurrent neural networks wth multple consecutve tmestamps (e.g. tmestamps and 3 tmestamps); the expermental results can be observed that the average error of locaton estmaton was 9.9 meters by the proposed moble postonng method wth tmestamps. Keywords: deep learnng; recurrent neural networks; moble postonng method; fngerprntng postonng method; receved sgnal strength. Introducton Wth the development of wreless networks and moble networks the technques of locatonbased servces (LBS) can provde the correspondng servces to the users accordng to users current locatons. LBS whch have played an mportant role n many felds requre the hgh accuracy of postonng technology [-3]. For the LBS n outdoor envronments global postonng system (GPS) and asssted GPS (A- GPS) are popular technques and meet most of the postonng requrements. However these technques may be no longer applcable f the problems of mult-path propagaton of wreless sgnals exst [0]. Furthermore hgher power consumptons are requred by these technques []. Therefore some studes proposed cellular-based postonng methods to analye the sgnals of cellular networks for locaton estmaton [ ]. Although cellular-based postonng methods can estmate the locatons of moble statons wthout GPS modules bg errors of estmated locatons may be obtaned. For the LBS n ndoor envronments W-F-based postonng methods are popular technques to detect and analye the receved sgnal strength ndcatons (RSSIs) from W-F access ponts (APs) [7 4 8-]. The fngerprntng postonng methods based on machne learnng algorthms were proposed to learnng the relatonshps among locatons and RSSIs for the estmaton of locatons. Although these methods can estmate the locatons of moble statons wthout GPS modules bg errors of estmated locatons may be obtaned. Although hgher precse estmated locatons can be obtaned by W-F-based postonng methods these methods may be nvald n outdoor envronments f the transmsson coverage of W-F APs s not enough. Some deep learnng methods (e.g. neural networks convolutonal neural networks recurrent neural networks etc.) have been appled to mprove the accuraces of estmaton locatons [ ]. For nstance a modfed probablty neural network was used for ndoor postonng and the 08 by the author(s). Dstrbuted under a Creatve Commons CC BY lcense.

2 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v of 0 accuraces of estmated locatons by the method were hgher than trangulaton technque [8]. An mproved neural network was traned wth the correlaton of the ntal parameters to acheve the hghest possble accuracy of the W-F-based postonng method n ndoor envronments []. Although cellular-based postonng methods can obtan estmated locatons n outdoor envronments the errors of estmated locatons may be larger. Furthermore W-F-based postonng methods can obtan hgher precse locatons but these methods may be not applcable n outdoor envronments. Therefore ths study proposed a moble postonng method to analye the network sgnals from heterogeneous networks (e.g. cellular networks and W-F networks) for the LBS n outdoor envronments. Furthermore the recurrent neural networks [4] are appled nto the proposed moble postonng method for the analyses of consecutve locatons and network sgnals (.e. tme seres data). The remander of the paper s organed as follows. Secton provdes the overvew of moble postonng methods and fngerprntng postonng methods. Secton 3 presents the proposed moble postonng system and method based on recurrent neural networks. The practcal expermental results and dscussons are llustrated n Secton 4. Fnally conclusons and future work are gven n Secton 5.. Related Work Moble postonng methods and fngerprntng postonng methods ncludes two stages: tranng stage and performng stage (shown n Fgure ). In tranng stage the RSSIs and locatons measured by the moble statons are matched and stored nto a fngerprntng database for tranng. Machne learnng methods can be performed to learn the relatonshps among RSSIs and locatons for the establshments of moble postonng models. In performng stage moble statons can detect the RSSIs of neghbor base statons and W-F APs whch can be adopted nto the traned models to estmate the locatons of these moble statons. Tranng Stage The RSSI of WF Access Pont The RSSI of WF Access Pont The RSSI n of WF Access Pont n The longtude and lattude of Locaton Fngerprntng Database Locaton : RSSI RSSI.. RSSI n Locaton : RSSI RSSI.. RSSI n Locaton m : RSSI RSSI.. RSSI n Performng Stage RSSI RSSI.. RSSI n Machne Learnng Methods The longtude and lattude of Estmated Locaton Fgure. Fngerprntng postonng method For tranng the moble postonng models some studes used k nearest neghbors Bayesan theory support vector machne neural networks convolutonal neural networks or recurrent neural networks to estmate locatons n accordance wth RSSIs. For nstance a probablstc postonng algorthm was proposed to store the probablty dstrbuton of RSSIs durng a certan tme n the fngerprntng database and the probable locatons of moble statons were calculated by a Bayesan theory system [4]. However the relatonshps among nputs were assumed as ndependent parameters so bg errors of estmated locatons may be obtaned f the nputs were not ndependent parameters. Some moble postonng methods based on k nearest neghbor algorthms can obtan hgher accuraces of estmated locatons but these methods requred more computaton tme n performng stage. Some neural networks have been proposed to analye the nterrelated nfluences of nputs for the mprovement of locaton estmaton [ 8-0] and convolutonal neural networks

3 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v 3 of 0 were appled to extract the features of spato metrcs []. Although the spato metrcs may be analyed by neural networks and convolutonal neural networks these methods cannot provde the solutons of temporal data analyses. Therefore ths study apples recurrent neural networks to analye the temporal data for mprovng the accuraces of estmaton locatons. 3. Moble Postonng System and Method The archtecture of the proposed moble postonng system s presented n Subsecton 3. and the concepts of the proposed moble postonng method are llustrated n Subsecton Moble Postonng System The proposed moble postonng system ncludes () moble statons () a moble postonng server (3) a database server and (4) a model server (shown n Fgure ). Each component n the proposed system s presented n the followng subsectons. Database Server Moble Staton Base Staton WF Access Pont Moble Postonng Server Collecton and Normalaton Moble Postonng Method De-normalaton and Estmaton Network Sgnals GPS Coordnates Model Server Recurrent Neural Networks Fgure. The proposed moble postonng system 3... Moble Statons In tranng stage moble statons can detect and receve the RSSIs of neghbor base statons and W-F APs from heterogeneous networks. GPS modules can be equpped nto the moble statons and estmate the locatons of moble statons (.e. coordnates). Then the moble statons can send the vectors of GPS coordnates (.e. longtudes and lattudes) and RSSIs to the moble postonng server for the collecton of network sgnals. In performng stage moble statons can send the detected RSSIs of neghbor base statons and W-F APs to the moble postonng server for locaton estmaton Moble Postonng Server In tranng stage the moble postonng server can receve GPS coordnates and network sgnals (.e. the RSSIs of base statons and W-F APs) from moble statons. These GPS coordnates and network sgnals can be sent to the database server for storng. The moble postonng server can execute the proposed moble postonng method to tran RNN models. The network sgnals can be used as the nput layer of the RNN models and the GPS coordnates can be used as the output layer of the RNN models. Once the RNN models have been traned these models can be sent to the model server for savng. In performng stage the moble postonng server can load the traned RNN models from the model server. When the moble postonng server receves network sgnals from moble statons these network sgnals can be adopted nto the traned RNN models for estmatng the locatons of moble statons Database Server

4 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v 4 of 0 The database server can store the vectors of coordnates (.e. longtudes and lattudes) and RSSIs from moble statons va the moble postonng server. These vectors can be quered and used to tran RNN models Model Server The model server can save the traned RNN models from the moble postonng server n tranng stage and the saved RNN models can be loaded for locaton estmaton by the moble postonng server. 3.. Moble Postonng Method The proposed moble postonng method ncludes () collecton and normalaton () the executon of moble postonng method based on recurrent neural networks (3) de-normalaton and estmaton. Each step n the proposed method s presented n the followng subsectons Collecton and Normalaton For the collecton of network sgnals and GPS coordnates the RSSIs of base statons from cellular networks (.e. R c n Equaton ()) and the GPS coordnates (.e. the moble staton at tme network at tme tme t t s defned as W-F networks) at tme t s defned as r w k t n Equaton ()) the RSSIs of W-F APs from W-F networks (.e. l R w n Equaton (3)) can be detected and collected by (shown n Fgure 3). The RSSI of the j-th base staton from a cellular r c j and the RSSI of the k-th W-F AP from a W-F network at. The RSSI dataset of heterogeneous networks (.e. cellular networks and s defned as (.e. a GPS coordnate) ncludes a longtude R (shown n Equaton (4)). Furthermore the locaton l x and a lattude l y. There are m locatons n dfferent base statons and n dfferent W-F APs detected n the experments. If the RSSIs of base statons or W-F APs cannot be detected the values of these RSSIs can be encoded as null. For nstance the moble staton cannot detect the RSSI of W-F AP at tme of r w s encoded as null. R r r... r c c c c n t n Fgure 3 so the value = () R = r r... r w w w w n l = l l x y R = R R c w = r r... r r r... r c c c n w w w n () (3) (4) l

5 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v 5 of 0 Base Staton Base Staton r c+ r c r c r w+ r w r w+ r w r w+ WF Access Pont WF Access Pont Fgure 3. The scenaro of network sgnal and GPS coordnate collecton For the normalaton of network sgnals and GPS coordnates the mnmum values and maxmum values of RSSIs and coordnates are consdered and adopted nto Equatons (5) (6) (7) and (8). The normaled RSSI of the j-th base staton from a cellular network at tme c j n accordance wth the mnmum value and maxmum value of the RSSIs (.e. t ( ) r c s defned as n Equaton (5)) from cellular networks; the normaled RSSI of the k-th W-F APs from a cellular network at tme t of the RSSIs (.e. s defned as ( ) r w and normaled longtude at tme maxmum value of longtudes (.e. normaled lattude at tme maxmum value of lattudes (.e. Locaton l at tme t Locaton l + at tme t + t t w k ( ) r + w and ( ) r + c n accordance wth the mnmum value and maxmum value n Equaton (6)) from W-F networks. Furthermore the s defned as ( ) l x and s defned as ( ) l y and x ( ) l + x ( ) l + y y n accordance wth the mnmum value and n Equaton (7)) from GPS coordnates and the n accordance wth the mnmum value and n Equaton (8)) from GPS coordnates. ( ) rc j rc f r ( ) ( ) c j null + ( + ) ( ) c = r r where r = max r r = mn r 0otherwse j c c c c p q c c p q pn qm pn qm (5) ( ) rw k rw f r ( ) ( ) w k null + ( + ) ( ) w = r r where r = max r r = mn r 0otherwse k w w w w p q w w p q pn qm pn qm (6) ( ) lx lx f l ( ) ( ) x null + ( + ) ( ) x = l l where l = max l l = mn l 0otherwse x x x x q x x q qm qm ( ) ly ly f l ( ) ( ) y null + ( + ) ( ) y = l l where l = max l l = mn l 0otherwse y y y y q y y q qm qm (7) (8)

6 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v 6 of Moble Postonng Method Based on Recurrent Neural Network The proposed moble postonng method adopts recurrent neural network algorthms to estmate the locatons of moble statons. The recurrent neural networks can be appled to extract the features of tme seres data so ths study consders and analyes the normaled RSSIs wth multple consecutve tmestamps. Subsecton 3... presents recurrent neural networks wth one tmestamp and Subsecton 3... descrbes recurrent neural networks wth multple consecutve tmestamps Recurrent Neural Networks wth One Tmestamp Ths subsecton shows the desgns and optmaton of recurrent neural networks wth one tmestamp. A smple case study of a recurrent neural network wth one tmestamp s llustrated n Fgure 4. The recurrent neural network s constructed wth an nput layer a recurrent hdden layer and an output layer. The nput layer ncludes the normaled RSSIs of two base statons and two W- F APs (.e. c c w and w) and the output layer ncludes the estmated normaled longtude and lattude (.e. x% and y%). The recurrent hdden layer ncludes a neuron and the ntal value of the neuron n the recurrent hdden layer s defned as h0. The value of the neuron n the recurrent hdden layer can be updated as h after calculatng the RSSIs n the frst tmestamp. The weghts of c c w w and h0 are and and v; the weghts of h for the outputs x% and respectvely. The bases of neurons n the hdden layer and the output layer are defned as b b and b3. The sgmod functon s elected as the actvaton functon of each neuron so the values of h0 h x% and can be calculated by Equatons (9) (0) () and (). Furthermore the y% loss functon s defned as Equaton (3) n accordance wth squared errors. y% are h 0 = 0 (9) h = s c + w + v h0 + b = s s = j= k= + e j j k k ( ) where ( ) (0) x%= s( h + b ) = s ( ) where s ( ) = + e y%= s( h + b3 ) = s ( 3 ) where s ( ) = + e E = ( x% x ) + ( y% y ) = + () () (3) b b 3 h 0 v h b c c w w Fgure 4. A recurrent neural network wth one tmestamp

7 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v 7 of 0 For the optmaton of recurrent neural network the learnng rate and a gradent descent method s appled to update each weght and bas. The updates of v and b and (3) respectvely. E = where are proved and calculated by Equatons (4) (5) (6) (7) (8) (9) (0) () () E E x% E y% x% y% 3 3 = x% x% h b b 3 (4) E = where E E x% E y% x% y% b 3 3 = y% y% h E = b b 3 3 = x% x% where E E x% E y% b x% b y% b b E = b b = y% y% where E E x% E y% b x% b y% b E = where E E x% h E y% 3 h x% h y% h 3 E x% E y% 3 h x h y 3 h % % % % % % = x x + y y h h c (5) (6) (7) (8)

8 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v 8 of 0 E = where E E x% h E y% 3 h x% h y% h 3 E x% E y% 3 h x h y 3 h % % % % % % = x x + y y h h c E = where E E x% h E y% 3 h x% h y% h 3 E x% E y% 3 h x h y 3 h % % % % % % = x x + y y h h w E = where E E x% h E y% h x% h y% h 3 3 E x% E y% 3 h x h y 3 h % % % % % % = x x + y y h h w E v= v where v E E x% h E y% h v x% h v y% h v 3 3 E x% E y% h x h y 3 h % % v 3 % % % % = x x + y y h h h 0 (9) (0) () ()

9 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v 9 of 0 b E = b b where E E x% h E y% h b x% h b y% h b 3 3 E x% E y% x% h y% h 3 3 h x% x% y% y% h h b = + (3) For the generalaton of recurrent neural network the number of base statons and the number of W-F APs can be extended as n and n n the nput layer (shown n Fgure 5). The value of h can be revsed and calculated by Equaton (4); the updates of by Equatons (5) and (6) respectvely. n n h = s c + w + v h0 + b = s s = j= k= + e j and k are proved and calculated j j k k ( ) where ( ) (4) E j = j where j E E x% h E y% 3 h x% h y% h j 3 j E x% E y% 3 h x h y 3 h % % j % % % % = x x + y y h h c j E k = k where k E E x% h E y% h x% h y% h 3 k 3 k E x% E y% 3 h x h y 3 h % % k % % % % = x x + y y h h w k (5) (6)

10 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v 0 of 0 b b 3 h 0 v h b c w Fgure 5. A generaled recurrent neural network wth one tmestamp Furthermore the number of neurons n the recurrent hdden layer can be extended for the extracton of tme seres data. The weght between each two neurons can be updated by the gradent descent method Two Tmestamps for Recurrent Neural Network Ths subsecton llustrates the desgns and optmaton of recurrent neural networks wth two consecutve tmestamps. A smple case study of a recurrent neural network wth two consecutve tmestamps s showed n Fgure 6. In the case the recurrent neural network s constructed wth an nput layer a recurrent hdden layer and an output layer. The nput layer ncludes four normaled RSSIs (.e. c c w and w) n the frst tmestamp and four normaled RSSIs (.e. c+ c+ w+ and w+) n the second tmestamp; the output layer ncludes the estmated normaled longtude and lattude (.e. x % + and y % + ) n the second tmestamp. The recurrent hdden layer ncludes a neuron and the ntal value of the neuron n the recurrent hdden layer s defned as h0 (shown n Equatons (9)). The value of the neuron n the recurrent hdden layer can be updated as h n the frst tmestamp and be updated as h n the second tmestamp. The weghts of Base Staton Base Staton W-F AP and W-F AP n each tmestamp are % x + and % y + are and and ; the weghts of h for the outputs respectvely. Furthermore the weght of the neurons n the recurrent hdden layer n least tmestamp s defned as v. In the case the bases of neurons n the hdden layer and the output layer are defned as b b and b3. The sgmod functon s elected as the actvaton functon of each neuron so the values of h h x% and y% can be calculated by Equatons (7) (8) (9) and (30). Furthermore the loss functon s defned as Equaton (3) n accordance wth squared errors. h = s c + w + v h0 + b = s s = j= k= + e j j k k ( ) where ( ) (7) h = s c + w + v h + b = s ( ) where s ( ) = j j + k k + j= k= + e x% = s( h + b ) = s( ) where s ( ) = + e + y% = s( h + b ) = s( ) where s ( ) = + e (8) (9) (30)

11 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v of 0 E = ( x% x ) + ( y% y ) = (3) b b 3 h v 0 h v h b b c c w w c + c + w + w + Fgure 6. A recurrent neural network wth two consecutve tmestamps For the optmaton of recurrent neural network wth two consecutve tmestamps the learnng rate and a gradent descent method s appled to update each weght and bas. The updates of b b 3 v and b (34) (35) (36) (37) (38) (39) (40) and (4) respectvely. E = where E E x% E y% x% y% = x% x% h + + are proved and calculated by Equatons (3) (33) (3) E = where E E x% E y% x% y% b = y% y% h + + E = b b where E E x% E y% b x% b y% b = x% x% + + (33) (34)

12 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v of 0 b E = b b where E E x% E y% b x% b y% b = y% y% + + E = where E E x% + h E y% + 3 h x% h y% h E x% + E y% + 3 h x% + h y% + 3 h h = x% + x% + + y% + y% + h h c + + v x% + x% + y% + y% + h h ( c + v h h c ) = + + (35) (36) E = where E E x% + h E y% + 3 h x% h y% h E x% + E y% + 3 h x% + h y% + 3 h h = x% + x% + + y% + y% + h h c + + v x% + x% + y% + y% + h h ( c + v h h c ) = + + E = where E E x% + h E y% + 3 h x% h y% h E x% + E y% + 3 h x% + h y% + 3 h h = x% + x% + + y% + y% + h h w + + v x% + x% + y% + y% + h h ( w + v h h w ) = + + (37) (38)

13 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v 3 of 0 E = where E E x% h E y% h x% h y% h E x% + E y% + 3 h x% + h y% + 3 h h = x% + x% + + y% + y% + h h w + + v x% + x% + y% + y% + h h ( w + v h h w ) = + + E v= v where v E E x% h E y% h v x% h v y% h v b E x% E y% x% h y% h h v h = x% + x% + + y% + y% + h h h + v v v x% + x% + y% + y% + h h ( h v h h h0 ) = + + E = b b where E E x% h E y% h b x% h b y% h b v E x% E y% x% + h y% h h b 3 3 = % + % + + % + % + + x x y y h h v b x% + x% + y% + y% + h h ( v h h ) = + + h (39) (40) (4) For the generalaton of recurrent neural network the number of base statons and the number of W-F APs can be extended as n and n n the nput layer (shown n Fgure 7). The values of h and h can be revsed and calculated by Equaton (4) and (43); the updates of and are proved and calculated by Equatons (44) and (45) respectvely. n n h = s c + w + v h0 + b = s s = j= k= + e j j k k ( ) where ( ) (4) j k n n h = s c + w + v h + b = s ( ) where s ( ) = j j + k k + j= k= + e (43)

14 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v 4 of 0 E j = j where j E E x% h E y% h x% h y% h j j E x% + E y% + 3 h x% + h y% + 3 h j h = x% + x% + + y% + y% + h h c j + + v j ( ) % % % % + = x x + y y h h c + v h h c j j E k = k where k E E x% h E y% h x% h y% h k k E x% + E y% + 3 h x% + h y% + 3 h k h = x% + x% + + y% + y% + h h wk + + v k x% + x% + y% + y% + h h ( wk + v h h wk ) = + + (44) (45) b b 3 h 0 v h v h b b c + w c + w + Fgure 7. A generaled recurrent neural network wth two consecutve tmestamps Furthermore the recurrent neural network can analye wth more consecutve tmestamps and the number of neurons n the recurrent hdden layer of the recurrent neural network can be extended for the extracton of tme seres data. The weght between each two neurons can be updated by the gradent descent method De-normalaton and Estmaton and For de-normalaton and estmaton the estmated normaled longtude and lattude (.e. y%) can be adopted nto Equatons (46) and (47) to retreve the estmated longtude and lattude (.e. l % x and l % y ). ( + ) ( ) ( ) lx = x ( lx lx ) + lx % % (46) x%

15 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v 5 of 0 ( + ) ( ) ( ) ( ) l% = y% l l + l (47) y y y y 4. Practcal Expermental Results and Dscusson Ths secton presents and dscusses the practcal expermental results. Practcal expermental envronments are llustrated n Subsecton 4. and practcal expermental results are showed n Subsecton 4.. Subsecton 4.3 dscussed the results of dfferent recurrent neural networks. 4.. Practcal Expermental Envronments In the practcal expermental envronments an Androd applcaton was mplemented and nstalled nto moble statons (e.g. Redm 5 runnng Androd platform 7..). The moble statons were carred out on a 5.6 km long road segment n Fuhou Unversty n Chna (shown n Fgure 8). The segment was traversed 8 tmes by moble statons to collect GPS coordnates and network sgnals (.e. the RSSIs of base statons and W-F APs). There are 455 records (.e. m = 455) 59 dfferent base statons (.e. n = 59) and 58 dfferent W-F APs (.e. n = 58) detected n the experments. Ths study selected 63 records ncludng GPS coordnates and RSSIs as tranng data and other 6 records were selected as testng data. 00 meters Me Q Lvng Area Zhong Me Lvng Area Chna Telecom Educatonal Buldngs of Fuhou Unversty The Teacher's Apartments of Fuhou Unversty The East Gate of Fuhou Unversty Fujan Agrculture and Forestry Unversty Lvng Area No. Fuhou Unversty Fuhou Unversty Fujan Communcatons Plannng and Desgn Insttute Lvng Area No. Fuhou Unversty Lvng Area No. 3 Fuhou Unversty The West Gate of Fuhou Unversty Alumn Buldng The South Gate of Fuhou Unversty Fuhou No. Hgh School Bo Sh Hou Lvng Area Fgure 8. Practcal expermental envronments 4.. Practcal Expermental Results For the evaluaton of the proposed moble postonng method 9 expermental cases wth dfferent tmestamp numbers (.e. tmestamp tmestamps and 3 tmestamps) and wth dfferent moble networks (.e. only cellular networks only W-F networks and cellular and W-F networks) were desgned and performed. There were 30 neurons n the recurrent hdden layer of the recurrent neural network for each expermental case. The practcal expermental results are showed n Table Fgure 9 Fgure 0 Fgure and Fgure. Table and Fgure 9 llustrated that the more precse locaton can be estmated by the proposed method wth heterogeneous networks (.e. cellular and W-F networks). The hgher locaton errors may be obtaned by the recurrent neural networks wth one tmestamp (.e. tradtonal neural networks) whch cannot extract the feature of tme seres data (shown n Table and Fgure 0). The lower locaton errors can be obtaned by the recurrent neural

16 CDF(%) Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v 6 of 0 networks wth multple consecutve tmestamps (e.g. tmestamps and 3 tmestamps); the expermental results can be observed that the average error of locaton estmaton was 9.9 meters by the proposed moble postonng method wth tmestamps. Table. The average errors of estmated locatons by the proposed moble postonng method (Unt: meters) Number of tmestamps Only cellular Only W-F cellular and W-F networks networks networks tmestamp tmestamps tmestamps meters Buldng No. 3 of Fuhou Unversty Buldng No. of Fuhou Unversty Educatonal Buldng No. 0 of Fuhou Unversty College of Mathematcs and Computer Scence Buldng No. of Fuhou Unversty The Restaurant of Fuhou Unversty G: GPS (a red pont); C: cellular networks (a green pont); W: W-F networks (a blue pont); CW: cellular and W-F networks (a yellow pont) Fgure 9. The estmated locatons by the proposed moble postonng method wth dfferent moble networks 00% 90% 80% 70% 60% 50% 40% 30% 0% 0% 0% Cell WF Cell+WF The error of estmated locaton (meters) Fgure 0. The cumulatve dstrbuton functon of locaton errors by the proposed moble postonng method wth tmestamp

17 CDF(%) Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v 7 of 0 00% 90% 80% 70% 60% 50% 40% 30% 0% 0% 0% Cell WF Cell+WF The error of estmated locaton (meters) Fgure. The cumulatve dstrbuton functon of locaton errors by the proposed moble postonng method wth tmestamps CDF(%) 00% 90% 80% 70% 60% 50% 40% 30% 0% 0% 0% Cell WF Cell+WF The error of estmated locaton (meters) Fgure. The cumulatve dstrbuton functon of locaton errors by the proposed moble postonng method wth 3 tmestamps 4.3. Dscussons The proposed moble postonng method used a traned recurrent neural network to smultaneously estmate longtudes and lattudes; n the recurrent neural network the estmated longtudes and lattudes were determned n accordance wth the same weghts n the nput layer and hdden layers. In addton ths study also consdered to separately tran two recurrent neural networks for estmatng longtudes and lattudes (shown n Fgures 3 and 4); the estmated longtudes and lattudes were determned n accordance wth dfferent weghts n these recurrent neural networks. The practcal expermental results ndcated that hgher precse locaton may be obtaned by the recurrent neural networks wth one tmestamp (.e. tradtonal neural network)(shown n Table ). However bg errors of estmated locatons may be obtaned by the recurrent neural networks wth multple consecutve tmestamps. The overfttng problems may exst f longtudes and lattudes are estmated by dfferent recurrent neural networks wth multple consecutve tmestamps. Therefore the nteracton effects of longtudes and lattudes should be analyed so they should be estmated by the same recurrent neural network for determnng hgher precse locatons. Table. The average errors of estmated locatons by the proposed moble postonng method (Unt: meters) Number of tmestamps Only cellular networks Only W-F networks cellular and W-F networks

18 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v 8 of 0 b h 0 v h b c c w w Fgure 3. A recurrent neural network wth one tmestamp for estmatng longtudes b 3 h 0 v h b c c w w Fgure 4. A recurrent neural network wth one tmestamp for estmatng lattudes 5. Conclusons and Future Work Ths secton summares and descrbes the contrbutons of ths study n Subsecton 5.. The lmtatons of the proposed method and future work are presented n Subsecton Conclusons In prevous studes cellular-based postonng methods can estmate locatons of moble statons n outdoor envronments but the accuraces of estmated locatons may be lower. Moreover W-Fbased postonng methods can precsely estmate the locatons moble statons but the transmsson coverage of W-F APs s not enough n outdoor envronments. Therefore a moble postonng system and a moble postonng method based on recurrent neural networks are proposed to analye the RSSIs from heterogeneous networks whch nclude cellular networks and W-F networks. The network sgnals from heterogeneous networks can be analyed to mprove the accuraces of estmaton locatons. Furthermore the RSSIs n multple consecutve tmestamps can be adopted nto recurrent neural networks for the analyses of tme seres data and locatons estmaton. In practcal expermental envronments the results showed that the average error of locaton estmaton was 9.9 meters by the proposed moble postonng method wth tmestamps. Therefore the proposed system and method can be appled to obtan LBS n outdoor envronments. 5.. Future Work Although the hgher accuraces of estmaton locatons can be obtaned by recurrent neural networks wth multple consecutve tmestamps some overfttng problems may exst. For nstance the hgher errors of estmated locatons were obtaned by recurrent neural networks wth 3

19 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v 9 of 0 tmestamps. Therefore overfttng solutons of tme seres data [5] can be nvestgated to mprove the accuraces of estmated locatons n the future. Author Contrbutons: Wu and Chen proposed and mplemented the methodology. Chen analyed and dscussed the practcal expermental results. Wu Chen and Zhang wrote the manuscrpt. Fundng: The research was funded by the Natural Scence Foundaton of Chna under the project of the Fujan Industry-Academy Cooperaton Project under Grant No. 07H6008 and the Natural Scence Foundaton of Fujan Provnce of Chna under the project of 08J079 and 07J075. Conflcts of Interest: The authors declare no conflct of nterest. References. Chen C.H.; Ln B.Y.; Ln C.H.; Lu Y.S.; Lo C.C. A green postonng algorthm for Campus Gudance System. Internatonal Journal of Moble Communcatons 0 0() 9-3 DOI: 0.504/IJMC Wu C.; Yang Z.; Xu Y.; Zhao Y.; Lu Y. Human moblty enhances global postonng accuracy for moble phone localaton. IEEE Transactons on Parallel and Dstrbuted Systems 05 6() 3-4 DOI: 0.09/TPDS Thejaswn M.; Rajalakshm P.; Desa U.B. Novel samplng algorthm for human moblty-based moble phone sensng. IEEE Internet of Thngs Journal 05 (3) 0-0 DOI: 0.09/JIOT Chen C.H. An arrval tme predcton method for bus system. IEEE Internet Thngs Journal 08 Early Access DOI: 0.09/JIOT Molna B.; Olvares E.; Palau C.E.; Esteve M. A multmodal fngerprnt-based ndoor postonng system for arports. IEEE Access DOI: 0.09/ACCESS Chen C.H.; Lee C.A.; Lo C.C. Vehcle localaton and velocty estmaton based on moble phone sensng. IEEE Access 06 4 pp DOI: 0.09/ACCESS Chen K.; Wang C.; Yn Z.; Jang H.; Tan G. Slde: towards fast and accurate moble fngerprntng for W-F ndoor postonng systems. IEEE Sensors Journal 08 8(3) 3-3 DOI: 0.09/JSEN La W.K.; Kuo T.H.; Chen C.H. Vehcle Speed Estmaton and Forecastng Methods Based on Cellular Floatng Vehcle Data. Appled Scences DOI: /app Lu D.; Sheng B.; Hou F.; Rao W.; Lu H. From wreless postonng to moble postonng: an overvew of recent advances. IEEE Systems Journal 04 8(4) DOI: 0.09/JSYST Tanuch D.; Lu X.; Naka D.; Maekawa T. Sprng model based collaboratve ndoor poston estmaton wth neghbor moble devces. IEEE Journal of Selected Topcs n Sgnal Processng 05 9() DOI: 0.09/JSTSP Cheng D.Y.; Chen C.H.; Hsang C.H.; Lo C.C.; Ln H.F.; Ln B.Y. The optmal samplng perod of a fngerprnt postonng algorthm for vehcle speed estmaton. Mathematcal Problems n Engneerng DOI: 0.55/03/ Mok E.; Cheung B.K.S. An mproved neural network tranng algorthm for W-F fngerprntng postonng. ISPRS Internatonal Journal of Geo-Informaton 03 (3) DOI: /jg Chen C.H.; Ln J.H.; Kuan T.S.; Lo K.R. A hgh-effcency method of moble postonng based on commercal vehcle operaton data. ISPRS Internatonal Journal of Geo-Informaton DOI: /jg Xa S.; Lu Y.; Yuan G.; Zhu M.; Wang Z. Indoor fngerprnt postonng based on W-F: an overvew. ISPRS Internatonal Journal of Geo-Informaton 07 6(5) 35 DOI: /jg Chen C.H.; Lo K.R. Applcatons of Internet of Thngs. ISPRS Internatonal Journal of Geo-Informaton DOI: /jg Lo C.L.; Chen C.H.; Kuan T.S.; Lo K.R.; Cho H.J. Fuel consumpton estmaton system and method wth lower cost. Symmetry DOI: /sym Chen C.H.; Al-Masr E.; Hwang F.J.; Ktordou D.; Lo K.R. Introducton to the specal ssue: applcatons of Internet of thngs. Symmetry DOI: /sym Chen C.Y.; Yn L.P.; Chen Y.J.; Hwang R.C. A modfed probablty neural network ndoor postonng technque. Proceedngs of 0 IEEE Internatonal Conference on Informaton Securty and Intellgent Control Yunln Tawan 4-6 Aug. 0 DOI: 0.09/ISIC

20 Preprnts ( NOT PEER-REVIEWED Posted: October 08 do:0.0944/preprnts v 0 of 0 9. Xu Y.; Sun Y. Neural network-based accuracy enhancement method for WLAN ndoor postonng. Proceedngs of 0 IEEE Vehcular Technology Conference Quebec Cty QC Canada 3-6 Sept. 0 DOI: 0.09/VTCFall Zhang T.; Man Y. The enhancement of WF fngerprnt postonng usng convolutonal neural network. Proceedngs of 08 Internatonal Conference on Computer Communcaton and Network Technology Wuhen Chna 9-30 June 08 DOI: 0.783/dtcse/CCNT08/4745. Zhu J.Y.; Xu J.; Zheng A.X.; He J.; Wu C.; L V.O.K. WIFI fngerprntng ndoor localaton system based on spato-temporal (S-T) metrcs. Proceedngs of 04 IEEE Internatonal Conference on Indoor Postonng and Indoor Navgaton Busan South Korea 7-30 Oct. 04 DOI: 0.09/IPIN Lukto Y.; Chrsmanto A.R. Recurrent neural networks model for WF-based ndoor postonng system. Proceedngs of 07 IEEE Internatonal Conference on Smart Ctes Automaton & Intellgent Computng Systems Yogyakarta Indonesa 8-0 Nov. 07 DOI: 0.09/ICON-SONICS Wang X.; Gao L.; Mao S.; Pandey S. DeepF: Deep learnng for ndoor fngerprntng usng channel state nformaton. Proceedngs of 05 IEEE Wreless Communcatons and Networkng Conference New Orleans LA USA 9- March 05 DOI: 0.09/WCNC LeCun Y.; Bengo Y.; Hnton G. Deep learnng. Nature DOI: 5. Chen C.H. Reducng the dmensonalty of tme-seres data wth deep learnng technques. Scence 08 eletter. Avalable onlne: (accessed on 0 Ocotober 08).