Unscented Particle Filtering Algorithm for Optical-Fiber Sensing Intrusion Localization Based on Particle Swarm Optimization

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1 TELKOMNIKA, Vol13, No1, March 015, pp 349~356 ISSN: , accredted A by DIKTI, Decree No: 58/DIKTI/Kep/013 DOI: 10198/TELKOMNIKAv Unscented Partcle Flterng Algorthm for Optcal-Fber Sensng Intruson Localzaton Based on Partcle Swarm Optmzaton Hua Zhang*, Xaopng Jang, Chenghua L College of Electroncs and Informaton Engneerng, Hube Key Laboratory of Intellgent Wreless Communcatons, South-Central Unversty for Natonaltes, Wuhan , Hube, Chna *Correspondng author, e-mal: zhanghua@malscueceducn Abstract To mprove the convergence and precson of ntruson localzaton n optcal-fber sensng permeter protecton applcatons, we present an algorthm based on an unscented partcle flter (UPF) The algorthm employs partcle swarm optmzaton (PSO) to mtgate the sample degeneracy and mpovershment problem of the partcle flter By comparng the present ftness value of partcles wth the optmum ftness value of the objectve functon, PSO moves partcles wth nsgnfcant UPF weghts towards the hgher lelhood regon and determnes the optmal postons for partcles wth larger weghts The partcles wth larger weghts results n a new sample set wth a more balanced dstrbuton between the prors and the lelhood Smulatons demonstrate that the algorthm speeds up convergence and mproves the precson of ntruson localzaton Keywords: optcal-fber sensor, ntruson localzaton, UPF, PSO 1 Introducton Optcal-fber sensor-based ntruson detecton technologes are wdely used n permeter securty protecton systems Recently, the optcal fber sensng technologes avalable for ntruson detecton nclude the nterferometer-based optcal fber sensors and the optcal tme doman reflectometry (OTDR)-based optcal fber sensors, and each of whch has characters [1]- [8] Among the technologes, the nterferometer-based optcal-fber sensors are preferred n ntruson detecton for ther hgh senstvty to vbratonal sgnals and low cost As s nown, t s mportant to localze the ntruder when an ntruson sgnal s detected n a permeter protecton system Generally, the underground ntruson sgnals to be detected are acoustc (or vbratonal) sgnals generated by the ntruder When an ntruson occurs, the tme of arrval (TOA) of the ntruson sgnal s used to locate the poston of the ntruder approxmately [9] As the nterferometer-based systems use consecutve laser pulses, the nterval between the laser beng sent out and the ntruson sgnal arrvng at the recever cannot be determned Thus, the TOA of the ntruson sgnal cannot be accurately measured, whch affects the precson of ntruson localzaton To get the precse TOAs of the ntruson sgnals, many sgnal processng algorthms were employed [11] However, the approaches suffer from the measurement errors for the fast speed of the laser propagatng n the optcal fber, the errors of the tme lmt the precson of the ntruson localzaton to tens of meters [1] Many researchers have wored on ths problem and varous sgnal processng algorthms have been employed to obtan a precse TOA n optcal-fber sensng localzaton [13],[14] To mprove the precson of ntruson localzaton, we have prevously used the geometrcal postons of the dstrbuted sensors and the dfferences n relatve TOAs to estmate the poston of the ntruder [15]-[16] State estmaton-based methods demonstrate hgh precson However, as the measurement equaton s nonlnear, the convergence speed s poor and the precson s subject to measurement errors In ths paper, a partcle flter s used to handle the problem of nonlnearty n optcal-fber sensng ntruson localzaton To avod the degeneracy problem and sample mpovershment after resamplng, we employ the unscented partcle flter (UPF) and use partcle swarm optmzaton (PSO) to mantan dversty n the partcles A seres of smulatons demonstrate that the proposed algorthm mproves precson and convergence when there s no pror ntruder locaton Receved October, 014; Revsed January, 015; Accepted January 0, 015

2 350 ISSN: Intruson localzaton n optcal-fber sensng permeter protecton In optcal-fber sensng permeter protecton systems, ntruders generate vbratonal sgnals that can be detected by the optcal-fber sensors After the detected sgnals have been processed and analyzed, the tme ntervals between the laser pulse beng sent and the 0-phase of the ntruson sgnal waveforms beng receved can be calculated Ths nterval s the tme that the vbratonal sgnals tae to propagate from the ntruder to the sensor, and s called the TOA of the ntruson sgnal Fgure 1 Dstances from ntruder to sensors are equal to the dstance that the acoustc sgnals travels from ntruder to sensors Fgure 1 llustrates a dstrbuted optcal-fber sensng permeter protecton system Let the moment at whch the ntruder generates the vbratonal sgnal be t 0, and the TOA be t The tme nterval (t-t0) ncludes the tme taen by the vbratonal sgnal to arrve at the sensor and the tme for the laser to propagate along the optcal fber As the sensor locatons are fxed, the propagaton tme of the laser n the optcal fber s almost constant and can be pre-calbrated Thus, the geometrcal relatonshp between the th sensor and the ntruder s: ( x - x) ( y- y ) ( z- z ) v ( t t T ) (1) I 0 where (x, y, z ) s the locaton of the th sensor and (x, y, z) s the locaton of the ntruder v I s the speed at whch the vbratonal sgnal generated by the ntruder s transported, t 0 s the moment at whch the ntruder generates the vbratonal sgnal, T s the tme taen by the laser to propagate along the optcal fber of the th sensor, and t s the moment at whch the ntruson sgnal n the th sensor s detected by the recever As the precse moment at whch the ntruder generates the vbratonal sgnal and the propagaton speed of the vbratonal sgnal are unnown (e, t 0 and v I are unnown), the poston of the ntruder cannot be computed drectly by solvng Equaton (1) In prevous wor, we used optmal estmaton and state estmaton methods to obtan the estmate of the ntruder s locaton ( xˆ, yz ˆ, ˆ) 1 Optmal estmaton-based localzaton If the ntruson sgnal s detected by more than two sensors, t 0 can be gnored by consderng the dstances between the sensors: ( x- x ( - ) ( - ) - - ( - ) ( - ) ) + y y + z z ( x x j ) + y y j + z z j = v I ( t -t j -( T - T j )) () where () returns the absolute value Then, (x, y, z) and I v can be computed by optmal estmaton technques such as the least-squares (L-S) method [15] However, the determnate TELKOMNIKA Vol 13, No 1, March 015 :

3 TELKOMNIKA ISSN: relatonshp n Equaton () does not consder nose n the parameters, resultng n mprecse estmates In partcular, when no more than four sensors detect the ntruson sgnal, the error n the locaton estmaton ncreases consderably State estmaton-based localzaton To use state estmaton methods to estmate and trac an ntruder s locaton, the state equatons and measurement model are deduced as follows The locaton and speed of the ntruder, the unnown speed of the vbratonal sgnal, and the moment at whch the ntruder generated the vbratonal sgnals are consdered as the state parameters, e, X [ x y z v 0] T x vy vz vi t To smplfy the problem, we assume that the speed at whch the ntruder s movng s almost constant, e, the varaton n speed s zero, and that the speed of the vbratonal sgnal s constant Zero-mean Gaussan nose s added to both the ntruder speed and the vbratonal sgnal The state equaton s then, Where X AX W (3) A (4) and W s the nose vector of the state parameters, whch have means of zero and covarance matrx R=dag( 1 8) The measurement parameters are the ponts at whch the ntruson sgnals arrve at the sensors, e, Y [ t1 t t ] T n From Equaton (1), we have 1 t ( x- x) ( y- y ) ( z- z ) t T (5) 0 vi Then, the measurement model can be wrtten as: Z GX ( ) V (6) where G() denotes the measurement functon vectors noted n Equaton (5) and V s the measurement nose vector, whch has mean m and covarance matrx Q=dag( t 1 t t ) n As the measurement equatons n Equaton (6) are nonlnear, the unscented Kalman flter (UKF) s used to obtan hgh precson [16] The algorthm yelds good performance n tracng the ntruder However, when there s no pror nowledge of the ntruson locaton, the algorthm s slow to converge 3 PSO-based UPF Algorthm for Intruson Localzaton UPF s a popular state estmaton algorthm for nonlnear systems In UPF, UKF s used to generate sophstcated proposed dstrbutons that seamlessly ntegrate the current observaton [18] The combnaton of UKF wth a partcle flter outperforms exstng partcle flters, albet at the cost of computatonal complexty UPF also suffers from the degeneracy Unscented Partcle Flterng Algorthm for Optcal-Fber Sensng Intruson (Hua Zhang)

4 35 ISSN: problem and the loss of partcle dversty As PSO s smple, fast, and effcent, t can be used to mprove the performance of the UPF algorthm 31 PSO algorthm PSO s an evolutonary computaton technque based on the behavor of ndvduals wthn a swarm [17] The ndvduals fnd the optmum soluton usng ther own prevous experence and that of ther neghbors Each ndvdual n the swarm tracs the coordnates n the problem space that are assocated wth the soluton acheved so far In the realzaton process of a PSO algorthm, each partcle corresponds to a canddate soluton to the optmzaton problem The drecton and dstance that the partcles move wthn the soluton space are determned by ther speed, and the objectve functon determnes the ftness value of each ntal populaton The partcles follow the current optmal partcle, and an optmal soluton s acheved after each generaton In each generaton, the partcles follow the optmal soluton p of the partcle tself, denoted as P ( 1,,, ) T b pb pb pbn, as well as the optmal soluton g of the whole populaton, denoted as G ( 1,,, ) T b gb gb gbn For a random partcle swarm contanng M partcles, the postons and veloctes of the th partcle n N-dmensonal space are X ( 1,,, ) T x x xn and V ( 1,,, ) T v v vn After determnng p and g, each partcle updates ts poston and velocty accordng to the followng equatons: v (1) w() v () cr()(p x ()) c r ()( g x ()) (7) 11 b b x (1) x () v () (8) where r 1 () ~U(0, 1) and r () ~U(0, 1) are used to gve the algorthm a stochastc nature, w () s the nertal weght, and c 1, c are acceleraton factors used to adjust the maxmum step sze of p and g 3 PSO-optmzed UPF for optcal-fber sensng ntruson localzaton In the PSO process, the partcle swarm searches for optmal solutons and determnes the optmal locaton by updatng the partcle veloctes When UPF s appled to the estmaton of the ntruson locaton, the PSO algorthm s used to optmze the partcles n UPF In the algorthm, the partcle populaton n the PSO supples the partcles for UPF PSO qucly fnds the target regon, whch ensures that the partcle set searches regons wth a hgh lelhood of contanng the optmal soluton The algorthm proceeds as follows: Step 1: Intalzaton Intalze the PSO parameters Set up the PSO parameters, such as the number of partcles N, acceleraton coeffcents C 1 and C, and the maxmum number of teratons Step : Intal samplng Sample N partcles {x 0, = 1,,, N} from the pror dstrbuton wth ntal weghts { w ( 1) 1 N, 1,,, N} Step 3: Importance samplng Sample partcles x () from the proposed dstrbuton: q(x() / x (1),Z ) N( xˆ (), x (), ˆ ()) (9) x() Step 4: Update weghts a Obtan system measurements b Accordng to the new measurements, calculate and normalze partcle weghts accordng to: TELKOMNIKA Vol 13, No 1, March 015 :

5 TELKOMNIKA ISSN: pz ( ()/ x()) px ( ()/ x(1)) w() w (1) (10) qx ( () / x(1), Z()) Step 5: Optmze the partcles by PSO a Resample the weghted partcles to obtan partcles { x, w } wth equal weghts 1 { x, N } Partcles wth smaller weghts are elmnated, and the number of partcles wth larger weghts ncreases b The majorty of partcles move towards the hgh-lelhood regon and are assgned a new weght by comparng the current postons wth the ftness value of the optmal partcles * * p pz ( / x ) pz ( / x) c Set the mnmum movement threshold α for the partcles If p, the flter partcles reman statonary; otherwse, the flter partcles adjust ther speed accordng to Equaton (7): v (1 ) w() v ( 1) c r(1)( x (1) x ( 1)) c r (1)( x (1) x ( 1)) (11) * * * * 11 p g where v ( 1 ) s the value of v ( 1 ) after teratons The speed determnes the drecton and dstance moved by the partcles d Redetermne the partcle postons accordng to Equaton (8) to obtan a new partcle set { x, w } Step 6: State estmaton Compute the posteror probablty estmaton of the target state at tme usng x N * xw 1 Step 7: Set = +1, return to Step 3, and contnue to estmate the posteror probablty of the target state at the next tme step In the above processes, PSO moves the partcles n the UPF towards areas of hgh lelhood Thus, the optmal poston s determned n the resamplng process by comparng the present ftness value wth the optmum ftness value of the objectve functon Modfyng the pror sample weghts such that the resultng partcles have larger weghts results n a new sample set that assumes a more balanced dstrbuton between the prors and the lelhood 4 Smulatons and Analyss To verfy the performance of the proposed algorthm, the convergence speed and precson of the proposed algorthm were compared wth that of the UKF algorthm and an L-S algorthm [15]-[16] The smulaton data n [15] are used, where the sensors are located n lnes and rows as shown n Fgure, and the ntervals between every par of the neghborng sensors are 50 meters The propagaton speed of the vbratonal sgnal generated by the ntruder was assumed to be a constant 1000 m/s The errors n TOAs were assumed to be below 01 ms, and the measurement nose was assumed to have zero mean and a covarance of 01 The ntruder was consdered to be movng wth a speed of 1 m/s, and the ntal R = dag(1,1,1,1,1,1,1,1) In our smulatons, the lelhood functon s defned as the objectve functon, and ths was assumed to have the posteror probablty functon 1 1 pz ( x) exp[ ( z 1/ z 1)], where z s the latest observaton and z 1 s the ( v) v predcted observaton Unscented Partcle Flterng Algorthm for Optcal-Fber Sensng Intruson (Hua Zhang)

6 354 ISSN: Fgure The locatons of the sensors for smulaton [15] 41 The convergence speed and precson of the algorthms Fgure 3 depcts the smulaton results and the statstcal results of the algorthms are lsted n table 1 As shown n the smulatons, the PSO algorthm optmzes the partcles n effcency and the partcle populaton n the PSO supples the partcles for UPF As PSO qucly fnds the target regon, the partcle set searches regons wth a hgh lelhood of contanng the optmal soluton As shown n Table 1, the proposed algorthm converges wthn 50 teratons Fgure 3 Smulaton results for each algorthm Where as the L-S and UKF algorthms requre more than 00 teratons Thus, the proposed algorthm has a reduced computatonal burden, whch maes t sutable for real-tme applcatons The errors gven by the dfferent algorthms are approxmately the same, although those from the proposed algorthm are less than 01 m after 50 teratons Ths demonstrates that the algorthm can also mprove the precson of detecton The smulatons demonstrate that the proposed algorthm outperforms the others n terms of both precson and convergence speed TELKOMNIKA Vol 13, No 1, March 015 :

7 TELKOMNIKA ISSN: Table 1 The statstcs of the algorthms Algorthms Error of the locaton Number of estmaton(meters) teratons(tmes) L-S[15] 03 >00 UKF[16] 01 >00 The proposed algorthm 007 <50 4 The robustness of the algorthm to the number of the sensors As n state-estmaton based algorthms, the precson s subject to the number of the sensors and the errors of the locaton estmaton under varous numbers of the sensors whch detected the ntruson are lsted n Table As shown n Table, to get hgher precson, the ntruder should be detected by more than 5 sensors smultaneously for L-S algorthm The number for the same precson n the UKF algorthm and the proposed algorthm are 3 Even when there s only one sensor whch can detect the ntruder, the proposed algorthm can trac the ntruder precsely It demonstrates that the proposed algorthm s robust to the number of the sensors used for locaton estmaton Table The statstcal errors wth varous numbers of sensors detectng the ntruson sgnals Algorthms L-S UKF The proposed algorthm Errors of the locaton Number of the sensors estmaton(meters) Concluson To mprove the convergence and precson of ntruson localzaton n optcal-fber sensng permeter protecton applcatons, we have proposed an algorthm based on PSOoptmzed UPF In the proposed algorthm, PSO s employed to mtgate the sample degeneracy and mpovershment problem of the partcle flter By comparng the present ftness value of the partcles wth the optmum ftness value of the objectve functon, PSO ensures partcles that have nsgnfcant UPF weghts move towards hgher lelhood regons and determnes the optmal poston of partcles wth larger weghts Smulatons have demonstrated that the proposed algorthm speeds up convergence and mproves the ntruson localzaton precson compared wth prevous methods Acnowledgements Ths wor was supported by the Key Technologes R&D Program of Wuhan Cty, Chna under Grant No and the General Program of Natonal Natural Scence Foundaton of Chna under Grant No References [1] Juarez JC, Maer, EW, et al Dstrbuted Fber-Optc Intruson Sensor System Journal of Lghtwave Technology 005; 3(6): [] Culshaw B The optcal fber Sagnac nterferometer: An overvew of ts prncples and applcatons Measurement Scence and Technology 006; 17: 1-16 [3] Par J Fber optc ntruson sensor usng coherent optcal tme doman reflectometer Appl Phys 003; 4: [4] Zhou Y, Jng SJ, et al Study on the dstrbuted optcal fber sensng technology for ppelne safety detecton and locaton Journal of Optoelectroncs Laser 008; 19(7): 9-94 Unscented Partcle Flterng Algorthm for Optcal-Fber Sensng Intruson (Hua Zhang)

8 356 ISSN: [5] Jahed NMS, Nurmohammad T, et al Enhanced resoluton fber optc stran sensor based on Mach- Zehnder nterferometer and dsplacement sensng prncples Proc of ELECO Internatonal Conference on Electrcal and Electroncs Engneerng 009; II: [6] Juarez JC Dstrbuted fber-optc ntruson sensor system Journal of Lghtwave Technology 005; 3: [7] Lnze N, Mégret P, et al Development of an Intruson Sensor Based on a Polarzaton-OTDR System IEEE Sensors Journal 01; 1(10): [8] L XL, Sun QZ, et al Hybrd TDM/WDM-Based Fber-Optc Sensor Networ for Permeter Intruson Detecton Journal of Lghtwave Technology 01; 30(8): [9] Zyczows M, Szustaows M, et al Fber optc permeter protecton sensor wth ntruder localzaton Proc of SPIE on Unmanned/Unattended Sensors and Sensor Networs 004; 5611: [10] Mcaulay AD, Wang J A Sagnac nterferometer sensor system for ntruson detecton and localzaton Proc of SPIE on Enablng Photonc Technologes for Aerospace Applcatons 004; 5435: [11] Zhang CX, L Q, et al Locaton algorthm for mult-dsturbances n fber-optc dstrbuted dsturbance sensor usng a Mach-Zehnder nterferometer Proc of Internatonal Conference on Optcal Communcatons and Networs 010; 574: [1] Kondrat M, Szustaows M, et al Two-nterferometer fber optc sensor wth dsturbance localzaton Proc of SPIE on Unattended Sensors and Sensor Networs 006; 6394: 1-7 [13] Zyczows M, Curapns W Fber optc sensor wth dsturbance localzaton n one optcal fber Proc of SPIE on Optcal Sensng Technology and Applcatons 007; 6585: 1-8 [14] Zhang Y, Chen JM Locaton method of Dstrbuted Fber-optc Permeter Securty System Based on Mach-Zehnder Interferometer Chnese Journal of Lasers 01; 39(6): 1-4 [15] Zhang H, Jang XP, et al Underground Intruson Localzaton and Identfcaton for Dstrbuted Optcal-Fber Sensng Permeter Protecton Internatonal Journal of Appled Mathematcs and Statstcs 013; 51(): [16] Zhang H, Jang XP, et al UKF-based Underground Intruson Localzaton Algorthm for Optcal-Fbre Sensng Permeter Protecton Compter Modellng & New Technologes 014; 18(3): [17] Zhang GY, Cheng YM, et al Partcle Flter Based on PSO Proc of the Internatonal Conference on Intellgent Computaton Technology and Automaton 008: [18] L M, Yuan LQ, et al Unscented Partcle Flterng wth Partcle Swarm Optmzaton for estmatng Nonlnear System Proc of the Thrd Internatonal Symposum on Electronc Commerce and Securty 010: TELKOMNIKA Vol 13, No 1, March 015 :