Performance Analysis of Direct Position Determination for Emitter Source Positioning

Transcription

1 American Journa of Signa Proceing 22,2(3): 4-45 DOI:.5923/j.ajp Performance Anayi of Direct Poition Determination for Emitter Source Poitioning Ling Huang *, Yiong Lu Schoo of Eectrica and Eectronic Engineering, Nanyang echnoogica Univerity, , Singapore Abtract hi paper preent the invetigation of performance of Direct Poition Determination (DPD) method for emitter ource poitioning. Singe and mutipe emitter cae are tudied with different ytem geometrie, array configuration and different emitter ocation. MUSIC and Maximum ikeihood agorithm are ued to proce received data and find out poibe region where emitter are. A impe earching method i then appied to reduce error and find out the fina etimated poition. From the reut, we can ee that DPD perform quite we at high Signa-to-Noie ratio (SNR). However at ow SNR, ytem geometrie and antenna configuration wi have apparent effect on the performance. In mutipe emitter cae, there i a minimum ditance imit between emitter for DPD to ceary eparate them. When emitter igna i hidden by other emitter, DPD performance degrade. Keyword DPD, MUSIC, Antenna Array, Emitter Poitioning. Introduction Location baed ervice are attracting more and more attention by ervice provider a we a by reearcher. Such traditiona ocation method a ime of Arriva (OA)[], Ange of Arriva (AOA)[2-4] and their derivative are widey ued in emitter ocaization and vehice navigation. hee method are two-tep ocation method meauring inge time or ange parameter at each bae tation (BS) eparatey and determining emitter ocation uing meaured parameter in a data centre. However, a probem caed meaurement-ource aociation probem i away aociated with thee method when mutipe emitter are to be ocaized. Such probem i caued by eparate determination of time or ange parameter at different bae tation with no information to recognize which parameter come from which emitter ource. Recenty, a new one-tep ocation method, Direct Poition Determination (DPD), ha been propoed by Anthony J. Wei in[5]. It i attractive for the high poitioning accuracy and advantage over traditiona ocation technique. Mot importanty, it i abe to ove the aociation probem in traditiona method. DPD ue exacty the ame data a traditiona method. It coect data at a bae tation and procee them at the ame time in data centre. By a 2-dimeniona earch, emitter poition are avaiabe on a 2-D pane. Wei ha tudied the * Correponding author: HUAN23@E.NU.EDU.SG (Ling Huang) Pubihed onine at Copyright 22 Scientific & Academic Pubihing. A Right Reerved performance of DPD for a inge radio frequency igna bycomparing with traditiona method, and performance of DPD in ocating mutipe emitter ource via comparion with traditiona method[5-8]. However, performance of DPD under other condition i not evauated. In thi paper, impact of different bae tation geometrie on performance of DPD in ocating inge emitter and performance of DPD on two different mutipe emitter ource ocation are invetigated. In ection 2, we decribe ytem geometry and igna mode in the poitioning ytem. Section 3 give a review of Wei DPD method a we a a earching method. Section 4 preent performance anayi of DPD in figure and tabe. 2. Sytem Geometry and Signa Mode Aume there are L bae tation and emitter in the ytem. Each bae tation i equipped with M antenna eement. For a rura environment, it i often aumed that no bockage between bae tation and emitter. In thi ituation, igna propagation mode i ine-of-ight (LOS). Signa o i due to ditance variation a we a environment noie and interference. L bae tation form an area inide which emitter are ocated randomy. Each bae tation i equipped with M-eement uniform inear antenna array (ULA) centred at bae tation. Ditance between antenna eement i et to be haf of igna waveength ( λ ). Antenna array aignment can be varied to different ange with repect to x-axi (axi pointing to the eat). hi ead to different receiving ange

2 42 Ling Huang et a.: Performance Anayi of Direct Poition Determination for Emitter Source Poitioning of received igna at different antenna array, hence varie accuracy of AOA information and accuracy of emitter poition. Poition of qth emitter i abeed a p q = ( xq, yq). Poition of centre of bae tation i abeed a p = ( x, y). he tranmitting igna ued in the ytem i a radio frequency (RF) igna. Denote emitter igna a t ( t ), t i the tarting tranmitting time. he received igna at th bae tation from emitter i the ummation of individua igna from each emitter and i expreed a: q q q q q q= r() t = b a ( p ) ( t τ ( p ) t ) + n () t () where a( pq) i the array repone of antenna array at th bae tation to qth emitter ource igna. D m i the ditance between qth emitter and the mth antenna eement at the th bae tation. j2 πd 2 / λ j πd( ) / ( ) [... M λ a p q = e e ] (2) bq repreent attenuation coefficient of path from qth emitter to th bae tation. τ ( p q) i the igna propagation time from qth emitter to th bae tation. ( xq x)2 + ( yq y)2 τ ( p q) = (3) c n () t incude noie and interference during igna propagation from emitter to th bae tation. In frequency domain, the above received igna i denoted a: jω ( ) ( ) ( ) k [ τ ( pq ) + tq ] k = bq q q ke + q= r a p n (4) 2π k where ωk =, k N N r i a M vector. k repreent index of Fourier coefficient and N repreent number of Fourier coefficient. r, q ( k ) and n are Fourier coefficient of repective igna. 3. Poitioning Agorithm 3.. Review of DPD Agorithm he key idea of DPD agorithm i to find the minimum difference between received igna and the idea repone igna at a bae tation. It reut in the optimum received igna and hence the optimum poition correponding to emitter igna in one tep. In DPD, a antenna eement at a bae tation pa the received igna to a data centre for proceing. A the information i proceed to form a data matrix containing both OA and AOA information. After a data decompoition method, earch dimenion of igna i reduced and the eigenvaue of data matrix can be found. Eigenvaue are aociated with igna pace and hence pace poition of emitter. Potting of cot function wi ceary how the mot poibe etimated emitter poition. Frequency domain received igna in matrix format i hown a foowing: r = A + n (5) where ( ) ( ) [ ( ) ( ) j j k,..., ( ) k k b e ωτ ωτ p A = a p p ba p e ] (6) j ( ) [ ( ) j kt ω,..., ( ) kt k ke ω = ] ke Written in thi format, time deay information and ange information are both embedded inide one matrix term. he entire received igna at th bae tation i a N M vector and expreed a: r = r(), r(),..., r ( N ) (7) [ ] Ue matrix P = p p 2... p to denote a the emitter poition. he difference between received igna and the idea igna repone i minimized uing a cot function: L N [ ( p ) ] P 2 r qa p q q (8) = k= q= j ( ) ( ) ( ) ( ) k q + t = q C k b ke ω τ he cot function require a mutidimeniona earch to find the minimum vaue. o reduce the earch compexity, Wei propoed a new cot function baed on MUSIC agorithm[8]: N F( Pb, ) = H(,, ) ( ) H a k PbU k U a( k, Pb(9), ) k= a( k, Pb, ) contain a the A term. U i a matrix containing eigenvector correponding to the arget eigenvaue of received igna correation matrix R : R = E[ r r H ] () In thi cae, F( Pb, ) require a 2( L ) + 2 dimeniona earch to obtain the maximum vaue correponding to the mot poibe emitter poition. In order to reduce the earch dimenion, Wei propoed a new repreentation of the cot function[8]. N F( P, b) = bhh H H( ) ( ) H Γ k U k U Γ Hb k = Γ = diag { a ( ) ( ) ( P) e jωτ k P,..., a ( ) j k L L P e ωτ P } () H = I L M he norm of = [ ],..., b b b L i aumed to be unity to maintain a unique oution. Hence, maximizing eigenvaue of equation (2) wi ead to the maxima of F( Pb., ) N D( P) = H H H ( ) H Γ U k U Γ H (2) k= herefore, F( Pb, ) reduce to: F( P) = λmax [ D( P )] (3) he earch dimenion i reduced to 2. For more than one emitter cae, thi approach wi find out the mot ignificant eigenvaue which correpond to the mot poibe emitter poition Searching Method

3 American Journa of Signa Proceing 22,2(3): We have ued a earching method for mutipe emitter cae. In order to find the etimated vaue of correponding emitter poition, we appied a grid and ub-grid earching method. he procedure i a foow: ) Coare grid earch: m grid ize. 2) Divide grid into maer quare area and earch inide each ma area. 3) Find out the peak inide each ma quare area: et area radiu to be R grid. 4) Find out the arget peak among a the peak and find out the correponding poition. 5) Arrange the reuted etimated poition in order of increment in x, y coordinate and compare with the actua emitter poition to find out the error performance. 6) Fine grid earch: m grid ize. 7) Repeat from tep 2 to Performance Anayi DPD performance on ocating inge and mutipe igna ha been evauated by Wei and ome reearcher. However, affect of different ytem geometrie and pecia emitter poition on DPD performance have not been tudied by any reearcher yet. In thi ection, DPD performance with different antenna configuration and different emitter poition are evauated. wo different antenna aignment are conidered: antenna array parae to x-axi and form 45 /35 with x-axi. Figure. 45 /35 aignment of antenna array In imuation, RF igna i aumed to be ent once ony. he performance evauation factor i the mi ditance between true emitter poition and etimated poition. mi ditance = ( xˆ x) 2 + ( yˆ y) 2 (4) Performance evauation i baed on mean and Root-Mean-Square (RMS) vaue of the mi ditance. K repreent number of imuation round. K mean = mi ditance (5) K k= K RMS = mi ditance2 (6) K Singe-emitter cae and mutipe-emitter cae are tudied eparatey in foowing ubection. It i aumed that the invetigation area i of 4 km by 4 km, and four bae tation are ocated at the corner of the area. Emitter are ocated randomy inide the quare area. 4.. Singe Emitter he poition of inge emitter i randomy generated. By varying the aignment of antenna array at each bae tation and the number of antenna eement of each array, DPD performance can be obtained. In comparion reut, RMS vaue and mean vaue of the mi ditance are hown. 2 Parae 45 degree Figure 2. Comparion of DPD performance with 5-eement parae antenna array and 45 /35 array 2 3BS 2BS (ame ide) BS (different ide) BS Figure 3. Comparion of DPD performance with different BS geometrie eement 4 eement 3 eement 2 eement Figure 4. Comparion of DPD performance with different number of antenna eement

4 44 Ling Huang et a.: Performance Anayi of Direct Poition Determination for Emitter Source Poitioning Figure 2 how effect of different antenna array aignment on DPD performance. Each array ha 5 antenna eement. When antenna array i forming 45 /35 with x-axi, the error i maer than the parae cae at ow SNR vaue. he reaon i that when antenna array i facing the centre of the invetigation area, mot of the area i on the broadide of the array. Whie for parae array, ony the ide of invetigation area are on it broadide. Hence ange information wi be more accurate when array are facing the centre of invetigation area. At high SNR vaue, performance are neary the ame. It i concuded that when channe condition i good, different aignment have ight effect on performance of ocation. However when channe condition i wore, performance of DPD depend argey on the aignment. Good aignment ead to accurate ange and deay information, whie bad aignment ead to inaccurate information and arger poitioning error. Figure 3 i the performance with different number of bae tation. Each bae tation i equipped with 5 antenna eement. Starting from four bae tation, DPD performance degrade with fewer bae tation. hi i obviou ince fewer bae tation reut in e accurate ange and time deay information. A noted, there are two poibe geometrie for two bae tation cae. When two of them are on one ide of the area, the performance i a itte better at ow SNR vaue than that when two of them are on different ide, meaning diagona poition. he reaon i that, in the atter cae two bae tation have very poor anguar eparation. hey wi obtain information ony from diagona direction, but no enough information from other direction. Hence ange information i greaty mied (a een ceary from Figure 5, AOA fai when bae tation are ocated at diagona poition) and DPD cannot perform we. Figure 4 how the DPD performance when number of antenna eement i varied. Starting from 5 eement, one eement i reduced each time with whoe antenna array away centred at bae tation. he pot indicate that when ize of antenna array decreae, DPD performance degrade epeciay at ow SNR vaue. mean error [m] mean error [m] BS on different ide 5 BS on ame ide DPD AOA OA DPD AOA OA Figure 5. Comparion of DPD with AOA and OA when two bae tation are ued 4.2. Mutipe Emitter When mutipe emitter are preented, performance of DPD become more intereting. Wei ony focued on invetigating DPD performance by comparing with traditiona method. Here we focu on invetigating DPD itef in pecific condition for eparating mutipe emitter. Figure 6 how two pecia ocation of mutipe emitter ource in the area with 45 /35 antenna array at bae tation. Antenna array equipped at bae tation i 5-eement uniform inear array. he invetigation area i divided into four quadrant (eparated by red dotted ine). S, S2 are emitter ource and 2 repectivey. (a) (b) Figure 6. Sytem geometrie: (a) two emitter ocated aong diagona ine, (b) two emitter ocated in different quadrant When two emitter are on the ame diagona ine, igna from them to bae tation at diagona poition wi be hidden by each other. Hence ome information wi be ot. From Figure 7, we can ee that when two emitter are far apart, DPD can eparate them eaiy. However, when they are too coe to each other, DPD wi mix them together. It i expected that there houd be a minimum ditance between them o that they can jut be eparated. We teted the minimum eparation ditance by varying ditance between two emitter aong one diagona ine in each imuation. One ocation error i determined by RMS vaue of imuated ocation error. Ditance increment tep i et to be 2 m emitter are eparated by one grid ize in both x and y direction. Figure 7. Cot function at SNR = 3 db: (a) emitter (, ) km, (, ) km on the ame diagona ine, eparated by around 2.8 km, (b) emitter (.35,.35) km, (.35,.35) km on the ame diagona ine, eparated by about.98 km, (c) 2-D contour pot of (a), (d) 2-D contour pot of (b)

5 American Journa of Signa Proceing 22,2(3): abe. Poitioning Error of Diagona Emitter Poition (SNR = 3 db) t Emitter 2 nd Emitter Poition (km) Error (m) Poition (km) Error (m) (, ) 24.4 (, ) (.8,.8) 2.2 (.8,.8) (.6,.6) (.6,.6) (.4,.4) (.4,.4) (.35,.35) 93.6 (.35,.35) 44.8 Shown in abe, poitioning error are increaing a eparation ditance decreae. When x, y eparation between emitter decreae to about 8 m repectivey, error increae abrupty. Error performance i reativey fat when emitter eparation ditance i above 8 2 m. A mentioned above, diagona bae tation wi mi ome information of emitter on that diagona ine. Whie when emitter are in different quadrant, it i expected that a bae tation are abe to acquire more information without any hiding and hadowing. It i ao expected that minimum eparation ditance between two emitter for thi cae wi be maer than previou cae. Figure 8 how cot function for two emitter ocating in different quadrant (aong y axi). he ditance between two emitter i 7 m. From the cot function in 8(b) and 8(d), we are abe to recognize two peak correponding to two etimated emitter poition. Hence in thi ituation, DPD can eparate them, however, with a bit arger error. Simiary from abe 2, error are ao increaing with decreaing ditance when ditance i above 8 m. When ditance reache 7 m, error i greaty increaed. abe 2. Poitioning Error of Non-diagona Emitter Poition (SNR = 3 db) t Emitter 2 nd Emitter Poition (km) RMS error (m) Poition (km) RMS error (m) (, ) 3. (, ) 6.43 (,.8) 2. (,.8) (,.6) 24. (,.6) (,.4). (,.4) 7.89 (,.35) 293. (,.35) Concuion DPD method generate very high poitioning accuracy even at ow SNR vaue. DPD performance degrade with decreaing SNR vaue. Antenna array aignment ao have impact on DPD performance. Compared with the impact on AOA and OA, it i much maer. Antenna array with 45 /35 aignment with repect to x-axi generate higher poitioning accuracy. Beide, the more bae tation with good ange eparation and more antenna eement we ue, the better DPD perform in ocating emitter. In mutipe emitter ource cae, DPD can ditinguih eaiy different emitter from each other when they are far enough, but mix them together when they are quite near. he minimum ditance between diagona emitter i arger than that between non-diagona emitter. ACKNOWLEDGEMENS he author wih to acknowedge the hep from Profeor Anthony J. Wei at e Aviv Univerity in Irae. REFERENCES [] M. I. Skonik, Introduction to radar ytem, McGraw-Hi, New York, NY, USA, 3 rd edition, 2. [2] R. G. Stanfied, Statitica theory of DF fixing, Journa IEE, vo. 94, Part 3A, no. 5, pp , 947. [3] D. J. orrieri, Statitica theory of paive ocation ytem, IEEE ran. on Aeropace and Eectronic Sytem, vo. 2, no. 2, pp , 984. [4] O. S. Raph, Mutipe emitter ocation and igna parameter etimation, IEEE ran. on Antenna and Propagation, vo. AP-34, No. 3, March 986. [5] A. J. Wei, Direct poition determination of narrowband radio frequency tranmitter, IEEE Signa Proceing Letter, vo., No. 5, pp , May 24. [6] A. Amar and A. J. Wei, Advance in direct poition determination, Proc. the 3rd IEEE Senor Array Mutichanne Signa Proceing Workhop (SAM24), Barceona, Spain, Juy 24. [7] A. J. Wei and A. Amar, Direct poition determination in the preence of mode error - known waveform, Eevier Journa on Digita Signa Proceing, No. 6, pp.52-83, 26. Figure 8. Cot function at SNR = 3 db: (a) emitter (, ) km, (, ) km inide different quadrant, eparated by 2 km, (b) emitter (,.35) km, (,.35) km in different quadrant, eparated by.7 km, (c) 2-D contour pot of (a), (d) 2-D contour pot of (b) [8] A. J. Wei and A. Amar, Direct poition determination of mutipe radio igna, EURASIP Journa on Appied Signa Proceing 25:, pp , January 25.