3D Position Estimation Performance Evaluation of a Hybrid Two Reference TOA/TDOA Multilateration System Using Minimum Configuration

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1 Internatonal Journal of Traff and Transportaton Engneerng 6, 5(4): 96- DOI:.593/j.jtte D Poston Estmaton Performane Evaluaton of a Hybrd Two eferene TOA/ Multlateraton System Usng Mnmum Confguraton Abdulmalk S. Yaro,*, Muazu J. Musa, Salsu San, Abdulrazaq Abdulazz Department of Eletral and Computer Engneerng, Ahmadu Bello Unversty, Zara, gera Federal Unversty Gusau, Zara oad Gusau, gera Abstrat A passve multlateraton survellane system estmate arraft loaton usng tme dfferene of arrval () wth a lateraton algorthm. It has advantage over multangulaton system as t an estmate arraft postons n 3 Dmenson (3D). In ths paper, two referene hybrd TOA/ lose form lateraton algorthm s develop usng the mnmum number of antenna statons for 3D poston estmaton (PE). Usng a trangular onfguraton, the performane n arraft PE of the developed lateraton algorthm s ompared wth the two fx referene lose form lateraton usng Monte Carlo smulaton for some seleted arraft loatons and TOA error standard devaton range of meters to meters. Smulaton results omparson shows that the performane of the hybrd TOA/ lateraton algorthm n arraft PE depends on the arraft loaton relatve to the antenna staton onfguraton. The hybrd system an only estmate arraft horzontal oordnate wth hgh auray outsde the antenna staton onstellaton. It fals ompare to the two fx referene lateraton algorthm to estmate the alttude of the arraft for at any loaton wthn or outsde the antenna staton onstellaton. Keywords Multlateraton, 3D poston estmaton, Hybrd TOA/, Mnmum onfguraton. Introduton Passve multlateraton (MLAT) survellane system estmate arraft loaton n two steps []. The frst step nvolves estmatng the tme dfferene of arrval () of the sgnal at antenna pars. The seond step nvolves usng the estmated measurements from the frst stage as nput to a poston estmaton (PE) algorthm known as lateraton. D or 3D arraft PE depends on the number of antenna deployed []. For a 3D arraft PE, a mnmum of 4 antennas are requred. Several tehnques for estmatng have been reported n lteratures [3-7] but the lassal approah use n ar traff survellane s the TOA approah [8]. estmaton usng the TOA approah nvolves a par wse dfferene of TOA measurements of the sgnal estmated at eah antenna. TOA of the sgnal s the tme taken for the transmtted sgnal from the arraft to be deteted at any of the antennas. Several tehnques for TOA estmaton has been reported n lteratures [9-3] but ths researh s foused on usng these TOA measurements for PE proess. Thus, the fous of ths researh s the lateraton algorthm. * Correspondng author: yaroabdulmalk@yahoo.om (Abdulmalk S. Yaro) Publshed onlne at Copyrght 6 Sentf & Aadem Publshng. All ghts eserved measurements when onverted to dstane results n hyperbol equatons. number of TOA measurements wll result n - hyperbol equatons [4]. In the hyperbol equaton, there s a nonlnear relatonshp between the measurements and the arraft loaton. To solve for the arraft loaton, a lnear relaton between the two parameters ( measurements and the arraft loaton) must be obtaned. Several artles have reported on how ths lnear relatonshp s obtaned whh resulted n the dfferent types of lateraton algorthm. The dfferent types of lateraton algorthms an be summarzed n to open form and lose form [5]. Open form lateraton algorthm nvolves the use of lnearzaton tehnques suh as Taylor seres method to lnearze the hyperbol equaton and a random ntal arraft loaton to be nputted whh s then refned usng the teraton method [4-9]. Ths approah suffers from onvergene ssue f the ntal arraft loaton nputted s far from the atual arraft loaton [9]. Close form lateraton algorthm lnearzed the two parameters through algebra manpulaton of the hyperbol equatons [-4]. Ths approah does not requre any ntal arraft loaton thus, do not suffer onvergene ssue. For ths reason, the lose form lateraton algorthm s adopted n ths work. The use of multple referene antenna to mprove the PE auray of the lateraton algorthm has been dsussed n [5]. PE usng hybrd TOA/ measurement has been

2 Internatonal Journal of Traff and Transportaton Engneerng 6, 5(4): dsussed n several artles [6-3]. The use of hybrd TOA/ to redue wreless sgnal overhead assoated wth TOA systems and number of antenna for system s presented n [6]. A omparson between hybrd TOA/ D postonng system and D system n terms of PE auray s done n [3]. It was founded out that D PE auray of the hybrd TOA/ system s superor to the D system for far area emtter loatons whle the opposte s sad for emtter loatons n the near area. In [], a performane evaluaton of a mnmum antenna onfguraton MLAT system for 3D PE s arred out. Ths work propose to mprove the PE auray of the MLAT system usng a two referene hybrd TOA/ lateraton algorthm. The 3D PE auray of the proposed hybrd system wll be evaluated and ompared wth two fx referene lateraton algorthm used n [] usng Monte Carlo smulaton for a trangular antenna onfguraton. The remnder of the paper s organzed as follows. The two referene hybrd TOA/ lateraton algorthm s desrbed n seton whh s then followed by smulaton results and dsusson n seton 3. Fnally the onluson from the researh s presented n seton 4.. Two eferene Hybrd TOA/ Lateraton Algorthm Ths seton gves a detal desrpton of the two referene hybrd TOA/ lateraton algorthm. It s assumed that the TOA measurements of the reeved sgnal have already been estmated at eah antenna. Let τ be the TOA measurement estmated at the -th antenna staton wth oordnates ( x, y, z ). The equaton for the TOA measurement of the sgnal at the -th antenna staton transmtted from an emtter loated at x = ( x, y, z) s τ ( x x ) ( ) ( ) + y y + z z = () 5 where = 3 km From eq., there s a nonlnear relatonshp between the arraft loaton (x) and the TOA measurement (τ). Takng the square of both sdes n eq. wll results to x x y y z z ( τ ) = + + () Further smplfaton of eq. wll results n Let ( ) ( ) ( x y z ) x y z xx yy zz ( τ ) = (3) τ = ( ) ( ) = x + y + z K = x + y + z Substtutng eq. 4 nto eq. 3, the resultng expresson s ( ) xx yy zz K For = 4, the TOA equatons are (4) = (5) ( ) = xx + yy + zz + K (6a) ( ) = xx + yy + zz + K (6b) ( ) = xx + yy + zz + K (6) ( ) = xx + yy + zz + K (6d) In eq. 6, the varable s a funton of the arraft loaton whh s unknown n passve systems. Subtratng eq. 6b from eq. 6a and 6d from 6 wll result nto two equaton. = + xx ( x) yy ( y) + ( zz z) + K K 3 4 = xx ( x) yy ( y) + ( zz z) + K K Eq. 7 and eq. 8 represent a lnear relatonshp between the TOA measurements and the arraft loaton. Usng eq. 7 and eq. 8 to solve for the arraft loaton wll not be suffent as there are 3 unknowns and equatons. Usng approah, addtonal equaton an be obtaned. The of reeved sgnal at two separate antenna statons an be obtaned by performng a parwse dfferene between the TOA measurements from eah antenna staton. Mathematally, measurement between the -th and the j-th antenna staton par s obtaned as τ = τ τ = j j ( x x ) + ( y y ) + ( z z ) ( x xj) + ( y yj) + ( z zj) Wth 4 antenna statons and = & = as referene par for obtanng the s, 4 number hyperbol equatons are obtaned as 3 x x y y z z x x y y z z (7) (8) (9) (a) (b)

3 98 Abdulmalk S. Yaro et al.: 3D Poston Estmaton Performane Evaluaton of a Hybrd Two eferene TOA/ Multlateraton System Usng Mnmum Confguraton 3 x x y y z z x x y y z z () (d) Further smplfaton eq. wll results n plane equatons n the form [] a34 = x b34 + y 34 + z d34 () a34 = x b34 + y 34 + z d34 () where the oeffents of eq. 4 and eq. 5 for and 3 j 4 are K K a34 = d d b d 34 x x = y y = z z = xj = xj x, yj = yj y, zj = zj z j j j j K = ( x + y + z ) ( x + y + z ) (3) Detal desrpton of the smplfaton an be found n []. Eq. and eq. are the addtonal equatons obtaned usng the approah. Combnng these equatons wth eq. 7 and eq. 8 wll result n the hybrd TOA/ lateraton algorthm as shown below n matrx form of eq. 4. Ax = b (4) where ( x x) ( y y) ( z z) ( x3 x4) ( y3 y4) ( z3 z4) x3 x4 y3 y4 z3 z4 (5a) A = x3 x4 y3 y4 z3 z ( K+ K) ( 3 4 K3 + K4) b = K4 K K4 K (5b) x = [ xyz,, ] T (5) The loaton of the emtter an be obtanng by solvng the nverse matrx eq. 4 gven the TOA measurements and oordnate of the antenna statons. The matrx eq. 4 s an over determned total least square (TLS) problem whh an be solved usng Sngular Value deomposton (SVD)... PE Estmaton Usng SVD TLS Let C be an augment of A and b mathematally expressed as C = [A,b] (6) Takng the SVD of C as [3] n+ T T C= UΣ V = uσ v (7) = The soluton to matrx eq. 4 s obtan as T x= v, n+ vnn, + v (8) n+, n+ 3. Smulaton esults and Dsusson In ths seton, the PE performane auray of the two referene hybrd TOA/ lateraton algorthm s ompared wth the two fx referene lateraton algorthm mplemented n []. Monte Carlo smulaton s used to generate results for omparson usng a trangular antenna staton onfguraton. Poston root mean square error (MSE) s used as the performane measure for the omparson. Horzontal oordnate MSE and the alttude MSE are mathematally expressed as Horzonal MSE = = ( ˆ ) ( ˆ x x) + y y (9a) ( zˆ z) Alttude = MSE = (9b) where ( xyz,, ) orrespond to the known arraft loaton and ( x, y, z) s the estmated arraft loaton at the -th Monte Carlo smulaton teraton. Monte Carlo smulaton results are obtaned after 5 teratons. The error n the TOA measurement error s assumed as to have a Gaussan dstrbuton wth zero mean and σ standard devaton. The estmated TOA measurement n dstane at the -th GS s ˆ = + (, σ ) () The dstrbuton for the antenna statons are shown n Fgure below

4 Internatonal Journal of Traff and Transportaton Engneerng 6, 5(4): antenna- antenna- antenna-3 antenna-4 y = sn( θ ) (b) Comparson between the two lateraton algorthms s performed for some seleted arraft loatons defned n Table below. Y-axs X-axs o. Table. Font Spefatons for A4 Papers Loaton ange (km) Bearng ( ) Alttude (km) A 3 5 B 3 3 C D 33 7 Fgure. Trangular antenna staton onfguraton wth km antenna par separaton Arraft loatons n survellane systems are defne n terms of range (), bearng (θ) and alttude (z) whh orresponds to the ylndral oordnate system (, θ, z). Converson from ylndral oordnate system to the Cartesan oordnate system ( x, y, z) an be done usng the equatons below. x= os( θ ) (a) By varyng the standard devaton of the error n the TOA from meters to meters, the horzontal oordnate and alttude MSE obtaned usng the two referene hybrd TOA/ lateraton algorthm s ompared wth the two fx referene lateraton algorthm n [] for arraft loatons defned n Table. Fgure shows the horzontal oordnate MSE omparson between the two lateraton algorthms. Comparson shows that for the seleted arraft loatons, there s a lnear relaton between the horzontal oordnate MSE and TOA error standard devaton. Horzontal oordnate MSE (meters) hybrd TOA/ TOA error standard devaton (meters) (a) Arraft loaton A Horzontal oordnate MSE (meters) hybrd TOA/ TOA error standard devaton (meters) (b) Arraft loaton B Horzontal oordnate MSE (meters) 5 5 hybrd TOA/.5.5 TOA error standard devaton (meters) () Arraft loaton C.5.5 TOA error standard devaton (meters) (b) Arraft loaton D Fgure. Horzontal oordnate MSE omparson between two referene hybrd TOA/ and two fx referene lateraton algorthm for some seleted arraft loatons Horzontal oordnate MSE (meters) 5 5 hybrd TOA/

5 Abdulmalk S. Yaro et al.: 3D Poston Estmaton Performane Evaluaton of a Hybrd Two eferene TOA/ Multlateraton System Usng Mnmum Confguraton Summary of horzontal oordnate MSE at TOA error standard devaton of meters an be seen n Table below. Table. Horzontal oordnate MSE omparson for dfferent emtter loaton at TOA error standard devaton of meters o. Arraft loaton Horzontal oordnate MSE (meters) Hybrd TOA/ A 5..4 B C D The Green fll-n n Table ndate the lateraton algorthm wth the least PE error among the two lateraton algorthms for eah arraft loatons. Arraft loaton A and B are wthn the antenna staton onstellaton. It an be seen that at these two loatons, the two fx referene lateraton algorthm estmate the arraft loatons wth less PE error ompared to that two referene hybrd TOA/ lateraton algorthm. For arraft loatons outsde the antenna staton onstellaton whh are ndated by loatons C and D, the two referene hybrd TOA/ obtaned the least PE error. Ths means that the performane omparson between the two lateraton algorthms depends on the loaton of the arraft. For arraft loatons wthn the antenna staton onstellaton, the two fx referene lateraton algorthm has the hgh horzontal oordnate PE auray ompared to the two referene hybrd TOA/. As for arraft loated outsde the antenna staton onstellaton, usng the two referene hybrd TOA/ lateraton algorthm wll estmate the horzontal oordnate wth hgher auray. Fgure 3 shows the alttude MSE omparson between the two lateraton algorthms for arraft loatons defned n Table. The same lnear relatonshp between the alttude MSE and the TOA error standard devaton an be observed. For all loatons ether wthn or outsde the antenna staton onstellaton, the two fx referene lateraton algorthm has the hgher alttude PE auray. The two referene hybrd TOA/ lateraton algorthm fal n ths regards due to hgh sensvty of the algorthm to nput nose. 5 3 hybrd TOA/ 5 hybrd TOA/ alttude MSE (meters) 5 5 alttude MSE (meters) PDE standard devaton (meters) PDE standard devaton (meters) (a) Arraft loaton A (b) Arraft loaton B hybrd TOA/.5 hybrd TOA/ alttude MSE (meters) PDE standard devaton (meters) () Arraft loaton C.5.5 PDE standard devaton (meters) (b) Arraft loaton D Fgure 3. Alttude MSE omparson between two referene hybrd TOA/ and two fx referene lateraton algorthm for some seleted arraft loatons alttude MSE (meters).5

6 Internatonal Journal of Traff and Transportaton Engneerng 6, 5(4): Conlusons In ths work, a two referene hybrd TOA/ lateraton algorthm for 3D arraft PE s developed usng the mnmum antenna staton MLAT onfguraton. The performane n PE of the developed algorthm s ompared wth the two fx referene lateraton usng Monte Carlo smulaton for some seleted arraft loatons and TOA error standard devaton range of meters to meters. Smulaton results shows that the performane omparson between the two lateraton algorthms depends on the loaton of the arraft. For arraft loatons wthn the antenna staton onstellaton, the two fx referene lateraton algorthm estmated the horzontal oordnate wth hgh auray ompared to the two referene hybrd TOA/ lateraton algorthm. Arraft loatons outsde the GS onstellaton are estmated wth hgh auray wth the two referene hybrd TOA/ lateraton algorthm. As for alttude estmaton, the two fx referene lateraton algorthm outperformed the two referene hybrd TOA/ lateraton algorthm. In prate, the two set of lateraton algorthms an be used alongsde to mprove the PE of the MLAT survellane system. The system an be onfgured to use the two fx referene lateraton algorthm to montor and estmate the arraft horzontal poston wthn the antenna onstellaton as well as alttude estmaton of arraft wthn and outsde the antenna onstellaton. For arraft montorng outsde the antenna onstellaton, the system an be onfgured to use the hybrd TOA/ lateraton algorthm. Thus, mprovng the overall 3D PE proess of the mnmum antenna staton MLAT system. Further work wll fous on mprovng the alttude estmaton proess of the hybrd TOA/ lateraton algorthm. EFEECES [] D. Dardar, E. Fallett, and M. Luse, Satellte and terrestral rado postonng tehnques: a sgnal proessng perspetve. Aadem Press,. [] W. H. L. even, T.J. Qulter,. Weedon, and. A. Hogendoorn, Wde area multlateraton, L, eport on EATMP TS 3, 4, 5. [3] Q. Lu, S. Han, and X. S. Ma, "esearh of tme delay estmaton based on hgher order statsts," In Appled Mehans and Materals, vol. 33, no. 9, pp , 4. [4] C. Knapp and G. Carter, "The generalzed orrelaton method for estmaton of tme delay," IEEE Transatons on Aousts, Speeh, and Sgnal Proessng, vol. 4, no. 4, pp. 3 37, 976. [5] H. Dou, Q. Le, W. L, Q. Xng, A new estmaton method n Three-satellte nterferene loalsaton, Internatonal Journal of Eletrons, vol. no. 4, pp , 5. [6] D. Oh, S. Km, S.-H. Yoon, and J.-W. Chong, "Two-Dmensonal espit-lke shft-nvarant TOA estmaton algorthm usng mult-band Chrp sgnals robust to arrer frequeny offset," IEEE Transatons on Wreless Communatons, vol., no. 7, pp , 3. [7] P. Marmarol, X. Falourd, and H. Lssek, "A Comparatve Study of Tme Delay Estmaton Tehnques for oad Vehle Trakng," n Proeedngs of the th Frenh Congress of Aousts and Annual IOA Meetng, Aousts. [8] G. Galat, M. Leonard, P. Magaro, and V. Pau, "Wde area survellane usng SS mode S Multlateraton: Advantages and lmtatons," European adar Conferene, 5. EUAD 5., pp. 5 9, 5. [9] X. L and K. Pahlavan, "Super-resoluton TOA estmaton wth dversty for ndoor Geoloaton," IEEE Transatons on Wreless Communatons, vol. 3, no., pp. 4 34, Jan. 4. [] Y. L, S. Go, H. Yoo, S. Km, and J.-W. Chong, "TOA estmaton algorthm based on shft-nvarant tehnque for mult-band sgnals," n AETA 3: eent Advanes n Eletral Engneerng and elated Senes. Sprnger Sene + Busness Meda, 4, pp [] K. Haneda, K.. Takzawa, J.. Takada, M. Dasht and P. Vankanen, "Performane evaluaton of threshold-based UWB rangng methods - Leadng edge vs. searh bak -," 9 3rd European Conferene on Antennas and Propagaton, Berln, 9, pp [] C. Steffes,. Kaune, S. au, and F. Fke, "Determnng Tmes of Arrval of Transponder Sgnals n a Sensor etwork usng GPS Tme Synhronzaton," n Jahrestagung der Gesellshaft für Informatk, Berln,. [Onlne]. Avalable: Aessed: ov., 6. [3] D. Oh, Y. L, S. Lu, S.-H. Yoon, and J.-W. Chong, "Dual shft nvarant TOA estmaton algorthm for mult-band sgnals," IEEE Communatons Letters, vol. 6, no., pp , Ot.. [4] I. A. Mantlla-Gavra, G. Galat, M. Leonard, and J. V. Balbastre-Tejedor, "Tme-dfferene-of-arrval regularsed loaton estmator for multlateraton systems," IET adar, Sonar & avgaton, vol. 8, no. 5, pp , 4. [5] I. A. Mantlla-Gavra, M. Leonard, G. Galat, and J. V. Balbastre-Tejedor, "Loalzaton algorthms for multlateraton (MLAT) systems n arport surfae survellane," Sgnal, Image and Vdeo Proessng, vol. 9, no. 7, pp , 4. [6] X. Qu and L. Xe, "An effent onvex onstraned weghted least squares soure loalzaton algorthm based on measurements," Sgnal Proessng, vol. 9, pp. 4 5, 6. [7] W. FOY, "Poston-loaton solutons by Taylor-Seres estmaton," IEEE Transatons on Aerospae and Eletron Systems, vol. AES-, no., pp , 976. [8] I. A. Mantlla-Gavra, M. Leonard, J. V. Balbastre-Tejedor, and E. de los eyes, "On the applaton of sngular value deomposton and Tkhonov regularzaton to ll-posed

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