DIRECTION OF ARRIVAL ESTIMATION

Size: px

Start display at page:

Download "DIRECTION OF ARRIVAL ESTIMATION"

Patience Garrett
6 years ago
Views:

1 Research Article DIRECTION OF ARRIVAL ESTIMATION Lalita Gupta, R P Sigh Address for correspodece Dept. of Electroics & Commuicatio Egieerig, Maulaa Azad Natioal Istitute of Techology, Bhopal MP gupta.lalita@gmail.com ABSTRACT Array Sigal Processig (ASP) is a relatively ew techique i Digital Sigal Processig (DSP) with may potetial applicatios i commuicatio ad speech processig. Directio of arrival (DOA) ca be estimated usig differet techiques evolved with ASP. It is observed that subspace method provides superior performace i resolvig closely spaced sources. INTRODUCTION sigals from relatively low frequecy Sigal Processig is oe of the fastest growig stream of Electrical Egieerig ad may applicatios, available i our day to day life, have bee developed usig this techology. Array sigal processig (ASP) is the techiques of DSP which has may potetial applicatios [1]. Sesor ASP has emerged as a active area of research ad is cetered o the ability to aalyze data collected at several sesors [1]. This paper addresses method to itroduce the topic ad ASPs practical implicatios. The most commo applicatios of array sigal processig ivolve detectig locatio of acoustic sigals [2] which is the focus of this paper. The sesors i this case are microphoes ad arragemet of microphoe positios is sigificat. We have cosidered a liear array to collect souds (0 to 8 khz) comig out from a specific directio. Array Sigal Processig Array processig cosists of usig the multi-chael observatios collected by a sesor array i a optimal maer i order to detect sigals or estimate their parameters. [2]. Arrays ca be arraged i a lie or a circle as show i Figure 1. Uiform liear array (ULA) where L umbers of sesors are spaced liearly with equal distace d is show i Figure 1(a). Figure 1(b) demostrates the uiform circular array (UCA) where L umbers of sesors are spaced circularly with equal amout of agle 2π / L. Adaptive beam formig, iterferece cacellatio, ad high-resolutio directio fidig are some of the importat areas of sesors array processig.

2 Fig. 1 Array arragemets (a) Uiform liear array, (b) Uiform circular array Spatial Frequecy Trasform we aalyze the spectrum of the spatial Like Discrete Fourier Trasform (DFT) frequecy as well. The Nyquist [2], Spatial Frequecy Trasform is the equivalet of the samplig rate to avoid sampled ad widowed spatial spatial aliasig implies that the distace equivalet. It is used to filter sigal i space. Spatial Aliasig betwee the sesors d should be less tha or equal to the half of the miimum wavelegth [3], i.e., d λ mi / 2 where It is well kow fact from the samplig λ mi is the miimum wavelegth theorem that aliasig occurs i the correspodig to the maximum frequecy domai if the sigal is ot frequecy f max. sampled at high eough rate (the miimum rate is Nyquist samplig rate give by the twice of the badwidth of This is due to the fact that the velocity of soud, v = fλ is fixed i a medium ad thus, whe the frequecy is maximum, the sigal). We have the same sort of cosideratios to take ito accout whe the wavelegth is miimum. Fig. 2 Visualizatio of Spatial Aliasig

3 Beamformig Beamformig is the process of combiig souds or electromagetic sigals that come from oly oe particular directio ad impiges differet sesors at the receiver. Due to the coheret combiig after the appropriate phase compesatio at each sesor the resultat sigal provides higher stregth. Thus, the resultat gai of the sesor would look like a large dumbbell shaped lobe aimed i the directio of iterest [3]. This importat cocept is used i differet commuicatio, voice ad soar applicatios [3]. Directio of Arrival (DOA) It is a process of fidig the exact locatio of the source from where the soud is comig. There are three ways of fidig the Directio of Arrival [3]: Spectral-based algorithm Covetioal beamformer Capo s beamformer Subspace-based methods Multiple Sigal Classificatio ESPRIT Root MUSIC Parametric Methods Determiistic Maximum Likelihood Method Stochastic Maximum Likelihood Method ESTIMATING DOA It is assumed that the array is liear with L sesors ad soud source is located at θ 0 away from the axis of the array as show i Figure 1. A useful property of the ULA is the delay from oe sesor to the ext is uiform across the array because of their equidistat spacig. Plaar siusoidal soud waves are cosidered to avoid complexity. Trigoometry reveals that the additioal distace the icidet sigal travels betwee sesors is d cosθ. Thus, the time delay betwee cosecutive sesors is give by, τ = d cosθ / c. Measuremet ad storage of elemet sigals u Multiplicatio by weightig factors ad additio for all y=w H u calculatio of output power yy* Searchig for maximum output Power as a fuctio of directio Directio for maximum power = bearig Fig. 3 Block Diagram for DOA*. If there are D sigals icidet o the array, the received iput data vector at a M-elemet array ca be expressed as a liear combiatio of the D icidet waveforms ad oise D w Weightig factors for all directios u = a ( φ l ) s l + = As + l= 1

4 where A is the matrix of steerig vectors A=[a(f 1 ) a(f 2 )... a(f D )] s=[s 1,..., s D ]' is the sigal vector, ad =[ 1,..., M ] is a oise vector with compoets of variace s 2. The DOAs of the multiple icidet sigals ca be estimated by locatig the peaks of a MUSIC spatial spectrum P MUSIC ( φ) = a H 1 ( φ) V V H a( φ) P s e u d o s p e c tru m E s tim a te via M U S IC Power (db) No r ma liz e d Fr e q u e c y ( π r a d /s a mp le ) 0 Power Spectral Desity Estimate via Burg -10 Power/frequecy (db/hz) Frequecy (khz)

5 EXPERIMENTS I this sectio we would like to itroduce the proposed experimet based o DOA. Here we have itroduced the sub space-based method ad subspacebased methods of estimatig DOA. CONCLUSION I this paper, priciples of Array Sigal Processig is itroduced for voice sigals to fid the locatio of source. Estimatio of a arbitrary locatio of sigal source ca be performed with moderate accuracy if the data collectio time is sufficietly log or the SNR is adequately high, ad the sigal model is sufficietly accurate. The algorithm fails if impigig sigals are highly correlated. REFERENCES 1. Moso H. Hayes, Statistical Digital Sigal Processig ad Modelig, Joh Wiley ad Sos, INC., Hery Stark, Joh W. Woods, Probability ad Radom Processes with Applicatio to Sigal Processig, Pearso Educatio, Hamid Krim ad Mats Viberg, Two Decades of Array Sigal Processig, IEEE Sigal Processig Magazie, pp , July, Ala V. Oppeheim, Ala S. Willsky ad S. Hamid Nawab, Sigals ad Systems, Pearso Educatio, Robert F. Coughli ad Frederick F. Driscoll, Operatioal Amplifiers ad Liear Itegrated Circuits, Pretice-Hall of Idia Private Limited, Joh G. Proakis ad Dimitris G. Maolakis, Digital Sigal Processig Priciples, Algorithms ad Applicatios,Pretice-Hall of Idia Private Limited, Frak Ayres, JR, Theory ad Problems of Matrices, McGraw-Hill Book Compay, New York, J.J.Shyk ad R.P.Gooch, The costat modulus array for cochael sigal copy ad directio fidig IEEE Tras. Sigal Processig; vol. 44, pp , Mar C. P. Mathews, M.D.Zoltoswki. Eigestructure techiques for 2-D agle estimatio with uiform circular array, IEEE Tras. o Sigal Processig, vol 42, o. 9, pp , Sep K M Patala, E.M.Friel, Mutual Couplig Effects ad Their Reductio i Widebad Directio of Arrival Estimatio, IEEE Trasactio o Aerospace ad Electroic Systems Vol. 30, No. 4 oct 1994.

Direction of Arrival Estimation Method in Underdetermined Condition Zhang Youzhi a, Li Weibo b, Wang Hanli c

Direction of Arrival Estimation Method in Underdetermined Condition Zhang Youzhi a, Li Weibo b, Wang Hanli c 4th Iteratioal Coferece o Advaced Materials ad Iformatio Techology Processig (AMITP 06) Directio of Arrival Estimatio Method i Uderdetermied Coditio Zhag Youzhi a, Li eibo b, ag Hali c Naval Aeroautical