A COMPARATIVE STUDY OF DOA ESTIMATION ALGORITHMS WITH APPLICATION TO TRACKING USING KALMAN FILTER

A COMPARATIVE STUDY OF DOA ESTIMATION ALGORITHMS WITH APPLICATION TO TRACKING USING KALMAN FILTER ABSTRACT Venu Madhava M 1, Jagadeesha S N 1, and Yerrswamy T 2 1 Department of Computer Scence and Engneerng, JNN College of Engneerng, Shmoga 2 Department of Computer Scence and Engneerng, KLE Insttute of Technology, Hubl Trackng the Drecton of Arrval (DOA) Estmaton of a movng source s an mportant and challengng task n the feld of navgaton, RADAR, SONAR, Wreless Sensor Networks (WSNs) etc. Trackng s carred out startng from the estmaton of DOA, consderng the estmated DOA as an ntal value, the Kalman Flter (KF) algorthm s used to track the movng source based on the moton model whch governs the moton of the source. Ths comparatve study deals wth analyss, sgnfcance of Non-coherent, Narrowband DOA (Drecton of Arrval) Estmaton Algorthms n percepton to trackng. The DOA estmaton algorthms Multple Sgnal Classfcaton (MUSIC), Root-MUSIC& Estmaton of Sgnal Parameters va Rotatonal Invarance Technque (ESPRIT) are consdered for the purpose of the study, a comparson n terms of optmalty wth respect to Sgnal to Nose Rato (SNR), number of snapshots and number of Antenna elements used and Computatonal complexty s drawn between the chosen algorthms resultng n an optmum DOA estmate. The optmum DOA Estmate s taken as an ntal value for the Kalman flter trackng algorthm. The Kalman flter algorthm s used to track the optmum DOA Estmate. KEYWORDS Drecton of arrval (DOA), MUSIC, Root-MUSIC, ESPRIT, Trackng, Kalman flter. 1. INTRODUCTION The Estmaton of Drecton of Arrval (DOA) and ts trackng, s the most sgnfcant area of array sgnal processng and fnds ts applcatons n the felds of RADAR, SONAR, Wreless Sensor Networks (WSN),Sesmology etc. [1]. Trackng the DOA Estmaton s estmatng the value of DOA of the sgnals from varous sources mpngng on the array of sensors at each scannng nstant of tme [2]. The trackng s performed n order to get correlated estmates at dfferent nstants of tme. The correlaton between the data s also known as data assocaton or estmate assocaton. In the frst step, the plane wave fronts from far feld are consdered to be fallng on the Unform Lnear Array (ULA) [11]. A partcular number of snapshots are collected and the DOA s estmated usng technques lke Multple SIgnal Classfcaton (MUSIC), Root- MUSIC and Estmaton of Sgnal Parameters va Rotatonal Invarance Technque (ESPRIT). All the three algorthms estmate the DOA of the sources whch are statonary but the estmaton of DOI : 10.5121/spj.2015.6602 13

DOA of the movng source s an mportant problem. In order to estmate the DOA of the movng target, the Estmated DOA wll Act as an ntal value to the Kalman flter algorthm and the Kalman flter algorthm tracks the DOA at each scannng nstant of tme based on the target moton model [2] [16].Unlke, ths method,music, Root-MUSIC or ESPRIT can be used to estmate the nstantaneous DOA estmate provded that there s no requrement of data assocaton and the process wll be slow. In the present study, we draw bref comparsons among the three most used DOA estmaton algorthms vz MUSIC [3], Root-MUSIC [4], ESPRIT [5]. These algorthms are also known as hgh resoluton DOA Estmaton algorthms. It s assumed that the Sgnals are non-coherent, narrowband sources. The DOA Estmaton s performed n multple source scenaros and trackng s performed on sngle source. 2. BACKGROUND AND FRAMEWORK Estmatng and trackng the sgnal parameters vz Tme, Frequency, Phase and DOA are nterestng and fnd applcatons n areas of RADAR, SONAR, Sesmology, Ar Traffc Control etc. There are varous types of estmaton technques such as classcal technques, Beam formng, Spectral based and parametrc approaches[6][13]. The Maxmum Lkelhood (ML) DOA estmaton technque [10] [13] was orgnally developed by R. A. Fsher n 1920 s. Under the sutable assumptons, t estmates the DOA of the ncomng sgnal wth the help of maxmzng the log-lkelhood functon of the sampled data sequences comng from a drecton. In the beamformng technque [13], the array s steered n one drecton and the output power s measured. We observe maxmum power when steered drecton and DOA of sgnal are n lne. These technques fnd out the output of the array by lnear combnaton of the data receved wth a weght vector. If the array weght vector s used then t s known as conventonal beam formng technque. In subspace based technques for DOA Estmaton such as MUSIC [3], we get a spectrum lke functon of nterested parameters, whose dstnct peaks are the nterested estmated parameters. Although MUSIC algorthm beng robust and computatonally less complex, t needs a search algorthm to dentfy the largest of the peaks. In Root-MUSIC [4] & ESPRIT [5], a search over all the parameters of nterest s carred out to get more accurate estmates beng computatonally expensve. In order to track the parameters, we have adaptve algorthms. These are n turn dvded manly nto two types; Least Mean Square (LMS)[2][6] are the types of algorthms whch converge at slow rates dependent on the number of step szes and Recursve Least Squares (RLS)[2][6] are the types of algorthms whch converge much quckly compared to the former type of algorthms. In the present lterature, one of the later (RLS) type of algorthm vz Kalman flter s used to track the DOA Estmaton of the movng target. The Kalman Flter algorthms proposed by R.E.Kalman n 1960 [16] are basc type of trackng algorthms whch consder the state-space model of the movng target to estmate the components of moton. Ths secton gves out the necessary framework to perform the trackng operaton of the optmum DOA Estmate. 2.1 System model Let us consder an ULA of M dentcal sensors on whch N narrow band sgnals are beng mpnged from the drectons θ 1,θ 2,θ 3, θ N. The th sgnal mpngng on the array as shown n 14

the Fg 1 s gven by S t S e N (1) j( t ) ( ) 1,2,3,, Where, S, ω, ϕ are the ampltude, frequency and phase of the sgnals of three parameters, phase ϕ s consdered to be a unformly dstrbuted random varable. Let us defne a column vector S(t) as Where T denotes Transpose. S( t) [ S ( t), S ( t),... S ( t)] T (2) 1 2 N The drecton vector of the th source s gven by Fg 1: Illustraton of the DOA Estmaton Model j1( ) 2( ) j ( M 1) ( M 1) ( ) j T a( ) [1, e, e,..., e ] 1,2,3, N (3) d Where, m ( m 1) sn m 1, 2,3 M (4) c d s the nter element spacng, c beng the propagaton velocty of the plane wave front. The nter element spacng s assumed to be less than or equal to half the wavelength of the sgnal mpngng. Ths assumpton s made n order to avod spatal alasng. Substtute (4) n (3) and replacng ω=2πf c, we get the array response vector for the ULA and t s gven by 2 2 j d sn( ) j ( M 1) d sn( ) T a( ) [1, e,..., e ] 1,2,3, N (5) Where, f c s the carrer frequency and λ ω s the wavelength and they are related by f c =c/ λ ω At the m th element, the receved sgnal s gven by 15

2 d xm( t) x1 ( t)exp( j ( m 1) sn( )) 1,2,3,, M (6) c Where x 1 (t) s the receved sgnal vector at the frst element of the ULA. The drecton vector matrx s gven by A [ a( ), a( ),... a( )] (7) 1 2 Assumng whte Gaussan nose n (t) at all the elements, the receved sgnal at the output of the array s gven by, x( t) [ x ( t), x ( t), x ( t),..., x ( t)] T 1 2 3 AS( t) n( t) Where, A s a MxN drecton or steerng vector matrx. If we dscretze the above, the nput sgnals of the array are dscrete n tme and the output of the array s gven by N M X ( k) AS( k) n( k) k 1,2,3,, K (9) Where, k s the sample nstance and K s the number of snapshots. The parameters of the sgnal from the source whch we are nterested n are spatal n nature. Hence they requre spatal correlaton matrx. (8) 2 R E{ X ( k) X H ( k)} AE[ S( k) S H ( k)] A H I AR A S H 2 I (10) Where, R s s the sgnal correlaton matrx, 2 s the Nose varance and I s the dentty matrx. Practcally, the correlaton matrx [7] s unknown and t has to be estmated from the array output data. If the underlyng processes are ergodc, then the statstcal expectaton can be replaced by tme average. Let us consder that, xk ( ) s the sgnal corrupted by nose havng K snapshots are receved at the output of the array. The receved sgnal xk ( ) s denoted by X whch s also known as stacked data matrx. The smlar stackng s appled to pure sgnal vector S(k) and the nose vector n(k) as S and N respectvely. Equaton (9) can be wrtten as X AS N (11) Where, X s the receved nose corrupted sgnal matrx of sze MxK, A s the drecton or steerng vector matrx of sze MxN, S s the sgnal matrx of sze NxK, N s the addtve whte Gaussan matrx of sze MxK. The ensemble correlaton matrx estmate s computed by K ˆ 1 H 1 H R x( k) x ( k) [ XX ] (12) K K k1 16

2.2. Subspace based technques The subspace based methods of DOA estmaton use the estmated correlaton matrx, decomposng t and carryng out the analyss on the decomposton. These technques were started from a paper publshed by V.T. Psarenko [14], later tremendously progressed by the ntroducton of MUSIC proposed by R.O.Schmdt and followed by ESPRIT by Roy and Kalath. These technques use the Egen decomposton of the estmated correlaton matrx nto sgnal and nose subspaces. The array output correlaton matrx s gven by ˆ [ ] H H 2 R AE SS A I H ARS A 2 I (13) 2 Where R s s the sgnal correlaton matrx s the nose varance and I s the dentty matrx. The correlaton matrx of (13) s decomposed usng Egen Value Decomposton (EVD) to obtan ˆ H R V V (14) Where, V s the untary matrx of Egen vectors of R as columns, s the dagonal matrx of Egen values of R. In the present lterature, we assume that the sources are uncorrelated and hence the rank of the correlaton matrx R s M and that of R S s N. Egen values of R: λ 1 λ 2 λ M Egen values of sgnal subspace R S : λ 1 λ 2 λ N. Remanng (M-N) Egen values corresponds to nose subspace. The columns of V are orthogonal. Hence, the correlaton matrx can also be decomposed as Rˆ V V H V V V V H H S S n n n Where V are sgnal Egen vectors, are sgnal Egen values both span the sgnal subspace E S. S S V n and n are nose Egen vectors and Egen values respectvely spannng the complement of sgnal subspace called nose subspace E n. 2.2.1 MUSIC MUSIC Stands for Multple SIgnal Classfcaton and t s a hgh resoluton DOA estmaton algorthm. It gves the estmate of DOA of sgnals as well as the estmate of the number of sgnals. In ths algorthm, the estmaton of DOA can be carred out by usng one of the subspaces ether nose or sgnal. The steps followed to estmate DOA usng MUSIC are as follows Step 1: Estmate the correlaton Matrx ˆR from the equaton (15) ˆ 1 H R [ XX ] (16) K 17

Step 2: Fnd the Egen decomposton of the estmated correlaton matrx usng the equaton followng Rˆ Vˆ ˆ Vˆ H (17) Step 3: Fnd the nose decomposton of V ˆ matrx to fnd the span of nose subspace V n Step 4: Plot the MUSIC functon P Musc as a functon of θ Step 5: The M Sgnal drectons are the M largest peaks of the plot. The MUSIC Algorthm along wth the requred number of operatons are summarsed n the table below Table 1: Summary of the MUSIC Algorthm Input to the algorthm θ, a(θ) No Operaton performed Complexty 1 Estmaton of Correlaton Matrx KM 2 2 Egen decomposton of correlaton Matrx O(M 3 ) 3 Selectng the (N-M) Egen par to obtan Nose subspace 4 Plottng the Musc functon and dentfyng M Large peaks of the plot ((M-N)MK 3 ) Total KM 2 +O(M 3 )+((M-N)MK 3 ) From the Table 1, t has been observed that, the MUSIC algorthm s havng the computatonal complexty of the order of M 3. Search algorthm s needed to decde the largest N peaks. Ths ncreases the computatonal complexty. 2.2.2 Root-MUSIC In order to overcome the necessty of comprehensve search algorthm to locate largest N peaks n the MUSIC algorthm, a new algorthm whch gves the results numercally has been developed. The algorthm s known as Root-MUSIC s a model based parametrc estmaton technque. It s also a polynomal rootng verson of the MUSIC algorthm. The algorthm operates n the followng steps. Step 1: Estmate the Correlaton Matrx R from the equaton ˆ 1 H R [ XX ] (19) K Step 2: Fnd the Egen decomposton of the estmated correlaton matrx usng the equaton followng 18

Rˆ Vˆ ˆ Vˆ H (20) Step 3: Fnd the nose decomposton of V matrx to fnd the nose subspace. Step 4: Fnd the C matrx usng C V V (21) H n n Step 5: Fnd C l by summng the l th dagonal of C usng C l C (22) nml m, n Step 6: Fnd the roots of the resultng polynomal n terms ( M 1) ( M 1) of (N-1) pars by l P( Z) C Z (23) Step 7: Of the (N-1) roots wthn the unt crcle, choose the M closest roots to the unt crcle. Step 8: Obtan the DOA usng the below formula c arcsn arg( Zn) dw The operaton of the root-music algorthm along wth the number of operatons for each mportant step s summarzed n the followng table Table 2: Summary of the operaton of Root-MUSIC algorthm Input to the algorthm θ, a(θ) No Operaton performed Complexty 1 Estmaton of Correlaton Matrx KM 2 2 Egen decomposton of correlaton Matrx O(M 3 ) l (24) 3 Selectng the (N-M) Egen par to obtan V n 4 Fndng the C Matrx gven by C V V H n n M 2 (M-N) 5 Fndng Cl C, nml m n M 6 Fndng roots of the polynomal 8M 2 K 7 Calculaton of DOA s Total KM 2 +O(M 3 )+M 2 (M-N)+M+8M 2 K From Table 2, we can see that the complexty of the operaton of the Root-MUSIC algorthm s of the order of M 3. 19

2.2.3 ESPRIT The algorthm s based on the rotatonal nvarance property of the sgnal subspace. Let us defne two sub-matrces, A 0 & A 1 by deletng the frst and last columns of steerng vectors matrx A respectvely. The matrces A 0 & A 1 are related by the followng equaton A A (25) 1 0 Where, ϕ s the dagonal matrx havng roots on ts dagonal. Here the DOA Estmaton problem gets reduced to fndng the matrx ϕ. Consderng the correlaton matrx R from eq (12), let us obtan a matrx R 0 whch s obtaned by deletng last column of R and smlarly we obtan a matrx R by deletng last column of R. Let us defne two matrces V S0 whch has N largest Egen vectors of R 0 as ts columns and smlarly V S1 s a matrx whch s havng N largest Egen vectors of R 1 as ts columns. The two matrces V S0 and V S1 are related by a unque non-sngular matrx ψ gven by V V (26) S1 S0 The same two matrces V S0 and V S1 are related to the steerng vector matrx by a non-sngular transformaton matrx wth the help of equatons gven below V Aand VS1 A1= A 0 (27) S 0 0 Substtutng eq(26) n (27) we get V A and A0 A 0 (28) S 0 0 ϕ s estmated usng least square problem, the dagonal elements of ϕ are the estmates of the polynomal. The DOA s obtaned usng (20). The algorthm, along wth the number of operatons needed s summarzed n the table below Table 3: Summary of operaton of ESPRIT Algorthm Input to the algorthm θ, a(θ) No Operaton performed Complexty 1 Estmaton of Correlaton Matrx KM 2 2 Egen decomposton of correlaton Matrx O(M 3 ) 3 ndng the sgnal subspace ormng the V S0 by deletng 1 st column of V S ormng the V S1 by deletng last column of V S O(N 3 ) 4 Usng Least squares solve the resultng equaton 5 Obtan estmate of MxM Matrx ψ Total KM 2 +O(M 3 )+O(N 3 ) It has been observed from Table 3 that, the ESPRIT algorthm s havng the computatonal complexty of the order of M 3 as well as N 3. By ths we can say that ths algorthm s computatonally most complex of the three algorthms whch are consdered for the study. 20

2.3 Trackng the DOA The Kalman flter (KF) algorthm proposed by R.E.Kalman s consdered as the basc of trackng algorthms used n optmum flterng of non-statonary sgnals. KF algorthm also known as dynamc flterng algorthm s consdered as an advantage over the Wener flter [2] [6] [16] whch fal to address the ssue of non-statonarty. In DOA trackng we use KF flter to track the optmum DOA estmate. The estmated DOA usng one of the procedures above wll act as an ntal estmate to the Kalman Flter algorthm. Based on the physcal model, the algorthm starts trackng the DOA Estmate. The KF algorthm s llustrated usng the followng steps. 2.3.1Trackng model Let us consder θ (t), ( k), ( k) ; =1,2,3...q gves us the DOA, Angular velocty and angular acceleraton of the q number of sources at tme T. The equatons governng the moton of the th source are gven by ( k1) ( k) 1( k) ( k 1) F ( k) ( k) 2 ( k1) ( k) 3( k) (29) Where Matrx F s gven by 2 T 1 T 2 F 0 1 T 0 0 1 Where T s the samplng duraton and ω (k), =1,2,3...q are random process nose responsble for the random dsturbances. It s assumed that ω (k) s zero mean whte Gaussan nose wth covarances ndcated as follows (30) T Q E[ ( k) ( k)] (31) In the trackng model llustrated above, we assume that the acceleraton remans constant throughout the samplng nterval. 2.3.2 Trackng Algorthm In the present study, sngle source s beng tracked. The trackng algorthm s llustrated as follows x (k) s the state of the q sources at k and s gven by 21

( k) x( k) ( k) 1,2,, q ( k) Usng equaton (29) the source moton governng model, we can wrte (30) as (32) x ( k 1) Fx ( k) ( k) (33) ˆ ( k ) s the optmum DOA Estmate of ( k) based on the data obtaned durng the nterval [(kt,(k+1)t]. Based on ths we can wrte the measurement equaton as ˆ ( k ) ( k ) ( k ) 1,2,3,, q (34) usng equatons (34) and consderng the optmum DOA Estmate, a Kalman flter s used to track the source s state estmate. The state estmaton s carred out usng the followng components. We can rewrte the equaton (34) as ( n) ˆ ( n ) h ( n ) ( n ) 1,2,3,, q ( n) Where h=[1,0,0] snce we are gong to track only angular poston, we neglect the angular veloctes and acceleraton and hence the h vector. Usng Equatons (32-35) the Kalman flter equaton can be wrtten as ˆ ˆ ( ) ( 1) n n n n ˆ ( ) ( 1) ( )[ ˆ( ) ˆ n n n n L n n ( n n 1)] ( ) ˆ n n ( n n1) The frst term n the RHS of (36) are predcted estmates, the predcton s carred out usng the measurements up to (n-1) T. The predcted state estmates of ˆ ( n n), ( n n), ( n n) are gven by [ ˆ ( 1), ˆ ( 1), ˆ n n n n ( n n 1)] respectvely. The Kalman gan L (n) acts as a weghted compensator s gven by T P ( n n 1) h L ( n) T hp( n n 1) h J Where, J s the th element of the Fsher nformaton Matrx. The Kalman flter recursons are carred out n the followng steps 1. In the frst nterval, one of the optmum procedures to obtan DOA s used to fnd the ntal estmate of DOA. 1 (35) (36) (37) 22

2. In the next step we use the optmum DOA estmate as the ntal value and start trackng the DOA Estmates. The Kalman flter algorthm s summarsed n Table 4 Table4: Summary of KF Algorthm No Step 1 Step 2 Step 3 Operaton performed Intalzaton of the KF Algorthm Tme recurson for n=1,2,3,. a)fndng the sgnal predcton b) Fndng the data predcton c) Determnaton of A pror error covarance d) Fndng the Kalman Gan e) Fndng the Sgnal Update f)determnaton of A posteror error covarance Obtanng the fltered estmate ( Output) 2.4 Results and Dscussons In ths secton, n order to demonstrate the numercal propertes, convergence characterstcs and drecton fndng abltes of the spectral based technque MUSIC and parametrc technques Root-MUSIC,ESPRIT have been compared for dfferent cases to decde optmum among them usng several smulatons. Later, the process of comparson s contnued by provdng DOA estmates to the Kalman flter trackng algorthm, where we observe whch technque makes the best estmate for the purpose of trackng. Fg 2 shows the Antenna Beam pattern for DOA Estmaton usng MUSIC Algorthm. In the present smulaton, three non-coherent, narrowband sources of equal power are mpngng from the broadsde of the array wth nose power 25dB SNR from the drectons -20º, 20º, 40º. The smulaton s carred out for 50 runs wth 50 snapshots. Fg 3 and Fg 4 shows the Hstogram plot of Root-MUSIC, ESPRIT algorthm respectvely. The smulatons carred out for three non-coherent, narrowband sources of equal power are mpngng from the broadsde of the array wth nose power 25dB SNR from the drectons -20º, 20º, 40º.The smulaton s carred out for 50 runs wth 50 snapshots. These algorthms gve the values of the estmated parameter n terms of numbers drectly. Table 5 shows that, all the algorthms work at less number of array elements. Snce we use three sources, four array elements are suffcent to estmate the DOA. However, as we ncrease the number of array elements there s no sgnfcant change n estmaton accuracy. Increase n the number of array elements ncreases the computatonal complexty due to the ncrease n the sze of the correlaton matrx and hence the cost. 23

Fg 2 : Antenna beam Pattern for DOA Estmaton usng MUSIC algorthm (Number of antenna elements=7,snr=25db,number of snapshots=50) Fg 3 : Hstogram plot for DOA Estmaton usng Root-MUSIC algorthm (Number of antenna elements=7,snr=25db,number of snapshots =50) 24

Hstogram Sgnal & Image Processng : An Internatonal Journal (SIPIJ) Vol.6, No.6, December 2015 1.5 Hstogram plot for ESPRIT DOA estmator 1 0.5 No of array elements Fg 4: Hstogram plot for DOA Estmaton usng ESPRIT algorthm (Number of antenna elements=7,snr=25db,number of snapshots =50) Table 5: Performance of the Algorthms for varyng number of array elements SNR=25dB, Snapshots=50, Sources are at {-20º,20º,40º} MUSIC Root-MUSIC ESPRIT -20º 20º 40º -20º 20º 40º -20º 20º 40º 7-19.91 19.89 39.86-19.9925 19.9744 39.9865-20.0208 19.9767 39.9757 21-19.90 19.90 39.87-19.9955 19.9948 39.9917-19.9969 19.9909 39.9956 50-19.89 19.86 39.77-19.9992 19.9999 39.9995-20.0021 19.9991 40.0026 100-19.51 19.53 39.70-20.0001 20.0003 39.9994-20.0001 20.0009 39.9980 200-19.46 19.43 39.37-20.0002 20.0001 40.0002-20.0017 19.9989 40.0006 No of snapshots 0-60 -40-20 0 20 40 60 Angle (Degrees) Table 6: Performance of the Algorthms for varyng number of snapshots SNR=25dB, Number of array elements=7, Sources are at {-20º,20º,40º} MUSIC Root-MUSIC ESPRIT -20º 20º 40º -20º 20º 40º -20º 20º 40º 1-13.12 12.8 31.2-28.25 15.69 29.13-28.99 12.7046 36.939 10-18.91 18.2 39.8-19.98 20.127 39.89-19.94 20.105 39.941 20-19.89 19.97 39.92-19.98 19.9897 39.968-20.0057 20.0052 39.9982 40-19.92 19.89 39.87-20.037 20.0144 40.022-20.0295 20.0010 39.9978 100-19.98 19.96 39.93-20.0096 19.9901 40.0182-20.0062 20.0211 40.0037 200-19.94 19.93 39.82-20.0018 20.0022 40.0128-20.0037 19.9993 40.0031 500-19.95 19.95 39.93-20.0006 19.9970 40.0071-19.9977 20.0022 40.0163 1000-19.96 19.97 39.96-20.0002 20.0107 40.0040-20.0013 19.9929 40.0054 Table 6 shows the performance of the DOA Estmaton algorthms for varyng number of snapshots. At sngle snapshot, all the algorthms won t perform accurately. As the number of snapshots gets ncreased to 10, 20 and further, the accuracy n the estmaton ncreases substantally and hence the computatonal complexty. However, Root-MUSIC and ESPRIT algorthms perform much better. Of the two (Root-MUSIC and ESPRIT) algorthms, ESPRIT algorthm performs best even at 10 snapshots. 25

SNR (db) Table 7: Performance of the Algorthms for varyng SNR Number of snapshots=50, Number of array elements=7, Sources are at {-20º,20º,40º} MUSIC Root-MUSIC ESPRIT -20º 20º 40º -20º 20º 40º -20º 20º 40º 1-19.12 21.2 38.3-19.8053 19.8053 39.1318-20.5167 19.9382 39.9006 2-20.91 19.1 39.4-19.2629 19.9044 39.6671-19.3558 19.9956 39.7850 5-20.43 19.13 40.25-20.1338 19.2283 40.0051-20.1967 19.1323 39.9528 10-19.18 19.63 39.65-19.9368 19.8121 39.9518-19.9845 19.9206 39.9025 25-19.89 19.88 40.23-19.9976 19.9751 40.0148-20.0001 19.9868 39.9958 50-19.81 19.86 39.87-19.9998 20.0001 39.9994-20.0037 19.9988 40.0007 80-19.91 19.97 39.93-20.0001 20.0006 40.0002-20.0000 20.0004 39.9999 90-19.94 19.99 39.99-20.000 20.0000 40.0000-20.0000 20.0000 40.0000 Table 7 shows the performance of the DOA Estmaton algorthms for varyng SNR. At low SNR, the accuracy of MUSIC algorthms s not good whereas the Root-MUSIC, ESPRIT algorthms perform relatvely well. As ncrease SNR, the accuracy n the estmaton ncreases n the case of MUSIC algorthm. However, Root-MUSIC and ESPRIT algorthms perform much better even at low SNR. Of the two (Root-MUSIC, ESPRIT) algorthms, ESPRIT performs much better. Later, a sngle movng source s consdered and ts estmated DOA s taken as an ntal value and s provded to the Kalman flter for the purpose of trackng. Here, 10º ntal value s assumed, the estmated DOA by all the three algorthms s gven to Kalman flter model for trackng and the performance s analysed for each algorthm. The Fgs 5,6 and 7depct the performance of Kalman flter algorthm for the ntal value estmated usng MUSIC, Root-MUSIC, and ESPRIT algorthms respectvely. The KF trackng algorthm s able to track the source whose ntal value s estmated by all the DOA Estmaton algorthms from 10º to 170º. Of the three algorthms consdered above, trackng the ntal estmate usng ESPRIT algorthm s found to be better compared to other two technques. Fg 5: Trackng the DOA Estmaton ( Intal Value MUSIC) usng Kalman Flter. 26

Fg 6: Trackng the DOA Estmaton (Intal Value Root-MUSIC) usng Kalman Flter. Fg 7: Trackng the DOA Estmaton (Intal Value ESPRIT) usng Kalman Flter. 2.5 Conclusons and future work The present study depcts that, all the three DOA Estmaton algorthms are capable of estmatng the DOA and amcably work wth Kalman flter algorthm to track the movng source. However, ESPRIT algorthm beng computatonally complex s hghly accurate and acts as best ntal estmate to the Kalman flter trackng algorthm. ESPRIT, can be used f abundant computatonal resources are avalable. Sutable modfcatons such as TLS [15]-ESPRIT can be an alternatve to ESPRIT. A Comparatve study of DOA Estmaton and Trackng of Multple, Coherent and Wdeband sources wll be addressed n further communcaton. REFERENCES [1] K. Hamd and M. Vberg, Two decades of array sgnal processng research, IEEE Sgnal Process. Mag., vol. 13, no. 4, pp. 67 94, 1996. [2] S Haykn Adaptve Flter Theory, 5 edton. Upper Saddle Rver, New Jersey: Prentce Hall, 2013. 27

[3] R. O. Schmdt, Multple emtter locaton and sgnal parameter estmaton, Antennas Propag. IEEE Trans. On, vol. 34, no. 3, pp. 276 280, 1986. [4] B. Fredlander, The root-music algorthm for drecton fndng wth nterpolated arrays, Sgnal Process., vol. 30, no. 1, pp. 15 29, 1993. [5] R. Roy and T. Kalath, ESPRIT-estmaton of sgnal parameters va rotatonal nvarance technques, Acoust. Speech Sgnal Process. IEEE Trans. On, vol. 37, no. 7, pp. 984 995, 1989. [6] M. H. Hayes, Statstcal dgtal sgnal processng and modelng. John Wley & Sons, 2009. [7] G. H. Golub and C. F. Van Loan, Matrx computatons, vol. 3. JHU Press, 2012. [8] Jagadeesha S. N. A Comparatve Study of Adaptve Algorthms wth Applcatons tobeamformng. PhD thess, Department of Electroncs and Computer Engneerng, Unversty of Roorkee, Roorkee, Inda, October 1994. [9] Yerrswamy.T, Drecton of arrval estmaton usng array sgnal processng technques PhD thess, Faculty of computer scence and engneerng, VTU, Inda, August2012. [10] A B Greshman,Sergy AV and K M Wong. Maxmum lkelhood drecton of arrval estmaton n unknown nose felds usng sparse sensor arrays. IEEE Trans on sgnal processng 53(1):34-43,2005 [11] Lal C. Godara. Applcaton of antenna array to moble communcatons part : Performance mprovement, feasblty, and system consderatons. IEEE Proc, Vol 85 no7 pp 1031 1060, 1997. [12] J. Capon. Hgh resoluton frequency-wavenumber spectrum analyss. In IEEE Proc,Vol 57,Pages 1408-1418,1969 [13] Satsh chandran Advances n Drecton of Arrval Estmaton Artech House,London,2010 [14] V.T.Psarenko. The retreval of harmoncs from a covarance functon. Geophyscs J Royal Astro, Sec, 33(3):347-366,1973 [15] Gene H Golub and C F Van loan. An analyss of the total least squares problem.siam,17(6):883-893,1980 [16] R.E.Kalman A new approach to lnear flterng and predcton problems Journal of Basc engneerng 82(1): 35-45 AUTHORS VenuMadhava.M receved hs B.E.,n Instrumentaton Technology and M.Tech., n Industral Electroncs, from Vsvesvaraya Technologcal Unversty, Belgaum, Karnataka Inda n 2004 and 2009 respectvely. He s currently workng towards hs Doctoral Degree from Vsvesvaraya Technologcal Unversty, Belgaum, Karnataka, Inda. At present he s workng as Assstant Professor, n the Department of Instrumentaton Technology,Proudhadevaraya Insttute of Technology,(Afflated to Vsvesvaraya Technologcal Unversty), Hospet, Karnataka, Inda. 28

Dr. S. N. Jagadeesha receved hs B.E., n Electroncs and Communcaton Engneerng, from Unversty B. D. T College of Engneerng., Davangere afflated to Mysore Unversty, Karnataka, Inda n 1979, M..E. from Indan Insttute of Scence (IISC), Bangalore, Inda specalzng n Electrcal Communcaton Engneerng., n 1987 and Ph.D. n Electroncs and Computer Engneerng., from Unversty of Roorkee (I.I.T, Roorkee), Roorkee, Inda n 1996. He s an IEEE member and Fellow, IETE. Hs research nterest ncludes Array Sgnal Processng, Wreless Sensor Networks and Moble Communcatons. He has publshed and presented many papers on Adaptve Array Sgnal Processng and Drecton-of-Arrval estmaton. Currently he s Professor n the Department of Computer Scence and Engneerng, Jawaharlal Nehru Natonal College of Engg. (Afflated to Vsvesvaraya Technologcal Unversty), Shmoga, Karnataka, Inda. Dr.Yerrswamy receved hs B.E. n Electroncs and Communcaton Engneerng, From RYMEC, Bellary afflated to Gulbarga Unversty, Gulbarga, Karnataka, Inda n 2000,M.Tech n Network and Internet Engneerng from JNNCE, Shmoga, Afflated to Vsvesvaraya Technologcal Unversty, Belgaum, Inda n 2005 and Ph.D n the Faculty of Computer and Informaton Scence form Vsvesvaraya Technologcal Unversty, Belgaum, Karnataka, Inda He s a member of ISTE. Hs research nterests ncludes Array Sgnal Processng, Wreless Sensor Networks, Cogntve Rados. He has publshed many papers n Drecton-of-Arrval estmaton and Array sgnal processng. Currently he s Professor n the Department of Computer scence and Engneerng, KLE Insttute of Technology, (Afflated to Vsvesvaraya Technologcal Unversty, Belgaum), Hubl, Karnataka, Inda 29