Objectives:Modified Gain Extended Kalman Filter (MGEKF) created by Song and Speyer [1] was turned out to be appropriate calculation for points just detached target following applications in air.Methods:As of late, roughly altered increases are displayed, which are numerically steady and exact [2]. In this paper, this enhanced MGEKF calculation is investigated for submerged applications with a few changes.Results:In submerged, the commotion in the estimations is high, turning rate of the stages is low and speed of the stages is likewise low when contrasted and the rockets in air. These attributes of the stage are concentrated on in detail and the calculation is adjusted appropriately to track applications in submerged.Conclusions:Monte-Carlo analysis comes about for two run of the mill situations are introduced with the end goal of clarification. From the outcomes it is watched that this calculation is especially reasonable for this nonlinear edges just detached target following

JAWHAR A

RAJYA LAKSHMI C

English

Innovare Academic Sciences: E-Journals

ISSN -  2347-1573 Vol 5, Issue 1, 2017INVESTIGATION OF NON-LINEAR MARITIME SIGNAL ESTIMATION SCHEME FOR PASSIVE ACOUSTIC AND ELECTROMAGNETIC UNDERWATER TRACKING AND UNDERWATER SURVEILLANCEJAWHAR A*, RAJYA LAKSHMI CDepartment of Electrical and Electronics Engineering, Sanketika Institute of Technology and Management, Visakhapatnam, Andhra Pradesh, India. Email: jawaharee@yahoo.comReceived: 26 October 2016, Revised and Accepted: 01 November 2016ABSTRACTObjectives: Modified gain extended Kalman filter (MGEKF) created by Song and Speyer was turned out to be an appropriate calculation for points just detached target following applications in air.Methods: As of late, roughly altered increases are displayed, which are numerically steady and exact. In this paper, this enhanced MGEKF calculation is investigated for submerged applications with a few changes.Results: In submerged, the commotion in the estimations is high, turning rate of the stages is low, and speed of the stages is likewise low when contrasted and the rockets in air. These attributes of the stage are concentrated on in detail, and the calculation is adjusted appropriately to track applications in submerged.Conclusions: Monte-Carlo analysis comes about for two run of the mill situations are introduced with the end goal of clarification. From the outcomes, it is watched that this calculation is, especially reasonable for this nonlinear edges just detached target following.Keywords: Estimation, Sonar, Kalman filter, Simulation, Modified gain, Angles-only target tracking.INTRODUCTIONIn the sea environment, three-dimensional (3D) edges just target movement examinations is by and large utilized. A spectator screens uproarious sonar orientation and heights from a transmitting target, which is thought to go in a consistent course with uniform speed. The estimations are removed from a solitary eyewitness and the spectator forms these estimations to discover target movement parameters such as go, course, bearing, rise, and speed of the objective. Here, the estimations are nonlinear; making the entire procedure nonlinear. Nonetheless, the changed increase broadened kalman channel (modified gain extended Kalman filter [MGEKF]) created by Song and Speyer [1-6], is the fruitful commitments in this field. MGEKF performs superior to anything EKF and also pseudo estimation channel. However, the adjusted pickup capacities was determined in light of the pseudo estimations. As of late, the adjusted pick up capacities are enhanced and exhibited by Longbin et al. [2-15], in which recipe of the bearing estimation is the same as in [1] and that of height estimation is more exact than the first.So far, the angles in azimuth alone are considered. Now elevation angles are also considered. A point P, as shown in Fig. 1 whose elements are x, y, z.A line from P is drawn onto xy plane. This line is parallel to Z axis. Let this line touch xy plane at P’(x,y). Let the angle of elevation, ϕ, be defined as the angle between +ve Z axis (or z up) and the line OP. Let the azimuth angle be the angle between True North and the line OP’. In Fig. 2a OPP’ is denoted as ϕ We can write the following equations.rz=r cos ϕ  rxy=r sin ϕ (1)Where, r is the distance from point 0 to P (in 3D space), rxy is the distance from point 0 to P’ (in two-dimensional space).Also rrByxy= cos  and rrBxxy= sinry=rxy cos B rx=rxy sin B (2)Substituting Equations (1) in (2),rx=r sinϕ sin B ry=r sin ϕ cos B (3)and rz=r cos ϕ.Where, r r +r +r r +rx2y2z xy2z2= =2r r rxy x2y= +2  (4)and rrBBBxy= =sincostan∴ Bearing, Brrxy= −tan 1  (5)tan = =r /rr /rrrxyzxyz{From (1)} (6) = −tan 1rrxyzLet the measurement be ZBtanrrtanrrmm1 xyB1 xyz= =++−−φσσφ (7)Considering the state vector as X x y z r r rs x y zT=      (8)Research Article47Innovare Journal of Eng. & Tech, Vol 5, Issue 1, 2017, 46-50 Jawhar and Lakshmi Then H=  h(X  X  h(B)  x  h(B)  y  h(B)  z  h(Bss∂∂∂∂∂∂∂∂∂)=  )  r  h(B)  r  h(B)  r  h( )  x  h( )  y  x y z∂∂∂∂∂∂ ϕ∂∂ ϕ∂∂ h( )  z  h( )  r  h( )  r  h( )  rx y zϕ∂∂ ϕ∂∂ ϕ∂∂ ϕ∂  (9)  h(B)  x  h(B)  y  h(B)  z =0  = =    IIIly ∂∂=∂∂=∂∂=hxhyhz( ) ( ) ( )    0  h(B)  r11+r r rx x y y==2 212y y y2 2y xy xy xyxy xyˆr r r1 1  cos B . . ˆr r r rr r= = =  − − −= − = = =  2y x xx2 2 2y xy xy xyxy y xyˆr r r  h(B) 1 1 sin B.r  ˆ  r r r rr r r∂∂=h Brz( )0    ∂ +  = = ⋅   ∂    = ⋅ = =2 22x yxy z2 2 2 zx z zxy zz x z x2 2xy xyr r  r r  h( ) 1 1 1  r r   x r1+r r r rˆ ˆr 2r r r cos sinBˆ2r r rr r  ∂= ⋅ ⋅ = ⋅ =∂y yz z2 2y z xy xyˆ ˆ2r rr rh( ) 1 cos cosBˆr r 2r r rr r     − − −= − =  2xyzxy2 2 2 2z zˆrr  h( ) 1 r sin sinr . = = ˆ  r rr r r r   −  ∴   −  xy xyˆ ˆ   cosB   sinB0 0 0 0ˆ ˆr rH=ˆ ˆˆ ˆ ˆcos   sinB cos   cosB   sin0 0 0 ˆ ˆ ˆr r r (10)Horizontal plane and bearing measurementsIf the range in horizontal plane is r rx y2 2+ , then the estimated range be:= +2 2xy x yr̂ r r  (11)Fig. 1: Target-observer geometryFig. 2: (a-c) Errors in target motion parameters for given scenariocba48Innovare Journal of Eng. & Tech, Vol 5, Issue 1, 2017, 46-50 Jawhar and Lakshmi As rx=rxy sin B =x xy ˆˆ ˆr r sin B ry=rxy cos B =y xyˆˆ ˆr r cos B  (12)rx sin B + ry cos B = rxy sin2B+rxy cos2B=rxy (13)x y xyˆ ˆ ˆr  sin B+r cosB=rBy adding +xy xyˆr r ,+ = + + +xy xy x y x yˆ ˆˆ ˆ ˆr r r sinB r cosB r sinB r sinBAdding both sides − − − +x y y yˆ ˆ ˆˆ ˆr sinB r cosB r cosB r cosB  to the above equation.+ − − + + −+ − − − − −xy xy x x y y x xy y x x y yˆ ˆˆ ˆ ˆr r r sinB r sinB r cosB r cosB=sinB(r r )ˆ ˆˆ ˆ ˆcosB(r r ) sinB(r r ) cosB(r r )= − − + − −x x y y ˆˆ ˆ(r r )(sinB sinB) (r r )(cosB cosB)  (14)Substituting for rx, xr̂  and ry, yr̂  on LHS of (14)+ − −− − =xy xy xy xyxy xyˆ ˆˆ ˆr r r  sinB sinB r sinB ˆ ˆˆ ˆsinB r cosBcosB r cosBcosB RHS  of (14)+ − −xy xy ˆ ˆˆ(r r )(1 sinB sin B cosB cos B) =RHS of (14)− − =xy xy ˆˆ(r +r )(1 cos(B B)) RHS  of (14)− − + − −+ =− −x x y yxy xyˆ ˆˆ ˆ(r r )(sinB sinB) (r r )(cosB cosB)ˆr r ˆ1 cos(B B) (15)By subtracting rxy from xyr̂ ,− = − − +xy xy x y x yˆ ˆ ˆˆ ˆ ˆr r r sinB r sinB r sinB+r cosB  (16)Adding both sides − − − −x x y yˆ ˆˆ ˆ ˆ ˆr sinB r sinB r cosB r cosB  to (16) and continuing the previous procedure,− + + − +− =+ −x x y yxy xyˆ ˆˆ ˆ(r r )(sinB sinB) (r r )(cosB cosB)ˆr r ˆ1 cos(B B) (17)Using (15) and (17), − − +   + + − +  xy x xy yˆ ˆsinB-sinB sinB+sinBˆ ˆ2r =( r -r ) ˆ ˆ1 cos(B-B) 1 cos(B-B)ˆ ˆcosB-cosB cosB+cosBˆ(r -r ) ˆ ˆ1 cos(B-B) 1 cos(B-B) (18)(18) can be simplified as:−−− − + −+ − − − − − +=− −2ˆ ˆsinB sinB sinB+sin Bˆ ˆ1 cos(B B) 1 cos(B B)ˆ ˆ ˆ ˆ1 cos(B B) (sinB sinB) (1 cos(B B)(sinB sin B) ˆ1 cos (B B)− −=−2ˆ ˆ2sinB cos (B B) 2sinBˆsin (B B)−= =−−2ˆ2cosB sin (B B) 2cosBˆˆ B sin (B B)sin (B B) (19)IIIly (ry− yr̂ )coefficient is simplified to − −−2ˆ ˆ2cos(B B)cos B 2cosBˆsin (B B)= −−2sinBˆsin(B B) (20)−−∴ = −− −y yx xxyˆˆ 2sinB(r r )2cosB(r r )ˆ2r ˆ ˆsin(B B) sin(B B) (21)(21) is rewritten as,− − −− = x x y yxyˆ ˆcosB(r r ) sinB(r r )ˆsin(B B)r̂ (22)Angle measurementtan− =1rrBxy generates − − −− = x x y yxyˆ ˆcosB(r r ) sinB(r r )ˆsin(B B)r̂tan− =1rrxyz  generates   − − −− = xy xy z zˆ ˆcos (r r ) sin (r r )ˆsin( )r(23)Where, rx → rxy, ry → rz, B → ϕ  rxy → rxyz (=r)−xy xyˆr r  is given by (17) as follows,− −− =+ −x x y yxy xyˆ ˆˆ ˆ(r r )(sinB + sin B)+(r r )(cosB +cosB)ˆr r ˆ1 cos(B B) (17)It is known that cos(p+q) + cos(p−q) =2cos p cos q,Here p+q=B p−q= B̂  giving ˆB+B  and −=ˆB Bp2So + −ˆ ˆB B B BˆcosB+cos B=2 cos cos2 2 (24)IIIly sin(p+q) + sin(p−q) = 2sin p sin q,+ −ˆ ˆB B B BˆsinB+sin B=2 sin sin2 2 (25)IIIly 1 2 2222+ =coscoscosααα= ,so −+ − 2ˆB Bˆ1 cos(B B) = 2 cos2 (26)Using (24), (25) and (26), equation (17) becomes,+ −−+ −+ −− =−x xy yxy xy2ˆ ˆ(B B) (B B)ˆ(r r )2sin cos2 2ˆ ˆ(B B) (B B)ˆ(r r )2cos cos2 2ˆr r ˆ(B B)2cos2+ +− + −=−x x y yˆ ˆ(B B) (B B)ˆ ˆ(r r )sin (r r )cos2 2ˆ(B B)cos2 (27)Substituting (27) in (23),      − −   x x y yz zˆ ˆ(B+B) (B+B)ˆ ˆ( r -r )sin +(r -r )coscos sin2 2ˆ ˆsin(  - )=  (r r )ˆˆ ˆr r(B-B)cos2 (28)49Innovare Journal of Eng. & Tech, Vol 5, Issue 1, 2017, 46-50 Jawhar and Lakshmi As  − ˆ  tend to zero and sin(  − ˆ )→(  − ˆ ) and sin ( − ˆB B )→( − ˆB B ). Equations (22) and (28) can be written in matrix form as,  − = −  ˆ(B B)ˆ(   )  −               −     −         xy xycosB sinB 0ˆ ˆr rˆ ˆB+B B+Bsin cos cos cos2 2 sinˆˆ ˆ rB+B B Bˆ ˆcos r cos r2 2  − −  − x xy yz zˆr rˆr rˆr r(29)True bearing is not available, if it is replaced by measured bearing,  − = −  ˆ(B B)ˆ(   )  −               −     −         m mxy xym mm mcosB sinB0ˆ ˆr rˆ ˆB +B B +Bsin cos cos cos2 2 sinˆˆ ˆ rB +B B Bˆ ˆcos r cos r2 2     − −  − x xy yz zˆr rˆr rˆr r (30)= g  − −  − x xy yz zˆr rˆr rˆr rWhere g is given by,g =   −               −     −         m mxy xym mm mcosB sinB0ˆ ˆr rˆ ˆB +B B +Bsin cos cos cos2 2 sinˆˆ ˆ rB +B B Bˆ ˆcos r cos r2 2 (31)Considering   x, y and z  also g is given by,g=  −  = =     + +         −    − −         m mˆ ˆxy xysin sinm mm mcosB sinB0 0 0 0ˆ ˆ ˆ ˆr r r rˆ ˆB B B Bcos   sin cos  cos2 2 sin0 0 0 ˆˆ ˆ rB B B Bˆ ˆr cos r cos2 2 (32)   −    −  xy xyˆ ˆ    cosB   sinB0 0 0 0ˆ ˆr rH=ˆ ˆˆ ˆ ˆcos   sinB cos   cosB   sin0 0 0 ˆ ˆ ˆr r r (33)Implementation of Kalman filterIt is assumed that the target is not changing depth.Let X x y r r rs x y zT=    (34)Where,  x y   are target (absolute) velocity components,Let X(0|0) be Xf(0|0) = f m mTm m mX [0|0] 10 10 10 15000 sin B sin15000 cos B sin 15000cos (35)P(0|0)=I (36)G(k+1)=P(k+1)HT(k+1)[H(k+1)P(k+1|k)HT(k+1)+r(k+1)] (37)Where, r(k+1) = σσ ϕ  k 1) 00  (k+1)B22( + (38)Where, B2  and σφ2  are input error bearing and elevation measurement covariances respectively.+ + + + − +ˆ ˆ ˆX(k+1|k+1)=X(k 1|k) k(k 1)[Z(k 1) h{x(k 1|k)}]  (39)Where, Z(k+1)=Bmm  (40)P(k+1|k+1) = (I−Gg)P(I−Gg) P(I−Gg)T + G r GT =(I−G(k+1)g)P(k+1|k)(I−G(k+1)gT) + G(k+1)r(k+1)GT(k+1) (41)For next cycle ˆ ˆx(k|k)=x(k+1|k+1)  (42)and P(k|k)=P(k+1|k+1) (43) +ˆ ˆx(k+1|k)= (k+1|k)x(k |k) B  (44)Where, B=000{x (k 1) x k)}{y (k 1) y k)}{z (k 1) z k)}0 00 00 0− + −− + −− + − ((( (45)P(k+1|k)=ϕ(k+1|k)P(k|k)ϕT(k+1|k)+Q(k+1) (46)Where, Q is plant covariance matrix.A maneuvering target and tracking using bearing and elevation measurements  x(k+1)=x k tx(k)( )+∫ ∫ ∫  t t0 0x(k+1)= x(k) dz+ x(k)dzx k x k x k t+tx(k)( ) ( ) ( ).+ − =122 x k x k tx k +tx(k)( ) ( ) ( )+ = +122 This can be easily remembered as,X t X t x(t )+ x(t )n n n n( ) ( )+ = +  22x Kt t x Kt tx kttx kt( ) ( ) ( ) ( )+ = + + 22or simply,x k x k tx ktx k( ) ( ) ( ) ( )+ = + +122 50Innovare Journal of Eng. & Tech, Vol 5, Issue 1, 2017, 46-50 Jawhar and Lakshmi IMPLEMENTATION OF THE ALGORITHM FOR UNDERWATER APPLICATIONThe above mentioned improved MGEKF algorithm is implemented for underwater passive target tracking as follows. In underwater, the variance of the noise in the measurements is very high, and so the measurements are preprocessed (averaging the measurements over some duration, say 20 seconds) to reduce the variance of the noise in the measurements. Hence, although the measurements are available every one second, the update of the solution is presented at every 20 seconds. This does not hamper the results as the vehicles move in water at very low speeds when compared with that of in air. The underlying target state vector is picked as takes after. As just bearing and height estimations are accessible, and there is no real way to figure the speed parts of the objective, these segments are each thought to be 10 m/s which is near the sensible speed of the vehicles in submerged. The scope of the day, say 15,000 m, is used in the computation of beginning position gauge of the objective is as:( )( ) ( )( ) ( ) ( )= =  Tm mTm m mX 0|0   x y z x y z10 10 10 15000 * sin B 0 * sin 015000 * sin 0 * cos B 0 15000 * cos 0Where, Bm(0) and m(0) are initial bearing and elevation measurements. The initial covariance matrix is chosen according the standard procedure [3].SIMULATION RESULTSPC calculation is produced and tried with recreated information to outline the execution of this estimator. Every single crude bearing and height estimations are adulterated by added substance zero mean Gaussian commotion with a r.m.s level of 1° and 0.3 separately and after that preprocessed over a time of 20 seconds. Relating to a strategic situation in which the objective is at the underlying scope of 19,000 yards (17373.6 m) at beginning bearing and height of 0° and 45° individually, the mistakes in assessments are plotted in Figs. 1, and 2(a-c) (on seawaters, as a rule range is communicated in yards and speed in tangles). The objective is thought to move at a consistent course of 140° at a speed of 25 bunches (12.875 m/s). Spectator is accepted to moving at a consistent speed of 7 bunches (3.605 m/s) with a pitch point of 45°. At last the outcomes have been troupe found the middle value of more than a few Monte Carlo runs. When all is said in done the blunder permitted in the evaluated target movement parameters in submerged is 8% in range assess, 3° in course gauge and three meters/sec in speed appraise. It is watched this required exactness is acquired from 240 seconds onwards thus this calculation is by all accounts particularly valuable for submerged aloof target following.REFERENCES1. Song TL, Speyer JL. A stochastic analysis of a modified gain extended kalman filter with applications to estimation with bearing only measurements. IEEE Trans Autom Control Ac 1985;30(10):940-9.2. Golkoki PHJ, Islam MA. An alternative derivation of the modified gain function of Song and Speyer. IEEE Trans on AC 1991;36:42.3. Longbin M, Qi L, Yiyu Z, Zhongkang S. Improvement of song and Speyer’s modified gain functions in angles only tracking. IEEE Trans Aerosp Electron Syst (to be Published).4. Chan YT, Rudnicki SW. Bearings - Only doppler bearing tracking using instrumental variables. IEEE Trans Aerosp Electron Syst 1992;28(4):1076-83.5. Jawahar A, Rao SK. Modified polar extended kalman filter (MP-EKF) for bearings - Only target tracking. Indian J Sci Technol 2016;9(26). DOI: 10.17485/ijst/2016/v9i26/90307.6. Jawahar A, Rao SK, Murthy AS, Srikanth KS, Das RP. Advanced submarine integrated weapon control system. Indian J Sci Technol 2015;8(35):1-3. DOI: 10.17485/ijst/2015/v8i35/82087.7. Jawahar A, Rao SK, Murthy AS, Srikanth KS, Das RP. Underwater passive target tracking in constrained environment. Indian J Sci Technol 2015;8(35). DOI: 10.17485/ijst/2015/v8i35/82264.8. Jawahar A, Rao SK, Karishma SB. Target estimation analysis using data association and fusion. Int J Oceans Oceanogr 2015;9(2):218-25.9. Jawahar A, Rao SK. Recursive multistage estimator for bearings only passive target tracking in ESM EW systems. Indian J Sci Technol 2015;8(26):74932, 1-5.10. Jawahar A. Feasible course trajectories for undersea sonar target tracking systems. Indian J Autom Artif Intell 2016;3(1):1-5.11. Jawahar A, Chakravarthi CV. Improved nonlinear signal estimation technique for undersea sonar-based naval applications. Innov J Eng Technol 2016;4(4):20-5.12. Jawahar A, Chakravarthi CV. Comparative analysis of non linear estimation schemes used for undersea sonar applications. Innov J Eng Technol 2016;4(4):14-9.13. Prasanna KL, Rao SK, Jagan BO, Jawahar A, Karishma SB. Data fusion in underwater environment. Int J Eng Technol (IJET) 2016;8(1):225-34.14. Prasanna KL, Rao SK, Jawahar A, Karishma SB. Modern estimation technique for undersea active target tracking. Int J Eng Technol 2016;8(2):791-803.15. Prasanna KL, Rao SK, Jawahar A, Karishma SB. Ownship strategies during hostile torpedo attack. Indian J Sci Technol 2016;9(16). DOI: 10.17485/ijst/2016/v9i16/85556.

INVESTIGATION OF NON-LINEAR MARITIME SIGNAL ESTIMATION SCHEME FOR PASSIVE ACOUSTIC AND ELECTROMAGNETIC  UNDERWATER TRACKING AND UNDERWATER SURVEILLANCE

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INVESTIGATION OF NON-LINEAR MARITIME SIGNAL ESTIMATION SCHEME FOR PASSIVE ACOUSTIC AND ELECTROMAGNETIC UNDERWATER TRACKING AND UNDERWATER SURVEILLANCE

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