 Open Access
 Total Downloads : 481
 Authors : Ashok Kumar.N, Dr.K.Raja Rajeswari, Dr.S.Koteswara Rao
 Paper ID : IJERTV2IS90468
 Volume & Issue : Volume 02, Issue 09 (September 2013)
 Published (First Online): 17092013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Underwater Passive Target Tracking from a Stationary Observer Using Modified Gain Extended Kalman Filter
Ashok Kumar.N 
Dr.K.RajaRajeswari 
Dr.S.Koteswara Rao 
M.Tech (Radar & 
Professor & Principal, 
Principal, 
Microwave Engg), 
Andhra University College 
Vignan institute of Engg 
Andhra University College 
of Engg for Women, 
for Women, 
of Engg(Autonomous), 
Visakhapatnam, 
Visakhapatnam, 
Visakhapatnam,India. 
India. 
India. 
ABSTRACT: Target tracking in underwater ,for a stationary observer, observability is less compared to moving observer. Modified Gain Extended Kalman Filter (MGEKF) developed by Song and Speyer [2] was proven to be suitable algorithm for angles only passive target tracking applications in air. In this paper, this improved MGEKF algorithm is explored for underwater applications with some modifications. In underwater, the noise in the measurements is very high, turning rate of the platforms is low and speed of the platforms is also low when compared with the missiles in air. These characteristics of the platform are studied in detail and the algorithm is modified suitably for tracking applications in underwater. Monte Carlo simulated results for one typical scenario is presented for the purpose of explanation. From the results it is observed that this algorithm is suitable for stationary observer in underwater passive target tracking using angles only measurements.

INTRODUCTION: In the ocean
environment, an observer monitors noisy sonar bearings and elevations from a radiating target.
Song and Speyer [2], was the successful contribution for angles only passive target tracking applications in air. This MGEKF algorithm was further improved by P.J. Galkowiski and M.A. Eslam [4]. In this paper, this improved MGEKF algorithm is explored for underwater applications with some modifications. In underwater, the noise in the measurements is very high, turning rate of the platforms is low and speed of the platforms is also low when compared with the missiles in air. These characteristics of the platform are studied in detail and the algorithm is modified suitably for tracking applications in underwater.
Section 2 deals with mathematical modelling of bearing and elevation measurements. Section 3 describes the implementation of the filter and section 4 is about the the results obtained in simulation.

MATHEMATICAL MODELING: Let a
target be at a point P and the observer be at the origin, as shown in Fig1. The measurement vector ,Z, is written as
B
B
tan1 rx
B r
m
m
The measurements are extracted from a single
Z= y
(1)
stationary observer and the observer processes
m
tan1 rxy
these measurements to find out target motion parametersViz., range, course, bearing,
rz
elevation and speed of the target. Here the
Where
B and
are zero mean, uncorrelated
measurements are nonlinear; making the whole process nonlinear. However, the modified gain extended kalman filter (MGEKF) developed by
normally distributed errors in the bearing (Bm) and elevation ( m ) measurements respectively.
Let the state vector be
Xs x y
T
z rx ry rz
(2)
simplified and the above equation is rewritten
The measurement matrix H is given by as
cosB
sinB
2cosB(r r ) 2sinB(r r )
0 0 0 r
r 0
2 rxy = x x – y y
(9)
H =
0 0 0
xy
cos sinB
xy
cos cosB
sin
(3)
sin(B B )
sin(B B )
r
r r
Again eqn. (9 ) is rewritten as
sin( B – B ) = cosB( rx rx ) sinB( ry ry )
(10)

HORIZONTAL PLANE AND BEARING MEASUREMENTS :
If the range in horizontal plane is
rx2 ry2 , then the estimated range be
rxy

ELEVATION ANGLE MEASUREMENT:
In the previous section , it is seen that
2 2
2 2
rxy rx ry (4)
tan1 rx
B generates
By adding
rxy
and
rxy
, eqn. (5) is obtained . ry
r + r = r sinB + r cosB + r sinB + r cosB
(5)
sin(B – B ) = cosB(rx rx ) sinB(ry ry )
. (11)
xy xy x y x y
rxy
adding both sides r
– r sinB – r sinB – r cosB + r cosB
to the above
Similarly
tan1
xy generates
x x y y
equation and after straight forward simplification, the following equations are obtained.
rz
sin( – ) = cos (rxy rxy ) sin (rz rz )
r
(12)
rxy
+ rxy
( rx – rx )(sinB – sinB ) + (ry – ry )(cosB – cosB )
=
1 cos(B – B )
After simple trigonometric manipulations, eqn.
rxy

rxy
(6)
( rx – rx )(sinB + sinB ) + (ry – ry )(cosB + cosB )
=
1 cos(B – B )

is written as
rxy – rxy =
(B + B )
(B + B )
using (6) and (7)
(7)
( rx – rx )sin
2
cos
+ (ry – ry )cos 2 (B – B )
2
(13)
2r
= ( r
– r )
sinB sinB

sinB + sinB
Substituting (13) in (12)
xy x
x 1 cos(B – B )
1 cos(B – B )
(8)
( r – r
)sin (B + B ) + (r
– r
)cos (B + B )
cosB – cosB
cosB + cosB
cos x x
2 y y 2
(ry – ry )
sin( – ) =
r
1 cos(B – B)
1 cos(B – B)
cos (B – B)
2
Eqn.(8) can be simplified as
sin (r
r )
sinB sinB sinB + sinB
r z z
1 cos(B – B ) 1 cos(B – B ) =
(1 cos(B – B )(sinB – sinB ) – (1 cos(B – B )(sinB + sinB ) 1 cos2 (B – B )
(14)
Eqn. (10) and eqn.(14) are rewritten in matrix
the coefficients of ( rx – rx ) and ( ry – ry )
are
form as
(B – B )
cos B
rxy
B + B

sinB 0
rxy
B + B
day, say 15000 meters, is utilized in the calculation of initial position estimate of the target is as
X(00)=[10 10 10 15000sin Bm (0)sin m(0)
sin cos
cos cos T
2
2
– sin
15000sin m(0)cos Bm(0) 15000cos m(0) ]
B – B
B – B
( – )
B – B
B – B
cos r
cos r
r
where Bm (0) and m(0) are initial bearing and
2
2
2
2
rx – rx
elevation measurements.
4. SIMULATION RESULTS :
r – r
(15)
All raw bearings and elevation
y y
rz – rz
As true bearing is ot available, it is replaced by
measured bearing in eqn.(15) and obtained eqn.(16) as follows.
measurements are corrupted by additive zero mean Gaussian noise with a r.m.s level of 0.3 degree. Corresponding to a tactical scenario in which the target is at the initial range of 20000 meters at initial bearing and elevation of 0.5 and 45 degrees respectively. The target is assumed to be moving at a constant course of 130 degrees. Observer is assumed to be stationary. The results have been ensemble
cosBm
rxy

sinBm rxy


averaged over several Monte Carlo runs. The errors
0 in estimates are plotted in Fig.2. It is observed that
this required accuracy is obtained from 800 seconds
B + B
B + B
(B – B )
sin m cos
cos Bm + B cos
.
2
2
onwards and so this algorithm seems to be very
( – )
– sin
much useful for underwater passive target tracking
B
– B
B – B
r
cos m r
cos m r
when observer is stationary, for a moving target.
2
2
2
2
REFERENCES:
rx – rx
rx – rx
[1]. S. Farahmand , G. Giannakis , G. Leus and Z.r – r = g
r – r
(16)
Tian "Sparsityaware Kalman tracking of target
y y
rz – rz
y y
rz – rz
signal strengthson a grid", Proc. 14th Int. Conf.
Inform. Fusion, pp.1 6 2011
[2].T.L.Song & J.L. Speyer," A stochastic AnalysisConsidering x, y and z also, g is
0
0
0
0
0
0
cosBm
m
m
rxy rs. sin
Bm B
given by
m
m
sinBm rxy rs.sin
Bm B
of a modified gain extended kalman filter with applications to estimation with bearing only measurements", IEEE Trans. Automatic Control
0 Vol. Ac 30, No.10, October 1985, PP 940949.
[3]. E. Masazade, M. Fardad and P. K. Varshney,
SparsityPromoting Extended Kalman Filtering
g
0 0 0
cos sin
2
cos cos
2
– sin
for Target Tracking in Wireless Sensor
Bm B
Bm B
r Networks, IEEE Signal Processing Letters, vol.
2
2
r cos
r cos
2
2
19, no.12, December 2012.
[4]. P.J. Galkowiski and M.A. Islam, An


IMPLEMENTATION OF THE ALGORTIHM :
The above mentioned improved algorithm is implemented using MGEKF (MGEKF equations are not given in this paper due to space constraint. These equations are available in [4].)for underwater passive target tracking as follows. As only bearing and elevation measurements are available, the velocity components of the target are assumed to be each 10 m/sec which is very close to the realistic speed of the vehicles in underwater. The range of the
alternate derivation of the Modified Gain Function of Song and Speyer ", IEEE Trans. Automatic Control Vol. 36, No.11, November 1991, PP 1323
1326.
Y
Z
rxyz
P(x,y,z)
rz
90
B
rxy
rx
P1(x,y)
ry
X
Fig.2(a). Error in range estimate versus time
Fig.2(c). Error in Course estimate verses time
Fig.1. A typical target observer geometry
Fig.2(b). Error in Speed estimate versus time