Aerospace and Electronic Systems Magazine December 2017 - 74

Target Tracking With 2-HFSWR Multisensor Surveillance System
For the constant turn (CT) model, the state equation is



( x − a)2 + y 2


1

 d1  
[(
)
]
−
⋅
+
⋅
x
a
v
y
v
x
y 
   ( x − a)2 + y 2
v

 1=

d2  
2
2
(
)
+
+
x
a
y

  

 v2  
1
[( x + a) ⋅ vx + y ⋅ v y ]

2
2
 ( x + a) + y


X (k + 1) = ACT X (k ) + BCT W (k )

where the transition matrices are

ACT

BCT


sin (ωT )
1
ω

0
cos (ωT )

=  1 − cos (ωT )
0
ω

0
sin
(ωT )

0
0

T 2 / 2
0

0
T

= 0
T 2/ 2

T
 0
 0
0


0 −
0
1
0
0

1 − cos (ωT )

ω

− sin (ωT )
sin (ωT )

ω

cos (ωT )
0


0

0


0

0
1 

Based on the above equation, the nonlinear measurement function
H ( X (k + 1)) can be determined accordingly.
However for maneuvering targets, the moving state varies frequently, it is inappropriate to describe the movement in one definite
model. In order to describe the motion process of the target effectively and precisely, it is appropriate to employ multiple models.

0

0
0

0
1 

IMMASTF

It should be noted that the parameters of CV and CT models
are time-variant. If the target moves at a different speed or turn rate
under different environment, the parameters of the system model
and the stochastic characteristics of the noises can be changed accordingly.

MEASUREMENT MODEL OF THE SYSTEM
Since the required parameters are just the distance and velocity
of vessels without azimuth measurement, the measurement is described as
Z(k  1)
  d1 (k  1) v1 (k  1) d 2 (k  1) v2 (k  1) T

where d1(k + 1) and d2(k + 1) are the radial location; v1(k + 1) and
v2(k + 1) are the radial velocity. While, for the whole motion process, the measurement model is
Z (k + 1) = H ( X (k + 1)) + V (k + 1)

The IMM algorithm is one of the most cost-efficient maneuvering
target tracking methods, which consists of input interaction, the
filter corresponding to each model, the probability updater and the
output fusion. The estimation of the state is based on the sum of the
weighted state estimation from each model
Moreover, the accuracy of STF algorithm depends on the precision of the established model, the accuracy of the initial value
and a priori statistical property, while these parameters are difficult
to be obtained in practice. Therefore, the idea of STF is combined
with the Saga-Husa adaptive filter together with the IMM algorithm
to improve the tracking performance under complex environment
with unknown statistical characteristics of observation noises.

STRONG TRACKING FILTER
The time-varying suboptimal fading factor λ(k + 1) is introduced
into the prediction error covariance of the STF to adjust the gain
matrix of the filter and make the residual error series orthogonal to
each other. Then covariance can be rewritten as
P ( k + 1| k ) = λ (k + 1) F ( k ) P ( k , k ) F T ( k ) + BQ ( k ) B T

However, the optimal value of the fading factor needs great
computational efforts, which is unsuitable for real-time processing.
Therefore, a suboptimal way of selecting the fading factor is given by
η (k + 1) η (k + 1) > 1
λ ( k + 1) = 
η (k + 1) ≤ 1
1

where the observation noise is

where

V (k + 1) =  vd1 (k + 1), vv1 (k + 1), vd2 (k + 1), vv2 (k + 1)  T

η (k + 1) =
vd1 (k + 1),vv1 (k + 1),vd 2 (k + 1) and vv2 (k + 1) are zero mean Gaussian
white noises with variances δ d1 ( k + 1), δ v1 (k + 1), δ d2 (k + 1), and
δ v2 ( k + 1), respectively.
Set the distance between the two radar stations as 2a. According to Figure 1, the geometrical relationship between the state and
the measurement is
72

tr[ N ( k + 1)]
tr[ M ( k + 1)]

with
N (k + 1) = V0 (k + 1) − H (k + 1)Q (k ) H T (k + 1) − β R(k + 1)
M (k + 1) = H (k + 1) F (k ) P (k ) F T (k ) H T ( k + 1)

IEEE A&E SYSTEMS MAGAZINE

DECEMBER 2017



Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine December 2017

No label
Aerospace and Electronic Systems Magazine December 2017 - No label
Aerospace and Electronic Systems Magazine December 2017 - Cover2
Aerospace and Electronic Systems Magazine December 2017 - 1
Aerospace and Electronic Systems Magazine December 2017 - 2
Aerospace and Electronic Systems Magazine December 2017 - 3
Aerospace and Electronic Systems Magazine December 2017 - 4
Aerospace and Electronic Systems Magazine December 2017 - 5
Aerospace and Electronic Systems Magazine December 2017 - 6
Aerospace and Electronic Systems Magazine December 2017 - 7
Aerospace and Electronic Systems Magazine December 2017 - 8
Aerospace and Electronic Systems Magazine December 2017 - 9
Aerospace and Electronic Systems Magazine December 2017 - 10
Aerospace and Electronic Systems Magazine December 2017 - 11
Aerospace and Electronic Systems Magazine December 2017 - 12
Aerospace and Electronic Systems Magazine December 2017 - 13
Aerospace and Electronic Systems Magazine December 2017 - 14
Aerospace and Electronic Systems Magazine December 2017 - 15
Aerospace and Electronic Systems Magazine December 2017 - 16
Aerospace and Electronic Systems Magazine December 2017 - 17
Aerospace and Electronic Systems Magazine December 2017 - 18
Aerospace and Electronic Systems Magazine December 2017 - 19
Aerospace and Electronic Systems Magazine December 2017 - 20
Aerospace and Electronic Systems Magazine December 2017 - 21
Aerospace and Electronic Systems Magazine December 2017 - 22
Aerospace and Electronic Systems Magazine December 2017 - 23
Aerospace and Electronic Systems Magazine December 2017 - 24
Aerospace and Electronic Systems Magazine December 2017 - 25
Aerospace and Electronic Systems Magazine December 2017 - 26
Aerospace and Electronic Systems Magazine December 2017 - 27
Aerospace and Electronic Systems Magazine December 2017 - 28
Aerospace and Electronic Systems Magazine December 2017 - 29
Aerospace and Electronic Systems Magazine December 2017 - 30
Aerospace and Electronic Systems Magazine December 2017 - 31
Aerospace and Electronic Systems Magazine December 2017 - 32
Aerospace and Electronic Systems Magazine December 2017 - 33
Aerospace and Electronic Systems Magazine December 2017 - 34
Aerospace and Electronic Systems Magazine December 2017 - 35
Aerospace and Electronic Systems Magazine December 2017 - 36
Aerospace and Electronic Systems Magazine December 2017 - 37
Aerospace and Electronic Systems Magazine December 2017 - 38
Aerospace and Electronic Systems Magazine December 2017 - 39
Aerospace and Electronic Systems Magazine December 2017 - 40
Aerospace and Electronic Systems Magazine December 2017 - 41
Aerospace and Electronic Systems Magazine December 2017 - 42
Aerospace and Electronic Systems Magazine December 2017 - 43
Aerospace and Electronic Systems Magazine December 2017 - 44
Aerospace and Electronic Systems Magazine December 2017 - 45
Aerospace and Electronic Systems Magazine December 2017 - 46
Aerospace and Electronic Systems Magazine December 2017 - 47
Aerospace and Electronic Systems Magazine December 2017 - 48
Aerospace and Electronic Systems Magazine December 2017 - 49
Aerospace and Electronic Systems Magazine December 2017 - 50
Aerospace and Electronic Systems Magazine December 2017 - 51
Aerospace and Electronic Systems Magazine December 2017 - 52
Aerospace and Electronic Systems Magazine December 2017 - 53
Aerospace and Electronic Systems Magazine December 2017 - 54
Aerospace and Electronic Systems Magazine December 2017 - 55
Aerospace and Electronic Systems Magazine December 2017 - 56
Aerospace and Electronic Systems Magazine December 2017 - 57
Aerospace and Electronic Systems Magazine December 2017 - 58
Aerospace and Electronic Systems Magazine December 2017 - 59
Aerospace and Electronic Systems Magazine December 2017 - 60
Aerospace and Electronic Systems Magazine December 2017 - 61
Aerospace and Electronic Systems Magazine December 2017 - 62
Aerospace and Electronic Systems Magazine December 2017 - 63
Aerospace and Electronic Systems Magazine December 2017 - 64
Aerospace and Electronic Systems Magazine December 2017 - 65
Aerospace and Electronic Systems Magazine December 2017 - 66
Aerospace and Electronic Systems Magazine December 2017 - 67
Aerospace and Electronic Systems Magazine December 2017 - 68
Aerospace and Electronic Systems Magazine December 2017 - 69
Aerospace and Electronic Systems Magazine December 2017 - 70
Aerospace and Electronic Systems Magazine December 2017 - 71
Aerospace and Electronic Systems Magazine December 2017 - 72
Aerospace and Electronic Systems Magazine December 2017 - 73
Aerospace and Electronic Systems Magazine December 2017 - 74
Aerospace and Electronic Systems Magazine December 2017 - 75
Aerospace and Electronic Systems Magazine December 2017 - 76
Aerospace and Electronic Systems Magazine December 2017 - 77
Aerospace and Electronic Systems Magazine December 2017 - 78
Aerospace and Electronic Systems Magazine December 2017 - Cover3
Aerospace and Electronic Systems Magazine December 2017 - Cover4
http://www.brightcopy.net/allen/aesm/34-2s
http://www.brightcopy.net/allen/aesm/34-2
http://www.brightcopy.net/allen/aesm/34-1
http://www.brightcopy.net/allen/aesm/33-12
http://www.brightcopy.net/allen/aesm/33-11
http://www.brightcopy.net/allen/aesm/33-10
http://www.brightcopy.net/allen/aesm/33-09
http://www.brightcopy.net/allen/aesm/33-8
http://www.brightcopy.net/allen/aesm/33-7
http://www.brightcopy.net/allen/aesm/33-5
http://www.brightcopy.net/allen/aesm/33-4
http://www.brightcopy.net/allen/aesm/33-3
http://www.brightcopy.net/allen/aesm/33-2
http://www.brightcopy.net/allen/aesm/33-1
http://www.brightcopy.net/allen/aesm/32-10
http://www.brightcopy.net/allen/aesm/32-12
http://www.brightcopy.net/allen/aesm/32-9
http://www.brightcopy.net/allen/aesm/32-11
http://www.brightcopy.net/allen/aesm/32-8
http://www.brightcopy.net/allen/aesm/32-7s
http://www.brightcopy.net/allen/aesm/32-7
http://www.brightcopy.net/allen/aesm/32-6
http://www.brightcopy.net/allen/aesm/32-5
http://www.brightcopy.net/allen/aesm/32-4
http://www.brightcopy.net/allen/aesm/32-3
http://www.brightcopy.net/allen/aesm/32-2
http://www.brightcopy.net/allen/aesm/32-1
http://www.brightcopy.net/allen/aesm/31-12
http://www.brightcopy.net/allen/aesm/31-11s
http://www.brightcopy.net/allen/aesm/31-11
http://www.brightcopy.net/allen/aesm/31-10
http://www.brightcopy.net/allen/aesm/31-9
http://www.brightcopy.net/allen/aesm/31-8
http://www.brightcopy.net/allen/aesm/31-7
https://www.nxtbookmedia.com