Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

Chapter 4 / Target Tracking
_ _
A
( Φ , Q )
V
V
: =
⎛
⎜ ⎡ 1 , ∆t
⎤
⎜ ⎢ ⎥
⎜ ⎢ ⎥
⎜ ⎢ ⎥
⎝ ⎣ 0 , 1 ⎦
(Vqt) represents the noise power spectral density in (m 2 /s 4 /Hz),
4.5.2 Constant Acceleration Filter
4-16
,
V
q
t
⋅
⎡
⎢
⎢
⎢
⎣
∆t
∆t
3
2
3
2
,
,
∆t
2
∆t
2
⎤
⎥
⎥
⎥
⎦
⎞
⎟
⎟
⎟
⎠
Equation 4.5-2
Target longitudinal acceleration is generally small compared with lateral
manoeuvring accelerations and target motion is best described by a constant
“g” turn - the circular dynamic model, Nabaa [N.4] . The acceleration is
directed along Target Velocity axes rather than Alignment axes, the state
transition and noise covariance matrices being,
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
∆t
8
5
∆t
⋅ T
20
4
⋅ T
∆t
6
3
A
TV
A
TV
⋅
⋅
⋅ T
A
A
L
A
L
A
TV
Φ
q
q
⋅
TV
TV
A
: =
q
⋅ T
⋅ T
TV
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎣
TV
A
TV
A
0
0
I
3
L
3x3
L
3x3
M
M
M
M
M
M
M
M
M
M
∆t
8
∆t
3
4
3
∆t
⋅ I
A
0
∆t
2
L
I
3
L
⋅ T
⋅ T
2
3
3x3
Q
A
A
TV
A
TV
⋅
⋅
⋅ T
M
M
M
M
M
: =
A
L
A
L
A
TV
q
q
⋅
A
2
TV
TV
−1
q
⋅ ∆t
⋅ I
∆t
⋅ I
⋅ T
⋅ T
TV
TV
A
TV
A
L
3
L
I
⋅ T
3
3
M
M
M
M
M
⋅ T
A
TV
A
TV
∆t
6
∆t
2
3
2
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎦
∆t
⋅ T
Equation 4.5-3
⋅ T
⋅ T
A
TV
L
A
TV
L
A
TV
⋅
⋅
⋅
A
A
A
q
q
q
TV
TV
TV
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
Equation 4.5-4
This noise matrix is diagonal and the elements of the PSD vector are
selected dependent upon the expected manoeuvring capability of the target,
TV
TV
[ q ] : = diag ( q )
A
A
Equation 4.5-5
Not only are the propagation equations more complex using directional
acceleration states they must be transformed into the Alignment frame
before IMM assimilation. As the IMM measurement updates are frequent