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

Chapter 4 / Target Tracking
_ _
The elements of the fully expanded system noise covariance matrix where
(σt) is the rms target acceleration uncertainty,
q
11
2 4 ⎛ 2
2 2 3
: = Sσt
⋅ SτC
⋅ ⎜ 1 − ϕ + 2 ⋅ β − 2 ⋅ β + ⋅ β − 4 ⋅ ϕ ⋅
⎝
3
12
S
2
t
3
SτC
2
2
( 1 + ϕ − 2 ⋅ ϕ + 2 ⋅ ϕ ⋅ β − 2 ⋅ β + )
q : = σ ⋅ ⋅
β
22
13
S
2
t
4-18
2
SτC
2
( 1 − 2 ⋅ ϕ ⋅ β − )
q : = σ ⋅ ⋅
ϕ
S
2
t
2
SτC
2
( −3
+ 4 ⋅ ϕ + 2 ⋅ β − )
q : = σ ⋅ ⋅
ϕ
23
S
2
t
S
C
2
( 1 − 2 ⋅ ϕ + )
q : = σ ⋅ τ ⋅
ϕ
33
S
2
t
S
C
2 ( 1 − 2 ⋅ )
q : = σ ⋅ τ ⋅ ϕ
When (β) is small these equations tend to the asymptotic form,
S
A
2
A
( 2 ⋅ σ τ ) Q
Q : =
⋅
S
t
S
C
A
β
⎞
⎟
⎠
Equation 4.5-11
Equation 4.5-12
Equation 4.5-13
Equation 4.5-14
Equation 4.5-15
Equation 4.5-16
Equation 4.5-17
The acceleration probability in the Singer model is uniformly distributed
between the maximum acceleration limit (± AMAX) with a probability of
(± PMAX); the no manoeuvre probability being (P0),
S
σ
2
t
2
( 1 + 4 ⋅ P − P ) 3
: = AMAX
⋅
MAX 0
Equation 4.5-18
If the maximum acceleration of a manned jet aircraft is 9 g for short periods
during evasion manoeuvres,
S
σ
t
: = 5 3 ⋅ A ≈
MAX
80 m / s
2
Equation 4.5-19
A drawback of this model is the apriori selection of maximum acceleration
and manoeuvre duration. In the context of the IMM this model is only