Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 27

Acito et al.
Thus

Now we can write HACD(yT, zT; i, j) as follows:

 Γˆ y
T
Γˆ 0,T = 
 Γˆ Ty z
 TT

HACD ( y T , zT ; i, j ) =

Γˆ 1,T

Γˆ yT zT 

Γˆ zT 
 R 0   Γˆ y Γˆ yz   RT 0 
⋅
=
= D ⋅ Γˆ 0 ⋅ DT
(47)
⋅ T
T
 0 K   Γˆ yz Γˆ z   0 K 
 Γˆ y
0   R 0   Γˆ y 0   RT 0 
T
T
=
=
⋅
 = D ⋅ Γˆ 1 ⋅ D
⋅
 0 Γˆ z   0 K   0 Γˆ z   0 K T 


T 


Notice that being both R and K full rank matrices and by exploiting the block matrix inversion formula, we conclude that D and DT
are invertible, so
Γˆ

−1
0,T

Γˆ

−1
1,T

( )
= (D )
= D

T

T

e T ( i, j ) ⋅ Γˆ d ,T ⋅ e T ( i, j ) =
T

T

⋅ Γˆ ⋅ D

−1

⋅ Γˆ ⋅ D

−1
0

−1
1

T

e T ( i, j ) ⋅ Γˆ 0,−1T ⋅ e T ( i, j ) =

SACD ( yT , zT ; i, j ) =

T

(48)

( ) ⋅ ( Γˆ

Γˆ d ,T = Γˆ 0,−1T − Γˆ 1,−1T = DT

JULY 2017, Part II of II

( )

= e ( i, j ) ⋅ DT ⋅ DT

and
−1

−1
0

)

( )

− Γˆ 1−1 ⋅ D−1 = DT

−1

⋅ Γˆ d ⋅ D−1 (49)

⋅ Γˆ d ⋅ D−1 ⋅ D ⋅ e ( i, j ) = (50)

Recalling that e ( i, j ) = e ( i, j ) − μˆ 0 and by comparing the expression in (50) with that in (12) we can conclude that .
Following the same reasoning as that leading to (50), we can
write SACD(yT, zT; i, j) as

−1

−1

−1

e ( i, j ) ⋅ Γˆ d ⋅ e ( i, j )

=

T

−1

( )

= e ( i, j ) ⋅ DT ⋅ DT

=

−1

⋅ Γˆ 0−1 ⋅ D−1 ⋅ D ⋅ e ( i, j ) =

(51)

e ( i, j ) ⋅ Γˆ 0−1 ⋅ e ( i, j )
T

Such an expression compared with the form the SACD test statistic
provided in the Subsection II-A.2 proves that SACD(yT, zT; i, j) =
SACD(y, z; i, j).

IEEE A&E SYSTEMS MAGAZINE

27



Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine July 2017 Tutorial XI

No label
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - No label
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - Cover2
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 1
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 2
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 3
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 4
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 5
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 6
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 7
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 8
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 9
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 10
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 11
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 12
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 13
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 14
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 15
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 16
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 17
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 18
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 19
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 20
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 21
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 22
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 23
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 24
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 25
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 26
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 27
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 28
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 29
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 30
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 31
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 32
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 33
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 34
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 35
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 36
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 37
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 38
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 39
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 40
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 41
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 42
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 43
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 44
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 45
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 46
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 47
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 48
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 49
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 50
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 51
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 52
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 53
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 54
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 55
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 56
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 57
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 58
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 59
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 60
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 61
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 62
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 63
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 64
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 65
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 66
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 67
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 68
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 69
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 70
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 71
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 72
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - Cover3
Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 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