moura f - 2008 - j physics - transition matrix_kalman_eit
TRANSCRIPT
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()k =
(+)k1
P()k = P
(+)k1
T +Qk1
Gk = P()k H
Tk (
()k )[Hk(
()k )P
()k H
Tk (
()k ) + Rk]
1
(+)k =
()k +Gk[vk Hk
()k ]
P(+)k = [IGkHk
()k ]P
()k
v
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P Q
H 1 R
GH
e p ep
ep
p P
2n n
X X+
(k)X
k k + m 1 X+
k + 1 k + m
X=(k) (k+1) . . . (k+m1)
X+ =
(k+1) (k+2) . . . (k+m)
(k) =
(k1)(k)
m > 2n X
= (X+XT)(XXT + I)1,
I
(k)
1
cj vj = Y1
cj vjcj Y
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300mm
n = 514 e = 32 p = 3240mm
126mm
object (k) =
35.0 , k 01050k + 35.0 , k > 0
m
basal = 35.0m
k = 0
object (k) =
35.0 , k < 0100.0 , k 0
m
basal = 35.0m.
0 = 35mI = 2mA 2
2
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0 500 1000 15000
50
100
150
200
250
300
350
iteration (k)
resistivity(
m)
estimated resistivityestimated basalobject real resistivitybasal real resistivity
0 500 1000 15000
50
100
150
200
250
300
350
iteration (k)
resistivity(
m)
estimated resistivityestimated basalobject real resistivitybasal real resistivity
3
3
ek =
k k,
k
ek =1
n
nXi=1
eik
ek =
vu
ut1
n1
nX
i=1
(eik ek)2,
n
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0 500 1000 15001
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
1
iteration (k)
error(m
)
0 500 1000 15001
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
1
iteration (k)
error(m
)
k = 1495
0.15 0.1 0.05 0 0.05 0.1 0.15
0.15
0.1
0.05
0
0.05
0.1
0.15
30
35
40
45
50
55
60
65
70
75
0.15 0.1 0.05 0 0.05 0.1 0.15
0.15
0.1
0.05
0
0.05
0.1
0.15
0
20
40
60
80
100
120
140
160
180
200
k = 1495
= 1.0
n
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1 0.5 0 0.5 1
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
real
imaginary
1 0.5 0 0.5 1
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
real
imaginary
= 1.0 = 0.01
(1.0, 0.0)
MAC > 0.5
0.15 0.1 0.05 0 0.05 0.1 0.15
0.15
0.1
0.05
0
0.05
0.1
0.15 z=1
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0.15 0.1 0.05 0 0.05 0.1 0.15
0.15
0.1
0.05
0
0.05
0.1
0.15 z=0.999
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0.05
0.1
= 1.0
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0.15 0.1 0.05 0 0.05 0.1 0.15
0.15
0.1
0.05
0
0.05
0.1
0.15 z=0.993
0.25
0.2
0.15
0.1
0.05
0
0.05
0.15 0.1 0.05 0 0.05 0.1 0.15
0.15
0.1
0.05
0
0.05
0.1
0.15 z=0.772
0.1
0.08
0.06
0.04
0.02
0
0.02
0.04
0.06
0.08
0.1
= 1.0
0 = 60m P0 = 101I
Qk
Qk =
Pk1 , k 3Qk1 , k > 3
,
H
k
Gk = k(P()k H
Tk [HkP
()k H
Tk +Rk]
1),
k
k =
0.1 , k < 50.5 , k < 81.0 , k 8
,
R
Rk Rk Rk
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4
R
Rk 102I 103I 104I 105I
P0 101I 101I 101I 101I
Q0 103P0 10
3P0 103P0 10
3P00 [m] 103 103 103 103
RkRk = 10
4I
0 50 100 150 200 250 30010
2
101
100
ob
servation
residue
(V)
iteration
residue
superior limit
0 50 100 150 200 250 30010
2
101
100
ob
servation
residue
(V)
iteration
residue
superior limit
0 50 100 150 200 250 30010
2
101
100
observation
residue
(V)
iteration
residue
superior limit
0 50 100 150 200 250 30010
3
102
101
100
observation
residue
(V)
iteration
residue
superior limit
4
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Q
Qk
Q
Rk 104I 104I
P0 101I 101I
Q0 103P0 10
5P00 [m] 103 105
k = 300Qk
0 50 100 150 200 250 30010
20
30
40
50
60
70
80
90
100
resistivity[
m]
iteration 0.15 0.1 0.05 0 0.05 0.1 0.15
0.15
0.1
0.05
0
0.05
0.1
0.15
20
30
40
50
60
70
80
0 50 100 150 200 250 30010
20
30
40
50
60
70
80
90
resistivity[m
]
iteration 0.15 0.1 0.05 0 0.05 0.1 0.15
0.15
0.1
0.05
0
0.05
0.1
0.15
25
30
35
40
45
50
55
60
65
70
Qkk = 300 k = 300
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k = 300
0 50 100 150 200 250 30010
20
30
40
50
60
70
80
90
100
110
resistivity[
m]
iteration
0 50 100 150 200 250 30010
3
102
101
100
observation
residue(V)
iteration
residuesuperior limit
0.15 0.1 0.05 0 0.05 0.1 0.15
0.15
0.1
0.05
0
0.05
0.1
0.15
30
40
50
60
70
80
k = 300
Rk
R
Rk 104I 106I
P0 101I 101I
Q0 105P0 10
5P00
[m] 105 105
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k = 300
0 50 100 150 200 250 30020
0
20
40
60
80
100
120
resistivity[
m]
iteration
0 50 100 150 200 250 30010
3
102
101
100
observation
residue
(V)
iteration
residuesuperior limit
0.15 0.1 0.05 0 0.05 0.1 0.15
0.15
0.1
0.05
0
0.05
0.1
0.15
30
40
50
60
70
80
k = 300
Rk
k = 800
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0 100 200 300 400 500 600 700 8000
10
20
30
40
50
60
70
resistivity[m
]
iteration
0 100 200 300 400 500 600 700 8000
20
40
60
80
100
120
resistivity[m
]
iteration
0 100 200 300 400 500 600 700 80010
5
104
103
102
101
100
observation
residue(V)
iteration
residue
superior limit
0 100 200 300 400 500 600 700 80010
5
104
103
102
101
100
observation
residue(V)
iteration
residue
superior limit
0.15 0.1 0.05 0 0.05 0.1 0.15
0.15
0.1
0.05
0
0.05
0.1
0.15
10
20
30
40
50
60
0.15 0.1 0.05 0 0.05 0.1 0.15
0.15
0.1
0.05
0
0.05
0.1
0.15
10
20
30
40
50
60
70
80
90
100
110
k = 800 k = 800
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