October 2011
Intermediate to advanced
749 pages
23h 36m
English
Content preview from Optimal Estimation of Dynamic Systems, 2nd Edition
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416 Optimal Estimation of Dynamic Systems
∂
h/
∂
x,aregivenby
∂
||ρ||
∂
x
=(
ρ
u
cos
φ
cosΘ −
ρ
e
sinΘ −
ρ
n
sin
φ
cosΘ)/||ρ|| (6.64a)
∂
||ρ||
∂
y
=(
ρ
u
cos
φ
sinΘ +
ρ
e
cosΘ −
ρ
n
sin
φ
sinΘ)/||ρ|| (6.64b)
∂
||ρ||
∂
z
=(
ρ
u
sin
φ
+
ρ
n
cos
φ
)/||ρ|| (6.64c)
∂
az
∂
x
=
1
(
ρ
2
n
+
ρ
2
e
)
(
ρ
e
sin
φ
cosΘ −
ρ
n
sinΘ) (6.65a)
∂
az
∂
y
=
1
(
ρ
2
n
+
ρ
2
e
)
(
ρ
e
sin
φ
sinΘ +
ρ
n
cosΘ) (6.65b)
∂
az
∂
z
= −
1
(
ρ
2
n
+
ρ
2
e
)
ρ
e
cos
φ
(6.65c)
∂
el
∂
x
=
1
||ρ||(||ρ||
2
−
ρ
2
u
)
1/2
||ρ||cos
φ
cosΘ −
ρ
u
∂
||ρ||
∂
x
(6.66a)
∂
el
∂
y
=
1
||ρ||(||ρ||
2
−
ρ
2
u
)
1/2
||ρ||cos
φ
sinΘ −
ρ
u
∂
||ρ||
∂
y
(6.66b)
∂
el
∂
z
=
1
||ρ||(||ρ||
2
−
ρ
2
u
)
1/2
||ρ||sin
φ
−
ρ
u
∂
||ρ||
∂
z
(6.66c)
The matrix
∂
h/
∂
x is given by
∂
h
∂
x
=
H
11
0
3×3
(6.67)
where
H
11
=
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
∂
||ρ||
∂
x
∂
||ρ||
∂
y
∂
||ρ||
∂
z
∂
az
∂
x
∂
az
∂
y
∂
az
∂
z
∂
el
∂
x
∂
el
∂
y
∂
el
∂
z
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
(6.68)
The least ...
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I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.