Global Positioning System Reference
In-Depth Information
Compute the Error State Estimate
The error state vector is
$
x
t
+
()
[
]
() ()
()
()
()()
$
+
$
−
$
−
x
t
=
x
t
+
K
t
y
t
−
H
t
x
t
1
1
1
1
1
1
computes to
−
18 101
5012
,
−
0
0
−
18 101
50
,
1.
()
()
()
$
−
y Hx
t
−
t
t
=
=
1
1
1
.
Multiplying by the gain matrix and adding in the previous error state vector yields
[
]
() ()
()
()
()()
$
+
$
−
$
−
x
t
=
x
t
+
K
t
y
t
−
H
t
x
t
1
1
1
1
1
1
0
0
0
0
−
199
.
0
E
−−
8
5 251
.
E
−
3
−
4900
.
E
−
13
−
5 252
.
E
−
3
−
18 101
5012
,
=
+
9999
.
E
−
1
−
2 878
.
E
−
3
.
1
.
174
E
−
12
9971
.
E
−
1
−
632
2 632
18 102 6
4997
2
.
−
.
,
=
−
.
.
2
Adjust the Covariance of the Current Estimate (
σ
)
The covariance of the new estimate is computed using the equation
()
[
] ()
()()
P
t
+
=−
I K
t
H
t
P
t
−
1
1
1
1
50070
.
9971
.
274 40
.
5464
.
9971
.
9972
.
5465
.
5465
.
()
[
] ()
()()
P
t
+
=−
I K
t
H
t
P
t
−
=
1
1
1
1
274 40
.
5464
.
15140
.
2995
.
5464
.
5464
.
2996
.
29
.96
Apply the Corrections and Reset the Error State Vector
(
)
x
x
ct
δ
δ
=
1527 397
,
,
+
−
2 63 1527 394
.
=
,
,
m
(
)
&
=+−
0
.
3
=−
.
6
ms
(
)
=+−
0
18 103
,
=−
18 103
,
m
u
&
ct
=+
0
4997
.
=
4997
.
ms
u
0
0
0
0
()
$
x
t
+
=
1
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