Fundamentals of Kalman Filtering and Applications to GNSS
Fundamentals of Kalman Filtering and Applications to GNSS
Fundamentals of Kalman Filtering and Applications to GNSS
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Example<br />
• Generating an exponentially correlated process as the<br />
solution <strong>to</strong> a differential equation driven by white noise<br />
<br />
<br />
w s<br />
<br />
w<br />
<br />
s<br />
2<br />
w<br />
2<br />
w<br />
<br />
<br />
x<br />
t<br />
<br />
generated as solution<br />
<strong>to</strong> differential equation<br />
driven by white noise<br />
x<br />
x w<br />
w<br />
Shaping Filter<br />
Representation<br />
1<br />
s <br />
<br />
<br />
Gs<br />
x<br />
<br />
x<br />
<br />
• PSD for x<br />
2<br />
<br />
G j<br />
<br />
<br />
1<br />
<br />
2 2<br />
<br />
<strong>Kalman</strong> <strong>Filtering</strong> Consultant Associates © 2011<br />
s<br />
w<br />
2<br />
w<br />
<br />
s<br />
2<br />
w<br />
2<br />
2 <br />
2 2<br />
<br />
<br />
<br />
<br />
e<br />
e<br />
s w<br />
<br />
2<br />
Remember for exponentially<br />
correlated noise<br />
<br />
<br />
s<br />
2<br />
e<br />
e<br />
2 s<br />
<br />
2<br />
<br />
e<br />
<br />
<br />
2 2<br />
<br />
Hence, x (t ) is exponentially<br />
correlated with<br />
2<br />
2<br />
s x ; corr. time <br />
1<br />
<br />
25