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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R<strong>and</strong>om Walk<br />
• A process x(t) is a r<strong>and</strong>om walk if it has a zero mean<br />
<strong>and</strong> an au<strong>to</strong>correlation function <strong>of</strong> the form<br />
– For t t t , we have E x t s t s .<br />
– Note<br />
• The variance <strong>of</strong> x(t) grows linearly with time<br />
• x(t) is non-stationary<br />
– Caution<br />
E<br />
2<br />
xt<br />
xt<br />
s minimum t<br />
<br />
1 2<br />
1 , t2<br />
2<br />
1 2<br />
<br />
2<br />
2<br />
s<br />
<br />
2 2<br />
t<br />
• The parameter has units <strong>of</strong> x per unit time.<br />
2<br />
• s is not a variance, but a variance growth rate.<br />
x<br />
<strong>Kalman</strong> <strong>Filtering</strong> Consultant Associates © 2011<br />
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