Kalman Filtering Tutorial
Kalman Filtering Tutorial
Kalman Filtering Tutorial
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What is a Covariance Matrix?<br />
The covariance of two random variables x1 and x2 is<br />
cov( x , x ) ≡ E[( x − x )( x − x )]<br />
1 2 1 1 2 2<br />
∞ ∞<br />
= ( x − x )( x − x ) p( x , x ) dx dx<br />
≡<br />
∫<br />
−∞<br />
∫<br />
−∞<br />
1 1 2 2 1 1 1 2<br />
where p is the joint probability density function of x1 and x2.<br />
6<br />
σ<br />
2<br />
x x<br />
The correlation coefficient is the normalised quantity<br />
ρ<br />
12<br />
2<br />
σ x1x2 ≡ ,<br />
−1 ≤ ρ12<br />
≤ + 1<br />
σ σ<br />
x x<br />
1 2<br />
1 2
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