1
$\begingroup$

I'm studying a special case of the Kalman filter, and the following problem has come up:

Suppose $H \in R^{d\times 1}$, and $R$ is a positive definite $d \times d$ matrix. How would I show that

$H^\top ( H H^\top + R)^{-1} H $ lies between 0 and 1?

Presumably there's an easy fact about matrix norms that I'm missing, but what's the right way to handle this expression?

$\endgroup$

1 Answer 1

1
$\begingroup$

In case anyone else ever encounters this problem, one can solve it using the Sherman-Morrison formula.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .