I am trying to follow the equations on page 12 of this document. How do we get from:
$P(x_t | u_{1:t}, z_{1:t})$
to:
$P(z_t | x_t, u_{1:t}, z_{1:t-1}) * P(x_t | u_{1:t}, z_{1:t-1})$?
I was expecting to see:
$P(x_t | u_{1:t}, z_{1:t}) = \cfrac{P(u_{1:t}, z_{1:t} | x_t) * P(x_t)}{P(u_{1:t}, z_{1:t})}$
via Bayes rule.