17. Markov Assumption for Motion Model: Quiz

Markov Assumption for Motion Model Quiz

What do you think about these two assumptions:

(a) Since we (hypothetically) know in which state the system is at time step t-1, the past observations z_{1:t-1} and controls u_{1:t-1} would not provide us additional information to estimate the posterior for x_t , because they were already used to estimate x_{t-1} . This means, we can simplify p(x_t|x_{t-1}, z_{1:t-1}, u_{1:t},m) to p(x_t|x_{t-1}, u_t, m) .

(b) Since u_t is “in the future” with reference to x_{t-1}, u_t does not tell us much about x_{t-1} . This means the term p(x_{t-1}|z_{1:t-1}, u_{1:t}, m) can be simplified to p(x_{t-1}|z_{1:t-1}, u_{1:t-1}, m) .