Content deleted Content added
m −sp |
m →Model: +. |
||
Line 21:
Using these assumptions the probability distribution over all states of the HMM can be written simply as:
:<math>p(\textbf{x}_0,\dots,\textbf{x}_k,\textbf{z}_1,\dots,\textbf{z}_k) = p(\textbf{x}_0)\prod_{i=1}^k p(\textbf{z}_i|\textbf{x}_i)p(\textbf{x}_i|\textbf{x}_{i-1}).</math>
However, when using the Kalman filter to estimate the state '''x''', the probability distribution of interest is associated with the current states conditioned on the measurements up to the current timestep. (This is achieved by marginalising out the previous states and dividing by the probability of the measurement set.)
| |||