# Equations for particle filter

The particle filter is based on the state and observation model equations

$$x_{t+1}=f_t(x_t, v_t)$$

$$y_t=h_t(x_t, u_t)$$

The idea is to randomly generate some particles then propagate them through the equations, resample, and normalize to get an estimate of the state $$x_t$$.

My question is: we need to know the state and observation model equations so why do we need the particle filter? I hope I am missing something because it seems like if this knowledge is required then why bother with particle filter, can't we just do ML estimation?