i am implrmrnting the particle filter, and i have some problem understanding the algorithm.
given the state equations: $$ x_k = f(x_{k-1},v_k) $$ $$ z_k=h(x_k,u_k) $$ where $v_k, u_k$ are process and measurement noise, $x_k$ is the current state estimate and $z_k$ is the current measurement estimation.
my understanding- i generate a set of particles around the initial guess. then i propagate them through the process equation ($f(;,;)$) to estimate next state for each particle.
after that, i propagate the new particles through the measurement equation to learn what would be the measurement, if this particle is the state. with that, i compute the probability for each particle to be the true state using the actual measurement, allowing me to resample around the most likly particles and take the mean of those particles as my next estimate.
if i am wrong in the steps, please correct me. if you have good sources, please let me know. assuming i am right in what i said - without knowing the actuall distribution of the process, i am guessing normal distribution. is that a correct assumption?
thanks, Joseph