you treat the prior set of particles as your proposed distribution and the observation as the weight for each particle, multiply them together and you will get the target, which is the posterior
If you do not have the map, then it is most likely a SLAM problem. And yes, you can solve that with a particle filter. See for example the paper by Grisetti et al., published in TRO 2007 on SLAM with Rao-Blackwellized Particle Filters.
In some of your lectures, you talk about some Introduction to Robotics Course. Are there any videos of that course too? I couldn't find it with a google search.
