The questions in this post do not appear to be related to Julia at all? Generally though
As long as the state of each particle is related to the measurement, and you can encode this relation through the measurement operator, the particle filter can infer the proper θ based on how well each particle’s θ agrees with the observed velocity. Particles that appear to have a worse fit will get a lower weight and eventually be removed through resampling.
I can’t quite answer this, you need to use your domain expertise to answer that. Generally, your post uses a lot of domain-specific language, since this is a forum for Julia programming, you may get better help if you could abstract away some of the domain details and focus on the math and code.