Particle Filters

Hello Community, For a homework I have to answer the following question but I can’t find a solution. My research has not helped me either. Can anyone help me with the following question ?

Convergence Errors
Can a particle filter also converge into a faulty position? Note down why this (can’t) happen. If
errors are possible, how could they be fixed?

Without knowing more context that question is impossible to answer. In particular, it does not seem well-posed. What does “a faulty position” mean? A particle filter can be used for evaluating the likelihood. If you have too few particles, the approximation will be poor. But that is not about convergence.

The context is about localisation of robots

So the question is not about estimating parameters but about filtering, i.e. finding realtime values for the state variables?