Partile filter code with an example of weight collapse in importance sampling methods

We propose an implementation of the particle filter in a quasi-static case in the example of Gaussian prior with independent and identically distributed prior states and observation errors. Weight collapse occurs in the particle filter when the number of model states and observations increases for a given ensemble size. In this example, we use a synthetic experiment to illustrate how weight collapse varies in the posterior distribution.This code provides a basis for the implementation of importance sampling methods and can be easily adapted to other problems.