Particle Filtering as a way to incorporate nonlinear observations into geostatistical simulation

Particle Filtering has been proposed as an alternative as a possible way to reconsiliate observations with nonstandard likelihood profiles. For that a population of simulations - called particles - is updated according to the random dynamic of the system increasing the population and then weighted and resampled according to their likelihood given the observation, resulting in a new population representing the conditional distribution given the observation.
Our idea is to use this for spatial random fields, where we have a spatial rather than a temporal randomness. The particles are conditional geostatististical simulations of a Gaussian Random Field given standard geostatistical data. Instead of a time update we use a random innovation updating each simulation to another simulation of the same random field by updating in directions driven by the current residual variability of the field as represented by the ”particle population”. By reweighting according to the likelihoods of the observations reconsilidated until now and resampling we get a new particle population now honoring the additional observations along with the original data.
We will demonstrate and check the performance and applicability of the method in simulated test cases, for relevant standard problems like interval observations and block observations of fields modeled as compositional, plurigaussian, or with a Gaussian anamorphosis.