Increasing computational power increases significance of Monte Carlo techniques, especially, its sequential variants forming among others the basis of particle filtering. The estimation version of this successful and powerful way suffers from degeneracy: the distribution of samples does not properly represent the underlying distribution. The referred research addresses this problem and treats it as an approximate recursive estimation implemented on a variable grid. The knowledge represented by samples and their weights is taken as a constrained list of values of an approximate posterior distribution. The remaining values are described by a flat, say uniform distribution. The updated posterior distribution goes out of this numerically feasible form and it is projected back. The procedure is repeated to a flattened updated distribution. The flattening avoids uncontrollable accumulation of errors caused by non-commutativity of the Bayes rule and the considered projection.The talk will describe basic ideas and open problems of the adopted approach.