Observed point data on a rectangleDofare represented by a doubly stochastic Poisson measureY. Its intensity is supposed to be a known function of a two-parameter processX, a semi-martingale of a Brownian sheet. As in the one-parameter case, the identification of the model goes through a recursive estimation ofX. For three types of exploration ofD— vertical, horizontal and diagonal—, we wish to derive filtering equations according to a partial ordering of. These are obtained by the reference probability method