The paper is devoted to a state filtering problem of Markov jump processes given the continuous and/or counting observations. All the transition intensity matrix, observation plan and counting intensity are parameterized by a random vector with uncertain distribution on a known support set. The estimation problem is formulated in minimax settings with a conditional optimality criterion. We reduce the initial minimax problem to a dual problem of constrained quadratic optimization. The corresponding numerical algorithm of minimax filtering is presented as well as its illustrative implementation in the monitoring of a TCP link status under uncertainty. (C) 2011 Elsevier Ltd. All rights reserved.