In this article, a diagnosis approach for partially observed labelled Petri nets is developed based on building a set of analytical redundancy relationships on a progressive horizon. A nominal model is used for fault detection based on a set of relationships linking the known data of the nominal behaviour. A fault model is used for fault isolation by establishing a set of relationships for each fault transition connecting the known data of the fault behaviour. The above-mentioned analytical redundancy relationships are established offline by eliminating unknown variables from the considered model. The proposed online procedure for fault diagnosis is polynomial with respect to the number of unobservable events.