This paper proposes an efficient marking estimation method for a subclass of time labeled Petri nets (TLPNs), in which each transition is associated with an infinite upper bound delay. The unobservable subnet of the considered subclass of TLPNs is backward-conflict-free, and all the output transitions of each conflict place are observable. The highlight of this method is that the markings set consistent with a given observation can be determined by a linear algebraic system based on the so-called slow-bound marking and fast-bound marking pairs. An algorithm to compute an online estimator is provided, and an example is given. By this method, the exhaustive construction of the full state space including the state class graph is avoided. This approach provides guidelines of sensor deployment in the design stage so that the online marking estimation problem can be efficiently solved.