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State tracking, i.e. estimating the state over time, is always an important problem in autonomous dynamic systems. Run-time requirements advocate for incremental estimation and memory limitations lead us to consider an estimation strategy that retains only one state out of the set of candidate estimates at each time step. This avoids the ambiguity of a high number of candidate estimates and allows the decision system to be fed with a clear input. However, this strategy may lead to dead-ends in the continuation of the execution. In this paper, we show that single-state trackability can be expressed in terms of the simulation relation between automata. This allows us to provide a complexity bound and a way to build estimators endowed with this property and, moreover, customizable along some correctness criteria. Our implementation relies on the Sat Modulo Theory solver MONOSAT and experiments show that our encoding scales up and applies to real world scenarios.

Model-Based Synthesis of Incremental and Correct Estimators for Discrete Event Systems