  We investigate decentralized state estimation for a discrete event system in
a setting where the information received at a coordinator may be corrupted or
tampered by a malicious attacker. Specifically, a system is observed by a set
of (local) observation sites (OSs) which occasionally send their recorded
sequences of observations to the coordinator that is in charge of estimating
the system state. The malfunctions and attacks, referred to as errors in this
paper, include symbol deletions, insertions and replacements, each of which
bears a positive cost. Two types of errors, global errors and local errors, are
proposed to describe the impact of errors on decentralized information
processing. Global errors occur when all OSs record the same error, while local
errors occur when different OSs record different errors. Distinguishing these
types of errors is important for a proper design of decentralized information
processing (so as to be more resilient and better equipped to handle errors and
failures). For each type of error, we propose two methods to efficiently
perform state estimation: one based on appropriately modifying the original
system and the other based on inferring the matching behavior of the original
system. For each method, we adopt an estimation-by-release methodology to
design an algorithm for constructing a corresponding synchronizer for state
estimation.
