While observers with asymptotic convergence guarantees can be used to design output feedback controllers when considering control tasks like stability, if state constraints relevant to safety exist, it is crucial to bound the estimation error at all times. In this paper, we propose an optimization-based design technique for bounded-error state estimators for affine systems that provide estimation guarantees in the presence of intermittent measurements. We treat the affine system as a switched system where the measurement equation switches between two modes based on whether a measurement exists or is missing, and model potential intermittent measurement patterns with a finite language that constrains the feasible mode sequences. By utilizing Q-parametrization, we show that an optimal estimator can be constructed that simultaneously provides an estimate of the continuous-state and implicitly estimates the specific missing data pattern (i.e., mode sequence), within the given language, according to the prefix observed so far. We illustrate with numerical examples that this approach significantly improves the achievable estimation bounds compared to earlier work.