In this paper, we consider the schedule-based network localization concept, which does not require synchronization among nodes and does not involve communication overhead. The concept makes use of a common transmission sequence, which enables each node to perform self-localization and to localize the entire network, based on noisy propagation-time measurements. We formulate the schedule-based localization problem as an estimation problem in a Bayesian framework. This provides robustness with respect to uncertainty in such system parameters as anchor locations and timing devices. Moreover, we derive a sequential approximate maximum a posteriori (AMAP) estimator. The estimator is fully decentralized and copes with varying noise levels. By studying the fundamental constraints given by the considered measurement model, we provide a system design methodology which enables a scalable solution. Finally, we evaluate the performance of the proposed AMAP estimator by numerical simulations emulating an impulse-radio ultra-wideband (IR-UWB) wireless network.