We propose a low-cost system for indoor self-localization of mobile devices using modulated LED ceiling lamps that are fully autonomous and broadcast their identifiers without any synchronization. The proposed self-localization method is designed to handle this lack of synchronization as well as the possibility of blocked line-of-sight connections or severe attenuation in real-world environments. This robustness is achieved by applying a suitable Bayesian signal model and by taking into account the inherent sparsity in detecting the concurrently visible lamps. The proposed estimator of the location approximates optimal Bayesian estimation while maintaining low complexity. Simulation results confirm a significant gain in performance compared to a classical matched-filter approach.