Mobile phone data collected by network operators can provide fundamental insights into individual and aggregate mobility of people, at unprecedented spatiotemporal scales. However, traditional call detail records (CDR) have fundamental issues because of low accuracy in both spatial and temporal dimensions, which limits their applicability for detailed studies on mobility, especially in urban scenarios. This paper focuses on a new generation of mobile phone passive data, individual cellular network signaling data, characterized by higher spatiotemporal resolutions than traditional CDR. A framework based on unsupervised hidden Markov model is designed for map-matching such data on a multimodal transportation network, aimed at accurately inferring the complex multimodal travel itineraries and popular paths people follow in their urban daily mobility. This information, especially if computed at large spatiotemporal scales, can represent a solid basis for studying actual and dynamic travel demand, to properly dimension multimodal transport systems and even perform anomaly detection and adaptive network control. The approach is evaluated in a case study based on real cellular traces collected by a major French operator in the city of Lyon, and a validation study at both microscopic and macroscopic levels proposed. The results show that this approach can properly handle sparse and noisy cell phone trajectories in complex urban environments. Moreover, the results are promising concerning popular paths detection and reconstruction of origin-destination matrices.