This paper studies the estimation of dynamic route choice behavior of drivers with incomplete fixed location-based sensor data, such as radio frequency identification (RFID) data. Unlike global positioning system (GPS) data providing continuous vehicle trajectories, the location-based RFID sensors record vehicles only when they pass by but may not record all vehicles. These bring challenges for route choice modeling since empty sensor observations will also influence the likelihood of routes that do not cross these sensors. Also, it requires the essential integration of dynamic traffic conditions into the modeling process as observation paths may share the same sensor detection sequence but exhibit different travel times. To address these challenges, the paper proposes a dynamic recursive logit model to estimate vehicle route choices with RFID data, enabling the characterization of the likelihood function of sensor observation paths without the need for path enumeration between consecutive detections. Also, we develop a probabilistic dynamic link utilization estimation method to infer the actual path of each vehicle from the available sensor observations. It serves as a validation process to ensure that the route choice behavior can comprehensively reflect traffic flow dynamics. The proposed methods are evaluated using both a simulated dataset on the Sioux Falls network and a collection of real-world RFID data in Chongqing, China. The simulation results show that the proposed method can recover true choice parameters and perform significantly better compared with static models. The real-world experimental results highlight its efficacy in aggregated link flow prediction and individual trajectory reconstruction.