Recent researchers have shown the potential benefits of using Lagrangian coordinates in modeling mobile sensor data such as GPS data. The convenience of vehicle traffic flow models provides flexibility in conducting traffic state estimation based on data collecting from moving sensors. In this paper, we propose a Lagrangian -space based travel time estimation model for the non-pipeline corridor. The model improves a previous presented Travel Time Transition Model (TTM) into non-pipeline cases by numerically implement its source term. A numerical experiment based on a simulation model of Nanbei Expressway in Shanghai, China is used to evaluate the proposed approach. The proposed model performs well and can track traffic breakdowns and recovery effectively. The Mean Absolute Percentage Error (MAPE) of the proposed estimator is 6.75%. 78.3% of the relative estimation errors are less than 10%. The estimation error is caused by the fluctuation of mainline traffic flow. Furthermore, the ramp flow term that numerically implements the analytic source term needs to be rescaled using a coefficient to reduce its impact on numerical error.

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