A new statistical algorithm is proposed in this paper with the aim of estimating fundamental diagram (FD) in actual traffic and dividing the traffic state. Traditional methods mainly focus on sensor data, but this paper takes random probe pairs as research objects. First, a mathematical method is proposed by using probe pairs data and the jam density to determine the FD on a stationary segment. Second, we applied it to the near-stationary probe traffic state set through linear regression and expectation maximisation iterative algorithm, estimating the free flow speed and the backward wave speed and dividing the traffic state based on the 95% confidence interval of the estimated FD. Finally, simulation and empirical analyses are used to verify the new algorithm. The simulation analysis results show that the estimation error corresponding to the free flow speed and the backward wave speed are 1.0668 km/h and 0.0002 km/h respectively. The empirical analysis calculates the maximum capacity of the road and divides the traffic into three states (free flow state, breakdown state, and congested state), which demonstrates the accuracy and practicability of the research in this paper, and provides a reference for urban traffic monitoring and government decision-making.
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