*Article* **Estimation of Traffic Stream Density Using Connected Vehicle Data: Linear and Nonlinear Filtering Approaches**

#### **Mohammad A. Aljamal 1, Hossam M. Abdelghaffar 2,3 and Hesham A. Rakha 1,***∗*


Received: 4 June 2020; Accepted: 17 July 2020; Published: 22 July 2020

**Abstract:** The paper presents a nonlinear filtering approach to estimate the traffic stream density on signalized approaches based solely on connected vehicle (CV) data. Specifically, a particle filter (PF) is developed to produce reliable traffic density estimates using CV travel-time measurements. Traffic flow continuity is used to derive the state equation, whereas the measurement equation is derived from the hydrodynamic traffic flow relationship. Subsequently, the PF filtering approach is compared to linear estimation approaches; namely, a Kalman filter (KF) and an adaptive KF (AKF). Simulated data are used to evaluate the performance of the three estimation techniques on a signalized approach experiencing oversaturated conditions. Results demonstrate that the three techniques produce accurate estimates—with the KF, surprisingly, being the most accurate of the three techniques. A sensitivity of the estimation techniques to various factors including the CV level of market penetration, the initial conditions, and the number of particles in the PF is also presented. As expected, the study demonstrates that the accuracy of the PF estimation increases as the number of particles increases. Furthermore, the accuracy of the density estimate increases as the level of CV market penetration increases. The results indicate that the KF is least sensitive to the initial vehicle count estimate, while the PF is most sensitive to the initial condition. In conclusion, the study demonstrates that a simple linear estimation approach is best suited for the proposed application.

**Keywords:** traffic density; connected vehicles; real-time estimation; particle filter; Kalman filter
