Higher-order traffic flow models describe the dynamics of non-equilibrium traffic (e.g., capacity drop, traffic oscillation). Therefore, a traffic state estimation (TSE) method based on higher-order models could have notable advantages over conventional method based on an equilibrium (first-order) model. First, they can encompass non-equilibrium traffic phenomena inherent to the nonlinearity of traffic flow. Second, they can directly fuse heterogeneous traffic data, such as flow measured by detectors and speed measured by probe vehicles. These features would be useful for large volumes of data. This article proposes a data-assimilation-based TSE method for capturing non-equilibrium traffic dynamics based on the Aw-Rascle-Zhang model, which is known as a physically-consistent higher-order model but not received as much attention as other models. The proposed method can efficiently and simply fuse heterogeneous data. Additionally, it is computationally efficient because it uses the extended Kalman filter with an analytical derivative. The features of the proposed method were investigated empirically and quantitatively using experimental dataset collected from actual traffic. We investigate the empirical relationship between the accuracy and amount of available data, and compare the proposed method with a conventional TSE method.