High-resolution spatiotemporal freeway traffic state estimation under sparse observations using METANET-EnKF data assimilation

The spatial sparsity of fixed sensing infrastructure fundamentally limits the reconstruction of high-resolution spatiotemporal traffic states. Under sparse observations, estimation performance is affected by initialization uncertainty, unmeasured boundary inputs, and spatial heterogeneity in traffic-flow relationships. This study investigates high-resolution freeway traffic state estimation using a METANET-Ensemble Kalman Filter (M-EnKF) data assimilation implementation. Building on established METANET-based recursive estimation and augmented-state treatments of unmeasured boundary variables, the implementation is configured for a challenging setting in which the ramp topology is known from the freeway geometry, ramp-flow measurements are not assimilated, and only sparse mainline loop measurements are used. A strong-constraint Four-Dimensional Variational (4D-Var) procedure is first used to provide a dynamically consistent initial condition for the subsequent EnKF recursion. Time-varying ramp-related boundary inputs at known ramp locations are represented as ramp-induced source/sink terms through an augmented-state EnKF update. In contrast, fundamental diagram (FD) parameters are not directly updated in the augmented EnKF state. Instead, they are adapted locally through a Gaussian approximation in which the random-walk prediction of each cell’s FD parameters provides the prior and the EnKF posterior density-speed estimate provides state-based evidence. Their combination yields the posterior FD-parameter estimate, which is then injected into METANET for the subsequent forecast cycle. Empirical evaluation using field data from the US-101 corridor shows that the resulting implementation improves estimation accuracy relative to physics-based models, data-driven baselines, and standard filtering approaches. The implementation achieves Mean Absolute Percentage Errors (MAPE) of 6.92% for flow and 4.75% for speed. Sensor-sparsity tests further show that the implementation remains robust under reduced mainline sensor availability. Ablation results indicate that 4D-Var initialization improves early-stage stability, augmented ramp-effect updating mitigates boundary-induced conservation mismatch, and cell-wise FD adaptation improves the representation of heterogeneous speed dynamics. Overall, the results support the effectiveness of the M-EnKF implementation for high-resolution freeway traffic state estimation under the evaluated sparse-sensing setting.