Q-Net: Queue Length Estimation via Kalman-based Neural Networks

TL;DR

Q-Net tackles the challenge of estimating queue length under partial observability by marrying a principled state-space model with an AI-augmented Kalman filter. It fuses loop-detector counts and aggregated floating car data through a learned Kalman gain (KalmanNet) and a spatially transferable measurement grouping scheme, yielding a data-efficient, interpretable solution suitable for real-time deployment. The approach demonstrates strong performance gains over baselines, robust transferability across adjacent road sections, and viable online operation for traffic control, all without costly sensing infrastructure. The work highlights a practical path toward scalable, privacy-preserving queue estimation in urban networks.

Abstract

Estimating queue lengths at signalized intersections is a long-standing challenge in traffic management. Partial observability of vehicle flows complicates this task despite the availability of two privacy preserving data sources: (i) aggregated vehicle counts from loop detectors near stop lines, and (ii) aggregated floating car data (aFCD) that provide segment-wise average speed measurements. However, how to integrate these sources with differing spatial and temporal resolutions for queue length estimation is rather unclear. Addressing this question, we present Q Net: a robust queue estimation framework built upon a state-space formulation. This formulation addresses key challenges in queue modeling, such as violations of traffic conservation assumptions. To overcome the limitations of standard filtering models in integrating diverse data sources, Q-Net employs an AI-augmented Kalman filter for estimation. Q-Net follows the Kalman predict-update framework and maintains physical interpretability, with internal variables linked to real-world traffic dynamics. Q-Net can be implemented in real-time, making it suitable for integration into queue-based traffic control systems. To achieve spatial transferability across road sections, we group aFCD measurements into fixed-size groups. This strategy ensures the dimension of Q-Net's learnable parameters is independent of section length. Evaluations on urban main roads in Rotterdam, the Netherlands, show that Q-Net outperforms baseline methods, accurately tracking queue formation and dissipation while correcting aFCD-induced delays. By combining data efficiency, interpretability, and strong transferability, Q Net makes accurate queue length estimation possible without costly sensing infrastructure like cameras or radar.

Figures (14)

• Figure 1: Layout of a signalized intersection, including the definitions of a lane, section, and ground truth queue length. Data are collected from inflow/outflow detectors and aFCD segments. The layout highlights two common sources of partially observed traffic flow: (i) lanes with combined directions at the upstream intersection of the study section, where part of the traffic flow does not proceed to the downstream area, (ii) unobserved traffic flow leaving or entering the study section. The leaving flow can be caused by infrastructure splits (e.g., elevated roads or tunnels) or vehicles entering neighboring buildings, while the entering flow consists of minor car movements from the surrounding environment.
• Figure 2: Queue estimation from net vehicle accumulation under unobserved traffic flow conditions for section N1-IN in Rotterdam on 2023-11-10.
• Figure 3: At time $t$, the Q-Net filtering framework takes three inputs: the previous a posteriori state estimate $\hat{x}_{t-1|t-1}$, cumulative vehicle counts $A_t, D_t$, and aFCD speed measurements $\mathbf{y}_{t}$, and produces one output: the current a posteriori state estimate $\hat{x}_{t|t}$. Predict:$A_t$ and $D_t$ are used to derive the control input (queue change) ${u}_{t}$, which predicts the a priori queue length $x_{t|t-1}$ and a priori speed measurements $\mathbf{\hat{y}_{t|t-1}}$ through the measurement model. Update: The predicted a priori speeds $\mathbf{\hat{y}_{t|t-1}}$ are compared with actual aFCD measurements $\mathbf{y}_{t}$, and the adapted KalmanNet calculates the Kalman gain $\mathcal{K}_t$ to update the a posteriori queue estimate $\hat{{x}}_{t|t}$.
• Figure 4: KalmanNet architecture for dynamic Kalman gain estimation. The top panel illustrates the overall KalmanNet pipeline, which takes in four temporal input features (forward evolution difference$\Delta \tilde{x}_{t-1}$, forward update difference$\Delta \hat{x}_{t-1}$, measurement difference$\Delta \tilde{\mathbf{y}}_t$, innovation difference$\Delta {\mathbf{y}}_t$) to estimate the Kalman gain. Intermediate representations ($\hat{Q}_t, \hat{\Sigma}_t, \hat{\mathbf{S}}_t$ and $\hat{\Sigma}_t^h$) are computed through sequential submodules. The lower panels detail the submodules a, b, c, d, and e.
• Figure 5: Local measurement grouping strategy for transferable Kalman gain estimation. aFCD speed measurements are grouped into fixed-size vectors consisting of the previous, current, and next segments. Each vector is processed by KalmanNet to obtain a local Kalman gain, and the final state update is computed as the sum of all local updates. This approach enables model transfer across road sections with different numbers of segments.