Robust estimation of traffic density with missing data using an adaptive-R extended Kalman filter

Traffic density is a crucial indicator of traffic congestion, but measuring it directly is often infeasible and hence, it is usually estimated based on other measurements. However, a challenge in measuring traffic parameters is the high probability of sensor failure, which results in missing measurement or missing data. To overcome this difficulty, in this paper, we propose a novel adaptive-R extended Kalman filter (AREKF) combined with a model-based data imputation technique to estimate traffic density. We show analytically that the AREKF is able to accurately estimate the density even when the noise covariance matrices are not accurately known. Microscopic traffic simulations demonstrated the efficacy of the AREKF, where the estimated density is fed into a real-time ramp metering control algorithm to control vehicle flow on a merging road, which is highly susceptible to traffic congestion. The results show that the proposed AREKF with data imputation is able to accurately estimate the traffic density even when data is missing, and the ramp-metering controller significantly improves the traffic flow and thus, alleviates congestion.