Multiple-clustering ARMAX-based predictor and its application to freeway traffic flow prediction

An adaptive predictor for a linear discrete time-varying stochastic system is proposed in this paper in order to forecast freeway traffic flow at a specific location over a one-hour horizon. Historical sensor data is first clustered by the K-means method to obtain the representative data pattern of the sensor. For each K-means cluster and using the clusters centroid as the exogenous input, the time-varying output of the sensor is subsequently modeled as an ARMAX stochastic process, and identified in real time using a recursive least squares (RLS) with forgetting factor algorithm. Based on the identified ARMAX model, a D-step ahead optimal predictor is generated for each cluster and its associated estimated error prediction variance calculated. The cluster and its associated ARMAX estimate that produces the smallest estimated D-step ahead error prediction variance is selected at each sampling time instant to generate the optimal D-step ahead predictor of the sensor output. The proposed technique is applied to empirical vehicle detector station (VDS) data to forecast both freeway mainline and on-ramp traffic flow at specific locations over a horizon of one hour. Results indicate that the proposed traffic flow predictor often offers superior flexibility and overall forecast performance compared to using either only historical data or only real-time sensor data on both normal commute days and days when unusual incidents occur.