A non-Gaussian Kalman Filter with application to the estimation of vehicular speed

Single Inductance Loop Detectors (ILDs) which provide online measurements of traffic volume and occupancy are widely used devices in road systems. Due to the nature of traffic flow, fast estimation and forecasting of vehicular speed using the data collected by an ILD are crucial to online road traffic management. In this paper statistical inference for vehicular speed is formulated as a dynamic generalized linear model with a reciprocal inverse Gaussian observational distribution. The formulation motivates us to extend the Gaussian Kalman filter to this non-Gaussian scenario. This results in a set of simple recursive formulae where the current estimate of the parameter of interest is updated as a weighted harmonic average of the previous estimate and the current observation. By applying the developed non-Gaussian Kalman filter to analyze traffic data collected by an ILD, we provide a competitive alternative to estimate vehicular speed at a minimum computational cost.