Numerical Integration for Future Vehicle Path Prediction

This paper proposes a shift from Kalman-like prediction routines for predicting the future state of a nonlinear dynamical system. Instead, this paper argues that, particularly in the vehicular path prediction environment, numerical integration of the nonlinear dynamics can provide more accurate predictions for significantly less computation time. This is particularly pertinent in the automotive domain where computation power and memory are kept at an affordable level. This work is motivated by future automotive safety systems which will leverage wireless communications to create current and future state maps of the driving environment. The ability of a vehicle to provide an estimate of its future position in an Earth Coordinate Frame is seen as a critical first piece of the larger collision avoidance puzzle. At a vehicle level, its nonlinear dynamics are nonstiff, smooth, and low enough in order that they lend themselves naturally to efficient numerical integration techniques. In contrast, techniques involving Kalman-like prediction are computationally heavy because of the large number of matrix computations required not only in the prediction, but in the real-time discretization of the continuous-time dynamics. The superiority of the numerical integration approach is illustrated in this paper through a comparison of various models and the prediction techniques on real-world driving data as well as an advanced safety system application that has been developed at the Toyota Technical Center.