Gaussian mixture approach to decision making for automotive collision warning systems

This paper proposes a practical probabilistic approach to collision decision making which is necessary for advanced automotive collision warning system (CWS) using FMCW radar. Most decision making algorithms assess the probable collisions based on the predicted collision position which is usually expressed as a nonlinear function of threat vehicle's position and velocity provided by FMCW radar. Since the predicted collision position has highly nonlinear statistics in general, it is one of main obstacles to improving the reliability of the collision probability computation and to developing real-time decision making algorithms. This motivates us to devise a Gaussian mixture method for collision probability calculation with the help of linear recursive time-to-collision (TTC) estimation. The suggested TTC estimator provides an accurate TTC estimate with small estimation error variance hence it enables us to approximate the probability density function of the predicted collision position as the weighted sum of just a few Gaussian distributions. Therefore, our approach could drastically reduce the inherent nonlinearity of collision decision making problem and computational complexity in collision probability calculation. Through the simulations for the typical engagement scenarios between the host and threat vehicles, the performance and effectiveness of the proposed algorithm is compared to those of the existing ones which require heavy computational burden.