A method was developed for determining the unknown initial velocity of vehicles in yaw based upon evidence of the vehicle’s trajectory. The problem is formulated as an optimization problem by minimizing the error between a simulation trajectory and the known vehicle trajectory as per tire marks.
A search simulation is coded in Matlab. An objective function is formulated based upon the error between the search simulation’ trajectories and the trajectory prescribed by the tire mark evidence. Initial conditions and step driver inputs are the design variables. A genetic algorithm routine coded in Matlab, GAOT (Genetic Algorithm Optimization Toolbox), is implemented to determine the solution vector that results in a simulation trajectory that minimizes the objective function.
Target simulations are created using EDVSM (Engineering Dynamics Vehicle Simulation Model). The optimization algorithm is implemented and errors in the resultant velocities are reported. Longitudinal velocity is determined to be the design variable to which the objective function is most sensitive.
Initial resultant velocities found through optimization are compared to initial resultant velocities found using the “Critical Speed Method”. The method herein is found to more accurately determine initial velocity, particularly when braking is involved.