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Before a car-following model can be applied in practice, it must first bevalidated against real data in a process known as calibration. This paperdiscusses the formulation of calibration as an optimization problem, andcompares different algorithms for its solution. The optimization consists of anarbitrary car following model, posed as either an ordinary or delaydifferential equation, being calibrated to an arbitrary source of trajectorydata which may include lane changes. Typically, the calibration problem issolved using gradient free optimization. In this work, the gradient of theoptimization problem is derived analytically using the adjoint method. Thecomputational cost of the adjoint method does not scale with the number ofmodel parameters, which makes it more efficient than evaluating the gradientnumerically using finite differences. Numerical results are presented whichshow that quasi-newton algorithms using the adjoint method are significantlyfaster than a genetic algorithm, and also achieve slightly better accuracy ofthe calibrated model.

Fast Calibration of Car Following models to Trajectory data using the Adjoint Method