Vehicle model identification by integrated prediction error minimization

We present a highly effective approach for the calibration of vehicle models. The approach combines the output error technique of system identification theory and the convolution integral solutions of linear systems and stochastic calculus. Rather than calibrate the system differential equation directly for unknown parameters, we calibrate its first integral. This integrated prediction error minimization (IPEM) approach is advantageous because it requires only low frequency observations of state, and produces unbiased parameter estimates that optimize simulation accuracy for the chosen time horizon. We address the calibration of models that describe both systematic and stochastic dynamics, such that uncertainties can be computed for model predictions. We resolve numerous implementation issues in the application of IPEM, such as the efficient linearization of the dynamics integral with respect to parameters, the treatment of uncertainty in initial conditions, and the formulation of stochastic measurements and measurement covariances. While the technique can be used for any dynamical system, we demonstrate its usefulness for the calibration of wheeled vehicle models used in control and estimation. Specifically we calibrate models of odometry, powertrain dynamics, and wheel slip as it affects body frame velocity. Experimental results are provided for a variety of indoor and outdoor platforms.