Derivation of the discrete-time constant turn rate and acceleration motion model

Abstract

For vehicle tracking in automotive applications there are a number of proposed motion models. One of those models is the constant turn rate and acceleration (CTRA) model. In the original paper where the model was introduced, the state prediction function was defined, but not the process noise. In this paper, a derivation of the process noise is made. For completeness, the discrete-time prediction model is also derived, using linearized discretization.