A new model for three-dimensional processes based on the trinion algebra is introduced for the first time. Compared
with the pure quaternion model, the trinion model is more compact and computationally more efficient, while having similar or
comparable performance in terms of adaptive linear filtering. Moreover, the trinion model can effectively represent the general
relationship of state evolution in Kalman filtering, where the pure quaternion model fails. Simulations on real-world wind
recordings and synthetic data sets are provided to demonstrate the potentials of this new modeling method
