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