Filtering and Tracking with Trinion-Valued Adaptive Algorithms

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

Quaternion MLP Neural Networks Based on the Maximum Correntropy Criterion

We propose a gradient ascent algorithm for quaternion multilayer perceptron (MLP) networks based on the cost function of the maximum correntropy criterion (MCC). In the algorithm, we use the split quaternion activation function based on the generalized Hamilton-real quaternion gradient. By introducing a new quaternion operator, we first rewrite the early quaternion single layer perceptron algorithm. Secondly, we propose a gradient descent algorithm for quaternion multilayer perceptron based on the cost function of the mean square error (MSE). Finally, the MSE algorithm is extended to the MCC algorithm. Simulations show the feasibility of the proposed method

A cyclo-stationary complex multichannel wiener filter for the prediction of wind speed and direction

This paper develops a linear predictor for application to wind speed and direction forecasting in time and across different sites. The wind speed and direction are modelled via the magnitude and phase of a complex-valued time-series. A multichannel adaptive filter is set to predict this signal, based on its past values and the spatio-temporal correlation between wind signals measured at numerous geographical locations. The time-varying nature of the underlying system and the annual cycle of seasons motivates the development of a cyclo-stationary Wiener filter, which is tested on hourly mean wind speed and direction data from 13 weather stations across the UK, and shown to provide an improvement over both stationary Wiener filtering and a recent auto-regressive approach