Novel Multivariate Nonlinear Signal Processing Methods for Modelling and Prediction

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Many natural phenomena are generated by complex mechanisms for which we do not know their generating mechanisms. We can however observe a few measurements which are available to us and which represent that phenomenon. For instance, we can measure wind speed and direction, but the behaviour of wind is influenced by general circulations of the atmosphere, together with some local factors, such as air pressure, humidity, temperature and landscape. These relationships are very difficult to understand, and the mathematical models to describe those data are very complex and often not sufficiently accurate. These observations, however, provide us with some imporant information, and the knowledge an understanding of their present and future behavior plays major role in human affairs. For instance, the knowledge about the future values of wind speed can help avoid train derailment and efficiency of wind farms.This project will show whether the understanding and successful use of the underlying nonlinear dynamics and signal modality characterisation, combined with advanced nonlinear modelling and forecasting will contribute to a reliable simultaneous estimation of the components of multivariate signals. We perform this research in the multidimensional mathematical framework with well defined algebraic operations. This will also help to mitigate theoretical and practical limitations in forecasting simultaneously nonstationary, nonlinear and non-Gaussian signals, such as wind, together with the improved efficiency of algorithms working under uncertainty and noise.The fact that we can avoid the emission of 1 kTon of CO2 per every 1000 GWh of wind energy production supports the commercial and environmental impact of this advanced nonlinear multivariate modelling research.