Quaternion Widely Linear Forecasting of Air Quality

In this paper, we propose a quaternion widely linear approach for the forecasting of environmental data, in order to predict the air quality. Specifically, the proposed approach is based on a fusion of heterogeneous data via vector spaces. A quaternion data vector has been constructed by concatenating a set of four different measurements related to the air quality (such as CO, NO\(_2\), SO\(_2\), PM\(_{10}\), an similar ones), then a Quaternion LMS (QLMS) algorithm is applied to predict next values from the previously ones. Moreover, when all the considered measurements are strongly correlated each other, the Widely Linear (WL) model for the quaternion domain is capable to benefit from correlations and to obtain improved accuracies in prediction. Some experimental results, evaluated on two different real world data sets, show the effectiveness of the proposed approach.