Identification of independent components using cumulants and coherences

The characterization of independent stationary stochastic components (sources), can theoretically be achieved by using the 2^nd and 4^th order cumulants of partially correlated measurements, which are linearly related to the components of interest. The general model supposes as many sources as measurements. The authors recall first why 4^th order cumulants achieve a solution, while 2^nd order cumulants fail. However, the main algorithms (Comon, Cardoso, Gaeta-Lacoume) are generally used with a 2 observations -2 independent components models, to avoid complexity of calculation. The authors first examine what is achieved when the number of independent components is not well estimated. They suggest a new algorithm for independent components identification, which enables more than two sources, and based on both 2^nd and 4^th order cumulants