In the present paper the authors generalize linear subspace identification theory to an analog theory for the subspace identification of bilinear systems. A major assumption they make is that the inputs of the system should be white and mutually independent. It is shown that in that case most of the properties of linear subspace identification theory can be extended to similar properties for bilinear systems. The link between the presented bilinear subspace method and Kalman filter theory is made. Finally, the practical relevance of the method is illustrated by making a direct comparison between linear and bilinear subspace identification methods when applied on data from a model of a distillation column.