On the realisation of 2-D linear systems with implicit latent variable models

In this paper a new latent variable model is proposed for the realisation of 2-D linear causal systems. For the general (n,m)-th order 2-D system, the latent variable model obtained here is implicit when nnem. Importantly however, even in this case the model is recursively computable. The advantage of this realisation is that its order is nm, which is much smaller than the orders of the existing latent variable realisations such as Fornasini-Marchesini (FM) models and Roesser model. In addition, given a particular 2-D system, an algorithm is developed for further reducing the size of the realisation.