Consistent identification of spatially interconnected systems

This paper presents an identification technique to consistently identify multi-dimensional systems with additive output colored noise in transfer function representation. The method is an extension of a one-dimensional refined instrumental variable method to multi-dimensional systems. It can be used to identify models for multi-dimensional systems with Box-Jenkins structure; the method may give estimates with minimum bias and variance. In this paper we consider a general multi-dimensional system, which may be separable or non-separable, causal, semi-causal (spatially interconnected systems) or non-causal. Furthermore the algorithm can handle boundary conditions. The effectiveness of the method is shown with application to simulation examples.