A stochastic subspace system identification algorithm for state-space systems in the general 2-D Roesser model form

摘要

The stochastic realisation problem is associated with fitting a state-space model to a given data-set so that the second-order statistics of the output of the system match those of the data. This problem has been well studied and documented in the 1-D case, but unfortunately not so in the 2-D case, despite the similarities. Until now, the main reason behind the lack of 2-D stochastic realisation algorithms is the fact that there is a strong coupling between horizontal and vertical states, which are difficult to separate. The only known way to separate the states is to assume the model to be causal, recursive, and separable-in-denominator (CRSD). Nevertheless, there is currently no known algorithm that can solve the general 2-D stochastic realisation problem. Such problem arises naturally in image modelling, where, given an image, one needs to fit a 2-D Kalman filter model to it. In this paper, we introduce a 2-D stochastic realisation algorithm for state-space models in the general 2-D Roesser form without using the CRSD assumption. The algorithm constructs a positive real 2-D Kalman filter model. We test the algorithm with three case studies, one of which is an image example.