A recursive algorithm for MIMO stochastic model estimation

Multivariable system identification is known to be a difficult problem. In part, this is due to the fact that, in general, the likelihood function is non-convex. The most commonly used class of procedures for off-line identification of multivariable systems is the method commonly known as sub-space. These methods avoid the non-convexity issue by using a multi-step procedure, which includes a singular value decomposition. Unfortunately, it is not easy to develop a recursive form of these sub-space algorithms due to the singular value decomposition step. Here, we borrow ideas from the sub-space methodologies to develop a novel recursive algorithm. We assume that the Kronecker invariants for the system are known. We also illustrate the performance of the algorithm via a simple example.