A recursive algorithm for simultaneous identification of model order and parameters

A recursive identification algorithm for SISO CARMA systems is presented based on an augmented information matrix (AIM). Decomposition of the AIM using UDU factorization provides simultaneous, recursive estimates of both the system parameters and the loss functions from order 0 to n, where n is the maximum possible order of the real process and U and D are upper and diagonal matrices, respectively. The most appropriate model order is then determined by examination of the loss functions. This approach results in a computationally efficient and numerically robust algorithm for systems of unknown or variable model order