New approach to model-order selection

A new, direct and practical scheme is proposed for determining the model orders of a system, its signal and disturbance using key properties of Kalman filter (KF). Unlike conventional methods, it enjoys the unique property of being both necessary and sufficient. The system is described by the Box–Jenkins model, whose accessible input and output are corrupted by unknown zero-mean white Gaussian-distributed disturbances and measurement noise. The signal and disturbance are outputs of asymptotically-stable linear time-invariant systems driven by an inaccessible input and a zero-mean white Gaussian noise process, respectively. Predictive analytics is used to estimate the input by exploiting its smoothness and the randomness of the noisy input. The system, signal, and disturbance models and their associated KFs are identified for various selected model orders by minimising the KF residuals so that these become zero-mean white noise processes. The selected model-order corresponds to the minimum-variance residual. Equivalently, the minimum order is selected when the number of poles or the output estimates of the identified models are all identical for all orders equal to, or exceeding the minimal order. The scheme is successfully evaluated and shown to outperform the commonly-used but only sufficient Akaike Information Criterion.