Recursive Identification of Noisy Autoregressive Models Via a Noise–Compensated Overdetermined Instrumental Variable Method

The aim of this paper is to develop a new recursive identification algorithm for autoregressive (AR) models corrupted by additive white noise. The proposed approach relies on a set of both low-order and high-order Yule–Walker equations and on a modified version of the overdetermined recursive instrumental variable method, leading to the estimation of both the AR coefficients and the additive noise variance. The main motivation behind our proposition is introducing model identification procedures suitable for implementation on edge-computing platforms and programmable logic controllers (PLCs), which are known to have limited capabilities and resources when dealing with complex mathematical computations (i.e., matrix inversion). Indeed, our development is focused on condition monitoring systems, with particular attention paid to their integration onboard industrial machinery. The performance of the recursive approach is tested using both numerical simulations and a laboratory case study. The obtained results are very promising.