Recursive parameter and state estimation methods for observability canonical state-space models exploiting the hierarchical identification principle

This study presents two recursive parameter and state estimation algorithms for state-space systems, considering the process noises and observation noises. Based on the Kalman filter and hierarchical identification principle, the authors propose a Kalman filtering-based hierarchical generalised stochastic gradient algorithm to jointly estimate the parameters and states of observability canonical state-space systems. With the aim of achieving more accurate parameter estimation, they present a Kalman filtering-based hierarchical multi-innovation generalised stochastic gradient algorithm by utilising a range of available data and more information at each recursion. Finally, the effectiveness of the proposed algorithms is validated through a numerical simulation example.