State filtering and parameter estimation for linear systems with d-step state-delay

This study considers the modelling and identification problems for linear systems based on canonical state space models with d-step state-delay. A recursive least-squares parameter identification algorithm is presented. The basic idea is to drive a parameter identification model for such d-step state-delay systems, to replace the unknown noise terms and unknown state variables in the formation vector with their estimated residuals and estimated states, and to compute the state estimates of the system in the state estimation algorithm using the estimated parameters. The simulation results indicate that the proposed parameter and state estimation algorithm can capture the dynamics of the system.