Results of least-squares identification algorithm for unstable systems

The convergence result of least-squares equation error identification algorithm applied to an unstable linear time-invariant system is given. It is shown that in order to obtain a uniform rate of convergence for all the parameter estimates of an ARMA model, an unbounded probing signal input is necessary. However, with the bounded probing signal input, the convergence of AR parameter estimates alone is ensured. Simulation results are included to illustrate the convergence behaviours.