An extension on the quantized input condition for FIR systems identification with quantized observations

This paper extends the quantized input condition in the identification for finite impulse response systems under quantized output observations, and investigates the convergence performance of the two-step estimation algorithm formed by combining the quasi-convex combination estimator and weighted least-squares optimization. We employ the limit inferior of the regressors´ frequencies of occurrences to character the input´s persistent excitation, under which the strong convergence and convergence rate of the algorithm are derived. It is interesting that the estimates can be asymptotically efficient with a suitable selection of the weighting matrix in the algorithm, even though the limit of Cramér-Rao lower bound times the data length does not exist as the data length goes to infinity. A numerical example is included to illustrate the main results obtained.