Estimation of IIR Systems with Binary-Valued Observations

Estimation and control problems with binary-valued observations exist widely in practical systems.However,most of the related works are devoted to finite impulse response(FIR for short)systems,and the theoretical problem of infinite impulse response(IIR for short)systems has been less explored.To study the estimation problems of IIR systems with binary-valued observations,the authors introduce a projected recursive estimation algorithm and analyse its global convergence properties,by using the stochastic Lyapunov function methods and the limit theory on double array martingales.It is shown that the estimation algorithm has similar convergence results as those for FIR systems under a weakest possible non-persistent excitation condition.Moreover,the upper bound for the accumulated regret of adaptive prediction is also established without resorting to any excitation condition.