Estimation of IIR Systems with Binary-Valued Observations  

作　　者：Ruifen DAI Lei GUO 

机构地区：[1]Data Science Institute,Shandong University,Jinan 250100,China [2]Key Laboratory of Systems and Control,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Chinese Annals of Mathematics,Series B》2023年第5期687-702,共16页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(No.12288201)。

摘　　要：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.

关 键 词：Binary-valued observations Infinite impulse response Adaptive estimation Double array martingales Adaptive prediction 

分 类 号：O231[理学—运筹学与控制论]