Iterative parameter identification of binary output FIR systems with measurement errors
GUO Jian
XUE Wen-chao
WANG Ting
ZHANG Ji-feng
Abstract：In this paper,we consider the problem of parameter identification for a class of finite impulse response(FIR)systems with binary outputs and measurement errors,where the measurement errors result in a certain probability of obtaining opposite values for the binary measurements.Firstly,for the considered FIR system,a maximum likelihood estimator(MLE)of the parameter is given,and the strong convergence and asymptotic normality of the MLE are proved under certain regularity conditions of the noise.In addition,by analysing the properties of the likelihood function,an iterative algorithm for solving the MLE is given based on the expectation-maximum(EM)method.In order to adapt to more general measurement error situations,an iterative solution algorithm with projection is given,and the boundedness of the iterative estimation sequence is theoretically proved.Further,a necessary and sufficient condition for the likelihood function to have a unique maximum point is obtained for a given number of observations,and the iterative estimation error is shown to converge to zero with an exponential rate under persistent excitation input conditions.Finally,the effectiveness of the proposed algorithm is verified based on numerical simulation results.
Keywords：binary-valued observationmaximum likelihood estimatesystem identificationstrong convergenceasymptotic normalityexponential rate
Publication Date：2024-07-28
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：10( 1197-1206 )