Stochastic adaptive pole-zero assignment with convergence analysis (Q1076655)

Given a multidimensional ARMAX model \(A(z)y_{n+1}=B(z)u_ n+C(z)w_{n+1}\), where \((u_ n)\) is a sequence of controls and \((w_ n)\) is a noise sequence, the problem is to estimate the vector \(\theta\) of unknown coefficients of the matrix polynomials A(z), B(z) and C(z). For a certain input sequence \((u^ o_ n)\) a sequence \((\theta_ n)\) of strongly consistent estimators for \(\theta\) is constructed by means of a stochastic gradient algorithm.