On Certain Convergence Questions in System Identification

摘要: This paper examines the asymptotic properties of maximum likelihood estimates unknown parameters and initial state linear, stable, constant coefficient, discrete time dynamic systems where plant noise observation are present. Necessary sufficient conditions obtained for system parameter to converge with probability one, be asymptotically normal in mean square. These require that representation unique impose a simple constraint on input sequence. Under these conditions, estimate is shown unbiased have finite covariance.