A new IV approach to the estimation of parameters of the linear system with noisy output data

A method with new instrumental variables of the IV (instrumental-variable) identification algorithm is proposed to estimate the unknown parameters of linear time-invariant single-input single-output systems with the output variables contaminated by noise. Since only the noisy observation and input signals are needed to obtain the instrumental variables and the knowledge of the measurement noise is not necessary, the algorithm is more easily to implement. The measurement noise may be colored Gaussian or independent and identically nonGaussian distributed. Strong consistency of the proposed method is proved under certain sufficient conditions. The limiting distribution of the parameter estimates is shown to be Gaussian asymptotically. An explicit expression of the covariance matrix for the parameter estimates is also given. Simulation results show that the unknown system is not restricted to be minimum phase and is allowed to contain all-pass components in its transfer function