Transfer function estimation with Kalman filter for processes with input and output noises

A solution is suggested to estimate the transfer function of an SISO (Single Input and Signal Output) system, in which the input and output are contaminated with measurement noises. The solution is based on maximum likelihood estimation (MLE) method, which has the properties of asymptotical efficiency and consistency. The solution combines Kalman filter and the MLE. Both the transfer function and the variances of the noises can be estimated. The estimate of the parameters in the transfer function or the estimate of the frequency response of the transfer function are unbiased. The algorithm overcomes the problems in algorithms using e.g. FFT and ARMAX identification which introduce bias in the transfer function estimate due to the noise in the input and the output. The algorithm is applied to estimation of MTC (moderate temperature coefficient) and the result is reasonable