Nonparametric identification assuming two noise sources: a deconvolution approach

Nonparametric identification of linear systems is investigated in this paper. Nonparametric identification is the estimation of the time record of the impulse response of the system. It is a deconvolution problem, i.e., inverse operation of the convolution of the impulse response and the excitation signal. The problem is ill posed, i.e., deconvolution amplifies the measurement noise to a great extent. The noise has to be suppressed with the price of a bias in the estimate. A tradeoff has to be found between the noisy and biased estimates. Because of the need for repeatability and to reduce the subjectivity, the level of noise reduction has to be set algorithmically. This paper introduces a method that optimizes the parameter(s) of deconvolution filters and, thus, controls the level of noise reduction. The proposed method assumes observation noise sources for both the measurement of the excitation signal and the system output.