A Stable Algorithm for Differentiating Noisy Signals in the Problem of Nonparametric Identification of Non-stationary Systems

We propose a new method for building an integral model of a non-stationary linear dynamic system. The method is based on identification of the model's transient characteristics using piecewise linear input signals. We obtained an explicit expression for the desired impulse function that includes second-order derivatives of the noisy output signal of the system. We developed an algorithm for stable differentiation of noisy output signals based on smoothing cubic splines. The issues of choosing the smoothing parameter using the condition of the minimum smoothing error are considered in detail. We carried out a computational experiment that showed a low methodological error of the identification algorithm and its acceptable resistance to measurement noise in practice.