AUTOREGRESSIVE SINESOID MODEL WITH FREQUENCY DRIFT - Maloied, Marina; Omelchuk, Igor; Omelchuk, Mykyta (Science-based technologies, 2024)
In technical systems, in addition to mechanical oscillations, it is also worth noting electrical sinusoidal processes in alternating current circuits, in electronic devices, in particular, in the industrial power supply network, oscillatory circuits, signal generators, communication systems, etc. In radar systems, sinusoidal signals with frequency drift can also be observed, for example, linear frequency-modulated or Doppler signal reflected from a maneuvering target, the speed of which has at least one derivative. Among the possible ones, in the future we limit ourselves to comparative studies of two types of SL-oscillations - harmonic (SG) with all constant parameters and sinusoid with linear frequency drift (SD). At the same time, we will consider two types of their mathematical models - trigonometric (T-models) and autoregressive (AR-models). The paper analyzes sine-like trigonometric models and features of their application. The peculiarities of the task of measuring the parameters of the movement of an object with uniform acceleration based on the estimation of the Doppler frequency of the radar probing signal reflected from it are considered. A synthesis of simplified and approximate ARD models was carried out. An important feature of the synthesized ARG model is the fact that only one parameter of the trigonometric model appears in it - the normalized frequency. The main merit of the synthesized simplified and approximate ARD models is their invariance to the amplitude and initial phase of the sinusoidal signal. This reduces the parametric dimension of the estimation problem from four to two parameters, which contributes to a significant improvement in the speed of calculations. Based on mathematical modeling, statistical errors were obtained for different sampling intervals in the triplet and sample size. Based on mathematical modeling, statistical errors were obtained for different sampling intervals in the triplet and sample size. The selection of pairs of triplets was probabilistic. Calculations show that the error of the obtained model does not exceed 8%.