AUTOREGRESSIVE SINESOID MODEL WITH FREQUENCY DRIFT
DOI:
https://doi.org/10.18372/2310-5461.62.18713Keywords:
autoregressive model, sinusoidal oscillation, radar system, frequency driftAbstract
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%.
References
Малоєд М. М. Оптимізація стабілізуючого управління математичним маятником. Електроніка та системи управління, 2011, №1(27), С. 78–83.
Omelchuk Iu., Chyrka A. Closed-Form ARMA-Based ML-Estimator of a Single-Tone Frequency. Circuits, Systems, and Signal Processing. 2018. V. 37 (8). P. 3441-3456.
Воронцов О. В. Заміна неперервних форм елементарних функціональних залежностей рекурентними формулами задання дискретних числових послідовностей. Геометричне та комп’ютерне моделювання: Збірник наук. праць. Харків: ХДУХТ, 2010. Вип. 27. С. 57–62.
Abe T. and Honda M. Sinusoidal model based on instantaneous frequency attractors. IEEE Trans. on Audio, Speech and Language Processing, July 2006, 14(4), P. 1292–300.
R.J. Mc. Aulay and T.F. Quatieri. Speech Analysis/Synthesis Based on a Sinusoidal Representation. IEEE Transactions on Acoustics, Speech, and Signal Processing. August 1986, V. 34 (4), P. 744-754.
S. Mann and S. Haykin. The chirplet transform: Physical considerations, IEEE Trans. Signal Process., 1995, V. 43, No. 11, 2745 p.
M. F. Ferreira. Dissipative Optical Solitons, Springer, 2022, 364 p.
Z. Despotovic A. R. The increasing energy efficiency of the vibratory conveying drives with electromagnetic excitation, International Journal of Electrical and Power Engineering, 2012, № 6 (1), P. 38-42.
V. Sinik, Z. Despotovic, I. Palinkas. Optimization of the operation and frequency control of electromagnetic vibratory feeders, Elektronika ir Elektrotechnika, 2016, №1, V. 22, P. 24-30.
Y. Yang, Q. Wang, Y. Hu, and others. Multiple Sine-Wave Superposition Drive for the Doubly Salient Motor Based on Fourier Linearization Modeling. IEEE Transactions on Power Electronics, April 2022, V. 37 (4), P. 4419 – 4430.
H. Chen, L. Liu, Y. Amirat, Z. Zhou. Model-Free Control for Doubly Salient Permanent Magnet-Generator-Based Tidal Stream Turbine Considering Flux-Weakening Operation. Journal of Marine Science and Engineering, 2023, V. 11(2), P. 1-26. doi:10.3390/jmse11122276.
