| Estimation of Frequencies of Sinusoids based on the Augmented Equivalent Systems |
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| Authors |
| | Ivanov D.V. |
| | Mitroshin D.I. |
| Date of publication |
| | 2020 |
| DOI |
| | 10.31114/2078-7707-2020-3-244-249 |
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| Abstract |
| | A large number of papers are devoted to the problem of estimating the frequencies of sinusoids from a finite number of discrete noisy measurements because of its widespread use in science and technology. Estimating the frequencies of sinusoids based on the total least-squares method (TLS) allows us to obtain more accurate estimates compared to the ordinary least-squares method (OLS). The most common algorithm for solving the total least squares problem is an algorithm based on a singular matrix decomposition. This algorithm has high computational complexity. An alternative method for solving the problem of complete least squares is the approach based on biased normal systems. The paper proposes an estimate of the frequencies of sinusoids from discrete measurements with noise based on augmented equivalent systems. The ability to obtain a solution of the complete least squares problem without finding the right singular vector and multiplying the data matrices is an undeniable advantage of frequency estimates based on augmented systems compared to solutions based on a singular matrix decomposition or a biased normal system, respectively.
The simulation results show that frequency estimates based on augmented systems are comparable in accuracy by solving the complete least squares problem based on a singular matrix decomposition and have a significantly lower condition number than a shifted normal system of equations. |
| Keywords |
| | Total Least Squares Method, Resolution, Frequency Estimation. |
| Library reference |
| | Ivanov D.V., Mitroshin D.I. Estimation of Frequencies of Sinusoids based on the Augmented Equivalent Systems // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2020. Issue 3. P. 244-249. doi:10.31114/2078-7707-2020-3-244-249 |
| URL of paper |
| | http://www.mes-conference.ru/data/year2020/pdf/D112.pdf |
