Abstract
In this article, a novel algorithm called integral linear least squares is proposed to estimate unknown parameters of a noisy damped complex/real sinusoidal signal in both one and two dimensions. Using the proposed innovative method, the problem of the nonlinear least squares algorithm in one dimension is transformed into a linear least squares algorithm. By the proposed algorithms, we can estimate the frequency, phase and amplitude of a sinusoidal signal corrupted by white Gaussian noise, with little complexity and high precision. In order to evaluate the performance and accuracy of our algorithm in one dimension, the Cramer–Rao lower bound (CRLB) is used. The proposed algorithm is able to achieve the CRLB criterion. In addition, the proposed algorithm is compared to other methods such as fast Fourier transform, maximum likelihood (ML) and derivation algorithm. Results show that the performance of proposed algorithm is very close to the ML method but with less computational complexity. Next, the proposed algorithm is developed to estimate unknown parameters of noisy two-dimensional damped sinusoidal models, including the noisy two-dimensional complex sinusoidal signal and noisy two-dimensional damped real sinusoidal signal. The simulation results indicate that the proposed algorithm is promising.
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References
Arablouei R, Doğançay K, Werner S (2015) Adaptive frequency estimation of three-phase power systems. Signal Process 109:290–300
Belega D, Petri D (2016) Accuracy analysis of the sine-wave parameters by means of the windowed three-parameter sine-fit algorithm. Digit Signal Process 50:12–23
Belega D, Petri D, Dallet D (2018) Amplitude and phase estimation of real-valued sine wave via frequency-domain linear least-squares algorithms. IEEE Trans Instrum Meas 67(5):1–13
Belega D, Petri D (2021) Fast procedures for accurate parameter estimation of sine-waves affected by noise and harmonic distortion. Digit Signal Process 114:1–17
Britos G, Ojeda S (2019) Robust estimation for spatial autoregressive processes based on bounded innovation propagation representations. Comput Stat 34:1315–1335
Campobello G, Segreto A, Donato N (2021) A novel low-complexity frequency estimation algorithm for industrial internet-of-things applications. IEEE Trans Instrum Meas. https://doi.org/10.1109/TIM.2020.3034629
Choqueuse V, Belouchrani A et al (2018) Frequency and phasor estimations in three-phase systems: maximum likelihood algorithms and theoretical performance. IEEE Trans Smart Grid 10(3):3248–3258
Djukanovic S, Popovic-Bugarian V (2020) Efficient and accurate detection and frequency estimation of multiple sinusoids. IEEE Access 7(1):1118–1125
Djukanovic S (2016) An accurate method for frequency estimation of a real sinusoid. IEEE Signal Process Lett 23(7):915–918
Elasmi-Ksibi R, Besbes H et al (2010) Frequency estimation of real-valued single-tone in colored noise using multiple autocorrelation lags. Signal Process 90(7):2303–2307
Fan L, Qi G et al (2020) Accurate frequency estimator of sinusoid based on interpolation of FFT and DTFT. IEEE Access 8(1):44373–44380
Kay S (1993) Fundamentals of statical signal processing: estimation theory, 2nd edn. Prentice-Hall Inc., United State of America
Kheirati Roonizi E, Sassi R (2016) A signal decomposition model-based Bayesian framework for ECG components separation. IEEE Trans Signal Process 64(3):665–674
Kuwalek P (2021) Estimation of parameters associated with individual sources of voltage fluctuations. IEEE Trans Power Deliv 36(1):351–361
Lin JQ, Chan S, Wu H (2022) A robust PAST-based ESPRIT algorithm with variable forgetting factor and regularization for frequencies/harmonics estimation in impulsive noise. IEEE Trans Instrum Meas. https://doi.org/10.1109/TIM.2022.3187728
Mahato B, Jana K, Thakura P (2019) Constant V/f control and frequency control of isolated winding induction motor using nine-level three-phase inverter. Iran J Sci Technol Trans Electr Eng 43:123–135
Mahdavi M, Gharehpetian G, Ghasemi A (2021) An enhanced converter-based diesel generator emulator for voltage and frequency control studies in laboratory-scale microgrids. Iran J Sci Technol Trans Electr Eng 45:945–957
Minjeong P, Sinsup C, Hee-Seok O (2013) The role of functional data analysis for instantaneous frequency estimation. Comput Stat 28:1965–1987
Narang M, Singh M (2019) Correlational analysis of heart rate variability band power and respiratory frequency to identify an optimal frequency band. Trans Inst Meas Control 41(14):4167–4175
Omelchuk I, Chyrka I (2018) A closed-form ARMA-based ML-estimator of a single-tone frequency. Circuits Syst Signal Process 37(8):3441–3456
Popovic P, Djukanovic S (2020) A low complexity model order and frequency estimation of multiple 2-D complex sinusoids. Digit Signal Process 104(2):1–9
Serbes A (2019) Fast and efficient sinusoidal frequency estimation by using the DFT coefficients. IEEE Trans Commun 67(3):2333–2342
So H, Chan F, Lau WH et al (2010) An efficient approach for two-dimensional parameter estimation of a single-tone. IEEE Trans Signal Process 58(4):1999–2009
So H, Chan F, Sun W (2012) Efficient frequency estimation of a single real tone based on principal singular value decomposition. Digit Signal Process 22(6):1005–1009
Song J, Mingotti A, Zhang J, Peretto L, Wen H (2022) Accurate damping factor and frequency estimation for damped real-valued sinusoidal signals. IEEE Trans Instrum Meas. https://doi.org/10.1109/TIM.2022.3220300
Pan P, Zhang Y, Deng Z, Qi W (2022) Deep learning-based 2-D frequency estimation of multiple sinusoidals. IEEE Trans Neural Netw Learn Syst 33(10):5429–5440
Tseng F, Sanpayao M, Wang T, Zhong M (2022) Low-complexity high-resolution frequency estimation of multi-sinusoidal signals. IEEE Trans Instrum Meas. https://doi.org/10.1109/TIM.2022.3187728
Wang P, Orlik P et al (2017) Parameter estimation of hybrid sinusoidal FM-polynomial phase signal. IEEE Signal Process Lett 24(1):66–70
Xu L (2022) Separable multi-innovation Newton iterative modeling algorithm for multi-frequency signals based on the sliding measurement window. Circuits Syst Signal Process 41:805–830
Xu L, Song G (2020) A recursive parameter estimation algorithm for modeling signals with multi-frequencies. Circuits Syst Signal Process 39(8):4198–4224
Yasar C (2020) Algebraic estimator of Parkinson’s tremor frequency from biased and noisy sinusoidal signals. Trans Inst Meas Control 43(3):679–686
Zayyani H, Dehghan M (2015) Frequency estimation of unbalanced three-phase power system using a new LMS algorithm. Iran J Electr Electron Eng 11(1):71–78
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Ghasemzadeh, S.V., Safarinejadian, B. Estimating Unknown Parameters of a Noisy Damped Real/Complex Sinusoidal Signal in Two Dimensions Based on the Integral Linear Least Squares Algorithm. Iran J Sci Technol Trans Electr Eng 47, 1225–1236 (2023). https://doi.org/10.1007/s40998-023-00603-y
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DOI: https://doi.org/10.1007/s40998-023-00603-y