Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates
Abstract
:1. Introduction
2. Scalar Parameter Estimation in Noise
Algorithm 1: AR Parameter estimation with noisy data. |
Input: , , Previous Conditions: , Compute
Update the covariance to obtain and compute . Return , , . |
- Ignore : Neglect the correlation structure and simply assume that . This gives the equivalent of taking a scalar measurement and is used as a sort of worst-case basis for comparison among the different algorithms.
- Use the correct value of : That is, assume that and and are known and compute according to (6). This provides a limit on best-case performance against which other methods can be compared.
- Use the estimate of : Using the correct values of and , compute the autocorrelation matrix using in (6).
- Estimate , fix and : With assumed values of and , compute the autocorrelation matrix using in (6).
- Estimate everything: Estimate the values of and , then use them with in (6).
3. Estimating the Variances
4. Vector Autoregressive Formulation
5. Some Results
6. Summary and Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A. Maximizing The Log Likelihood Function for Estimating Variances
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Case | Order | Pole Locations |
---|---|---|
1 | 3 | , , |
2 | 3 | , , |
3 | 3 | , , |
4 | 6 | , , |
5 | 6 | , , |
6 | 6 | , , |
d | |||
---|---|---|---|
2 | −5.9 | −5.8 | 11.1 |
3 | −12.4 | −12.5 | 4.5 |
4 | −17.5 | −17.5 | −0.6 |
5 | −20.6 | −20.6 | −3.9 |
6 | −22.6 | −22.7 | −5.9 |
7 | −23.9 | −24.0 | −7.2 |
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Moon, T.K.; Gunther, J.H. Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates. Entropy 2020, 22, 572. https://doi.org/10.3390/e22050572
Moon TK, Gunther JH. Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates. Entropy. 2020; 22(5):572. https://doi.org/10.3390/e22050572
Chicago/Turabian StyleMoon, Todd K., and Jacob H. Gunther. 2020. "Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates" Entropy 22, no. 5: 572. https://doi.org/10.3390/e22050572
APA StyleMoon, T. K., & Gunther, J. H. (2020). Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates. Entropy, 22(5), 572. https://doi.org/10.3390/e22050572