# A Closed-Form ARMA-Based ML-Estimator of a Single-Tone Frequency

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## Abstract

The new synthesis methodology for single-tone frequency estimation is proposed on the basis of the maximum likelihood (ML) method and autoregressive moving average (ARMA) models. The novel frequency estimator for the scenario with a strongly correlated interference and an additive white Gaussian noise is synthesized in a closed form. The assumption about a constant value of that interference allows to simplify the mixture and transform it to ARMA (3,3) model. The synthesized estimator is invariant to the interference power when it is actually constant (has a unitary correlation coefficient). The particular and much more usual scenario without the interference and just with the noise is considered as well. For that case, the ML-estimator synthesized using the proposed methodology is equal to the existing modified least squares estimator. It is shown that the proposed ML-estimator has an advantage over the known one when the interference is present in the mixture.

## Keywords

Single-tone harmonic Autoregressive moving average model Frequency estimation Maximum likelihood Strongly correlated interference## References

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