An iterative algorithm for single-frequency estimation

Abstract

An algorithm for the estimation of the frequency of a complex sinusoid in noise is proposed. The estimator consists of multiple applications of lowpass filtering and decimation, frequency estimation by linear prediction, and digital heterodyning. The estimator has a significantly reduced threshold relative to existing phase-based algorithms and performance close to that of maximum likelihood estimation. In addition, the mean-squared error performance is within 0.7 dB of the Cramér-Rao bound (CRB) at signal-to-noise ratios (SNRs) above threshold. Unlike many autocorrelation and phase-based methods, the proposed algorithm's performance is uniform across a frequency range of to . The computational complexity of the algorithm is shown to be favorable compared with maximum likelihood estimation via the fast Fourier transform (FFT) algorithm when significant zero-padding is required.

A Filter Structure for Arbitrary Re-Sampling Ratio Conversion of a Discrete Signal

“…This problem has been studied using many methods, such as the autocorrelation function and maximum likelihood estimation [9][10][11][12][13]. For our method, the frequency deviation can be estimated using (6).…”

Adding Sensitivity to the MLBF Doppler Centroid Estimator

“…A more accurate estimator was proposed by Brown and Wang in 2002 [13], which is called the ILP method. This method uses iterative processing that successively reduces the filter bandwidth to improve the ACCC estimator.…”

“…13 As a result, when RCMC is applied before look extraction, the beat signal can be expressed as As the phase of the beat signal is constant in azimuth [compare (36) with (10)], the beat signal has zero frequency, and the information used to obtain a Doppler estimate has been lost. 13 Note that the R(η) dependence in the first exponential term still remains, because it was created by the demodulation process and is not affected by the RCMC. However, this phase term does not provide any information to the MLBF algorithm, as it is not dependent on range frequency.…”

Accurate Frequency Estimation for Real Harmonic Sinusoids

“…iv) Repeat ii) and iii) until the absolute difference between successive fundamental frequency estimates is less than , where is a small positive constant. It is noteworthy that as in many iterative frequency estimation algorithms [22], [23], there is no guarantee of convergence for the proposed method, although extensive simulation results have been performed to illustrate its global convergence for sufficiently large signal-to-noise ratio (SNRs) and/or data lengths.…”