Direct estimation of noisy sinusoids using abductive networks

Spectral estimation techniques have been used for many years. In many cases, their complexity warrants investigating machine-learning alternatives where intensive computations are required only during training, with actual estimation simplified and speeded up. This allows using simple portable apparatus for fast and automated estimation in real time. We propose using abductive network machine learning for estimating both the amplitude and frequency of a single sine wave in the presence of additive Gaussian noise. Models synthesized by training on 1000 representative simulated sinusoids were evaluated on 500 new cases. With no phase variations and a signal to noise ratio of 7 dB, average absolute percentage errors for the sinusoid amplitude and period are 8.4% and 3.6%, respectively. Effects of the range of frequency variations and the noise level on the complexity and accuracy of the models were investigated. Amplitude and period estimates show signs of bias at a signal to noise ratio of 3 dB. Error variances track the Cramer-Rao bounds at high noise levels, with no thresholding observed down to 0 dB. The method is compared with a neural network model and with conventional discrete Fourier transform (DFT) based techniques and a Prony's based approach. The new approach is particularly useful when only a small portion of the sinusoid cycle is measured.