High resolution adaptive estimator of sinusoidal based on covariance matrix reconstruction

Exponentially decaying sinusoidal signal is often observed in engineering and research fields. In some practical applications, the frequencies of multiple signals are close to each other. It would face a challenging task to resolve these crowded signals processed by discrete Fourier transformation, especially in the case of the lack of sampling time and the fast-decaying signals. The Localised Capon estimator (LoCapE) has demonstrated its advantage in improving the resolution of exponentially decaying sinusoidal signals. However, the amplitude and the frequency of each component extracted by the LoCapE are not accurate due to the effect from interference components. Here, we improve the LoCapE method by reconstructing the interference-plus-noise covariance matrix instead of the signal covariance matrix. Experimental results on simulated and real exponentially decaying sinusoidal data show that the proposed method is more accurate in extracting parameters at the lack of sampling points.