Performance Weighted Blended Spectral Estimation

Abstract

A classic approach to power spectrum estimation is to apply a time domain window to a signal and then compute the discrete Fourier transform (DFT). The window provides a trade o between the resolution of the estimator, and the ability to detect a quiet signal when loud signals are also present. There are many windows available, and there is often no single window that provides the best balance between resolution and dynamic range. Analysts can often improve their estimates by combining spectra from multiple windowed DFTs. This thesis proposes a performance weighted blended (PWB) spectrum estimator that automates the work of an analyst by blending an ensemble of estimators. The proposed estimator is an adaptation of Buck and Singer's performance weighted blended beamformer. A sensor array samples a signal in space and a beamformer calculates a spatial frequency spectrum. Since planewave beamforming is analogous to spectral estimation, Buck and Singer's approach can be used to blend windowed DFTs. Thus the same approach can be used to blend windowed DFTs. When an ensemble spectral estimators are constrained to have unity gain in the look direction, then any di erence in their estimates is due to noise or interference. With this in mind, accumulated power output was chosen as the performance metric for the PWB estimator. This estimator is guaranteed to perform as well or better than the best performing estimator in the ensemble as the number of data blocks goes to in nity. The PWB estimator was tested on complex exponential signals with uniformly distributed random phase in complex Gaussian white noise and experimental data. Results show that the PWB estimator is able to exhibit improved resolution in regions of the spectrum where there are loud signals, and improved dynamic range in regions where there are quiet signals. Simulations also show that the PWB estimator is able to outperform a minimum power distortionless response (MPDR) estimator when it is calculated using the sample statistics. Since the estimator as it was originally proposed was not robust enough for use with real data, methods to improve robustness will be presented. The algorithm was evaluated using data from a hydrophone mounted on an underwater glider. The experiments show that the PWB algorithm is able approximate the performance of the best estimator in the ensemble as long as certain restrictions on its parameters are respected.