Performance of the stochastic MV-PURE estimator in highly noisy settings |
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| Authors: | Tomasz Piotrowski Isao Yamada |
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| Institution: | 1. Department of Informatics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Torun, Poland;2. Department of Communications and Computer Engineering, Tokyo Institute of Technology, Tokyo 152-8550, Japan |
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| Abstract: | The stochastic minimum-variance pseudo-unbiased reduced-rank estimator (stochastic MV-PURE estimator) has been developed to provide linear estimation with robustness against high noise levels, imperfections in model knowledge, and ill-conditioned systems. In this paper, we investigate the theoretical performance of the stochastic MV-PURE estimator under varying levels of additive noise. We prove that the mean-square-error (MSE) of this estimator in the low signal-to-noise (SNR) region is much smaller than that obtained with its full-rank version, the minimum-variance distortionless estimator, and the gap becomes larger as the noise level increases. These results shed light on the excellent performance of the stochastic MV-PURE estimator in highly noisy settings obtained in simulations so far. Furthermore, we extend previous numerical simulations to show how the insight gained from the results of this paper can be used in practice. |
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