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NTIA Report TR-02-395Estimation of System Gain and Bias Using Noisy Observations with Known Noise Power RatioSeptember 2002Stephen D. Voran |
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Abstract: The identification of linear systems from input and output observations is an important and well-studied topic. When both the input and output observations are noisy, the resulting problem is sometimes called the "errors in variables" problem. Existing work on this problem deals with the identification of multivariate systems and thus results in algorithms that are necessarily somewhat complex and often involve iteration. In this report we treat an important special case of the problem: estimation of a system bias and a system gain from noisy observations of system input and output. In addition, we invoke an input-output noise power ratio constraint. This constraint can also be interpreted as a parameter that moves the problem in a continuous fashion between two limiting cases, each of which is a conventional least-squares problem. We do not model the input signal, and we place minimal restrictions on the input and output observation noises. We develop five different low-complexity closedform solutions to the problem. The final two are the most satisfying and we explore these further through simulations. Our original motivation for working on this problem came from the need to calibrate objective and subjective estimates of perceived video or speech quality. We expect that our solutions may also find applications in remote sensing, active noise reduction, echo cancellation, channel estimation, and channel equalization. |
Keywords: gain estimation; bias estimation; linear system identification; input noise; errors in variables; total least squares; extended least squares; audio quality estimation; speech quality estimation; video quality estimation |
Disclaimer: Certain commercial equipment, components, and software are identified in this report to specify adequately the technical aspects of the reported results. In no case does such identification imply recommendation or endorsement by the National Telecommunications and Information Administration, nor does it imply that the equipment or software identified is necessarily the best available for the particular application or uses. |
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