Optimal Determination of the Equilibrium Displacement of a Damped Harmonic Oscillator in the Presence of Thermal Noise

Details Optimal Determination of the Equilibrium Displacement of a Damped Harmonic Oscillator in the Presence of Thermal Noise Optimal Determination of the Equilibrium Displacement of a Damped Harmonic Oscillator in the Presence of Thermal Noise

2004-12-17

arxiv.org/abs/physics/0412102v1

Rev.Sci.Instrum.76:085106,2005

Physics

Data Analysis, Statistics and Probability

12 pages, 6 figures, submitted to Review of Scientific Instruments, revtex4

Scientific paper

10.1063/1.1994985

Using a matched filter technique, we derive the minimum variance, unbiased estimator for the equilibrium displacement of a damped harmonic oscillator in thermal equilibrium when interactions with the thermal bath are the leading source of noise. We compare the variance in this optimal estimator with the variance in other, commonly used estimators in the presence of pure thermal noise and pure white noise. We also compare the variance in these estimators for a mixture of white and thermal noise. This result has implications for experimental design and the collection and analysis of data.

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