Poisson 잡음 하에서의 지수 감소 함수 인자 추정시의 Cramer-Rao bound

• Accepted : 2012.12.04
• Published : 2013.01.01
• 42 12

Abstract

We computed Cramer-Rao bound for estimating amplitude and decay parameters of exponentially decaying function under Poisson noise. Since Cramer-Rao bound is the lowest variance bound for any unbiased estimator, the computed Cramer-Rao bound can be used for evaluating the performance of estimators under Poisson noise. In addition, we show that the performance of maximum-likelihood estimator is close to the Cramer-Rao bound by simulations.

Keywords

Cramer-Rao bound;Maximum-likelihood estimator;Poisson noise

References

1. S. L. Tantum and L. M. Collins, "A parameter transformation and Cramer-Rao bounds for estimating decay rates from exponential signals," in IGARSS '02. 2002 IEEE International, vol. 4, pp.2568-2571, (2002).
2. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Kluwer Academic/Plenum Publishers, 1999), 2nd ed.
3. A. U. Jibia, M-J. E. Salami, O. O. Khalifa and F.A.M. Elfaki, "Cramer-Rao Lower Bound for Parameter Estimation of Multiexponential Signals," in IWSSIP 2009, pp.1-5 (2009).
4. A. Papoulis, Probability, Random variables, and Stochastic Processes (McGraw-Hill, Inc, 2002), 4th ed.
5. P. Hall, and B. Selinger, "Better estimates of exponential decay parameters", J. Phys. Chem. vol. 85, No. 20, pp.2941-2946 (1981). https://doi.org/10.1021/j150620a019
6. H. Van Trees, Detection, Estimation, and Modulation Theory, no. v. in Detection, Estimation, and Modulation Theory (John Wiley & Sons, 2001).

Acknowledgement

Supported by : 한국과학재단