|
|
- 2016
测量不确定度估计的极限费舍尔信息方法
|
Abstract:
极限费舍尔信息（EFI）是源于极限物理信息理论下的一种信息测度。由于在测量实践中，很难一一准确且高效地定义与补偿所有影响测量结果的因素并估计测量不确定度。因此，该文提出了采用根据EFI推导的概率密度函数（PDFs）来估计被测量的测试边界信息，即待测系统的测量不确定度。该方法能够根据不同的不确定度影响因素以及待测系统的物理规则更加动态地刻画测量不确定性。从物理应用角度进行了详细的数理推导与讨论，相比不考虑物理意义的数学模型，该方法更适用于实际应用。最后，用两组实例验证了该EFI方法的有效性。
| [1] | BIPM, IEC, IFCC, et al. Evaluation of measurement data-guide to the expression of uncertainty in measurement JCGM 100:2008[EB/OL].[2015-03-15]. http://www.bipm.org/utils/common/documents/jcgm/.JCGM_100_2008_E.pdf. |
| [2] | BIPM, IEC, IFCC, et al. International vocabulary of metrology-basic and general concepts and associated terms (VIM) JCGM 200:2008[EB/OL].[2015-03-20]. http://www.bipm.org/en/publications/guides/vim.html. |
| [3] | MAURIS G, BERRAH L, FOULLOY L, et al. Fuzzy handling of measurement errors in instrumentation[J]. IEEE Transactions on Instrument and Measurement, 2000, 49(1):89-93. |
| [4] | MAURIS G, LASSERRE V, FOULLOY L. A fuzzy approach for the expression of uncertainty in measurement[J]. Measurement, 2001, 29(3):165-177. |
| [5] | URBANSKY M, WASOWSKI J. Fuzzy approach to the theory of measurement inexactness[J]. Measurement, 2003, 34(1):67-74. |
| [6] | FERRERO A, SALICONE S. The random-fuzzy variables:a new approach to the expression of uncertainty in measurement[J]. IEEE Transactions on Instrument and Measurement, 2004, 53(5):1370-1377. |
| [7] | MAKALIC E, SCHMIDT D F. Fast computation of the Kullback-Leibler divergence and exact Fisher information for the first-order moving average model[J]. IEEE Signal Processing Letter, 2010, 17(4):391-393. |
| [8] | FERRERO A, RAMBA R, SALICONE S. A method based on random fuzzy variables for on-line estimation of the measurement uncertainty of DSP-based instruments[J]. IEEE Transactions on Instrument and Measurement, 2009, 53(5):1362-1369. |
| [9] | FERRERO A, SALICONE S. Modeling and processing measurment uncertainty within the theory of evidence:Mathematics of random-fuzzy variables[J]. IEEE Transactions on Instrument and Measurement, 2007, 56(3):704-716. |
| [10] | FRIEDEN A R. Science from Fisher information-a unification[M]. NewYork:Cambridge University Press, 2004. |
| [11] | ZHANG Jiang-fan, BLUM R S, LU Xuan-xuan, et al. Asymptotically optimum distributed estimation in the presence of attacks[J]. IEEE Transactions on Signal Processing, 2014, 63(5):1086-1101. |
| [12] | GUO Sheng-han. Analysis of data-based methods for approximating fisher information in the scalar case[C]//The 49 Annual Conference on Information Sciences and Systems. Baltimore, USA:IEEE, 2015:1-5. |
| [13] | FRIEDEN B, GATENBY R, ROBERT A. Exploratory data analysis using Fisher information[M]. London:Springer, 2007. |
| [14] | DANTONA G. Expanded uncertainty and coverage factor computation by higher order moments analysis[C]//The 21 IEEE Instrumentation and Measurement Technology Conference. Como, Italy:IEEE, 2004:234-238. |
| [15] | COHEN M. The Fisher information and convexity[J]. IEEE Transactions on Information Theory, 1968, 14(4):591-592. |
| [16] | GELFAND I M, FOMIN S V. Calculus of variations[M]. New York:Dover Publications, 2000. |
| [17] | FRIEDEN B R. Applications to optics and wave mechanics of the criterion of maximum Cramer-Rao bound[J]. Journal of Modern Optics, 1988, 35(8):1297-1316. |
| [18] | WANG Zhu-xi. Special functions[M]. Singapore:World Scientific, 1989. |
| [19] | VALLEE O, SOARES M. Airy functions and applications to physics[M]. Singapore:World Scientific, 2004. |
| [20] | FERRERO A, SALICONE S. The construction of randomfuzzy variables from the available relevant metrological information[J]. IEEE Transactions on Instrument and Measurement, 2009, 58(2):365-374. |
| [21] | FERRERO A, SALICONE S. Uncertainty:Only one mathematical approach to its evaluation and expression?[J]. IEEE Transactions on Instrument and Measurement, 2012, 61(8):2167-2178. |
| [22] | IUCULANO G, NIELSEN L, ZANOBINI A, et al. The principle of maximum entropy applied in the evaluation of the measurement uncertainty[J]. IEEE Transactions on Instrument and Measurement, 2007, 56(3):717-722. |
| [23] | SONG Xiu-feng, WILLETT P, ZHOU Sheng-li. On Fisher information reduction for range-only location with imperfect detection[J]. IEEE Transaction on Aerospace and Electronic Systems, 2012, 48(4):3694-3702. |
| [24] | YILMAZ Y, WANG Xiao-dong. Sequential decentralized parameter estimation under randomly observed fisher information[J]. IEEE Transactions on Information Theory, 2013, 60(2):1281-1300. |
| [25] | HUBER P J. Robust statistics:a review[J]. The Annals of Mathematical Statistics, 1972, 43(3):1041-1167. |
| [26] | FLETCHER R. Practical methods of optimization[M]. New York:Wiely, 1991. |
| [27] | SCALES L E. Introduction to nonlinear optimization[M]. London:Macmillan, 1985. |
