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Journal ArticleDOI

Optimal Estimation of Calibration Parameters in Polarimetric Microwave Radiometers

03 Oct 2008-IEEE Transactions on Geoscience and Remote Sensing (IEEE)-Vol. 46, Iss: 10, pp 3223-3237

TL;DR: It is demonstrated that Bayesian estimation decreases the root-mean-square error of the estimates by a factor of two, and the method is extended to estimate several hardware component parameters of interest in system calibration.

AbstractMethods for internal calibration of a certain class of microwave polarimetric radiometers are presented by Piepmeier. In that work, the calibration parameters are estimated algebraically. We demonstrate that Bayesian estimation decreases the root-mean-square error of the estimates by a factor of two. This improvement is obtained by using knowledge of the noise structure of the measurements and by utilizing all of the information provided by the measurements. Drawbacks are the increased complexity of the method and an increase in computation. We also extend the method to estimate several hardware component parameters of interest in system calibration. more

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01 Jan 2009
Abstract: IMPROVING ACCURACY IN MICROWAVE RADIOMETRY VIA PROBABILITY AND INVERSE PROBLEM THEORY Derek L. Hudson Electrical and Computer Engineering Doctor of Philosophy Three problems at the forefront of microwave radiometry are solved using probability theory and inverse problem formulations which are heavily based in probability theory. Probability theory is able to capture information about random phenomena, while inverse problem theory processes that information. The use of these theories results in more accurate estimates and assessments of estimate error than is possible with previous, non-probabilistic approaches. The benefits of probabilistic approaches are expounded and demonstrated. The first problem to be solved is a derivation of the error that remains after using a method which corrects radiometric measurements for polarization rotation. Yueh [1] proposed a method of using the third Stokes parameter TU to correct brightness temperatures such as Tv and Th for polarization rotation. This work presents an extended error analysis of Yueh’s method. In order to carry out the analysis, a forward model of polarization rotation is developed which accounts for the random nature of thermal radiation, receiver noise, and (to first order) calibration. Analytic formulas are then derived and validated for bias, variance, and root-mean-square error (RMSE) as functions of scene and radiometer parameters. Examination of the formulas reveals that: 1) natural TU from planetary surface radiation, of the magnitude expected on Earth at L-band, has a negligible effect on correction for polarization rotation; 2) RMSE is a function of rotation angle Ω, but the value of Ω which minimizes RMSE is not known prior to instrument fabrication; and 3) if residual calibration errors can be sufficiently reduced via postlaunch calibration, then Yueh’s method reduces the error incurred by polarization rotation to negligibility. The second problem addressed in this dissertation is optimal estimation of calibration parameters in microwave radiometers. Algebraic methods for internal calibration of a certain class of polarimetric microwave radiometers are presented by Piepmeier [2]. This dissertation demonstrates that Bayesian estimation of the calibration parameters decreases the RMSE of the estimates by a factor of two as compared with algebraic estimation. This improvement is obtained by using knowledge of the noise structure of the measurements and by utilizing all of the information provided by the measurements. Furthermore, it is demonstrated that much significant information is contained in the covariance information between the calibration parameters. This information can be preserved and conveyed by reporting a multidimensional pdf for the parameters rather than merely the means and variances of those parameters. The proposed method is also extended to estimate several hardware parameters of interest in system calibration. The final portion of this dissertation demonstrates the advantages of a probabilistic approach in an empirical situation. A recent inverse problem formulation, sketched in [3], is founded on probability theory and is sufficiently general that it can be applied in empirical situations. This dissertation applies that formulation to the retrieval of Antarctic air temperature from satellite measurements of microwave brightness temperature. The new method is contrasted with the curvefitting approach which is the previous state-of-the-art. The adaptibility of the new method not only results in improved estimation but is also capable of producing useful estimates of air temperature in areas where the previous method fails due to the occurence of melt events.

1 citations

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20 Dec 2004
TL;DR: This chapter discusses Monte Carol methods, the least-absolute values criterion and the minimax criterion, and their applications to functional inverse problems.
Abstract: 1 The general discrete inverse problem 2 Monte Carol methods 3 The least-squares criterion 4 Least-absolute values criterion and minimax criterion 5 Functional inverse problems 6 Appendices 7 Problems References Index

4,634 citations

"Optimal Estimation of Calibration P..." refers background or methods in this paper

  • ...The current practice of reporting only the mean and variance for each parameter is equivalent, in effect, to reporting independent 1-D marginal Gaussian pdfs for the parameters [6]....


  • ...The only joint pdf that can logically be reconstructed from marginal pdfs is the product of the marginal pdfs (this follows from [6])....


  • ...In general, the most complete answer to an estimation problem is a joint pdf on the variables of interest [6], in our case, (21)....


  • ...A numerical alternative is to simply report a large number of samples because most, if not all, calculations done with a posterior pdf can be done using these samples [6]....


  • ...Sampling p(m|v) by the Rejection Method Samples of the posterior pdf p(m|v) can be generated by the well-known rejection method [6], [7]....


Abstract: Foreword Preface Part I. Principles and Elementary Applications: 1. Plausible reasoning 2. The quantitative rules 3. Elementary sampling theory 4. Elementary hypothesis testing 5. Queer uses for probability theory 6. Elementary parameter estimation 7. The central, Gaussian or normal distribution 8. Sufficiency, ancillarity, and all that 9. Repetitive experiments, probability and frequency 10. Physics of 'random experiments' Part II. Advanced Applications: 11. Discrete prior probabilities, the entropy principle 12. Ignorance priors and transformation groups 13. Decision theory: historical background 14. Simple applications of decision theory 15. Paradoxes of probability theory 16. Orthodox methods: historical background 17. Principles and pathology of orthodox statistics 18. The Ap distribution and rule of succession 19. Physical measurements 20. Model comparison 21. Outliers and robustness 22. Introduction to communication theory References Appendix A. Other approaches to probability theory Appendix B. Mathematical formalities and style Appendix C. Convolutions and cumulants.

4,390 citations

01 Aug 1982

3,426 citations

"Optimal Estimation of Calibration P..." refers background in this paper

  • ...As shown in [5], I , J , and K can be rewritten as sums of independent samples...


  • ...during one interval is independent of the realization during the next interval [5])....


Journal ArticleDOI
Abstract: This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. Now results are discussed, along with the application of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book is not restricted to one particular discipline but rather will be of interest to scientists working in any area where inference from incomplete information is necessary.

1,265 citations