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.
Abstract: Methods 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.
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01 Jan 2009
TL;DR: In this article, a probabilistic approach was proposed to estimate the air temperature of a microwave radiometer by using the third Stokes parameter TU to correct the brightness temperature for polarization rotation.
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.
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TL;DR: Four calibration algorithms are studied for microwave polarimeters that use hybrid coupler-based correlators and the four-look calibration algorithm was found to be most sensitive to the correlated calibration source.
Abstract: Four calibration algorithms are studied for microwave polarimeters that use hybrid coupler-based correlators: (1) conventional two-look of hot and cold sources; (2) three looks of hot and cold source combinations; (3) two-look with correlated source; and (4) four-look combining methods (2) and (3). The systematic errors are found to depend on the polarimeter component parameters and accuracy of calibration noise temperatures. A case study radiometer in four different remote sensing scenarios was considered in light of these results. Applications for ocean surface salinity, ocean surface winds, and soil moisture were found to be sensitive to different systematic errors. Finally, a standard uncertainty analysis was performed on the four-look calibration algorithm, which was found to be most sensitive to the correlated calibration source.
19 citations
"Optimal Estimation of Calibration P..." refers methods in this paper
...This technique is introduced in [1] for microwave radiometers which use a hybrid coupler to synthesize ±45◦ linear polarizations from vertical and horizontal signals....
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...Then, with V T2 v and V T 1 v in hand, we can form v by derotating (left multiplying by V ) because V [ V T1 v V T2 v ] = V (V Tv) = (V V T)v = v. (22) With the simulated voltages, we then use the method of Piepmeier [1], as summarized in Section III, to algebraically estimate the ten calibration parameters....
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...ALGEBRAIC ESTIMATION (PIEPMEIER’S METHOD [1])...
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...The algebraic method of [1] for estimating channel...
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...In the remainder of this paper, we improve on the method of [1]....
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TL;DR: An extended error analysis of the estimation of Tv, Th, and TQ equiv Tv - Th by Yueh's method is presented, revealing that natural TU from planetary surface radiation, of the magnitude expected on Earth at L-band, has a negligible effect on correction for polarization rotation.
Abstract: Yueh proposed a method of using the third Stokes parameter TU to correct brightness temperatures such as Tv and Th for polarization rotation This paper presents an extended error analysis of the estimation of Tv, Th, and TQ equiv Tv - Th by Yueh's method In order to carry out the analysis, we first develop a forward model of polarization rotation that accounts for the random nature of thermal radiation, receiver noise, and (to first order) calibration Analytic formulas are then derived for the bias, standard deviation (STD), and root-mean-square error (RMSE) of estimated TQ, Tv, and Th, as functions of scene and radiometer parameters These formulas are validated through independent calculation via Monte Carlo simulation 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 Omega, but the value of Omega that 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
4 citations