# Optimal Estimation of Calibration Parameters in Polarimetric Microwave Radiometers

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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### "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]....

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

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

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...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]....

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...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]....

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### "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...

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

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