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AMT | Articles | Volume 12, issue 5
Atmos. Meas. Tech., 12, 2967–2977, 2019
https://doi.org/10.5194/amt-12-2967-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
Atmos. Meas. Tech., 12, 2967–2977, 2019
https://doi.org/10.5194/amt-12-2967-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 29 May 2019

Research article | 29 May 2019

The cost function of the data fusion process and its application

Simone Ceccherini et al.

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Cited articles

Aires, F., Aznay, O., Prigent, C., Paul, M., and Bernardo, F.: Synergistic multi-wavelength remote sensing versus a posteriori combination of retrieved products: Application for the retrieval of atmospheric profiles using MetOp-A, J. Geophys. Res., 117, D18304, https://doi.org/10.1029/2011JD017188, 2012. 
Calisesi, Y., Soebijanta, V. T., and Oss, R. V.: Regridding of remote soundings: formulation and application to ozone profile comparison, J. Geophys. Res., 110, D23306, https://doi.org/10.1029/2005JD006122, 2005. 
Ceccherini, S.: Equivalence of measurement space solution data fusion and complete fusion, J. Quant. Spectrosc. Ra., 182, 71–74, 2016. 
Ceccherini, S. and Ridolfi, M.: Technical Note: Variance-covariance matrix and averaging kernels for the Levenberg-Marquardt solution of the retrieval of atmospheric vertical profiles, Atmos. Chem. Phys., 10, 3131–3139, https://doi.org/10.5194/acp-10-3131-2010, 2010. 
Ceccherini, S., Carli, B., Pascale, E., Prosperi, M., Raspollini, P., and Dinelli, B. M.: Comparison of measurements made with two different instruments of the same atmospheric vertical profile, Appl. Opt., 42, 6465–6473, 2003. 
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We have analytically calculated the expected value and the variance of the cost function that is minimized in the complete data fusion and propose a procedure that uses these quantities to constrain the values of the inconsistency covariance matrices. These matrices have to be added to the error covariance matrices of the measurements in order to fuse measurements that are inconsistent because of different vertical grids, not perfect time and space coincidence and different forward model errors.
We have analytically calculated the expected value and the variance of the cost function that is...
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