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Computerized ionospheric tomography is a highly ill-posed inverse problem, and regularization tends to stabilize the problem to provide a unique solution. When a regularization method is used, the choice of an optimal parameter is a key issue. In this article, we propose an adaptive regularization method for 3-D ionospheric tomography based on the U-curve. The proposed approach uses a U-curve method to determine the optimal regularization parameter from Global Navigation Satellite Systems (GNSS) observation data. Comparative case studies are investigated based on GNSS simulated observations and real measurements. The simulation results indicate that the proposed method is superior to the adaptive regularization method based on the L-curve. In addition, we further validate the tomographic results with actual ionosonde station data. The results demonstrate the reliability and superiority of the proposed method compared to traditional methods. [ABSTRACT FROM AUTHOR]

Previous work on multiple-input multiple-output (MIMO) radar waveform design in colored noise based on minimizing minimum mean-square error (MMSE) and normalized mean-square error (NMSE) only considered the optimization of the singular value of the waveform matrix, while the optimization of singular vectors, which forms a basis of singular value optimization, was not stressed enough. In this correspondence, we revisit the waveform design problem for MIMO radar in colored noise based on MMSE and NMSE respectively. Further results for the optimal solutions under both criteria are derived. We prove the optimality of “matching” with the target and colored noise for the singular vectors of the transmitted waveform. Moreover, to obtain minimum MMSE/NMSE, the pairing of the eigenvectors of the target and noise should be carefully designed, where the optimal pairing of the eigenvectors based on MMSE is fixed while the optimal pairing based on NMSE changes according to the transmitted power, the strength of the target, and noise. [ABSTRACT FROM PUBLISHER]