This letter addresses the problem of the nonunitary joint block diagonalization of a given set of complex matrices whose potential applications stem from the blind separation of convolutive mixtures of sources and from the array processing. The proposed algorithm is based on the algebraic optimization of a least-mean-square criterion. One of its advantage is that a pre-whitening stage is no more compulsorily required when this algorithm is applied in the blind source separation context. Computer simulations are provided in order to illustrate its behavior in three cases: when exact block-diagonal matrices are built, then when they are progressively perturbed by an additive Gaussian noise and, finally, in the context of blind separation of convolutive mixtures of temporally correlated sources with estimated correlation matrices. A comparison with a classical orthogonal joint block diagonalization algorithm is also performed, and a new performance index is introduced to measure the performance of the separation.

The separation problem of an instantaneous mixture of deterministic or random source signals is addressed. We show that the separation can be realized through the nonorthogonal joint diagonalization of spatial quadratic time-frequency matrices. One advantage of the proposed method is that it does not require any whitening stage, and thus, it is intended to work even with a class of correlated signals. We also propose a general automatic time-frequency point selection procedure for the determination of the above matrices to be joint diagonalized. An analytical example and computer simulations are provided in order to illustrate the effectiveness of the proposed approach and to compare it with classical ones.

Solar irradiance data from high-quality ground-based measurements are primordial for different solar energy applications. In order to achieve the required accuracy, quality control procedures are of great benefit. A variety of approaches have been proposed. In this sense, some approaches propose a visual representation of the routine, while others only provide a time series of binary flag values, and do not propose any specific visualization of the flagged data as opposed to non-flagged ones. In this regard, the present paper puts forward a complete routine including several quality control procedures for solar irradiance measurements by providing visual support for these different approaches. The visual tool in question was validated using five years research data with 10 minutes resolution of the global, diffuse and direct components of solar irradiation collected from three ground-based weather stations in Morocco. This visual tool puts forth a more precise idea of the measurement quality by detecting various errors, such as time shifts, outliers identification; either with one or two components, or consistency tests between the three components of solar radiation when available. The proposed tool can be regarded as a means of improving the detection rate of abnormal data as a first step in diagnosing the prominent causes of error.