TY - JOUR
T1 - Two-dimensional sampling-recovery algorithm of a realization of gaussian processes on the input and output of linear systems
AU - Kazakov, Vladimir
AU - Enciso, Mauro A.
AU - Mendoza, Francisco
N1 - Publisher Copyright:
© 2020 by the authors.
PY - 2020/10
Y1 - 2020/10
N2 - Based on the application of the conditional mean rule, a sampling-recovery algorithm is studied for a Gaussian two-dimensional process. The components of such a process are the input and output processes of an arbitrary linear system, which are characterized by their statistical relationships. Realizations are sampled in both processes, and the number and location of samples in the general case are arbitrary for each component. As a result, general expressions are found that determine the optimal structure of the recovery devices, as well as evaluate the quality of recovery of each component of the two-dimensional process. The main feature of the obtained algorithm is that the realizations of both components or one of them is recovered based on two sets of samples related to the input and output processes. This means that the recovery involves not only its own samples of the restored realization, but also the samples of the realization of another component, statistically related to the first one. This type of general algorithm is characterized by a significantly improved recovery quality, as evidenced by the results of six non-trivial examples with different versions of the algorithms. The research method used and the proposed general algorithm for the reconstruction of multidimensional Gaussian processes have not been discussed in the literature.
AB - Based on the application of the conditional mean rule, a sampling-recovery algorithm is studied for a Gaussian two-dimensional process. The components of such a process are the input and output processes of an arbitrary linear system, which are characterized by their statistical relationships. Realizations are sampled in both processes, and the number and location of samples in the general case are arbitrary for each component. As a result, general expressions are found that determine the optimal structure of the recovery devices, as well as evaluate the quality of recovery of each component of the two-dimensional process. The main feature of the obtained algorithm is that the realizations of both components or one of them is recovered based on two sets of samples related to the input and output processes. This means that the recovery involves not only its own samples of the restored realization, but also the samples of the realization of another component, statistically related to the first one. This type of general algorithm is characterized by a significantly improved recovery quality, as evidenced by the results of six non-trivial examples with different versions of the algorithms. The research method used and the proposed general algorithm for the reconstruction of multidimensional Gaussian processes have not been discussed in the literature.
KW - Basic function
KW - Conditional mean rule
KW - Covariance function
KW - Cross-covariance function
KW - Error recovery function
KW - Sampling recovery algorithm of a realization of multidimensional gaussian process
UR - http://www.scopus.com/inward/record.url?scp=85092467487&partnerID=8YFLogxK
U2 - 10.3390/E22101079
DO - 10.3390/E22101079
M3 - Artículo
AN - SCOPUS:85092467487
SN - 1099-4300
VL - 22
JO - Entropy
JF - Entropy
IS - 10
M1 - 1079
ER -