Content uploaded by Vadym Slyusar
Author content
All content in this area was uploaded by Vadym Slyusar on Aug 21, 2018
Content may be subject to copyright.
End matrix products in radar applications
Abstract
This paper is the first publication about concept of face-splittiing product of matrices and his properties, which dated on December 1996.
In this article was used the old version of English translation the origin term "торцевое произведение", which was introduced by Vadym Slyusar. In next publications was used translation as face-splitting product.
... In addition to the classical set of these operations, due to the objective demands for technological applications of systems analysis a lot of unconventional procedures of matrix multiplication should be introduced in practice. In particular, we mean the generalized Kronecker products with respect to columns and rows [1,2], left and fight almost Kronecker products [2], and also the family of face products of matrices [3][4][5]. ...
... According to [3][4][5], we will call the pxgs matrix A 13 B specified by the equality ...
... The symmetric complement of the face variant of multiplication is its transposed modification. According to [3][4][5] a21"b21 a22"b22 a23"b23 J It is worthy of note that, for expressions (1) and (2), we can write the law of inversion of the order of matrices [5]. This law is similar to the well-known property of transposition of generalized Kronecker products with respect to rows and columns [1] ...
This article continued the description of properties of the face-splitting product of matrices, which was proposed by Vadym Slyusar in 1996.
... (2) OP Here, is the Neudecker derivative of the matrix P with respect to the vector Y, which is composed of unknown OY parameters of the signals of M sources, 1R8 is a unit (RxR)-matrix, and | is the symbol of Kronecker product. The Fisher matrix in general form can be used to form the Cramer-Rao low bound, achievable by a multicoordinate singleor multiposition radar-tracking system in a multsignal situation. ...
... The Fisher matrix in general form can be used to form the Cramer-Rao low bound, achievable by a multicoordinate singleor multiposition radar-tracking system in a multsignal situation. As was mentioned in [2], it is sufficient to use in expression (2) instead of the matrix P its value represented by a face-splitting matrix product, and to appropriately adjust the dimension of the matrix 1RR. ...
... The Fisher matrix in general form can be used to form the Cramer-Rao low bound, achievable by a multicoordinate singleor multiposition radar-tracking system in a multsignal situation. As was mentioned in [2], it is sufficient to use in expression (2) instead of the matrix P its value represented by a face-splitting matrix product, and to appropriately adjust the dimension of the matrix 1RR. ...
Expressions for blocks of the information Fisher matrix are presented based on factorization of the Neudecker derivative of
a transposed face-splitting matrix product.
... To collect Big Data from sensors and preprocessing these data before Machine Learning (ML) procedure, it is proposed to form data sets with the help of the face-splitting matrix product (Slyusar, 1998;Slyusar, 1999). The 1 st stage of such processing is the building of incidence matrices for every engine mode or for every partial network inside the structure of DECS. ...
... Moving on to the problem of analyzing combinations of sensor readings in a sequence of modes, as indicated in (Bischof, 2020), it is necessary to use the facesplitting product of the matrices for this. In particular, the co-occurrence matrix for the analysis of triple combinations can be formed on the basis of the 1 st incidence matrix and its version in the form of the facesplitting product (symbol □ (Slyusar, 1998;Slyusar, 1999)): ...
This report is considered different aspects of the concept of the networked distributed engine control system (DECS) of future air vehicles. These aspects include the following: the structure of multiple networks similar to NATO Generic Vehicle Architecture (NGVA), the role of Artificial Intelligence (AI) in DECS, and the use Augmented Reality (AR) as Human-Machine Interface between AI and pilots. Deployment of AI solutions for monitoring equipment in on-board infrastructure can be provided on physical or virtual servers and in the clouds. In this case, it is possible to use various methods of alerting the pilot and ground personnel on the basis of AR. The use of AI allows covering an unlimited set of scenarios, to provide an assessment of the likelihood of equipment failure, classification alarm is normal, and recognition of the development of defects. To collect Big Data from sensors and the pre-processing of this data before a machine learning (ML) procedure it is proposed to form data sets with the help of the face-splitting matrix product. To decrease the time of reaction of Neural Networks it has been suggested the implementation of advanced tensor-matrix theory on the basis of penetrating face product of matrices. Other important results of the report are a possible version of the AR data format for DECS and a proposal about the use of non-orthogonal frequency discrete multiplexing (N-OFDM) signals to data transfer via fibre optics.
... To collect Big Data from sensors and preprocessing these data before Machine Learning (ML) procedure, it is proposed to form data sets with the help of the face-splitting matrix product [9,10]. The 1st stage of such processing is the building of incidence matrices for every engine mode or for every partial network inside the structure of DECS. ...
... Moving on to the problem of analyzing combinations of sensor readings in a sequence of modes, as indicated in [11], it is necessary to use the face-splitting product of the matrices for this. In particular, the co-occurrence matrix for the analysis of triple combinations can be formed on the basis of the 1st incidence matrix and its version in the form of the face-splitting product (symbol □ [9,10] ...
This report is considered different aspects of the concept of the networked distributed engine control system (DECS) of future air vehicles. These aspects include the following: the structure of multiple networks similar to NATO Generic Vehicle Architecture (NGVA), the role of Artificial Intelligence (AI) in DECS, and the use Augmented Reality (AR) as Human-Machine Interface between AI and pilots. Deployment of AI solutions for monitoring equipment in on-board infrastructure can be provided on physical or virtual servers and in the clouds. In this case, it is possible to use various methods of alerting the pilot and ground personnel on the basis of AR. The use of AI allows covering an unlimited set of scenarios, to provide an assessment of the likelihood of equipment failure, classification alarm is normal, and recognition of the development of defects. To collect Big Data from sensors and the pre-processing of this data before a machine learning (ML) procedure it is proposed to form data sets with the help of the face-splitting matrix product. To decrease the time of reaction of Neural Networks it has been suggested the implementation of advanced tensor-matrix theory on the basis of penetrating face product of matrices. Other important results of the report are a possible version of the AR data format for DECS and a proposal about the use of non-orthogonal frequency discrete multiplexing (N-OFDM) signals to data transfer via fibre optics.
В работе предложена совокупность новых тензорноматричных операций для обработки данных в нейронных сетях.
This presentation is devoted to the tensor-matrix theory of the traditional approach to multichannel signal parameters measurements based analytical model of signals and the tensor-matrix theory of Neural Networks for Mechanical Measurements.
This presents the basic concepts of matrix operations that can be used for ultrasonic, sonar, radar systems, wireless communications, and more systems with digital beamforming. It is intended for individuals in the field who wish to gain a general view of this area. For additional information, read the references on the final slides.
This paper propose the concept of synthesis of LDPC and Polar Codes on the basis of Face-Splitting product of matrices
ResearchGate has not been able to resolve any references for this publication.