scholarly journals Matrix expressions defi ning the oblique projector

2019 ◽  
Vol 23 (133) ◽  
pp. 107-113
Author(s):  
A.M. Vetoshkin ◽  
◽  
A.A. Shum ◽  
Keyword(s):  
Oblique Projector

scholarly journals DOA Estimation without Source Number for Cyber-Physical Interactions

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Jianzhong Li ◽  
Xiaobo Gu ◽  
Ruidian Zhan ◽  
Xiaoming Xiong ◽  
Yuan Liu
Keyword(s):  
A Priori ◽  
Doa Estimation ◽  
A Priori Knowledge ◽  
Second Order Statistics ◽  
Oblique Projector ◽  
Physical Interactions ◽  
Simulation Results ◽  
The Impact ◽  
The Relationship ◽  
Source Number

In this paper, a direction of arrival (DOA) estimator is proposed to improve the cyber-physical interactions, which is based on the second-order statistics without a priori knowledge of the source number. The impact of noise will firstly be eliminated. Then the relationship between the processed covariance matrix and the steering matrix is studied. By applying the elementary column transformation, an oblique projector will be designed without the source number. At last, a rooting method will be adopted to estimate the DOAs with the constructed projector. Simulation results show that the proposed method performs as well as other methods, which requires that the source number must be known.

Equivalence of zero-forcing detector and oblique projector

2008 ◽  
Vol 44 (6) ◽  
pp. 425 ◽  
Author(s):  
J. Li ◽  
X.D. Zhang
Keyword(s):  
Zero Forcing ◽  
Oblique Projector

scholarly journals Characterisation of k-Class estimation in simultaneous equation models

1969 ◽  
Vol 74 (3) ◽  
pp. 307-310
Author(s):  
José F. Burguete ◽  
Esteban Burguete
Keyword(s):  
Estimation Method ◽  
Simultaneous Equation ◽  
Equation Model ◽  
Geometric Characterization ◽  
Simultaneous Equation Model ◽  
Oblique Projector ◽  
Linear Simultaneous Equation ◽  
Whole Space ◽  
Simultaneous Equation Models

This paper presents the direct geometric characterization of the k-Class estimation method in a linear simultaneous equation model. The concept of oblique projector is used. The paper also exhibits several estimators generated by projecting along subspaces of the whole space along which this class is projected.

scholarly journals Strictly oblique projectors and their properties

2020 ◽  
Vol 24 (5) ◽  
pp. 122-127
Author(s):  
A.M. Vetoshkin ◽  
◽  
A.A. Shum ◽  
Keyword(s):  
Practical Problem ◽  
Null Space ◽  
Full Rank ◽  
Oblique Projection ◽  
Unitary Similarity ◽  
Oblique Projector ◽  
Matrix Expression

In this paper, strictly oblique projectors are defined as projectors that cannot be represented as the sum of two projectors, one of which is a nonzero orthoprojector. A theorem is proved that each projector can be represented in a unique way as the sum of a strictly oblique projector and an orthoprojector. The properties of such projectors are given. For example: if the projector is strictly oblique, then its Hermitian adjoint is also strictly oblique; the rank of a strictly oblique projector is at most n/2, where n is the order of the projector matrix; the property of the projector to be strictly oblique is preserved with a unitary similarity. The work is a continuation of the previous work of the authors, the main result of which is such a matrix expression for an arbitrary projector: where A and B are two matrices of full rank whose columns define range and the null space of this projector. Based on this result, the article shows that the strictly oblique part of any projector P is given by the expression: P(P – P+P)+P. And equality P = P(P – P+P)+P is a criterion that the projector P is a strictly oblique projector. The decomposition of the projector obtained in the work is applied to the practical problem of oblique projection onto the plane

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