scholarly journals Estimation of Two-Dimensional Non-Symmetric Incoherently Distributed Source with L-Shape Arrays

Sensors ◽  
2019 ◽  
Vol 19 (5) ◽  
pp. 1226 ◽  
Author(s):  
Tao Wu ◽  
Zhenghong Deng ◽  
Yiwen Li ◽  
Zhengxin Li ◽  
Yijie Huang
Keyword(s):  
Array Signal Processing ◽  
Gaussian Mixture ◽  
Source Model ◽  
Point Sources ◽  
Gaussian Component ◽  
Two Dimensional ◽  
Distributed Source ◽  
One Dimensional ◽  
Sample Covariance ◽  
Incoherently Distributed Source

In the field of array signal processing, distributed sources can be regarded as an assembly of point sources within a spatial distribution. In this study, a two-dimensional (2D) non-symmetric incoherently distributed (ID) source model is proposed; we explore the estimation of a 2D non-symmetric ID source using L-shape arrays. The 2D non-symmetric ID source is established by modeling the angular power density function (APDF) as a Gaussian mixture model. Estimation of the non-symmetric distributed source is proposed based on the expectation maximization (EM) framework. The proposed EM iterative framework contains three steps in the process of each circle. Firstly, the nominal azimuth and nominal elevation of each Gaussian component are obtained from the phase parts of elements in sample covariance matrices. Then the angular spreads can be solved through a one-dimensional (1D) search by the original generalized Capon estimator. Finally, weights of each Gaussian component are obtained by solving the least-squares estimator. Simulations are conducted to verify the effectiveness of the estimation technique.

scholarly journals Estimation for Two-Dimensional Nonsymmetric Coherently Distributed Source in L-Shaped Arrays

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Tao Wu ◽  
Zhenghong Deng ◽  
Qingyue Gu ◽  
Jiwei Xu
Keyword(s):  
Expectation Maximization ◽  
Two Dimensional ◽  
Signal Distribution ◽  
Distributed Source ◽  
One Dimensional ◽  
Least Squares Estimators ◽  
Iterative Calculation ◽  
Symmetric Source ◽  
Relationship Of ◽  
The Relationship

We explore the estimation of a two-dimensional (2D) nonsymmetric coherently distributed (CD) source using L-shaped arrays. Compared with a symmetric source, the modeling and estimation of a nonsymmetric source are more practical. A nonsymmetric CD source is established through modeling the deterministic angular signal distribution function as a summation of Gaussian probability density functions. Parameter estimation of the nonsymmetric distributed source is proposed under an expectation maximization (EM) framework. The proposed EM iterative calculation contains three steps in each cycle. Firstly, the nominal azimuth angles and nominal elevation angles of Gaussian components in the nonsymmetric source are obtained from the relationship of rotational invariance matrices. Then, angular spreads can be solved through one-dimensional (1D) searching based on nominal angles. Finally, the powers of Gaussian components are obtained by solving least-squares estimators. Simulations are conducted to verify the effectiveness of the nonsymmetric CD model and estimation technique.

scholarly journals Estimation for Two-Dimensional Incoherently Distributed Source in Double L-Shape Arrays

2019 ◽  
Vol 37 (4) ◽  
pp. 838-845
Author(s):  
Tao Wu ◽  
Zhenghong Deng ◽  
Jiwei Xu ◽  
Qingyue Gu
Keyword(s):  
Point Sources ◽  
Estimation Accuracy ◽  
Two Dimensional ◽  
Simulation Experiments ◽  
Experimental Conditions ◽  
Invariance Properties ◽  
Peak Finding ◽  
Incoherently Distributed Sources ◽  
Taylor Series Expansions ◽  
Incoherently Distributed Source

Distributed sources can be regarded as an assembly of point sources within a spatial distribution. In this paper, we explore the estimation of the two-dimensional incoherently distributed sources using double L-shape arrays. The rotational invariance properties of the nominal elevation and nominal elevation are firstly obtained by taking first-order Taylor series expansions with regard to the generalized steering vectors of two pairs of parallel subarrays. The rotation operators can be solved based on signal subspace. Then the nominal elevation and nominal elevation can be obtained from parameters matching method. Estimation of direction of arrival can be used in multi-source scenario and needn't peak-finding search. Lastly the angular spreads can be solved through two-dimensional Capon search based on nominal angles. The simulation experiments show that the proposed method has good performance on the estimation of two-dimensional incoherently distributed sources. Investigating different experimental conditions, sources with different angular spreads, simulations are conducted to validate better estimation accuracy of the proposed method.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

State-of-the-Art of Modeling Surface Water Impoundments

1982 ◽  
Vol 14 (1-2) ◽  
pp. 241-261 ◽  
Author(s):  
P A Krenkel ◽  
R H French
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
State Of The Art ◽  
Rate Coefficients ◽  
Two Dimensional ◽  
One Dimensional ◽  
Integral Energy ◽  
Range Of Values ◽  
Dimensional Integral ◽  
Water Impoundment

The state-of-the-art of surface water impoundment modeling is examined from the viewpoints of both hydrodynamics and water quality. In the area of hydrodynamics current one dimensional integral energy and two dimensional models are discussed. In the area of water quality, the formulations used for various parameters are presented with a range of values for the associated rate coefficients.

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

Modifications of the Godunov method for computing disturbance propagation in an elastic body

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Godunov Method ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Order Accuracy ◽  
One Dimensional ◽  
Disturbance Propagation ◽  
Linear Waves ◽  
Longitudinal And Shear Waves ◽  
Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

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