scholarly journals Sparse Array Design for DOA Estimation of Non-Gaussian Signals: From Global Postage-Stamp Problem Perspective

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Changbo Ye ◽  
Luo Chen ◽  
Beizuo Zhu
Keyword(s):  
Design Problem ◽  
Doa Estimation ◽  
Second Order ◽  
Sensor Location ◽  
Postage Stamp ◽  
Array Design ◽  
Sparse Array ◽  
Physical Sensors ◽  
Physical Sensor ◽  
Non Gaussian

In this paper, a sparse array design problem for non-Gaussian signal direction of arrival (DOA) estimation is investigated. Compared with conventional second-order cumulant- (SOC-) based methods, fourth-order cumulant- (FOC-) based methods achieve improved DOA estimation performance by utilizing all information from received non-Gaussian sources. Considering the virtual sensor location of vectorized FOC-based methods can be calculated from the second order difference coarray of sum coarray (2-DCSC) of physical sensors, it is important to devise a sparse array design principle to obtain extended degree of freedom (DOF). Based on the properties of unfolded coprime linear array (UCLA), we formulate the sparse array design problem as a global postage-stamp problem (GPSP) and then present an array design method from GPSP perspective. Specifically, for vectorized FOC-based methods, we divide the process of obtaining physical sensor location into two steps; the first step is to obtain the two consecutive second order sum coarrays (2-SC), which can be modeled as GPSP, and the solutions to GPSP can also be utilized to determine the physical sensor location sets without interelement spacing coefficients. The second step is to adjust the physical sensor sets by multiplying the appropriate coprime coefficients, which is determined by the structure of UCLA. In addition, the 2-DCSC can be calculated from physical sensors directly, and the properties of UCLA are given to confirm the degree of freedom (DOF) of the proposed geometry. Simulation results validate the effectiveness and superiority of the proposed array geometry.

scholarly journals Highly Accurate Multi-Invariance ESPRIT for DOA Estimation with a Sparse Array

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Chen Gu ◽  
Hong Hong ◽  
Yusheng Li ◽  
Xiaohua Zhu ◽  
Jin He
Keyword(s):  
Doa Estimation ◽  
Invariance Property ◽  
Two Dimensional ◽  
Sparse Array ◽  
Half Wavelength ◽  
Vector Sensors ◽  
Matrix Blocks ◽  
Simulation Results ◽  
Non Gaussian ◽  
Array Geometry

This paper proposes a multi-invariance ESPRIT-based method for estimation of 2D direction (MIMED) of multiple non-Gaussian monochromatic signals using cumulants. In the MIMED, we consider an array geometry containing sparse L-shaped diversely polarized vector sensors plus an arbitrarily-placed single polarized scalar sensor. Firstly, we define a set of cumulant matrices to construct two matrix blocks with multi-invariance property. Then, we develop a multi-invariance ESPRIT-based algorithm with aperture extension using the defined matrix blocks to estimate two-dimensional directions of the signals. The MIMED can provide highly accurate and unambiguous direction estimates by extending the array element spacing beyond a half-wavelength. Finally, we present several simulation results to demonstrate the superiority of the MIMED.

Pattern search-based sparse array design for unambiguous DOA estimation

2015 ◽  
Author(s):  
Xianxiang Yu Xianxiang Yu ◽  
Cuiguo Long Cuiguo Long ◽  
Shangwei Gao Shangwei Gao ◽  
Lingjiang Kong Lingjiang Kong
Keyword(s):  
Doa Estimation ◽  
Pattern Search ◽  
Array Design ◽  
Sparse Array

Non‐Gaussian Properties of Second‐Order Random Waves

1993 ◽  
Vol 119 (2) ◽  
pp. 344-364 ◽  
Author(s):  
Sau‐Lon James Hu ◽  
Dongsheng Zhao
Keyword(s):  
Second Order ◽  
Random Waves ◽  
Non Gaussian

Maximum Correntropy Criterion Constrained Kalman Filter

2017 ◽  
Author(s):  
Seyed Fakoorian ◽  
Mahmoud Moosavi ◽  
Reza Izanloo ◽  
Vahid Azimi ◽  
Dan Simon
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
State Constraints ◽  
Statistical Information ◽  
Second Order ◽  
System Model ◽  
Error Covariance ◽  
Inequality State ◽  
Maximum Correntropy Criterion ◽  
Non Gaussian

Non-Gaussian noise may degrade the performance of the Kalman filter because the Kalman filter uses only second-order statistical information, so it is not optimal in non-Gaussian noise environments. Also, many systems include equality or inequality state constraints that are not directly included in the system model, and thus are not incorporated in the Kalman filter. To address these combined issues, we propose a robust Kalman-type filter in the presence of non-Gaussian noise that uses information from state constraints. The proposed filter, called the maximum correntropy criterion constrained Kalman filter (MCC-CKF), uses a correntropy metric to quantify not only second-order information but also higher-order moments of the non-Gaussian process and measurement noise, and also enforces constraints on the state estimates. We analytically prove that our newly derived MCC-CKF is an unbiased estimator and has a smaller error covariance than the standard Kalman filter under certain conditions. Simulation results show the superiority of the MCC-CKF compared with other estimators when the system measurement is disturbed by non-Gaussian noise and when the states are constrained.

Effect of Sparse Array Geometry on Estimation of Co-array Signal Subspace

2021 ◽  
Vol 35 (11) ◽  
pp. 1435-1436
Author(s):  
Mehmet Hucumenoglu ◽  
Piya Pal
Keyword(s):  
Covariance Matrix ◽  
Estimation Error ◽  
Doa Estimation ◽  
Singular Value ◽  
Signal Subspace ◽  
Sparse Array ◽  
Subspace Estimation ◽  
Signal Covariance Matrix ◽  
Special Case ◽  
Array Geometry

This paper considers the effect of sparse array geometry on the co-array signal subspace estimation error for Direction-of-Arrival (DOA) estimation. The second largest singular value of the signal covariance matrix plays an important role in controlling the distance between the true subspace and its estimate. For a special case of two closely-spaced sources impinging on the array, we explicitly compute the second largest singular value of the signal covariance matrix and show that it can be significantly larger for a nested array when compared against a uniform linear array with same number of sensors.

scholarly journals Central DOA Estimation Method for Exponential-Type Coherent Distributed Source Based on Fourth-Order Cumulant

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Hao Li ◽  
Weijia Cui ◽  
Bin Ba ◽  
Haiyun Xu ◽  
Yankui Zhang
Keyword(s):  
Fourth Order ◽  
Exponential Type ◽  
Complexity Analysis ◽  
Estimation Method ◽  
Doa Estimation ◽  
Estimation Accuracy ◽  
Distributed Source ◽  
Sparse Array ◽  
Fourth Order Cumulant ◽  
Array Aperture

The performance of direction-of-arrival (DOA) estimation for sparse arrays applied to the distributed source is worse than that applied to the point source model. In this paper, we introduce the coprime array with a large array aperture into the DOA estimation algorithm of the exponential-type coherent distributed source. In particular, we focus on the fourth-order cumulant (FOC) of the received signal which can provide more useful information when the signal is non-Gaussian than when it is Gaussian. The proposed algorithm extends the array aperture by combining the sparsity of array space domain with the fourth-order cumulant characteristics of signals, which improves the estimation accuracy and degree of freedom (DOF). Firstly, the signal-received model of the sparse array is established, and the fourth-order cumulant matrix of the received signal of the sparse array is calculated based on the characteristics of distributed sources, which extend the array aperture. Then, the virtual array is constructed by the sum aggregate of physical array elements, and the position set of its maximum continuous part array element is obtained. Finally, the center DOA estimation of the distributed source is realized by the subspace method. The accuracy and DOF of the proposed algorithm are higher than those of the distributed signal parameter estimator (DSPE) algorithm and least-squares estimation signal parameters via rotational invariance techniques (LS-ESPRIT) algorithm when the array elements are the same. Complexity analysis and numerical simulations are provided to demonstrate the superiority of the proposed method.

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