scholarly journals Sea Clutter Covariance Matrix Estimation and Its Application to Whitening Filter

2021 ◽  
Vol 21 (2) ◽  
pp. 134-142
Author(s):  
Sanghyun Choi ◽  
Hoongee Yang ◽  
Jimin Song ◽  
Hyeonmu Jeon ◽  
Jongmann Kim ◽  
...  
Keyword(s):  
Covariance Matrix ◽  
Estimation Algorithm ◽  
Doppler Spectrum ◽  
Accurate Estimation ◽  
Sea Clutter ◽  
Matrix Estimation ◽  
Range Cell ◽  
Sample Covariance ◽  
Whitening Filter ◽  
Mutual Independence

The accurate estimation of clutter covariance matrix (CCM) is essential in designing a radar detector/filter to suppress sea clutter. This estimation might not be easily accomplished because of the scarcity of valid training vectors adjacent to the range cell under test (CUT). We propose a new CCM estimation algorithm that is derived by modeling time-series clutter returns into a clutter Doppler spectrum in the frequency domain and exploiting mutual independence among spectral components. To justify its excellence over the conventional sample covariance matrix (SCM) algorithm, we design two filters—a maximum signal-to-interference-plus-noise ratio (SINR)-based filter and a whitening filter—that use the estimated CCMs and compare their performance in a numerically simulated sea clutter scenario. Comparisons are made by showing the eigenvector spectra of the estimated CCMs and the frequency responses and outputs of the filters. Moreover, SINRs at the target Doppler bin are examined and compared with a theoretical, analytically derived SINR.

scholarly journals Covariance Matrix Estimation under Total Positivity for Portfolio Selection*

2020 ◽  
Author(s):  
Raj Agrawal ◽  
Uma Roy ◽  
Caroline Uhler
Keyword(s):  
Covariance Matrix ◽  
Total Positivity ◽  
General Purpose ◽  
Shrinkage Estimators ◽  
Positive Dependence ◽  
Matrix Estimation ◽  
Sample Covariance ◽  
Totally Positive ◽  
Markowitz Portfolio ◽  
Previous State

Abstract Selecting the optimal Markowitz portfolio depends on estimating the covariance matrix of the returns of N assets from T periods of historical data. Problematically, N is typically of the same order as T, which makes the sample covariance matrix estimator perform poorly, both empirically and theoretically. While various other general-purpose covariance matrix estimators have been introduced in the financial economics and statistics literature for dealing with the high dimensionality of this problem, we here propose an estimator that exploits the fact that assets are typically positively dependent. This is achieved by imposing that the joint distribution of returns be multivariate totally positive of order 2 (MTP2). This constraint on the covariance matrix not only enforces positive dependence among the assets but also regularizes the covariance matrix, leading to desirable statistical properties such as sparsity. Based on stock market data spanning 30 years, we show that estimating the covariance matrix under MTP2 outperforms previous state-of-the-art methods including shrinkage estimators and factor models.

scholarly journals Novel Diagonal Reloading Based Direction of Arrival Estimation in Unknown Non-Uniform Noise

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Hao Zhou ◽  
Guoping Hu ◽  
Junpeng Shi ◽  
Ziang Feng
Keyword(s):  
Covariance Matrix ◽  
Degrees Of Freedom ◽  
Direction Of Arrival ◽  
Estimation Algorithm ◽  
Doa Estimation ◽  
Main Diagonal ◽  
Sample Covariance ◽  
Uniform Noise ◽  
Negative Effect ◽  
Signal Covariance Matrix

Nested array can expand the degrees of freedom (DOF) from difference coarray perspective, but suffering from the performance degradation of direction of arrival (DOA) estimation in unknown non-uniform noise. In this paper, a novel diagonal reloading (DR) based DOA estimation algorithm is proposed using a recently developed nested MIMO array. The elements in the main diagonal of the sample covariance matrix are eliminated; next the smallest MN-K eigenvalues of the revised matrix are obtained and averaged to estimate the sum value of the signal power. Further the estimated sum value is filled into the main diagonal of the revised matrix for estimating the signal covariance matrix. In this case, the negative effect of noise is eliminated without losing the useful information of the signal matrix. Besides, the degrees of freedom are expanded obviously, resulting in the performance improvement. Several simulations are conducted to demonstrate the effectiveness of the proposed algorithm.

scholarly journals On the Assessment of Non-Local Multi-Looking in Detection of Persistent Scatterers Using SAR Tomography

2020 ◽  
Vol 12 (19) ◽  
pp. 3195
Author(s):  
Hossein Aghababaei
Keyword(s):  
Covariance Matrix ◽  
Super Resolution ◽  
Covariance Matrix Estimation ◽  
Ratio Test ◽  
Matrix Estimation ◽  
Persistent Scatterers ◽  
Sample Covariance ◽  
Permanent Scatterers ◽  
Non Local ◽  
The Impact

Synthetic aperture radar (SAR) tomography has shown great potential in multi-dimensional monitoring of urban infrastructures and detection of their possible slow deformations. Along this line, undeniable improvements in SAR tomography (TomoSAR) detection framework of multiple permanent scatterers (PSs) have been observed by the use of a multi-looking operation that is the necessity for data’s covariance matrix estimation. This paper attempts to further analyze the impact of a robust multi-looking operation in TomoSAR PS detection framework and assess the challenging issues that exist in the estimation of the covariance matrix of large stack data obtained from long interferometric time series acquisition. The analyses evaluate the performance of non-local covariance matrix estimation approaches in PS detection framework using the super-resolution multi-looked Generalized Likelihood Ratio Test (GLRT). Experimental results of multi-looking impact assessment are provided using two datasets acquired by COSMO-SkyMED (CSK) and TerraSAR-X (TSX) over Tehran, Iran, and Toulouse, France, respectively. The results highlight that non-local estimation of the sample covariance matrix allows revealing the presence of the scatterers, that may not be detectable using the conventional local-based framework.

scholarly journals A Sparse-Based Off-Grid DOA Estimation Method for Coprime Arrays

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 3025 ◽  
Author(s):  
Weijian Si ◽  
Fuhong Zeng ◽  
Changbo Hou ◽  
Zhanli Peng
Keyword(s):  
Covariance Matrix ◽  
Estimation Error ◽  
Estimation Method ◽  
Doa Estimation ◽  
Sample Covariance Matrix ◽  
Estimation Methods ◽  
Matrix Estimation ◽  
Estimation Process ◽  
Sample Covariance ◽  
Coprime Arrays

Recently, many sparse-based direction-of-arrival (DOA) estimation methods for coprime arrays have become popular for their excellent detection performance. However, these methods often suffer from grid mismatch problem due to the discretization of the potential angle space, which will cause DOA estimation performance degradation when the target is off-grid. To this end, we proposed a sparse-based off-grid DOA estimation method for coprime arrays in this paper, which includes two parts: coarse estimation process and fine estimation process. In the coarse estimation process, the grid points closest to the true DOAs, named coarse DOAs, are derived by solving an optimization problem, which is constructed according to the statistical property of the vectorized covariance matrix estimation error. Meanwhile, we eliminate the unknown noise variance effectively through a linear transformation. Due to finite snapshots effect, some undesirable correlation terms between signal and noise vectors exist in the sample covariance matrix. In the fine estimation process, we therefore remove the undesirable correlation terms from the sample covariance matrix first, and then utilize a two-step iterative method to update the grid biases. Combining the coarse DOAs with the grid biases, the final DOAs can be obtained. In the end, simulation results verify the effectiveness of the proposed method.

scholarly journals An Efficient Hardware Accelerator for the MUSIC Algorithm

Electronics ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 511 ◽  
Author(s):  
Hui Chen ◽  
Kai Chen ◽  
Kaifeng Cheng ◽  
Qinyu Chen ◽  
Yuxiang Fu ◽  
...  
Keyword(s):  
Real Time ◽  
Covariance Matrix ◽  
High Precision ◽  
Estimation Algorithm ◽  
Cmos Technology ◽  
Spectral Peak ◽  
Access Time ◽  
Music Algorithm ◽  
Matrix Estimation ◽  
Peak Search

As a classical DOA (direction of arrival) estimation algorithm, the multiple signal classification (MUSIC) algorithm can estimate the direction of signal incidence. A major bottleneck in the application of this algorithm is the large computation amount, so accelerating the algorithm to meet the requirements of high real-time and high precision is the focus. In this paper, we design an efficient and reconfigurable accelerator to implement the MUSIC algorithm. Initially, we propose a hardware-friendly MUSIC algorithm without the eigenstructure decomposition of the covariance matrix, which is time consuming and accounts for about 60% of the whole computation. Furthermore, to reduce the computation of the covariance matrix, this paper utilizes the conjugate symmetry property of it and the way of iterative storage, which can also lessen memory access time. Finally, we adopt the stepwise search method to realize the spectral peak search, which can meet the requirements of 1° and 0.1° precision. The accelerator can operate at a maximum frequency of 1 GHz with a 4,765,475.4 μm2 area, and the power dissipation is 238.27 mW after the gate-level synthesis under the TSMC 40-nm CMOS technology with the Synopsys Design Compiler. Our implementation can accelerate the algorithm to meet the high real-time and high precision requirements in applications. Assuming that the case is an eight-element uniform linear array, a single signal source, and 128 snapshots, the computation times of the algorithm in our architecture are 2.8 μs and 22.7 μs for covariance matrix estimation and spectral peak search, respectively.

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