scholarly journals Estimation accuracy of covariance matrices when their eigenvalues are almost duplicated

2018 ◽  
Vol 7 ◽  
Author(s):  
Kantaro Shimomura ◽  
Kazushi Ikeda
Keyword(s):  
Covariance Matrix ◽  
Estimation Method ◽  
Estimation Accuracy ◽  
Essential Information ◽  
The Matrix ◽  
The Difference ◽  
Processing Techniques ◽  
Monotonic Property ◽  
Signal Processing Techniques ◽  
Special Case

The covariance matrix of signals is one of the most essential information in multivariate analysis and other signal processing techniques. The estimation accuracy of a covariance matrix is degraded when some eigenvalues of the matrix are almost duplicated. Although the degradation is theoretically analyzed in the asymptotic case of infinite variables and observations, the degradation in finite cases are still open. This paper tackles the problem using the Bayesian approach, where the learning coefficient represents the generalization error. The learning coefficient is derived in a special case, i.e., the covariance matrix is spiked (all eigenvalues take the same value except one) and a shrinkage estimation method is employed. Our theoretical analysis shows a non-monotonic property that the learning coefficient increases as the difference of eigenvalues increases until a critical point and then decreases from the point and converged to the distinct case. The result is validated by numerical experiments.

Impact of AMSU-A Radiances in a Column Ensemble Kalman Filter

2018 ◽  
Vol 146 (12) ◽  
pp. 3949-3976 ◽  
Author(s):  
Herschel L. Mitchell ◽  
P. L. Houtekamer ◽  
Sylvain Heilliette
Keyword(s):  
Covariance Matrix ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Microwave Sounding Unit ◽  
The Matrix ◽  
Microwave Sounding ◽  
Background Temperature ◽  
The Difference

Abstract A column EnKF, based on the Canadian global EnKF and using the RTTOV radiative transfer (RT) model, is employed to investigate issues relating to the EnKF assimilation of Advanced Microwave Sounding Unit-A (AMSU-A) radiance measurements. Experiments are performed with large and small ensembles, with and without localization. Three different descriptions of background temperature error are considered: 1) using analytical vertical modes and hypothetical spectra, 2) using the vertical modes and spectrum of a covariance matrix obtained from the global EnKF after 2 weeks of cycling, and 3) using the vertical modes and spectrum of the static background error covariance matrix employed to initiate a global data assimilation cycle. It is found that the EnKF performs well in some of the experiments with background error description 1, and yields modest error reductions with background error description 3. However, the EnKF is virtually unable to reduce the background error (even when using a large ensemble) with background error description 2. To analyze these results, the different background error descriptions are viewed through the prism of the RT model by comparing the trace of the matrix , where is the RT model and is the background error covariance matrix. Indeed, this comparison is found to explain the difference in the results obtained, which relates to the degree to which deep modes are, or are not, present in the different background error covariances. The results suggest that, after 2 weeks of cycling, the global EnKF has virtually eliminated all background error structures that can be “seen” by the AMSU-A radiances.

scholarly journals A Novel ULA-Difference-Coarray-Based DOA Estimation Method for General Coherent Signals

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhang Chen ◽  
Hao Wu ◽  
Yongxiang Liu
Keyword(s):  
Good Accuracy ◽  
Linear Array ◽  
Estimation Method ◽  
Doa Estimation ◽  
Estimation Accuracy ◽  
Coherent Signals ◽  
Low Snr ◽  
Sample Covariance ◽  
Lower Complexity ◽  
The Difference

In this article, a difference-coarray-based direction of arrival (DOA) method is introduced, which utilizes the uniform linear array (ULA) in a novel fashion to address the problem of DOA estimation for coherent signals. Inspired by the coarray-based estimators employed in cases of sparse arrays, we convert the sample covariance matrix of the observed signals into the difference coarray domain and process the signals using a spatial smoothing technique. The proposed method exhibits good accuracy and robustness in both the uncorrelated and coherent cases. Numerical simulations verify that the ULA difference coarray- (UDC-) based method can achieve good DOA estimation accuracy even when the SNR is very low. In addition, the UDC-based method is insensitive to the number of snapshots. Under extremely challenging conditions, the proposed UDC-ES-DOA method is preferred because of its outstanding robustness, while the UDC-MUSIC method is suitable for most moderate cases of lower complexity. Due to its demonstrated advantages, the proposed method is a promising and competitive solution for practical DOA estimation, especially for low-SNR or snapshot-limited applications.

Matlab-Based Formant Estimation

2014 ◽  
Vol 577 ◽  
pp. 798-801
Author(s):  
Jiao Yan Luo ◽  
Xiang E Sun
Keyword(s):  
Signal Processing ◽  
Estimation Method ◽  
Digital Signal ◽  
Speech Signal Processing ◽  
Short Time Fourier Transform ◽  
Transform Method ◽  
Processing Techniques ◽  
Short Time ◽  
Matlab Programming ◽  
Signal Processing Techniques

In the study of speech digital signal processing, the resonance peak is the major characteristics in reflecting track resonant. In order to be more conducive to the future development of speech signal processing techniques, three methods of the formant estimation are introduced in the article, namely, Short-time Fourier Transform method, Cepstrum, LPC estimation method. These methods are compared and analyzed by means of MATLAB programming, and it is concluded that LPC method is the best method, which can estimate the formant peaks more accurate.

scholarly journals A Time-Efficient and Accurate Open Circuit Voltage Estimation Method for Lithium-Ion Batteries

Energies ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1803 ◽  
Author(s):  
Yingjie Chen ◽  
Geng Yang ◽  
Xu Liu ◽  
Zhichao He
Keyword(s):  
Lithium Ion Batteries ◽  
Open Circuit Voltage ◽  
Estimation Method ◽  
Nonlinear Function ◽  
Lithium Ion ◽  
Open Circuit ◽  
Constant Current ◽  
Estimation Accuracy ◽  
Battery Modeling ◽  
The Difference

The open circuit voltage (OCV) of lithium-ion batteries is widely used in battery modeling, state estimation, and management. However, OCV is a function of state of charge (SOC) and battery temperature (Tbat) and is very hard to estimate in terms of time efficiency and accuracy. This is because two problems arise in normal operations: (1) Tbat changes with the current (I), which makes it very hard to obtain the data required to estimate OCV—terminal voltage (U) data of different I under the same Tbat; (2) the difference between U and OCV is a complex nonlinear function of I and is very difficult to accurately calculate. Therefore, existing methods have to design special experiments to avoid these problems, which are very time consuming. The proposed method consists of a designed test and a data processing algorithm. The test is mainly constant current tests (CCTs) of large I, which is time-efficient in obtaining data. The algorithm solves the two problems and estimates OCV accurately using the test data. Experimental results and analyses showed that experimental time was reduced and estimation accuracy was adequate.

scholarly journals A Hybrid Method for SOC Estimation of Power Battery

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Jiliang Yi ◽  
Xuechun Zhou ◽  
Jin Zhang ◽  
Zhongqi Li
Keyword(s):  
Hybrid Method ◽  
Estimation Method ◽  
Threshold Value ◽  
Least Square ◽  
Convergence Time ◽  
Equivalent Model ◽  
Estimation Accuracy ◽  
Soc Estimation ◽  
Power Battery ◽  
The Difference

The accuracy of battery state of charge (SOC) is crucial for solving the problems such as overcharge, overdischarge, and mileage anxiety of electric vehicle power battery. In this study, an SOC estimation method using a hybrid method (HM) based on threshold switching is proposed, which combines the advantages of the extended Kalman filter (EKF) and the ampere hour integration (AHI) to improve the estimation accuracy and convergence speed. First, the parameters of the second-order RC equivalent model are identified using the least square. Then, the equation of EKF for updating the state variable is reconstructed by using the identified parameters to solve the problem of multiple iterations caused by the uncertainty of the initial value. Finally, the difference between the estimated voltage and the sampling voltage is used as the threshold value for switching between the AHI and the EKF to estimate the SOC of the battery. Simulation results show that the estimated SOC error of the proposed algorithm is less than 1.6% and the convergence time is within 70 s. Experiments under different SOC initial values are carried out to prove the advantages of the proposed method.

scholarly journals Highway Reliability Management Model Based on Depth Recursion for Transportation Demand

CONVERTER ◽  
2021 ◽  
pp. 470-481
Author(s):  
Guozhen Sang
Keyword(s):  
Transition Probability ◽  
Estimation Method ◽  
Sampling Technique ◽  
Reliability Estimation ◽  
Estimation Accuracy ◽  
Optimal Test ◽  
Transportation Demand ◽  
Reliability Management ◽  
Model Based ◽  
The Difference

An effective estimation method for the highway reliability management according to the Zhukov usage model based on the recursive test is put forward. This method makes use of the important sampling technique to ensure that under the conditions of the unbiased reliability estimation, the depth recursion is used to measure the difference between the operation profile and the distribution of the zero variance sampling, to correct the test profile by adjusting the transition probability between all the states through the heuristic iterative process. It has proved theoretically that the reliability of the estimation using the modified test profile test is unbiased estimate with the variance of 0. Finally, the heuristic iterative algorithm for the generation of the optimal test profile of the highway reliability estimation is given. The simulation results show that the method put forward in this paper can significantly reduce the variance of the estimate compared with the Newton algorithm, and can increase the speed of the recursive test while improving the estimation accuracy at the same time. The research done in this paper can effectively meet the requirements of the transportation industry in the tertiary industry.

scholarly journals Gridless DOA Estimation for Minimum-Redundancy Linear Array in Nonuniform Noise

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Changyun Qi ◽  
Gong Zhang ◽  
Jiawen Yuan
Keyword(s):  
Covariance Matrix ◽  
Linear Array ◽  
Estimation Method ◽  
Doa Estimation ◽  
Residual Energy ◽  
Estimation Accuracy ◽  
Two Stages ◽  
Signal Covariance Matrix ◽  
Toeplitz Structure ◽  
True Signal

A gridless direction-of-arrival (DOA) estimation method to improve the estimation accuracy and resolution in nonuniform noise is proposed in this paper. This algorithm adopts the structure of minimum-redundancy linear array (MRA) and can be composed of two stages. In the first stage, by minimizing the rank of the covariance matrix of the true signal, the covariance matrix that filters out nonuniform noise is obtained, and then a gridless residual energy constraint scheme is designed to reconstruct the signal covariance matrix of the Hermitian Toeplitz structure. Finally, the unknown DOAs can be determined from the recovered covariance matrix, and the number of sources can be acquired as a byproduct. The proposed algorithm can be regarded as a gridless version method based on sparsity. Simulation results indicate that the proposed method has higher estimation accuracy and resolution compared with existing algorithms.

scholarly journals A Study on the Amplitude Comparison Monopulse Algorithm

2020 ◽  
Vol 10 (11) ◽  
pp. 3966
Author(s):  
Minjeong Kim ◽  
Daseon Hong ◽  
Sungsu Park
Keyword(s):  
Monte Carlo ◽  
Numerical Simulations ◽  
Least Squares ◽  
Estimation Method ◽  
Prediction Equation ◽  
Least Squares Estimation ◽  
Estimation Accuracy ◽  
Prediction Equations ◽  
Special Case ◽  
Rms Errors

This paper presents two amplitude comparison monopulse algorithms and their covariance prediction equation. The proposed algorithms are based on the iterated least-squares estimation method and include the conventional monopulse algorithm as a special case. The proposed covariance equation is simple but predicts RMS errors very accurately. This equation quantitatively states estimation accuracy in terms of major parameters of amplitude comparison monopulse radar, and is also applicable to the conventional monopulse algorithm. The proposed algorithms and covariance prediction equations are validated by the numerical simulations with 100,000 Monte Carlo runs.

scholarly journals Underdetermined DOA Estimation for Wideband Signals via Focused Atomic Norm Minimization

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 359 ◽  
Author(s):  
Juan Shi ◽  
Qunfei Zhang ◽  
Weijie Tan ◽  
Linlin Mao ◽  
Lihuan Huang ◽  
...  
Keyword(s):  
Information Theory ◽  
Signal Processing ◽  
Covariance Matrix ◽  
Estimation Method ◽  
Doa Estimation ◽  
Estimation Methods ◽  
Estimation Accuracy ◽  
Norm Minimization ◽  
Atomic Norm ◽  
Virtual Array

In underwater acoustic signal processing, direction of arrival (DOA) estimation can provide important information for target tracking and localization. To address underdetermined wideband signal processing in underwater passive detection system, this paper proposes a novel underdetermined wideband DOA estimation method equipped with the nested array (NA) using focused atomic norm minimization (ANM), where the signal source number detection is accomplished by information theory criteria. In the proposed DOA estimation method, especially, after vectoring the covariance matrix of each frequency bin, each corresponding obtained vector is focused into the predefined frequency bin by focused matrix. Then, the collected averaged vector is considered as virtual array model, whose steering vector exhibits the Vandermonde structure in terms of the obtained virtual array geometries. Further, the new covariance matrix is recovered based on ANM by semi-definite programming (SDP), which utilizes the information of the Toeplitz structure. Finally, the Root-MUSIC algorithm is applied to estimate the DOAs. Simulation results show that the proposed method outperforms other underdetermined DOA estimation methods based on information theory in term of higher estimation accuracy.

A Digital Watermarking Algorithm Based on the Wavelet Bit Plane Coding

2013 ◽  
Vol 821-822 ◽  
pp. 1438-1441
Author(s):  
Gao Yan ◽  
Yan Liang ◽  
Xin Zhou ◽  
Chun Xia Qi
Keyword(s):  
Image Processing ◽  
Digital Watermarking ◽  
Original Image ◽  
A Algorithm ◽  
Bit Plane Coding ◽  
Bit Plane ◽  
The Difference ◽  
Bit Planes ◽  
Processing Techniques ◽  
Signal Processing Techniques

In this paper a algorithm of digital image watermark based on wavelet bit plane is introduced, and the original image is not required for detecting the watermarking. The digital watermark is embedded by changing information of some bit planes in DWT images at different resolutions. The watermark can be extracted on the difference bit plane values of subimages of the decomposed watermarked image which is then mapped to an image with a few shades of gray. Experimental results show that the watermark is robust to several signal processing techniques, including JPEG compression and some image processing operations

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