scholarly journals LARGE INFORMATION PLUS NOISE RANDOM MATRIX MODELS AND CONSISTENT SUBSPACE ESTIMATION IN LARGE SENSOR NETWORKS

2012 ◽  
Vol 01 (02) ◽  
pp. 1150006 ◽  
Author(s):  
WALID HACHEM ◽  
PHILIPPE LOUBATON ◽  
XAVIER MESTRE ◽  
JAMAL NAJIM ◽  
PASCAL VALLET
Keyword(s):  
Covariance Matrix ◽  
Estimation Method ◽  
Singular Values ◽  
Subspace Methods ◽  
Localization Function ◽  
Random Matrix Models ◽  
Order Of Magnitude ◽  
Source Signal ◽  
Subspace Estimation ◽  
Empirical Covariance

In array processing, a common problem is to estimate the angles of arrival of K deterministic sources impinging on an array of M antennas, from N observations of the source signal, corrupted by Gaussian noise. In the so-called subspace methods, the problem reduces to estimate a quadratic form (called "localization function") of a certain projection matrix related to the source signal empirical covariance matrix. The estimates of the angles of arrival are then obtained by taking the K deepest local minima of the estimated localization function. Recently, a new subspace estimation method has been proposed, in the context where the number of available samples N is of the same order of magnitude than the number of sensors M. In this context, the traditional subspace methods tend to fail because they are based on the empirical covariance matrix of the observations which is a poor estimate of the source signal covariance matrix. The new subspace method is based on a consistent estimator of the localization function in the regime where M and N tend to +∞ at the same rate. However, the consistency of the angles estimator was not addressed, and the purpose of this paper is to prove this consistency in the previous asymptotic regime. For this, we prove the property that the singular values of M × N Gaussian information plus noise matrix escape from certain intervals is an event of probability decreasing at rate [Formula: see text] for all p. A regularization trick is also introduced, which allows to confine these singular values into certain intervals and to use standard tools as Poincaré inequality to characterize any moments of the estimator. These results are believed to be of independent interest.

scholarly journals An Enhanced Smoothed L0-Norm Direction of Arrival Estimation Method Using Covariance Matrix

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4403
Author(s):  
Ji Woong Paik ◽  
Joon-Ho Lee ◽  
Wooyoung Hong
Keyword(s):  
Covariance Matrix ◽  
Phased Array ◽  
Null Space ◽  
Estimation Method ◽  
Direction Of Arrival ◽  
Estimation Algorithm ◽  
Doa Estimation ◽  
Direction Of Arrival Estimation ◽  
Improve Performance ◽  
Space Projection

An enhanced smoothed l0-norm algorithm for the passive phased array system, which uses the covariance matrix of the received signal, is proposed in this paper. The SL0 (smoothed l0-norm) algorithm is a fast compressive-sensing-based DOA (direction-of-arrival) estimation algorithm that uses a single snapshot from the received signal. In the conventional SL0 algorithm, there are limitations in the resolution and the DOA estimation performance, since a single sample is used. If multiple snapshots are used, the conventional SL0 algorithm can improve performance in terms of the DOA estimation. In this paper, a covariance-fitting-based SL0 algorithm is proposed to further reduce the number of optimization variables when using multiple snapshots of the received signal. A cost function and a new null-space projection term of the sparse recovery for the proposed scheme are presented. In order to verify the performance of the proposed algorithm, we present the simulation results and the experimental results based on the measured data.

scholarly journals Refinement of the ice absorption spectrum in the visible using radiance profile measurements in Antarctic snow

2016 ◽  
Author(s):  
Ghislain Picard ◽  
Quentin Libois ◽  
Laurent Arnaud
Keyword(s):  
Absorption Coefficient ◽  
Fiber Optics ◽  
Estimation Method ◽  
Radiative Transfer Model ◽  
Transfer Model ◽  
Snow Layer ◽  
Antarctic Snow ◽  
Order Of Magnitude ◽  
The Difference ◽  
The Antarctic

Abstract. Ice is a highly transparent material in the visible. According to the most widely used database (Warren and Brandt, 2008; IA2008), the ice absorption coefficient reaches values lower than 10−3 m−1 around 400 nm. These values were obtained from a radiance profile measured in a single snow layer at Dome C in Antarctica. We reproduced this experiment using a fiber optics inserted in the snow to record 56 profiles from which 70 homogeneous layers were identified. Applying the same estimation method on every layer yields 70 ice absorption spectra with a significant variability and overall larger than IA2008 by one order of magnitude. We devise another estimation method based on Bayesian inference. It reduces the statistical variability and confirms the higher absorption, around 2 × 10−2 m−1 near the minimum at 440 nm. We explore potential instrumental artifacts by developing a 3D radiative transfer model able to explicitly account for the presence of the fiber in the snow. The simulation results show that the radiance profile is indeed perturbed by the fiber intrusion but the error on the ice absorption estimate is not larger than a factor 2. This is insufficient to explain the difference between our new estimate and IA2008. Nevertheless, considering the number of profiles acquired for this study and other estimates from the Antarctic Muon and Neutrino Detector Array (AMANDA), we estimate that ice absorption values around 10−2 m−1 at the minimum are more likely than under 10−3 m−1. We provide a new estimate in the range 400–600 nm for future modeling of snow, cloud, and sea-ice optical properties. Most importantly we recommend that modeling studies take into account the large uncertainty of the ice absorption coefficient in the visible.

RECURSIVE UPDATING OF ERROR COVARIANCE MATRIX IN SUBSPACE METHODS

2006 ◽  
Vol 39 (1) ◽  
pp. 285-290 ◽  
Author(s):  
Yoshinori Takei ◽  
Hidehito Nanto ◽  
Shunshoku Kanae ◽  
Zi-Jiang Yang ◽  
Kiyoshi Wada
Keyword(s):  
Covariance Matrix ◽  
Subspace Methods ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Recursive Updating

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 Improvements to a long-term Rayleigh-scatter lidar temperature climatology by using an optimal estimation method

2018 ◽  
Vol 11 (11) ◽  
pp. 6043-6058 ◽  
Author(s):  
Ali Jalali ◽  
Robert J. Sica ◽  
Alexander Haefele
Keyword(s):  
Traditional Method ◽  
Middle Atmosphere ◽  
Density Measurement ◽  
Estimation Method ◽  
Optimal Estimation ◽  
Temperature Profiles ◽  
Vertical Resolution ◽  
Order Of Magnitude ◽  
Lidar Equation ◽  
Model Temperature

Abstract. Hauchecorne and Chanin (1980) developed a robust method to calculate middle-atmosphere temperature profiles using measurements from Rayleigh-scatter lidars. This traditional method has been successfully used to greatly improve our understanding of middle-atmospheric dynamics, but the method has some shortcomings regarding the calculation of systematic uncertainties and the vertical resolution of the retrieval. Sica and Haefele (2015) have shown that the optimal estimation method (OEM) addresses these shortcomings and allows temperatures to be retrieved with confidence over a greater range of heights than the traditional method. We have calculated a temperature climatology from 519 nights of Purple Crow Lidar Rayleigh-scatter measurements using an OEM. Our OEM retrieval is a first-principle retrieval in which the forward model is the lidar equation and the measurements are the level-0 count returns. It includes a quantitative determination of the top altitude of the retrieved temperature profiles, the evaluation of nine systematic plus random uncertainties, and the vertical resolution of the retrieval on a profile-by-profile basis. Our OEM retrieval allows for the vertical resolution to vary with height, extending the retrieval in altitude 5 to 10 km higher than the traditional method. It also allows the comparison of the traditional method's sensitivity to two in-principle equivalent methods of specifying the seed pressure: using a model pressure seed versus using a model temperature combined with the lidar's density measurement to calculate the seed pressure. We found that the seed pressure method is superior to using a model temperature combined with the lidar-derived density. The increased altitude capability of our OEM retrievals allows for a comparison of the Rayleigh-scatter lidar temperatures throughout the entire altitude range of the sodium lidar temperature measurements. Our OEM-derived Rayleigh temperatures are shown to have improved agreement relative to our previous comparisons using the traditional method, and the agreement of the OEM-derived temperatures is the same as the agreement between existing sodium lidar temperature climatologies. This detailed study of the calculation of the new Purple Crow Lidar temperature climatology using the OEM establishes that it is both highly advantageous and practical to reprocess existing Rayleigh-scatter lidar measurements that cover long time periods, during which time the lidar may have undergone several significant equipment upgrades, while gaining an upper limit to useful temperature retrievals equivalent to an order of magnitude increase in power-aperture product due to the use of an OEM.

scholarly journals Estimating model error covariance matrix parameters in extended Kalman filtering

2014 ◽  
Vol 21 (5) ◽  
pp. 919-927 ◽  
Author(s):  
A. Solonen ◽  
J. Hakkarainen ◽  
A. Ilin ◽  
M. Abbas ◽  
A. Bibov
Keyword(s):  
Covariance Matrix ◽  
Weather Prediction ◽  
Estimation Method ◽  
Model Error ◽  
Tuning Parameter ◽  
Extended Kalman Filtering ◽  
Error Covariance Matrix ◽  
Nonlinear Dynamical ◽  
Error Covariance

Abstract. The extended Kalman filter (EKF) is a popular state estimation method for nonlinear dynamical models. The model error covariance matrix is often seen as a tuning parameter in EKF, which is often simply postulated by the user. In this paper, we study the filter likelihood technique for estimating the parameters of the model error covariance matrix. The approach is based on computing the likelihood of the covariance matrix parameters using the filtering output. We show that (a) the importance of the model error covariance matrix calibration depends on the quality of the observations, and that (b) the estimation approach yields a well-tuned EKF in terms of the accuracy of the state estimates and model predictions. For our numerical experiments, we use the two-layer quasi-geostrophic model that is often used as a benchmark model for numerical weather prediction.

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.

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