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Journal articles on the topic 'Minimum norm estimation'

Author: Grafiati

Published: 14 April 2023

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1

Stein, Michael L. "Minimum Norm Quadratic Estimation of Spatial Variograms." Journal of the American Statistical Association 82, no. 399 (September 1987): 765–72. http://dx.doi.org/10.1080/01621459.1987.10478497.

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2

Kim, June Sic, Joo Man Han, Kwang Suk Park, and Chun Kee Chung. "Distribution-based minimum-norm estimation with multiple trials." Computers in Biology and Medicine 38, no. 11-12 (November 2008): 1203–10. http://dx.doi.org/10.1016/j.compbiomed.2008.09.004.

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3

Iwaki, S., and S. Ueno. "Minimum-Norm Source Estimation in MEG with Temporal Information." Journal of the Magnetics Society of Japan 22, no. 4_2 (1998): 773–76. http://dx.doi.org/10.3379/jmsjmag.22.773.

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4

Ermolaev, V. T., and A. B. Gershman. "Fast algorithm for minimum-norm direction-of-arrival estimation." IEEE Transactions on Signal Processing 42, no. 9 (1994): 2389–94. http://dx.doi.org/10.1109/78.317860.

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5

Xu, Peiliang. "The value of minimum norm estimation of geopotential fields." Geophysical Journal International 111, no. 1 (October 1992): 170–78. http://dx.doi.org/10.1111/j.1365-246x.1992.tb00563.x.

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6

Nov, Yuval, and Ori Davidov. "Minimum-norm estimation for a bi-exponential survival model." Statistics & Probability Letters 80, no. 7-8 (April 2010): 648–53. http://dx.doi.org/10.1016/j.spl.2009.12.022.

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7

Nenonen, J. T., M. S. Hämäläinen, and R. J. Iimoniemi. "Minimum-norm estimation in a boundary-element torso model." Medical & Biological Engineering & Computing 32, no. 1 (January 1994): 43–48. http://dx.doi.org/10.1007/bf02512477.

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8

Willis, A. J., R. de Mello Koch, and J. Nicolson. "Minimum norm target estimation algorithm for phased array radar." Electronics Letters 28, no. 4 (1992): 358. http://dx.doi.org/10.1049/el:19920224.

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9

Marshall, R. J., and K. V. Mardia. "Minimum norm quadratic estimation of components of spatial covariance." Journal of the International Association for Mathematical Geology 17, no. 5 (July 1985): 517–25. http://dx.doi.org/10.1007/bf01032106.

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10

Mardia, K. V. "Minimum norm quadratic estimation of components of spatial covariance." Mathematical Geology 18, no. 2 (February 1986): 267. http://dx.doi.org/10.1007/bf00898290.

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11

Chen*, Y. Q., Adam Chrzanowski, and M. Kavouras. "Assessment of observations using minimum norm quadratic unbiased estimation (minque)." CISM journal 44, no. 1 (April 1990): 39–46. http://dx.doi.org/10.1139/geomat-1990-0004.

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Estimation of the variances and covariances of observations in geodetic and engineering surveys of high precision is of great importance for proper weighting of the observations in their subsequent processing and for better understanding of sources of errors and their modeling. The authors have adopted from modern statistics the Minimum Norm Quadratic Unbiased Estimation (MINQUE) method for the variance-covariance component estimation. The method has successfully been implemented in modeling the error propagation in geodetic leveling, in determination of error components and weighting of measurements with the Global Positioning System, and in an assessment of a triangulateration network observed with different EDM instruments.

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12

Uchida, S., A. Tachikawa, K. Goto, K. Iramina, and S. Ueno. "Current Source Estimation in Rats with Coronary Occlusion by Minimum Norm Estimation." Journal of the Magnetics Society of Japan 25, no. 4−2 (2001): 1123–26. http://dx.doi.org/10.3379/jmsjmag.25.1123.

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13

Shi, Yi Ran, Yan Tao Tian, Lan Xiang Zhu, and Li Fei Deng. "The MUSIC Minimum Norm Method for Linear Polarized Array Parameter Estimation." Applied Mechanics and Materials 411-414 (September 2013): 1559–63. http://dx.doi.org/10.4028/www.scientific.net/amm.411-414.1559.

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This paper used signal Cyclostationarity and MUSIC minimum norm method to estimate DOA and polarization parameters with linear polarization array. Cyclostationarity statistics have the advantage of limiting different frequencies of signal cycle stationary colored noise and inhibit both the minimum norm loop correlation function and estimation error. This paper also verifies the effectiveness of the method through simulation experiments.

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14

Jiao, Huiping, Xiao Zhang, and Chao Wei. "$ L_{\infty} $-norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise." AIMS Mathematics 8, no. 1 (2023): 2083–92. http://dx.doi.org/10.3934/math.2023107.

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<abstract><p>This paper is concerned with $ L_{\infty} $-norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise. By applying the Gronwall-Bellman lemma, Chebyshev's inequality and Taylor's formula, the minimum distance estimator is established and the consistency and asymptotic distribution of the estimator are derived when a small dispersion coefficient $ \varepsilon\rightarrow 0 $.</p></abstract>

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15

Wu, Xiaoyong, Guohua Zou, and Jianwei Chen. "Unbiased invariant minimum norm estimation in generalized growth curve model." Journal of Multivariate Analysis 97, no. 8 (September 2006): 1718–41. http://dx.doi.org/10.1016/j.jmva.2006.05.007.

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16

Kleffe, Jürgen, and Ragnar Norberg. "MINIMUM NORM ESTIMATION OF VARIANCE COMPONENTS FOR LIFE INSURANCE DATA." Communications in Statistics - Theory and Methods 30, no. 8-9 (July 31, 2001): 1591–603. http://dx.doi.org/10.1081/sta-100105686.

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17

Gershman, A. B. "Direction-of-arrival estimation by using generalised minimum-norm approach." Electronics Letters 27, no. 16 (1991): 1485. http://dx.doi.org/10.1049/el:19910929.

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18

Pitkänen, Minna, Elisa Kallioniemi, Petro Julkunen, Maria Nazarova, Jaakko O. Nieminen, and Risto J. Ilmoniemi. "Minimum-Norm Estimation of Motor Representations in Navigated TMS Mappings." Brain Topography 30, no. 6 (July 18, 2017): 711–22. http://dx.doi.org/10.1007/s10548-017-0577-8.

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19

Kleffe, Jürgen, and Ragnar Norberg. "Minimum Norm Estimation Under Parameter Constraints with an Application to Insurance." Statistics 31, no. 3 (January 1998): 215–34. http://dx.doi.org/10.1080/02331889808802637.

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20

Ng, B. P. "Constraints for linear predictive and minimum-norm methods in bearing estimation." IEE Proceedings F Radar and Signal Processing 137, no. 3 (1990): 187. http://dx.doi.org/10.1049/ip-f-2.1990.0028.

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21

Omati, M., M. M. Omati, and M. H. Bastani. "BUILDING RECONSTRUCTION BASED ON A SMALL NUMBER OF TRACKS USING NONPARAMETRIC SAR TOMOGRAPHIC METHODS." ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences X-4/W1-2022 (January 14, 2023): 617–22. http://dx.doi.org/10.5194/isprs-annals-x-4-w1-2022-617-2023.

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Abstract. Nowadays, the synthetic aperture radar (SAR) tomography (TomoSAR) technique plays a notable role in the 3D reconstruction of urban buildings through several SAR acquisitions with slightly different positions. Nonparametric-based TomoSAR spectral estimation algorithms usually work well when a large number of SAR observations. In this study, with a limited number of SAR images, we have assessed the efficiency of the nonparametric spectral estimation methods, including maximum entropy (ME), singular value decomposition (SVD), linear prediction (LP), Capon, minimum norm (MN), and beamforming (BF) in the reconstruction of the third dimension of urban buildings. The experiments are conducted on both simulated and TerraSAR-X stripmap images to indicate the effectiveness of the LP proposed estimation algorithm. The analysis of the results proves that by minimizing the average output signal power over the antenna array elements, the LP spectral estimation achieves the discrimination of distinct scatterers inside an image pixel. In addition, this low computational estimator improves the sidelobe suppression and the height estimates of the scatterers in the complex multiple-scattering urban environment. Compared to SVD, maximum entropy, Capon, minimum norm, and beamforming, the height of the Eskan tower in Tehran, Iran, obtained with the LP technique, is considerably near to field-based measurement.

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22

Lau, C. K. E., R. S. Adve, and T. K. Sarkar. "Minimum norm mutual coupling compensation with applications in direction of arrival estimation." IEEE Transactions on Antennas and Propagation 52, no. 8 (August 2004): 2034–41. http://dx.doi.org/10.1109/tap.2004.832511.

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23

Konttila, Teijo, Ville Mäntynen, and Matti Stenroos. "Comparison of minimum-norm estimation and beamforming in electrocardiography with acute ischemia." Physiological Measurement 35, no. 4 (March 12, 2014): 623–38. http://dx.doi.org/10.1088/0967-3334/35/4/623.

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24

Pitkänen, Minna, Elisa Kallioniemi, Petro Julkunen, Maria Nazarova, Jaakko O. Nieminen, and Risto J. Ilmoniemi. "Erratum to: Minimum-Norm Estimation of Motor Representations in Navigated TMS Mappings." Brain Topography 30, no. 6 (September 6, 2017): 723. http://dx.doi.org/10.1007/s10548-017-0587-6.

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25

Hincapié, Ana-Sofía, Jan Kujala, Jérémie Mattout, Sebastien Daligault, Claude Delpuech, Domingo Mery, Diego Cosmelli, and Karim Jerbi. "MEG Connectivity and Power Detections with Minimum Norm Estimates Require Different Regularization Parameters." Computational Intelligence and Neuroscience 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/3979547.

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Minimum Norm Estimation (MNE) is an inverse solution method widely used to reconstruct the source time series that underlie magnetoencephalography (MEG) data. MNE addresses the ill-posed nature of MEG source estimation through regularization (e.g., Tikhonov regularization). Selecting the best regularization parameter is a critical step. Generally, once set, it is common practice to keep the same coefficient throughout a study. However, it is yet to be known whether the optimal lambda for spectral power analysis of MEG source data coincides with the optimal regularization for source-level oscillatory coupling analysis. We addressed this question via extensive Monte-Carlo simulations of MEG data, where we generated 21,600 configurations of pairs of coupled sources with varying sizes, signal-to-noise ratio (SNR), and coupling strengths. Then, we searched for the Tikhonov regularization coefficients (lambda) that maximize detection performance for (a) power and (b) coherence. For coherence, the optimal lambda was two orders of magnitude smaller than the best lambda for power. Moreover, we found that the spatial extent of the interacting sources and SNR, but not the extent of coupling, were the main parameters affecting the best choice for lambda. Our findings suggest using less regularization when measuring oscillatory coupling compared to power estimation.

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26

Zuo, Ming, Shuguo Xie, Xian Zhang, and Meiling Yang. "DOA Estimation Based on Weighted l1-norm Sparse Representation for Low SNR Scenarios." Sensors 21, no. 13 (July 5, 2021): 4614. http://dx.doi.org/10.3390/s21134614.

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In this paper, a weighted l1-norm is proposed in a l1-norm-based singular value decomposition (L1-SVD) algorithm, which can suppress spurious peaks and improve accuracy of direction of arrival (DOA) estimation for the low signal-to-noise (SNR) scenarios. The weighted matrix is determined by optimizing the orthogonality of subspace, and the weighted l1-norm is used as the minimum objective function to increase the signal sparsity. Thereby, the weighted matrix makes the l1-norm approximate the original l0-norm. Simulated results of orthogonal frequency division multiplexing (OFDM) signal demonstrate that the proposed algorithm has s narrower main lobe and lower side lobe with the characteristics of fewer snapshots and low sensitivity of misestimated signals, which can improve the resolution and accuracy of DOA estimation. Specifically, the proposed method exhibits a better performance than other works for the low SNR scenarios. Outdoor experimental results of OFDM signals show that the proposed algorithm is superior to other methods with a narrower main lobe and lower side lobe, which can be used for DOA estimation of UAV and pseudo base station.

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27

Xu, Keni, and Wenhong Liu. "Generalized Weighted Adaptive Time Delay Estimation Algorithm Based on Minimum Average P Norm." Journal of Electrical and Electronic Engineering 9, no. 5 (2021): 161. http://dx.doi.org/10.11648/j.jeee.20210905.13.

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28

Wang, J. Z. "Minimum-norm least-squares estimation: magnetic source images for a spherical model head." IEEE Transactions on Biomedical Engineering 40, no. 4 (April 1993): 387–96. http://dx.doi.org/10.1109/10.222331.

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29

Holm, Sverre. "On the relationship between minimum norm and linear prediction for spatial spectrum estimation." Signal Processing 85, no. 1 (January 2005): 227–30. http://dx.doi.org/10.1016/j.sigpro.2004.10.010.

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30

Huang, Sheng-Juan, and Guang-Hong Yang. "Fault Estimation for Fuzzy Delay Systems: A Minimum Norm Least Squares Solution Approach." IEEE Transactions on Cybernetics 47, no. 9 (September 2017): 2389–99. http://dx.doi.org/10.1109/tcyb.2016.2586968.

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31

Mukerjee, Rahul. "Optimality of balanced designs for minimum norm quadratic unbiased estimation of variance components." Metrika 37, no. 1 (December 1990): 181–88. http://dx.doi.org/10.1007/bf02613519.

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32

Garcia-Calva, Tomas A., Daniel Morinigo-Sotelo, Oscar Duque-Perez, Arturo Garcia-Perez, and Rene de J. Romero-Troncoso. "Time-Frequency Analysis Based on Minimum-Norm Spectral Estimation to Detect Induction Motor Faults." Energies 13, no. 16 (August 7, 2020): 4102. http://dx.doi.org/10.3390/en13164102.

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In this work, a new time-frequency tool based on minimum-norm spectral estimation is introduced for multiple fault detection in induction motors. Several diagnostic techniques are available to identify certain faults in induction machines; however, they generally give acceptable results only for machines operating under stationary conditions. Induction motors rarely operate under stationary conditions as they are constantly affected by load oscillations, speed waves, unbalanced voltages, and other external conditions. To overcome this issue, different time-frequency analysis techniques have been proposed for fault detection in induction motors under non-stationary regimes. However, most of them have low-resolution, low-accuracy or both. The proposed method employs the minimum-norm spectral estimation to provide high frequency resolution and accuracy in the time-frequency domain. This technique exploits the advantages of non-stationary conditions, where mechanical and electrical stresses in the machine are higher than in stationary conditions, improving the detectability of fault components. Numerical simulation and experimental results are provided to validate the effectiveness of the method in starting current analysis of induction motors.

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33

Suraci, Stefano S., Leonardo C. Oliveira, Ivandro Klein, and Ronaldo R. Goldschmidt. "Introducing covariances of observations in the minimum L1-norm, is it needed?" Journal of Geodetic Science 12, no. 1 (January 1, 2022): 65–74. http://dx.doi.org/10.1515/jogs-2022-0135.

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Abstract The most common approaches for assigning weights to observations in minimum L1-norm (ML1) is to introduce weights of p or p \sqrt{p} , p being the weights vector of observations given by the inverse of variances. Hence, they do not take covariances into consideration, being appropriated only to independent observations. To work around this limitation, methods for decorrelation/unit-weight reduction of observations originally developed in the context of least squares (LS) have been applied for ML1, although this adaptation still requires further investigations. In this article, we presented a deeper investigation into the mentioned adaptation and proposed the new ML1 expressions that introduce weights for both independent and correlated observations; and compared their results with the usual approaches that ignore covariances. Experiments were performed in a leveling network geometry by means of Monte Carlo simulations considering three different scenarios: independent observations, observations with “weak” correlations, and observations with “strong” correlations. The main conclusions are: (1) in ML1 adjustment of independent observations, adaptation of LS techniques introduces weights proportional to p \sqrt{p} (but not p); (2) proposed formulations allowed covariances to influence parameters estimation, which is unfeasible with usual ML1 formulations; (3) introducing weighs of p provided the closest ML1 parameters estimation compared to that of LS in networks free of outliers; (4) weighs of p \sqrt{p} provided the highest successful rate in outlier identification with ML1. Conclusions (3) and (4) imply that introducing covariances in ML1 may adversely affect its performance in these two practical applications.

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34

Shi, Yi Ran, Yan Tao Tian, Lan Xiang Zhu, and Li Fei Deng. "Cyclic Relation Method for DOA and Polarization Parameters Estimation of Arbitrary Polarized Array." Applied Mechanics and Materials 397-400 (September 2013): 2330–34. http://dx.doi.org/10.4028/www.scientific.net/amm.397-400.2330.

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Focus on the estimation for DOA and polarization parameters of electromagnetic sensor array, this paper proposes the method that uses cyclic relation function to substitute for covariance matrix. Because cyclic statistic is less sensitive to stable noise and any cyclic stable noise with different cyclic frequency, the method proposed is immune to any stable color noise. This method use minimum norm method to solve the spectrum function. So this method can restrict the effect of the cyclic relation matrix estimating error. Computer simulation experiments prove the performance of this method.

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35

Zhu, Jun, and Bruce S. Weir. "Mixed model approaches for diallel analysis based on a bio-model." Genetical Research 68, no. 3 (December 1996): 233–40. http://dx.doi.org/10.1017/s0016672300034200.

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SummaryA MINQUE(l) procedure, which is minimum norm quadratic unbiased estimation (MINQUE) method with 1 for all the prior values, is suggested for estimating variance and covariance components in a bio-model for diallel crosses. Unbiasedness and efficiency of estimation were compared for MINQUE(l), restricted maximum likelihood (REML) and MINQUE(θ) which has parameter values for the prior values. MINQUE(l) is almost as efficient as MINQUE(θ) for unbiased estimation of genetic variance and covariance components. The bio-model is efficient and robust for estimating variance and covariance components for maternal and paternal effects as well as for nuclear effects. A procedure of adjusted unbiased prediction (AUP) is proposed for predicting random genetic effects in the bio-model. The jack-knife procedure is suggested for estimation of sampling variances of estimated variance and covariance components and of predicted genetic effects. Worked examples are given for estimation of variance and covariance components and for prediction of genetic merits.

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36

Niu, Chao, Yongshun Zhang, and Jianrong Guo. "Low angle estimation in diffuse multipath environment by time‐reversal minimum‐norm‐like technique." IET Radar, Sonar & Navigation 11, no. 10 (October 2017): 1483–87. http://dx.doi.org/10.1049/iet-rsn.2017.0015.

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37

Nikolaevskaya, E. A., and A. N. Khimich. "Error estimation for a weighted minimum-norm least squares solution with positive definite weights." Computational Mathematics and Mathematical Physics 49, no. 3 (March 2009): 409–17. http://dx.doi.org/10.1134/s0965542509030038.

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38

Shi, Fangquan, Lianjie Shu, Aijun Yang, and Fangyi He. "Improving Minimum-Variance Portfolios by Alleviating Overdispersion of Eigenvalues." Journal of Financial and Quantitative Analysis 55, no. 8 (October 24, 2019): 2700–2731. http://dx.doi.org/10.1017/s0022109019000899.

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In portfolio risk minimization, the inverse covariance matrix of returns is often unknown and has to be estimated in practice. Yet the eigenvalues of the sample covariance matrix are often overdispersed, leading to severe estimation errors in the inverse covariance matrix. To deal with this problem, we propose a general framework by shrinking the sample eigenvalues based on the Schatten norm. The proposed framework has the advantage of being computationally efficient as well as structure-free. The comparative studies show that our approach behaves reasonably well in terms of reducing out-of-sample portfolio risk and turnover.

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39

Uchida, S., K. Iramina, K. Goto, and S. Ueno. "A comparison of iterative minimum norm estimation and current dipole estimation for magnetic field measurements from small animals." IEEE Transactions on Magnetics 36, no. 5 (2000): 3724–26. http://dx.doi.org/10.1109/20.908953.

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40

Zhu, Lan Xiang, Yao Wu Shi, Yi Ran Shi, and Li Fei Deng. "Using Single-Cycle-Related Electromagnetic Vector Sensors to Estimation DOA and Polarization Parameters." Advanced Materials Research 684 (April 2013): 424–28. http://dx.doi.org/10.4028/www.scientific.net/amr.684.424.

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This paper proposes a new algorithm for joint estimation of Directions-Of-Arrival (DOA’s) and polarization parameters of the single electromagnetic vector sensor. Based on the cyclostationary properties of the signal,the algorithm uses minimum norm method to strike the signal steering vector solution, and then gets the estimation of DOA and polarization parameters. Besides limiting the distribution of additional stationary noise and interference signals on various frequencies, this algorithm also restraints the estimation error of the noise subspace singular vector with outstanding results. Computer simulation verified the effectiveness of the algorithm.

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41

Keele, J. W., and W. R. Harvey. "Estimation of Components of Variance and Covariance by Symmetric Differences Squared and Minimum Norm Quadratic Unbiased Estimation: a Comparison." Journal of Animal Science 67, no. 2 (1989): 348. http://dx.doi.org/10.2527/jas1989.672348x.

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42

Yaesh, I., and U. Shaked. "Game theory approach to optimal linear state estimation and its relation to the minimum H/sub infinity /-norm estimation." IEEE Transactions on Automatic Control 37, no. 6 (June 1992): 828–31. http://dx.doi.org/10.1109/9.256343.

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43

Liu, Ming-Ming, Chun-Xi Dong, Yang-Yang Dong, and Guo-Qing Zhao. "Superresolution 2D DOA Estimation for a Rectangular Array via Reweighted Decoupled Atomic Norm Minimization." Mathematical Problems in Engineering 2019 (July 8, 2019): 1–13. http://dx.doi.org/10.1155/2019/6797168.

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This paper proposes a superresolution two-dimensional (2D) direction of arrival (DOA) estimation algorithm for a rectangular array based on the optimization of the atomic l0 norm and a series of relaxation formulations. The atomic l0 norm of the array response describes the minimum number of sources, which is derived from the atomic norm minimization (ANM) problem. However, the resolution is restricted and high computational complexity is incurred by using ANM for 2D angle estimation. Although an improved algorithm named decoupled atomic norm minimization (DAM) has a reduced computational burden, the resolution is still relatively low in terms of angle estimation. To overcome these limitations, we propose the direct minimization of the atomic l0 norm, which is demonstrated to be equivalent to a decoupled rank optimization problem in the positive semidefinite (PSD) form. Our goal is to solve this rank minimization problem and recover two decoupled Toeplitz matrices in which the azimuth-elevation angles of interest are encoded. Since rank minimization is an NP-hard problem, a novel sparse surrogate function is further proposed to effectively approximate the two decoupled rank functions. Then, the new optimization problem obtained through the above relaxation can be implemented via the majorization-minimization (MM) method. The proposed algorithm offers greatly improved resolution while maintaining the same computational complexity as the DAM algorithm. Moreover, it is possible to use a single snapshot for angle estimation without prior information on the number of sources, and the algorithm is robust to noise due to its iterative nature. In addition, the proposed surrogate function can achieve local convergence faster than existing functions.

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44

Reijonen, Jusa, Laura Saisanen, Minna Pitkanen, Meri Julkunen, Risto J. Ilmoniemi, Petteri Nieminen, and Petro Julkunen. "Minimum-Norm Estimation of TMS-Activated Motor Cortical Sites in Realistic Head and Brain Geometry." IEEE Transactions on Neural Systems and Rehabilitation Engineering 30 (2022): 441–54. http://dx.doi.org/10.1109/tnsre.2022.3151678.

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45

Xu, Fangwei, Chuan Wang, Qin Shu, Zhiquan Ma, Hongru Zheng, and Anqing Peng. "Study on the Estimation of Utility Harmonic Impedance Based on Minimum Norm of Impedance Difference." IEEE Access 8 (2020): 207389–96. http://dx.doi.org/10.1109/access.2020.3033388.

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46

Iwaki, Sunao, and Shoogo Ueno. "Weighted minimum-norm source estimation of magnetoencephalography utilizing the temporal information of the measured data." Journal of Applied Physics 83, no. 11 (June 1998): 6441–43. http://dx.doi.org/10.1063/1.367732.

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47

Bücker, H. Martin, and Roland Beucker. "Using automatic differentiation for the solution of the minimum p-norm estimation problem in magnetoencephalography." Simulation Modelling Practice and Theory 12, no. 2 (May 2004): 105–16. http://dx.doi.org/10.1016/j.simpat.2003.11.004.

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48

Stenroos, Matti, and Olaf Hauk. "Minimum-norm cortical source estimation in layered head models is robust against skull conductivity error." NeuroImage 81 (November 2013): 265–72. http://dx.doi.org/10.1016/j.neuroimage.2013.04.086.

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49

Molins, A., S. M. Stufflebeam, E. N. Brown, and M. S. Hämäläinen. "Quantification of the benefit from integrating MEG and EEG data in minimum ℓ2-norm estimation." NeuroImage 42, no. 3 (September 2008): 1069–77. http://dx.doi.org/10.1016/j.neuroimage.2008.05.064.

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50

Wang, Bao Feng. "Robust Estimation for Discrete Time-Varying Uncertain Systems with Observation Losses in Networked Control System." Applied Mechanics and Materials 336-338 (July 2013): 628–32. http://dx.doi.org/10.4028/www.scientific.net/amm.336-338.628.

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In this paper, we deal with the robust minimum variance filtering problem for discrete time-varying systems with observation losses. The system under consideration is subjected to time-varying norm-bounded parameter uncertainties in both the state and output matrices, and the observation losses are described by a Bernoulli process with a known probability. An upper bound on the variance of the state estimation error is first found under certain probability of missing observations and admissible parameter uncertainties. Then, a robust filter is derived by minimizing the prescribed upper bound in the sense of the matrix norm. It is shown that the desired filter can be obtained in terms of the solutions to two discrete Riccati difference equations.

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