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Journal articles on the topic 'Multiparameter estimation'

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Published: 2 March 2024

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1

Miyazaki, Jisho, and Keiji Matsumoto. "Imaginarity-free quantum multiparameter estimation." Quantum 6 (March 10, 2022): 665. http://dx.doi.org/10.22331/q-2022-03-10-665.

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Multiparameter quantum estimation is made difficult by the following three obstacles. First, incompatibility among different physical quantities poses a limit on the attainable precision. Second, the ultimate precision is not saturated until you discover the optimal measurement. Third, the optimal measurement may generally depend on the target values of parameters, and thus may be impossible to perform for unknown target states. We present a method to circumvent these three obstacles. A class of quantum statistical models, which utilizes antiunitary symmetries or, equivalently, real density matrices, offers compatible multiparameter estimations. The symmetries accompany the target-independent optimal measurements for pure-state models. Based on this finding, we propose methods to implement antiunitary symmetries for quantum metrology schemes. We further introduce a function which measures antiunitary asymmetry of quantum statistical models as a potential tool to characterize quantumness of phase transitions.

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2

Jensen, D. R. "Vector efficiency in multiparameter estimation." Linear Algebra and its Applications 151 (June 1991): 143–55. http://dx.doi.org/10.1016/0024-3795(91)90360-9.

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3

Alam, Khursheed, and Amitava Mitra. "Component risk in multiparameter estimation." Annals of the Institute of Statistical Mathematics 38, no. 3 (December 1986): 399–410. http://dx.doi.org/10.1007/bf02482526.

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4

Datta, Animesh, Rafał Demkowicz-Dobrzański, and Jing Liu. "Quantum multiparameter estimation and metrology—preface." Journal of Physics A: Mathematical and Theoretical 54, no. 46 (October 26, 2021): 460301. http://dx.doi.org/10.1088/1751-8121/ac0d6b.

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5

Kragten, J., P. C. de Jagher, and L. G. Decnop-Weever. "Non-linear multiparameter estimation in spectrophotometry." Analytica Chimica Acta 180 (1986): 457–72. http://dx.doi.org/10.1016/0003-2670(86)80025-3.

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6

Gorgucci, Eugenio, V. Chandrasekar, and Gianfranco Scarchilli. "Radar and Surface Measurement of Rainfall during CaPE: 26 July 1991 Case Study." Journal of Applied Meteorology 34, no. 7 (July 1, 1995): 1570–77. http://dx.doi.org/10.1175/1520-0450-34.7.1570.

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Abstract Conventional usage of multiparameter radar measurements for rainfall estimation has been associated with tracking the variability of the raindrop size distribution. The use of multiparameter radar measurements in a statistical framework to estimate rainfall is presented in this paper. The techniques developed in this paper are applied to the radar and rain gauge measurement of rainfall observed on 26 July 1991, during the Convection and Precipitation Electrification program. Conventional pointwise estimates of rainfall are also compared. The probability matching procedure, when applied to the radar and surface measurements shows that multiparameter radar algorithms can match the probability distribution functions better than the reflectivity based algorithms, thereby indicating the potential of multiparameter radar measurements for statistical approach to rainfall estimation.

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Cimini, Valeria, Ludovica Ruggiero, Ilaria Gianani, Marco Sbroscia, Tecla Gasperi, Emanuele Roccia, Luca Mancino, et al. "Multiparameter Approach to Dynamic Quantum Phase Estimation." Proceedings 12, no. 1 (December 4, 2019): 55. http://dx.doi.org/10.3390/proceedings2019012055.

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We have applied techniques of quantum phase estimation to the dynamical tracking of the optical activity of a solution of sucrose undergoing acid hydrolysis. We adopt a multiparameter approach that makes the estimation reliable and robust against setup instabilities.

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8

Gianani, Ilaria, and Claudia Benedetti. "Multiparameter estimation of continuous-time quantum walk Hamiltonians through machine learning." AVS Quantum Science 5, no. 1 (March 2023): 014405. http://dx.doi.org/10.1116/5.0137398.

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The characterization of the Hamiltonian parameters defining a quantum walk is of paramount importance when performing a variety of tasks, from quantum communication to computation. When dealing with physical implementations of quantum walks, the parameters themselves may not be directly accessible, and, thus, it is necessary to find alternative estimation strategies exploiting other observables. Here, we perform the multiparameter estimation of the Hamiltonian parameters characterizing a continuous-time quantum walk over a line graph with n-neighbor interactions using a deep neural network model fed with experimental probabilities at a given evolution time. We compare our results with the bounds derived from estimation theory and find that the neural network acts as a nearly optimal estimator both when the estimation of two or three parameters is performed.

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Liu, Jing, Haidong Yuan, Xiao-Ming Lu, and Xiaoguang Wang. "Quantum Fisher information matrix and multiparameter estimation." Journal of Physics A: Mathematical and Theoretical 53, no. 2 (December 18, 2019): 023001. http://dx.doi.org/10.1088/1751-8121/ab5d4d.

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10

Karlen, Walter, S. Raman, J. M. Ansermino, and G. A. Dumont. "Multiparameter Respiratory Rate Estimation From the Photoplethysmogram." IEEE Transactions on Biomedical Engineering 60, no. 7 (July 2013): 1946–53. http://dx.doi.org/10.1109/tbme.2013.2246160.

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11

Cheng, Ming-Yen, Wenyang Zhang, and Lu-Hung Chen. "Statistical Estimation in Generalized Multiparameter Likelihood Models." Journal of the American Statistical Association 104, no. 487 (September 2009): 1179–91. http://dx.doi.org/10.1198/jasa.2009.tm08430.

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12

Lin, Jin-Guan, Kong-Sheng Zhang, and Yan-Yong Zhao. "Nonparametric estimation of multivariate multiparameter conditional copulas." Journal of the Korean Statistical Society 46, no. 1 (March 2017): 126–36. http://dx.doi.org/10.1016/j.jkss.2016.08.003.

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13

Aerts, Marc, and Gerda Claeskens. "Local Polynomial Estimation in Multiparameter Likelihood Models." Journal of the American Statistical Association 92, no. 440 (December 1997): 1536–45. http://dx.doi.org/10.1080/01621459.1997.10473675.

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14

Pan, Wenyong, Kristopher A. Innanen, Gary F. Margrave, Michael C. Fehler, Xinding Fang, and Junxiao Li. "Estimation of elastic constants for HTI media using Gauss-Newton and full-Newton multiparameter full-waveform inversion." GEOPHYSICS 81, no. 5 (September 2016): R275—R291. http://dx.doi.org/10.1190/geo2015-0594.1.

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In seismic full-waveform inversion (FWI), subsurface parameters are estimated by iteratively minimizing the difference between the modeled and the observed data. We have considered the problem of estimating the elastic constants of a fractured medium using multiparameter FWI and modeling naturally fractured reservoirs as equivalent anisotropic media. Multiparameter FWI, although promising, remains exposed to a range of challenges, one being the parameter crosstalk problem resulting from the overlap of Fréchet derivative wavefields. Parameter crosstalk is strongly influenced by the form of the scattering pattern for each parameter. We have derived 3D radiation patterns associated with scattering from a range of elastic constants in general anisotropic media. Then, we developed scattering patterns specific to a horizontal transverse isotropic (HTI) medium to draw conclusions about parameter crosstalk in FWI. Bare gradients exhibit crosstalk, as well as artifacts caused by doubly scattered energy in the data residuals. The role of the multiparameter Gauss-Newton (GN) Hessian in suppressing parameter crosstalk is revealed. We have found that the second-order term in the multiparameter Hessian, which is associated with multiparameter second-order scattering effects, can be constructed with the adjoint-state technique. We have examined the analytic scattering patterns for HTI media with a 2D numerical example. We have examined the roles played by the first- and second-order terms in multiparameter Hessian to suppress parameter crosstalk and second-order scattering artifacts numerically. We have also compared the multiparameter GN and full-Newton methods as methods for determining the elastic constants in HTI media with a two-block-layer model.

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15

Conlon, Lorcán O., Ping Koy Lam, and Syed M. Assad. "Multiparameter Estimation with Two-Qubit Probes in Noisy Channels." Entropy 25, no. 8 (July 26, 2023): 1122. http://dx.doi.org/10.3390/e25081122.

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This work compares the performance of single- and two-qubit probes for estimating several phase rotations simultaneously under the action of different noisy channels. We compute the quantum limits for this simultaneous estimation using collective and individual measurements by evaluating the Holevo and Nagaoka–Hayashi Cramér-Rao bounds, respectively. Several quantum noise channels are considered, namely the decohering channel, the amplitude damping channel, and the phase damping channel. For each channel, we find the optimal single- and two-qubit probes. Where possible we demonstrate an explicit measurement strategy that saturates the appropriate bound and we investigate how closely the Holevo bound can be approached through collective measurements on multiple copies of the same probe. We find that under the action of the considered channels, two-qubit probes show enhanced parameter estimation capabilities over single-qubit probes for almost all non-identity channels, i.e., the achievable precision with a single-qubit probe degrades faster with increasing exposure to the noisy environment than that of the two-qubit probe. However, in sufficiently noisy channels, we show that it is possible for single-qubit probes to outperform maximally entangled two-qubit probes. This work shows that, in order to reach the ultimate precision limits allowed by quantum mechanics, entanglement is required in both the state preparation and state measurement stages. It is hoped the tutorial-esque nature of this paper will make it easily accessible.

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16

D’Aurelio, Simone Evaldo, Mauro Valeri, Emanuele Polino, Valeria Cimini, Ilaria Gianani, Marco Barbieri, Giacomo Corrielli, et al. "Experimental investigation of Bayesian bounds in multiparameter estimation." Quantum Science and Technology 7, no. 2 (March 7, 2022): 025011. http://dx.doi.org/10.1088/2058-9565/ac5124.

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Abstract Quantum parameter estimation offers solid conceptual grounds for the design of sensors enjoying quantum advantage. This is realised not only by means of hardware supporting and exploiting quantum properties, but data analysis has its impact and relevance, too. In this respect, Bayesian methods have emerged as an effective and elegant solution, with the perk of incorporating naturally the availability of a priori information. In this article we present an evaluation of Bayesian methods for multiple phase estimation, assessed based on bounds that work beyond the usual limit of large samples assumed in parameter estimation. Importantly, such methods are applied to experimental data generated from the output statistics of a three-arm interferometer seeded by single photons. Our studies provide a blueprint for a more comprehensive data analysis in quantum metrology.

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17

Shi, Hanyu, Zhiqiang Xiao, Qian Wang, and Dongxing Wu. "Multiparameter Estimation From Landsat Observations With Topographic Consideration." IEEE Transactions on Geoscience and Remote Sensing 59, no. 9 (September 2021): 7353–69. http://dx.doi.org/10.1109/tgrs.2021.3057377.

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18

Kull, Ilya, Philippe Allard Guérin, and Frank Verstraete. "Uncertainty and trade-offs in quantum multiparameter estimation." Journal of Physics A: Mathematical and Theoretical 53, no. 24 (June 1, 2020): 244001. http://dx.doi.org/10.1088/1751-8121/ab7f67.

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19

Bakmou, Lahcen, Mohammed Daoud, and Rachid ahl laamara. "Multiparameter quantum estimation theory in quantum Gaussian states." Journal of Physics A: Mathematical and Theoretical 53, no. 38 (August 26, 2020): 385301. http://dx.doi.org/10.1088/1751-8121/aba770.

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Roccia, Emanuele, Ilaria Gianani, Luca Mancino, Marco Sbroscia, Fabrizia Somma, Marco G. Genoni, and Marco Barbieri. "Entangling measurements for multiparameter estimation with two qubits." Quantum Science and Technology 3, no. 1 (November 1, 2017): 01LT01. http://dx.doi.org/10.1088/2058-9565/aa9212.

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21

Ghosh, Dibakar. "Nonlinear-observer–based synchronization scheme for multiparameter estimation." EPL (Europhysics Letters) 84, no. 4 (November 2008): 40012. http://dx.doi.org/10.1209/0295-5075/84/40012.

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22

Speiser, Bernd. "Multiparameter estimation: extraction of information from cyclic voltammograms." Analytical Chemistry 57, no. 7 (June 1985): 1390–97. http://dx.doi.org/10.1021/ac00284a047.

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23

Chrostowski, Andrzej, Rafał Demkowicz-Dobrzański, Marcin Jarzyna, and Konrad Banaszek. "On super-resolution imaging as a multiparameter estimation problem." International Journal of Quantum Information 15, no. 08 (December 2017): 1740005. http://dx.doi.org/10.1142/s0219749917400056.

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We consider the problem of characterizing the spatial extent of a composite light source using the super-resolution imaging technique based on mode demultiplexing when the centroid of the source is not known precisely. We show that the essential features of this problem can be mapped onto a simple qubit model for joint estimation of a phase shift and a dephasing strength.

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24

Sinha, Swati, Tummalapalli Venkata Chandrasekhar Sarma, and Mary Lourde Regeena. "Estimation of Doppler Profile Using Multiparameter Cost Function Method." IEEE Transactions on Geoscience and Remote Sensing 55, no. 2 (February 2017): 932–42. http://dx.doi.org/10.1109/tgrs.2016.2616918.

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25

Roccia, Emanuele, Valeria Cimini, Marco Sbroscia, Ilaria Gianani, Ludovica Ruggiero, Luca Mancino, Marco G. Genoni, Maria Antonietta Ricci, and Marco Barbieri. "Multiparameter approach to quantum phase estimation with limited visibility." Optica 5, no. 10 (September 24, 2018): 1171. http://dx.doi.org/10.1364/optica.5.001171.

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26

Elhaj, Alaref, Mohamad Alzayed, and Hicham Chaoui. "Multiparameter Estimation-Based Sensorless Adaptive Direct Voltage MTPA Control for IPMSM Using Fuzzy Logic MRAS." Machines 11, no. 9 (August 28, 2023): 861. http://dx.doi.org/10.3390/machines11090861.

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This paper introduces a parameter-estimation-based sensorless adaptive direct voltage maximum torque per ampere (MTPA) control strategy for interior permanent magnet synchronous machines (IPMSMs). In direct voltage control, the motor’s electrical parameters, speed, and rotor position are of great significance. Thus, any mismatch in these parameters or failure to acquire accurate speed or position information leads to a significant deviation in the MTPA trajectory, causing high current consumption and hence affecting the performance of the entire control system. In view of this problem, a fuzzy logic control-based cascaded model reference adaptive system (FLC-MRAS) is introduced to mitigate the effect of parameter variation on the tracking of the MTPA trajectory and to provide precise information about the rotor speed and position. The cascaded scheme consists of two parallel FLC-MRAS for speed and multiparameter estimation. The first MRAS is utilized to estimate motor speed and rotor position to achieve robust sensorless control. However, the speed estimator is highly dependent on time-varying motor parameters. Therefore, the second MRAS is designed to identify the quadratic inductance and permanent magnet flux and continuously update both the speed estimator and control scheme with the identified values to ensure accurate speed estimation and real-time MTPA trajectory tracking. Unlike conventional MRAS, which uses linear proportional-integral controllers (PI-MRAS), an FLC is adopted to replace the PI controllers, ensuring high estimation accuracy and enhancing the robustness of the control system against sudden changes in working conditions. The effectiveness of the proposed scheme is evaluated under different speed and torque conditions. Furthermore, a comparison against the conventional PI-MRAS is extensively investigated to highlight the superiority of the proposed scheme. The evaluation results and our quantitative assessment show the ability of the designed strategy to achieve high estimation accuracy, less oscillation, and a faster convergence rate under different working conditions. The quantitative assessment reveals that the FLC-MRAS can improve the estimation accuracy of speed, permanent magnet flux, and quadratic inductance by 19%, 55.8% and 44.55%, respectively.

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Razavian, Sholeh, Matteo G. A. Paris, and Marco G. Genoni. "On the Quantumness of Multiparameter Estimation Problems for Qubit Systems." Entropy 22, no. 11 (October 23, 2020): 1197. http://dx.doi.org/10.3390/e22111197.

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The estimation of more than one parameter in quantum mechanics is a fundamental problem with relevant practical applications. In fact, the ultimate limits in the achievable estimation precision are ultimately linked with the non-commutativity of different observables, a peculiar property of quantum mechanics. We here consider several estimation problems for qubit systems and evaluate the corresponding quantumnessR, a measure that has been recently introduced in order to quantify how incompatible the parameters to be estimated are. In particular, R is an upper bound for the renormalized difference between the (asymptotically achievable) Holevo bound and the SLD Cramér-Rao bound (i.e., the matrix generalization of the single-parameter quantum Cramér-Rao bound). For all the estimation problems considered, we evaluate the quantumness R and, in order to better understand its usefulness in characterizing a multiparameter quantum statistical model, we compare it with the renormalized difference between the Holevo and the SLD-bound. Our results give evidence that R is a useful quantity to characterize multiparameter estimation problems, as for several quantum statistical model, it is equal to the difference between the bounds and, in general, their behavior qualitatively coincide. On the other hand, we also find evidence that, for certain quantum statistical models, the bound is not in tight, and thus R may overestimate the degree of quantum incompatibility between parameters.

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Koch, Brandon, David M. Vock, Julian Wolfson, and Laura Boehm Vock. "Variable selection and estimation in causal inference using Bayesian spike and slab priors." Statistical Methods in Medical Research 29, no. 9 (January 15, 2020): 2445–69. http://dx.doi.org/10.1177/0962280219898497.

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Unbiased estimation of causal effects with observational data requires adjustment for confounding variables that are related to both the outcome and treatment assignment. Standard variable selection techniques aim to maximize predictive ability of the outcome model, but they ignore covariate associations with treatment and may not adjust for important confounders weakly associated to outcome. We propose a novel method for estimating causal effects that simultaneously considers models for both outcome and treatment, which we call the bilevel spike and slab causal estimator (BSSCE). By using a Bayesian formulation, BSSCE estimates the posterior distribution of all model parameters and provides straightforward and reliable inference. Spike and slab priors are used on each covariate coefficient which aim to minimize the mean squared error of the treatment effect estimator. Theoretical properties of the treatment effect estimator are derived justifying the prior used in BSSCE. Simulations show that BSSCE can substantially reduce mean squared error over numerous methods and performs especially well with large numbers of covariates, including situations where the number of covariates is greater than the sample size. We illustrate BSSCE by estimating the causal effect of vasoactive therapy vs. fluid resuscitation on hypotensive episode length for patients in the Multiparameter Intelligent Monitoring in Intensive Care III critical care database.

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29

Zhu, Beizuo, Weiyang Chen, and Luo Chen. "Electromagnetic Vector Sparse Nested Array: Array Structure Design, Off-Grid Parameter Estimation Algorithm." Mathematical Problems in Engineering 2021 (March 26, 2021): 1–14. http://dx.doi.org/10.1155/2021/5525221.

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In this paper, a new array structure of sparse nested array (SNA) for electromagnetic vector sensor is designed. An electromagnetic vector sensor is composed of six spatially colocated, orthogonally oriented, diversely polarized antennas, which can measure three-dimensional electric and magnetic field components. By introducing sparse factor (SF) between every adjacent sensor, the proposed SNA has flexibility of extending the array aperture and reducing the mutual coupling effect. Meanwhile, a low-complexity multiparameter estimation algorithm is proposed for SNA. First, the vectorization operation for array manifold ensures the large degrees of freedom for multiparameter estimation, where the initial coarse estimates decrease search range. In addition, the improved off-grid orthogonal matching pursuit method obtains joint direction of arrival (DOA) and polarization estimates with a relatively small overcomplete dictionary because this off-grid method achieves high performance even if the estimates do not fall on the grid of the dictionary. Theoretical analysis and simulation results verify the superiority of the proposed array structure and the algorithm.

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30

Katariya, Vishal, and Mark M. Wilde. "RLD Fisher information bound for multiparameter estimation of quantum channels." New Journal of Physics 23, no. 7 (July 1, 2021): 073040. http://dx.doi.org/10.1088/1367-2630/ac1186.

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31

Ghosh, Dibakar, and Bidyut K. Bhattacharyya. "Generalized synchronization-based multiparameter estimation in modulated time-delayed systems." AIP Advances 1, no. 3 (September 2011): 032144. http://dx.doi.org/10.1063/1.3631773.

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32

Warsza, Zygmunt, and Jacek Puchalski. "Matrix Estimation of Uncertainty of Indirect Multiparameter Measurements with Examples." Pomiary Automatyka Robotyka 22, no. 2 (June 30, 2018): 31–39. http://dx.doi.org/10.14313/par_228/31.

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33

Küchler, Uwe, and Vyacheslav A. Vasiliev. "On guaranteed parameter estimation of a multiparameter linear regression process." Automatica 46, no. 4 (April 2010): 637–46. http://dx.doi.org/10.1016/j.automatica.2010.01.003.

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34

Liu, Chao, and Feiyang Zhou. "A Mutiparameter Joint Estimation Algorithm for Dual-Polarized Cylindrical Conformal Array in the Presence of Mutual Coupling." International Journal of Antennas and Propagation 2022 (February 8, 2022): 1–12. http://dx.doi.org/10.1155/2022/7321449.

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In this article, we proposed a multiparameter joint estimation algorithm based on the dual-polarized cylindrical conformal array (DCCA) in the presence of mutual coupling. Using the characteristic of the dual-polarized cylindrical conformal array, 2D direction-of-arrival (DOA) estimation can be divided into 1D estimations of elevation and azimuth. Sensors on the boundary of the DCCA are set as auxiliary sensors to eliminate the influence of mutual coupling. Then, elevation can be estimated by the generalized eigenvalues utilizing signal subspace eigenvectors (GEESE). After that, polarization sensitivity can be eliminated by projection transformation and the proposed dual-polarized forward-backward smoothing algorithm. Consequently, a dual-polarized spatial spectrum can be developed to estimate the azimuth based on the estimated elevation. Furthermore, the angles of the signals can be reestimated to improve the accuracy of DOA estimation. Simulation results confirm the effectiveness of the proposed algorithm.

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35

Dupuy, Bastien, Stéphane Garambois, Amir Asnaashari, Hadi M. Balhareth, Martin Landrø, Alexey Stovas, and Jean Virieux. "Estimation of rock physics properties from seismic attributes — Part 2: Applications." GEOPHYSICS 81, no. 4 (July 2016): M55—M69. http://dx.doi.org/10.1190/geo2015-0492.1.

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The estimation of quantitative rock physics properties is of great importance for reservoir characterization and monitoring in [Formula: see text] storage or enhanced oil recovery as an example. We have combined the high-resolution results of full-waveform inversion (FWI) methods with rock physics inversion. Because we consider a generic and dynamic rock physics model, our method is applicable to most kinds of rocks for a wide range of frequencies. The first step allows determination of viscoelastic effective properties, i.e., quantitative seismic attributes, whereas the rock physics inversion estimates rock physics properties (porosity, solid frame moduli, fluid phase properties, or saturation). This two-step workflow is applied to time-lapse synthetic and field cases. The sensitivity tests that we had previously carried out showed that it can be crucial to use multiparameter inputs to accurately recover fluid saturations and fluid properties. However, due to the limited data availability and difficulties in getting reliable multiparameter FWI results, we are limited to acoustic FWI results. The synthetic tests are conclusive even if they are favorable cases. For the first time-lapse fluid substitution synthetic case, we first characterize the rock frame parameters on the baseline model using P-wave velocity estimations obtained by acoustic FWI. Then, we obtain an accurate estimation of fluid bulk modulus from the time-lapse P-wave velocity. In the Marmousi synthetic case, the rock frame properties are accurately recovered for the baseline model, whereas the gas saturation change in the monitor model is not estimated correctly. On the field data example (time-lapse monitoring of an underground blowout in the North Sea), the estimation of rock frame properties gives results on a relatively narrow range, and we use this estimation as a starting model for the gas saturation inversion. We have found that the estimation of the gas saturation is not accurate enough, and the use of attenuation data is then required. However, the uncertainty on the estimation of baseline rock frame properties is not critical to monitor gas saturation changes.

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Kivanc, Omer Cihan, and Salih Baris Ozturk. "Sensorless PMSM Drive Based on Stator Feedforward Voltage Estimation Improved With MRAS Multiparameter Estimation." IEEE/ASME Transactions on Mechatronics 23, no. 3 (June 2018): 1326–37. http://dx.doi.org/10.1109/tmech.2018.2817246.

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Len, Yink Loong. "Multiparameter estimation for qubit states with collective measurements: a case study." New Journal of Physics 24, no. 3 (March 1, 2022): 033037. http://dx.doi.org/10.1088/1367-2630/ac599d.

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Abstract Quantum estimation involving multiple parameters remains an important problem of both theoretical and practical interest. In this work, we study the problem of simultaneous estimation of two parameters that are respectively associate with the length and direction of the Bloch vector for identically prepared qubit states that is confined to a plane, where in order to obtain the optimal estimation precision for both parameters, collective measurements on multiple qubits are necessary. Upon treating N qubits as an ensemble of spin-1/2 systems, we show that simultaneous optimal estimation for both parameters can be attained asymptotically with a simple collective measurement strategy—first, we estimate the length parameter by measuring the populations in spaces corresponding to different total angular momentum values j, then we estimate the direction parameter by performing a spin projection onto an optimal basis. Furthermore, we show that when the state is nearly pure, for sufficiently but not arbitrarily large N, most information will be captured in the largest three j-subspaces. Then, we study how the total angular-momentum measurement can be realized by observing output signatures from a Bell multiport setup, either exactly for N = 2, 3, or approximately when the qubits are nearly pure for other N values. We also obtain numerical results that suggest that using a Bell multiport setup, one can distinguish between projection onto the j = N/2 and j = N/2 − 1 subspaces from their respective interference signatures at the output.

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Cheng, Xin, Kun Jiao, Dong Sun, and Denes Vigh. "Multiparameter estimation with acoustic vertical transverse isotropic full-waveform inversion of surface seismic data." Interpretation 4, no. 4 (November 1, 2016): SU1—SU16. http://dx.doi.org/10.1190/int-2016-0029.1.

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Obtaining accurate depth-migrated images demands an anisotropic representation of the earth. As a prominent tool for building high-resolution earth models, full-waveform inversion (FWI) therefore must not only account for anisotropy during wavefield simulation but also reconstruct the anisotropy fields. We have developed an inversion strategy to perform acoustic multiparameter FWI of surface seismic data in transversely isotropic media with a vertical axis of symmetry (VTI). During the early era of FWI practice, most studies only invert for the most dominant parameter, that is, the vertical velocity, and the rest of the model parameters are either ignored or kept constant. Recently, more and more emphases focus on inverting for more parameters, such as for the vertical velocity and the anisotropy fields; these are referred to as multiparameter inversion. Due to the dominant influence of the vertical velocity on the kinematics of surface seismic data, we have developed a hierarchical approach to invert for the vertical velocity first, but we kept the anisotropy fields unchanged and only switched to joint inversion of the vertical velocity and the anisotropy fields when the inversion for the vertical velocity approaches convergence. In addition, we have illustrated the necessity of incorporating the diving and reflection energy during inversion to mitigate the nonuniqueness of the solutions caused by the coupling between the vertical velocity and the anisotropy fields. We also demonstrate the success of our method for VTI FWI using synthetic and real data examples based on marine surface seismic acquisition. Our results show that incorporation of multiparameter anisotropy inversion produced better focused migration images.

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Dey, Dipak K., and Chung Younshik. "Multiparameter estimation in truncated power series distributions under the stein's loss." Communications in Statistics - Theory and Methods 20, no. 1 (January 1991): 309–26. http://dx.doi.org/10.1080/03610929108830499.

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40

Hoekstra, Robert M., and Thomas C. Chenier. "A simulation study of stopping times in bayesian sequential multiparameter estimation." Sequential Analysis 17, no. 3-4 (January 1998): 219–37. http://dx.doi.org/10.1080/07474949808836410.

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41

Gupta, Anirban Das. "Simultaneous Estimation in the Multiparameter Gamma Distribution Under Weighted Quadratic Losses." Annals of Statistics 14, no. 1 (March 1986): 206–19. http://dx.doi.org/10.1214/aos/1176349850.

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42

Huang, Debin, Guojing Xing, and Diek W. Wheeler. "Multiparameter estimation using only a chaotic time series and its applications." Chaos: An Interdisciplinary Journal of Nonlinear Science 17, no. 2 (June 2007): 023118. http://dx.doi.org/10.1063/1.2732495.

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43

Lai, Chunyan, Guodong Feng, Ze Li, and Narayan C. Kar. "Computation-Efficient Decoupled Multiparameter Estimation of PMSMs From Massive Redundant Measurements." IEEE Transactions on Power Electronics 35, no. 10 (October 2020): 10729–40. http://dx.doi.org/10.1109/tpel.2020.2980315.

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44

Tsui, Kam-Wah. "Multiparameter estimation for some multivariate discrete distributions with possibly dependent components." Annals of the Institute of Statistical Mathematics 38, no. 1 (December 1986): 45–56. http://dx.doi.org/10.1007/bf02482499.

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45

Colombo, Daniele, Diego Rovetta, Taqi Al-Yousuf, Ernesto Sandoval, Ersan Turkoglu, and Gary McNeice. "Multiple joint wavefield inversions: Theory and field data implementations." Leading Edge 39, no. 6 (June 2020): 411–21. http://dx.doi.org/10.1190/tle39060411.1.

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Accurate velocity models for the near surface and overburden are needed for seismic processing and reliable depth imaging. Seismic with multiphysics data, well logs, and geology information need to be quantitatively integrated to obtain high-resolution velocity models. We detail our development and application of the joint wavefield inversion software platform, which enables flexible algorithmic schemes for the integration of multiparameter data and constraints. Inversion is performed in cascade or simultaneously using a variety of input data to constrain the velocity field reconstruction at multiple scales. Coupling mechanisms based on structure similarity together with rock-physics relations are optimally combined to boost resolution and enhance accuracy of the inverted velocity models. Ill-posed inversion problems are then solved using extensive geologic and rock-physics regularization instead of relying on smoothness constraints alone. We detail workflows and algorithms to guide the application of multiparameter joint inversion for velocity model building whether the input data are seismic traveltimes, electromagnetics (time/frequency domains), gravity, and/or surface waves. Extensive applications of multiparameter joint inversion are presented for a variety of complex geologic scenarios in which various multiparameter coupling strategies are illustrated. Robust velocity modeling and enhanced seismic imaging in time and depth domains are obtained as a result, proving the importance of multiphysics integration for reliable earth model parameter estimation.

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46

Zheng, Hepeng, Zuhang Wu, Lifeng Zhang, Yanqiong Xie, and Hengchi Lei. "Improving Radar Rainfall Estimations with Scaled Raindrop Size Spectra in Mei-Yu Frontal Rainstorms." Sensors 20, no. 18 (September 14, 2020): 5257. http://dx.doi.org/10.3390/s20185257.

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Hydrological calibration of raw weather radar rainfall estimation relies on in situ rainfall measurements. Raindrop size distribution (DSD) was collected during three typical Mei-Yu rainstorms in July 2014 using three particle size velocity (Parsivel) DSD sensors along the Mei-Yu front in Nanjing, Chuzhou, and the western Pacific, respectively. To improve the radar precipitation estimation in different parts of the Mei-Yu front, a scaling method was adopted to formulate the DSD model and further derive the Z–R relations. The results suggest a distinct variation of DSDs in different parts of the Mei-Yu front. Compared with statistical radar Z–ARb relations obtained by mathematical fitting techniques, the use of a DSD model fitting based on a scaling law formulation theoretically shows a significant improvement in both stratiform (33.9%) and convective (2.8%) rainfall estimations of the Mei-Yu frontal system, which indicates that using a scaling law can better reflect the DSD variations in different parts of the Mei-Yu front. Polarimetric radar has indisputable advantages with multiparameter detection ability. Several dual-polarization radar estimators are also established by DSD sensor data, and the R(ZH, ZDR) estimator is proven to be more accurate than traditional Z–R relations in Mei-Yu frontal rainfall, with potential applications for operational C-band polarimetric radar.

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47

Candeloro, Alessandro, Matteo G. A. Paris, and Marco G. Genoni. "On the properties of the asymptotic incompatibility measure in multiparameter quantum estimation." Journal of Physics A: Mathematical and Theoretical 54, no. 48 (November 10, 2021): 485301. http://dx.doi.org/10.1088/1751-8121/ac331e.

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Abstract We address the use of asymptotic incompatibility (AI) to assess the quantumness of a multiparameter quantum statistical model. AI is a recently introduced measure which quantifies the difference between the Holevo and the symmetric logarithmic derivative (SLD) scalar bounds, and can be evaluated using only the SLD operators of the model. At first, we evaluate analytically the AI of the most general quantum statistical models involving two-level (qubit) and single-mode Gaussian continuous-variable quantum systems, and prove that AI is a simple monotonous function of the state purity. Then, we numerically investigate the same problem for qudits (d-dimensional quantum systems, with 2 < d ⩽ 4), showing that, while in general AI is not in general a function of purity, we have enough numerical evidence to conclude that the maximum amount of AI is attainable only for quantum statistical models characterized by a purity larger than μ min = 1 / ( d − 1 ) . In addition, by parametrizing qudit states as thermal (Gibbs) states, numerical results suggest that, once the spectrum of the Hamiltonian is fixed, the AI measure is in one-to-one correspondence with the fictitious temperature parameter β characterizing the family of density operators. Finally, by studying in detail the definition and properties of the AI measure we find that: (i) given a quantum statistical model, one can readily identify the maximum number of asymptotically compatible parameters; (ii) the AI of a quantum statistical model bounds from above the AI of any sub-model that can be defined by fixing one or more of the original unknown parameters (or functions thereof), leading to possibly useful bounds on the AI of models involving noisy quantum dynamics.

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Qi, Hong, Chun-Yang Niu, Teng Jia, Da-Lin Wang, and Li-Ming Ruan. "Multiparameter estimation in nonhomogeneous participating slab by using self-organizing migrating algorithms." Journal of Quantitative Spectroscopy and Radiative Transfer 157 (May 2015): 153–69. http://dx.doi.org/10.1016/j.jqsrt.2015.01.003.

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49

Jones, John, and Chiewchar Narathong. "Estimation of variance and covariance components in linear models containing multiparameter matrices." Mathematical and Computer Modelling 11 (1988): 1097–100. http://dx.doi.org/10.1016/0895-7177(88)90664-4.

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50

Lwin, T., and J. S. Maritz. "Empirical Bayes approach to multiparameter estimation: with special reference to multinomial distribution." Annals of the Institute of Statistical Mathematics 41, no. 1 (March 1989): 81–99. http://dx.doi.org/10.1007/bf00049111.

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