Reliable amplitude and frequency estimation for biased and noisy signals |
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| Affiliation: | 1. Institut Néel, CNRS et Université Joseph Fourier BP 166, F 38042 Grenoble Cedex 9, France;2. Faculté des Sciences et Techniques de Tanger, BP 416 Tanger, Université Abdelmalek Essaâdi, Morocco;3. Institute of Physics and National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China;4. National Laboratory for Solid State Microstuctures, Department of Physics, Nanjing University, 210093 Nanjing, China;1. Department of Sciences and Technology, University of Faroe Islands, Nóatún 3, FO-100 Tórshavn, Faroe Islands;2. Research Institute of Mathematics, Seoul National University, Seoul 08826, Republic of Korea;1. Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, PR China;2. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences Beijing, 100190, PR China;3. Department of Applied Mathematics, South China Agricultural University, Guangzhou 510642, PR China;1. Department of Finance and Quantitative Methods, Bradley University, Peoria, IL, 61625, USA;2. Engineering Physics, Bradley University, Peoria, IL, 61625, USA;1. Higher School of Economics, Department of Computer Science, Russian Federation;2. Samara University, Chair of Algebra and Geometry, Russian Federation;1. Department of Mathematics and Statistics, Loyola University Maryland, Baltimore, Maryland 21210, USA;2. College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, PR China |
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| Abstract: | Robust estimation of the amplitude, frequency and bias of unknown noisy sinusoidal signals is considered in this paper. It is only assumed that the measurements noise is bounded without any additional information such as stationarity, uncorrelation or type of distribution. In this context, the aim is to compute the set of all admissible values that are consistent with the measurements and with the error bound. The estimation problem is formulated as a Constraint Satisfaction Problem (CSP) where the amplitude, frequency and bias constitute the variables and a function relating them to the output is the constraint. Interval constraint propagation techniques are used to solve, in a guaranteed way, this problem. In order to illustrate the principle and the efficiency of the approach, numerical simulations are provided. |
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