scholarly journals Solutions to inverse moment estimation problems in dimension 2, using best constrained approximation

2020 ◽  
pp. 105520
Author(s):  
Juliette Leblond ◽  
Elodie Pozzi
Keyword(s):  
Moment Estimation ◽  
Constrained Approximation ◽  
Estimation Problems ◽  
Dimension 2 ◽  
Inverse Moment

scholarly journals Set-membership identifiability of nonlinear models and related parameter estimation properties

2016 ◽  
Vol 26 (4) ◽  
pp. 803-813 ◽  
Author(s):  
Carine Jauberthie ◽  
Louise Travé-MassuyèEs ◽  
Nathalie Verdière
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
Dynamic System ◽  
Nonlinear Models ◽  
Differential Algebra ◽  
Related Parameter ◽  
Set Membership ◽  
Estimation Problems ◽  
The Mathematical Model

Abstract Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.

scholarly journals DoA Estimation Using Neural Tangent Kernel under Electromagnetic Mutual Coupling

Electronics ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 1057
Author(s):  
Qifeng Wang ◽  
Xiaolin Hu ◽  
Xiaobao Deng ◽  
Nicholas E. Buris
Keyword(s):  
Mutual Coupling ◽  
Deep Neural Network ◽  
Doa Estimation ◽  
Antenna Element ◽  
Root Finding ◽  
Multiple Signal ◽  
Estimation Problems ◽  
Limiting Case ◽  
Signal Doa Estimation ◽  
Polynomial Root Finding

Antenna element mutual coupling degrades the performance of Direction of Arrival (DoA) estimation significantly. In this paper, a novel machine learning-based method via Neural Tangent Kernel (NTK) is employed to address the DoA estimation problem under the effect of electromagnetic mutual coupling. NTK originates from Deep Neural Network (DNN) considerations, based on the limiting case of an infinite number of neurons in each layer, which ultimately leads to very efficient estimators. With the help of the Polynomial Root Finding (PRF) technique, an advanced method, NTK-PRF, is proposed. The method adapts well to multiple-signal scenarios when sources are far apart. Numerical simulations are carried out to demonstrate that this NTK-PRF approach can handle, accurately and very efficiently, multiple-signal DoA estimation problems with realistic mutual coupling.

scholarly journals Counting and equidistribution in quaternionic Heisenberg groups

2021 ◽  
pp. 1-38
Author(s):  
JOUNI PARKKONEN ◽  
FRÉDÉRIC PAULIN
Keyword(s):  
Hyperbolic Geometry ◽  
Quaternion Algebra ◽  
Rational Points ◽  
Hyperbolic Spaces ◽  
Heisenberg Groups ◽  
Arithmetic Groups ◽  
Hermitian Forms ◽  
Dimension 2 ◽  
Counting Formula ◽  
The Relationship

Abstract We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over ${\mathbb{Q}}$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.

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