Introduction to More Complex Estimation Problems

1992 ◽  
pp. 162-215
Author(s):  
Carl-Erik Särndal ◽  
Bengt Swensson ◽  
Jan Wretman
Keyword(s):  
Estimation Problems

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 Optimal Linear Estimators for Time-Delay Systems with Fading Measurements and Correlated Noises

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Yazhou Li ◽  
Jiayi Li ◽  
Xin Wang
Keyword(s):  
Time Delay ◽  
Minimum Variance ◽  
Delay Systems ◽  
Multiplicative Noises ◽  
Linear Estimators ◽  
Discrete Linear Systems ◽  
Estimation Problems ◽  
Optimal Linear ◽  
State Augmentation ◽  
Correlated Noises

The optimal linear estimation problems are investigated in this paper for a class of discrete linear systems with fading measurements and correlated noises. Firstly, the fading measurements occur in a random way where the fading probabilities are regulated by probability mass functions in a given interval. Furthermore, time-delay exists in the system state and observation simultaneously. Additionally, the multiplicative noises are considered to describe the uncertainty of the state. Based on the projection theory, the linear minimum variance optimal linear estimators, including filter, predictor, and smoother are presented in the paper. Compared with conventional state augmentation, the new algorithm is finite-dimensionally computable and does not increase computational and storage load when the delay is large. A numerical example is provided to illustrate the effectiveness of the proposed algorithms.

Causation Entropy Identifies Sparsity Structure for Parameter Estimation of Dynamic Systems

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Pileun Kim ◽  
Jonathan Rogers ◽  
Jie Sun ◽  
Erik Bollt
Keyword(s):  
Parameter Estimation ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Measurement Data ◽  
Relative Magnitude ◽  
Initial Guess ◽  
Series Data ◽  
System Parameters ◽  
Estimation Problems ◽  
System States

Parameter estimation is an important topic in the field of system identification. This paper explores the role of a new information theory measure of data dependency in parameter estimation problems. Causation entropy is a recently proposed information-theoretic measure of influence between components of multivariate time series data. Because causation entropy measures the influence of one dataset upon another, it is naturally related to the parameters of a dynamical system. In this paper, it is shown that by numerically estimating causation entropy from the outputs of a dynamic system, it is possible to uncover the internal parametric structure of the system and thus establish the relative magnitude of system parameters. In the simple case of linear systems subject to Gaussian uncertainty, it is first shown that causation entropy can be represented in closed form as the logarithm of a rational function of system parameters. For more general systems, a causation entropy estimator is proposed, which allows causation entropy to be numerically estimated from measurement data. Results are provided for discrete linear and nonlinear systems, thus showing that numerical estimates of causation entropy can be used to identify the dependencies between system states directly from output data. Causation entropy estimates can therefore be used to inform parameter estimation by reducing the size of the parameter set or to generate a more accurate initial guess for subsequent parameter optimization.

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