Exploiting dynamical coherence: A geometric approach to parameter estimation in nonlinear models

2010 ◽  
Vol 374 (26) ◽  
pp. 2618-2623 ◽  
Author(s):  
Leonard A. Smith ◽  
Milena C. Cuéllar ◽  
Hailiang Du ◽  
Kevin Judd
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Models ◽  
Geometric Approach ◽  
Dynamical Coherence

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 Design of delayed fractional state variable filter for parameter estimation of fractional nonlinear models

2018 ◽  
Vol 94 (4) ◽  
pp. 2697-2713 ◽  
Author(s):  
Walid Allafi ◽  
Ivan Zajic ◽  
Kotub Uddin ◽  
Zhonghua Shen ◽  
James Marco ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Models ◽  
State Variable ◽  
State Variable Filter

scholarly journals Combinatorial Algorithm In Linear Model

2018 ◽  
Vol 196 ◽  
pp. 03017
Author(s):  
Jana Ižvoltová ◽  
Peter Pisca
Keyword(s):  
Parameter Estimation ◽  
Linear Model ◽  
Markov Models ◽  
Nonlinear Models ◽  
The Other ◽  
Estimation Methods ◽  
Combinatorial Algorithm ◽  
Alternative Approach ◽  
Parameter Estimation Methods ◽  
Iterative Numerical Methods

Gauss-jacobi combinatorial algorithm is an alternative approach to traditional iterative numerical methods, which is primary oriented for parameter estimation in nonlinear models. The combinatorial algorithm is often exploited for outlier diagnosis in nonlinear models, where the other parameter estimation methods lose their efficiency. The paper describes comparison of both of gauss-jacobi combinatorial and gauss-markov models executed on parameter estimation process of levelling network for the reason to find the efficiency of combinatorial algorithm in simply linear model.

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