scholarly journals Modeling and Parameter Estimation of Partially Coherent Signals in Radio Engineering Systems

2021 ◽  
Vol 7 (3) ◽  
pp. 16-24
Author(s):  
E. Glushankov ◽  
D. Kirik ◽  
A. Lyalina
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
Differential Equations ◽  
A Priori ◽  
Spatial Coherence ◽  
High Accuracy ◽  
Engineering Systems ◽  
Coherent Signals ◽  
Radio Engineering ◽  
Partially Coherent

The problem of modeling signals of various spatial coherence in radio engineering systems is considered. First, a mathematical model for spatially coherent signals in the form of stochastic differential equations is constructed, followed by its study in the Simulink environment. The following is a method for constructing a mathematical model for a more general case – partially coherent signals, and its accuracy is also evaluated. Based on the developed models, an algorithm for estimating the parameters of partially coherent signals is synthesized. Based on the obtained dependence of the sensitivity of the model to deviation from a priori data, conclusions are drawn about a sufficiently high accuracy of estimation using synthesized algorithms.

Estimation of lateral-directional aerodynamic derivatives from flight data using conventional and neural based methods

2014 ◽  
Vol 118 (1210) ◽  
pp. 1453-1479 ◽  
Author(s):  
R. Kumar ◽  
A. K. Ghosh
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
A Priori ◽  
Estimation Methods ◽  
Control Input ◽  
Feed Forward Neural Network ◽  
Additional Advantage ◽  
Flight Data ◽  
Aerodynamic Derivatives ◽  
Different Types

Abstract The paper presents the estimation of lateral-directional aerodynamic derivatives (parameters) using conventional and neural based methods from real flight data of Hansa-3 aircraft. The conventional methods such as least squares (LS) and maximum likelihood (ML) require an a priori postulation of mathematical model to estimate the parameters. Whereas the neural-based method such as Neural-Gauss-Newton (NGN) is an algorithm that utilises feed forward neural network and Gauss-Newton optimisation to estimate the parameters and does not require any a priori postulation of mathematical model or solution of equations of motion. In the paper, the LS, ML and NGN methods are applied to lateral-directional flight data in order to estimate parameters. The results obtained in terms of lateral-directional aerodynamic derivatives are reasonably accurate to establish LS, ML and NGN as parameter estimation methods along with NGN method having an additional advantage of non-requirement of a priori mathematical model. The paper also highlights the effect of different types of control inputs on parameter estimation. For this, three types of control inputs were used to generate real flight data. The ailerons and rudder were deflected in the first, the ailerons were deflected while keeping rudder at trim condition in the second and the rudder was deflected while keeping ailerons at trim condition in the third type of control input to generate the real flight data. The paper presents the effect of three different types of control inputs in terms of aerodynamic parameters estimated through conventional and neural based methods using flight data generated through these inputs.

scholarly journals The study of a mathematical model of surface reactions

2014 ◽  
Vol 55 ◽  
Author(s):  
Algirdas Ambrazevičius ◽  
Gintaras Puriuškis
Keyword(s):  
Mathematical Model ◽  
Carbon Monoxide ◽  
Nitrous Oxide ◽  
Differential Equations ◽  
Classical Solution ◽  
A Priori Estimates ◽  
Surface Reactions ◽  
A Priori ◽  
Coupled System ◽  
Priori Estimates

We prove the a priori estimates of a classical solution to a coupled system of parabolic and ordinary differential equations, the latter being determined on the boundary of the domain. This system describes the model of surface reactions between carbon monoxide and nitrous oxide.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

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 A priori bounds of the solution of a one point IBVP for a singular fractional evolution equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Said Mesloub ◽  
Hassan Eltayeb Gadain
Keyword(s):  
Differential Equations ◽  
Evolution Equation ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Initial Boundary ◽  
A Priori Bounds ◽  
Fractional Evolution Equation ◽  
Priori Estimates ◽  
Initial Boundary Value

Abstract A priori bounds constitute a crucial and powerful tool in the investigation of initial boundary value problems for linear and nonlinear fractional and integer order differential equations in bounded domains. We present herein a collection of a priori estimates of the solution for an initial boundary value problem for a singular fractional evolution equation (generalized time-fractional wave equation) with mass absorption. The Riemann–Liouville derivative is employed. Results of uniqueness and dependence of the solution upon the data were obtained in two cases, the damped and the undamped case. The uniqueness and continuous dependence (stability of solution) of the solution follows from the obtained a priori estimates in fractional Sobolev spaces. These spaces give what are called weak solutions to our partial differential equations (they are based on the notion of the weak derivatives). The method of energy inequalities is used to obtain different a priori estimates.

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