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Related Concept Videos

State Space Representation01:27

State Space Representation

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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

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This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
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Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
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Design of Nonlinear Autoregressive Exogenous Model Based Intelligence Computing for Efficient State Estimation of

Wasiq Ali1,2, Wasim Ullah Khan3, Muhammad Asif Zahoor Raja4

  • 1School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China.

Entropy (Basel, Switzerland)
|May 5, 2021
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Summary

This study introduces a deep learning approach using a nonlinear autoregressive exogenous (NARX) neural network for precise underwater passive target state estimation. The NARX model demonstrates superior performance compared to traditional filters in tracking moving objects with limited data.

Keywords:
artificial neural networkintelligent computingmeasurement noisenonlinear autoregressive with exogenous input (NARX)nonlinear filteringstate estimation

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Area of Science:

  • Underwater acoustics
  • Artificial intelligence
  • Signal processing

Background:

  • Real-time motion parameter extraction for underwater passive targets typically relies on nonlinear filtering techniques.
  • Existing methods often associate nonlinear passive measurements with linear target kinetics within a state-space framework.
  • Improving tracking accuracy and minimizing position error for dynamic passive objects remains a challenge.

Purpose of the Study:

  • To present an intelligent computing paradigm utilizing a nonlinear autoregressive exogenous (NARX) feedback neural network for accurate state estimation of underwater passive targets.
  • To leverage deep learning strengths for enhanced feature estimation and reduced position error in dynamic passive object tracking.
  • To evaluate the performance of the NARX-based supervised learning approach in bearings-only tracking scenarios.

Main Methods:

  • Development of a deep learning model based on a nonlinear autoregressive exogenous (NARX) feedback neural network.
  • Application of NARX-based supervised learning for estimating the real-time state of a passive moving object following a semi-curved path.
  • Performance evaluation through Monte Carlo simulations under six different standard deviation scenarios of white Gaussian measurement noise.

Main Results:

  • The proposed NARX feedback neural network scheme effectively estimates the real-time state of underwater passive targets.
  • Root mean square error (RMSE) in rectangular coordinates was computed to quantify the accuracy of the estimated versus real positions.
  • The NARX model demonstrated superior state estimation capabilities compared to conventional nonlinear filters like the spherical radial cubature Kalman filter and unscented Kalman filter.

Conclusions:

  • Intelligent computing using NARX-based deep learning offers a capable alternative for underwater passive target state estimation.
  • The NARX model shows significant potential in improving tracking accuracy and minimizing position errors in challenging underwater environments.
  • The study validates the effectiveness of the proposed NARX feedback neural network over traditional filtering algorithms for bearings-only tracking.