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Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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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Extraction: Partition and Distribution Coefficients01:14

Extraction: Partition and Distribution Coefficients

The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
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Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
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Estimation of the Physical Quantities01:05

Estimation of the Physical Quantities

On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
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Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...

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Related Experiment Video

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Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
08:42

Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method

Published on: September 3, 2021

Direction-of-arrival estimation based on joint sparsity.

Junhua Wang1, Zhitao Huang, Yiyu Zhou

  • 1School of Electronic Science and Engineering, NUDT, Changsha 410073, China. skysword_wjh@126.com

Sensors (Basel, Switzerland)
|December 14, 2011
PubMed
Summary

This study introduces a novel Joint-Sparse Direction-of-Arrival (DOA) estimation algorithm. The method efficiently estimates DOA with fewer snapshots and unknown source numbers, improving resolution and handling coherent sources.

Keywords:
Direction-of-Arrivalcompressed sensingjoint-sparsemultiple measure vectorsquasi-Newton methods

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A Methodology for Capturing Joint Visual Attention Using Mobile Eye-Trackers
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Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
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A Methodology for Capturing Joint Visual Attention Using Mobile Eye-Trackers
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Published on: January 18, 2020

Area of Science:

  • Signal Processing
  • Array Signal Processing
  • Electromagnetics

Background:

  • Direction-of-Arrival (DOA) estimation is crucial for sensor array applications.
  • Existing DOA algorithms often require a known number of sources and numerous snapshots.
  • Coherent sources and limited data present significant challenges in DOA estimation.

Purpose of the Study:

  • To develop a robust DOA estimation algorithm that overcomes limitations of existing methods.
  • To address the challenge of estimating DOA with a reduced number of snapshots.
  • To improve DOA estimation resolution and performance with coherent sources.

Main Methods:

  • Direction-of-Arrival (DOA) estimation is formulated as a joint-sparse recovery problem.
  • An arctan function approximates the norm to represent joint sparsity.
  • A quasi-Newton method is employed to solve the minimization problem for DOA estimation.

Main Results:

  • The proposed Joint-Sparse DOA algorithm requires a minimal number of snapshots.
  • The number of sources does not need to be known a priori.
  • Improved resolution and effective handling of coherent sources were demonstrated through simulations.

Conclusions:

  • The Joint-Sparse DOA algorithm offers significant advantages over conventional methods.
  • It provides a flexible and efficient approach for DOA estimation in various scenarios.
  • The algorithm shows promise for applications requiring high-resolution DOA estimation with limited data.