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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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When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
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A Reduced Complexity Acoustic-Based 3D DoA Estimation with Zero Cyclic Sum.

Rigel Procópio Fernandes1, José Antonio Apolinário1,2, José Manoel de Seixas3

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This study introduces a two-stage direction of arrival (DoA) estimation method that uses secondary peaks in cross-correlation. The refined approach achieves 94.0% accuracy in acoustic drone detection.

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Area of Science:

  • Acoustics
  • Signal Processing
  • Array Signal Processing

Background:

  • Accurate direction of arrival (DoA) estimation is crucial for surveillance, security, and spatial audio.
  • Existing methods may struggle with complex acoustic environments and identifying all relevant signal features.

Purpose of the Study:

  • To develop an innovative, reduced-complexity DoA estimation method.
  • To enhance DoA accuracy by utilizing secondary peaks in cross-correlation functions.
  • To validate the method's effectiveness in challenging acoustic scenarios, such as drone detection.

Main Methods:

  • A two-stage approach is proposed, starting with a low-complexity zero cyclic sum (ZCS) cost function for exhaustive time delay search.
  • The second stage employs a least-squares (LS) solution on a subset of promising time delay combinations identified by the ZCS function.
  • The method was applied to acoustic-based drone DoA estimation using a four-microphone array.

Main Results:

  • The ZCS method alone achieved 89.4%±2.7% accuracy.
  • The combined ZCS and LS method significantly improved accuracy to 94.0%±3.1%.
  • The approach demonstrated effectiveness with both simulated and real-world acoustic data.

Conclusions:

  • The proposed two-stage DoA estimation method offers a viable alternative for complex acoustic environments.
  • Leveraging secondary cross-correlation peaks enhances DoA estimation accuracy.
  • The ZCS-LS approach provides a computationally efficient yet accurate solution for critical DoA applications.