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Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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Wavelet-Variance-Based Estimation for Composite Stochastic Processes.

Stéphane Guerrier1, Jan Skaloud, Yannick Stebler

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Summary
This summary is machine-generated.

A novel wavelet variance (WV) estimation method for composite Gaussian processes in time series analysis is introduced. This approach offers a practical alternative to likelihood-based methods, proving effective for complex models in engineering and science.

Keywords:
Allan varianceKalman filterSignal processingTime series

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Area of Science:

  • Statistics
  • Signal Processing
  • Time Series Analysis

Background:

  • Composite Gaussian processes are crucial for modeling complex time series in engineering and natural sciences.
  • Classical likelihood-based estimation methods can be computationally intensive or infeasible for intricate models.

Purpose of the Study:

  • To introduce a new, practical estimation method for parameters of composite Gaussian process time series models.
  • To provide an alternative to traditional maximum likelihood estimation (MLE) and least squares estimation (LSE).

Main Methods:

  • The proposed method optimizes a criterion based on the standardized distance between sample and model-based wavelet variances (WV).
  • Wavelet variances (WV) decompose the variance process across scales, capturing diverse stochastic model features.
  • Asymptotic properties of the estimator were derived, and simulation studies compared it against MLE and LSE.

Main Results:

  • The new estimator demonstrates consistency under verifiable conditions for composite models.
  • Simulation studies indicate competitive or superior performance compared to MLE and LSE for various models.
  • The method was successfully applied to estimate parameters in gyroscope data from inertial navigation systems.

Conclusions:

  • The proposed wavelet variance-based estimation method is a viable and effective alternative for complex time series models.
  • This technique offers practical advantages in implementation and applicability, particularly in fields like inertial navigation.
  • The study validates the estimator's theoretical properties and practical utility through simulations and real-world data analysis.