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Optimal Input Signal Design for Data-Centric Estimation Methods.

Sunil Deshpande1, Daniel E Rivera

  • 1Control Systems Engineering Laboratory (CSEL), Arizona State University, Tempe, AZ, USA. Doctoral student in the electrical engineering program at Arizona State.

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Summary
This summary is machine-generated.

This study introduces optimal input signal design for data-centric estimation methods, improving local modeling accuracy. The new method enhances data informativeness for better function approximation from noisy data.

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Area of Science:

  • Control Systems Engineering
  • Statistical Signal Processing
  • Machine Learning

Background:

  • Data-centric estimation methods, including Model-on-Demand and Direct Weight Optimization, are crucial for approximating unknown functions from noisy data.
  • These methods iteratively build local function approximations using regressors at each operating point.
  • Optimizing the input signals is key to generating informative data for these local modeling procedures.

Purpose of the Study:

  • To design optimal input signals that maximize the informativeness of data for local modeling procedures.
  • To specifically address the distribution of regressor vectors within the input signal design.
  • To evaluate the proposed method for linear time-invariant systems under amplitude constraints.

Main Methods:

  • Formulation of an optimization problem for input signal design, focusing on regressor vector distribution.
  • Application of semidefinite relaxation methods to solve the resulting optimization problem.
  • Comparison with classical Pseudorandom Binary Sequence (PRBS) input design.

Main Results:

  • The proposed input signal design method yields more informative data compared to traditional PRBS.
  • Demonstrated benefits in the context of local modeling for function estimation.
  • Effective handling of amplitude constraints on the input signal.

Conclusions:

  • Optimal input signal design significantly enhances the performance of data-centric estimation methods.
  • The proposed approach provides a systematic way to generate informative data for local modeling.
  • Semidefinite relaxation offers a viable solution for optimizing input signals under constraints.