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Area of Science:

  • Control Systems Engineering
  • Signal Processing
  • Statistical Inference

Background:

  • Dynamic systems are often affected by output outliers and heavy-tailed noise, degrading estimation accuracy.
  • Conventional Maximum A Posteriori (MAP) estimation methods can be sensitive to such data anomalies.
  • Robust filtering techniques are crucial for reliable system performance in real-world applications.

Purpose of the Study:

  • To develop a robust recursive filter for discrete-time linear dynamic systems prone to output outliers.
  • To introduce a novel weight matrix within the MAP estimation framework for improved outlier detection and filtering.
  • To enhance filtering performance by precisely determining the weight matrix based on noise characteristics.

Main Methods:

  • Incorporation of a weight matrix into the conventional MAP estimation for innovation whitening and variance adjustment.
  • Development of two constrained optimization problems to derive the weight matrix, considering environmental noise.
  • Implementation of a convex optimization approach to minimize the estimation upper bound of the error covariance matrix.
  • Formulation of a min-min optimization problem with a concave cost function for modified MAP estimation.
  • Application of a Semidefinite Program (SDP) for effective outlier detection.

Main Results:

  • The proposed weight matrix significantly influences innovation whitening and asymptotic variance, enabling effective outlier detection.
  • Constrained optimization approaches yield a more precise weight matrix, leading to substantial improvements in filtering performance.
  • The convex optimization method minimizes the error covariance matrix upper bound.
  • The min-min optimization approach provides an alternative for robust estimation.
  • Simulation results demonstrate the filter's effectiveness in dynamic systems with measurement outliers.

Conclusions:

  • The proposed recursive filter effectively handles discrete-time linear dynamic systems with output outliers and heavy-tailed noises.
  • The introduced weight matrix and constrained optimization methods enhance outlier detection and filtering accuracy.
  • The filter offers a robust solution for improving the performance of dynamic systems operating under noisy conditions.