Measurement-outlier robust Kalman filter for discrete-time dynamic systems

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.