Minimax Regret filter for uncertainty Single-Input Single-Output systems: simulation study

Abstract

The Kalman filter, widely used since its introduction in 1960, assumes Gaussian random disturbances. However, this assumption can be inappropriate in non-Gaussian contexts, leading to suboptimal performance. Researchers have proposed robust filters like minimax filters to address this limitation, but these filters can overly conservative estimates. This research introduces a novel approach that combines unknown-but-bounded dynamics for the state process and stochastic processes for the measurement equation along with a Minimax Regret framework to improve state estimation in one-dimensional linear dynamic models. We evaluate the proposed method through two simulation studies. The first study optimizes the hyperparameter value using Grid Search. In contrast, the second compares the performance of the proposed method with conventional methods, including the Kalman filter and a robust version of the RobKF filter implemented in R software, using a suitable performance metric such as mean squared error. The results demonstrate the superiority of the proposed algorithm.

Keywords

• Minimax regret approach
• Unknown-but-bounded
• Unknown distribution error
• Grid hyperparameter optimization