KalMRACO: Unifying Kalman Filter and Model Reference Adaptive Control for Robust Control and Estimation of Uncertain Systems

TL;DR

KalMRACO combines Kalman filtering and MRAC to enable robust control and estimation of uncertain systems without requiring prior system parameter knowledge, demonstrated on an underwater vehicle.

Contribution

It unifies Kalman filter and MRAC using the reference model as the Kalman system model, reducing the need for known system parameters.

Findings

Superior tracking of reference model state

Convergence of observer states

Effective noise mitigation

Abstract

A common assumption when applying the Kalman filter is a priori knowledge of the system parameters. These parameters are not necessarily known, and this may limit real-world applications of the Kalman filter. The well-established Model Reference Adaptive Controller (MRAC) utilizes a known reference model and ensures that the input-output behavior of a potentially unknown system converges to that of the reference model. We present KalMRACO, a unification of the Kalman filter and MRAC leveraging the reference model of MRAC as the Kalman filter system model, thus eliminating, to a large degree, the need for knowledge of the underlying system parameters in the application of the Kalman filter. We also introduce the concept of blending estimated states and measurements in the feedback law to handle stability issues during the initial transient. KalMRACO is validated through simulations and lab trials on an underwater vehicle. Results show superior tracking of the reference model state, observer state convergence, and noise mitigation properties.