Bias-VarianceTrade-off in Kalman Filter-Based Disturbance Observers

TL;DR

This paper explores the bias-variance trade-off in Kalman filter-based disturbance observers with partial disturbance model knowledge, proposing two novel estimators to improve estimation accuracy in practical scenarios.

Contribution

It introduces two new estimators, MKCKF-DOB and IMMKF-DOB, addressing the bias-variance trade-off in KF-DOB with incomplete disturbance models.

Findings

Simulations confirm the effectiveness of the proposed estimators.

The paper clarifies the relationship between SISE and KF-DOB.

Proposes methods to improve disturbance estimation accuracy.

Abstract

The performance of disturbance observers is strongly influenced by the level of prior knowledge about the disturbance model. The simultaneous input and state estimation (SISE) algorithm is widely recognized for providing unbiased minimum-variance estimates under arbitrary disturbance models. In contrast, the Kalman filter-based disturbance observer (KF-DOB) achieves minimum mean-square error estimation when the disturbance model is fully specified. However, practical scenarios often fall between these extremes, where only partial knowledge of the disturbance model is available. This paper investigates the inherent bias-variance trade-off in KF-DOB when the disturbance model is incomplete. We further show that SISE can be interpreted as a special case of KF-DOB, where the disturbance noise covariance tends to infinity. To address this trade-off, we propose two novel estimators: the multi-kernel correntropy Kalman filter-based disturbance observer (MKCKF-DOB) and the interacting multiple models Kalman filter-based disturbance observer (IMMKF-DOB). Simulations verify the effectiveness of the proposed methods.