Multi-Scaled Unscented Kalman Filter

TL;DR

This paper introduces a multi-scaled Unscented Kalman Filter that allows different scaling for each state dimension, improving estimation accuracy in nonlinear systems with diverse state behaviors.

Contribution

It proposes a novel multi-scaling approach for UKF, enabling tailored sigma point spreading per state dimension, supported by a rigorous mathematical foundation.

Findings

Enhanced estimation accuracy in nonlinear systems

Effective handling of multi-dimensional states with diverse behaviors

Validated improvements through experiments on two nonlinear systems

Abstract

The unscented Kalman filter (UKF) is a commonly used algorithm capable of estimating the states of nonlinear dynamic systems. It carefully chooses a set of sample points, called sigma points that capture the nonlinear system states posterior mean and covariance. The filter is based on the scaled unscented transform, where the scaling parameters impact the spreading of the sigma points, determining the estimated model capturing. In its current form, the UKF employs a single set of scaling parameters shared by all sigma points. Because states in multi-dimensional models often exhibit substantially different behaviors, this imposes a critical limitation: the standard UKF parameters cannot be tuned to extend the spread for one dimension while reducing it for another. To bridge this gap, we propose the multi-scaled UKF to enable spreading differently per state, while maintaining the key properties of the sigma points and UKF. A rigorous mathematical foundation is provided, introducing a novel theoretical approach to multi-scaling. The benefits of this approach are demonstrated through two distinct nonlinear dynamic systems. Consequently, our multi-scaled UKF captures the nonlinear behavior of multi-dimensional states more effectively, leading to improved estimation accuracy.