UKF Parameter Tuning for Local Variation Smoothing

Abstract

The unscented Kalman filter (UKF) is a method to solve nonlinear dynamic filtering problems, which internally uses the unscented transform (UT). The behavior of the UT is controlled by design parameters, seldom changed from the values suggested in early UT/UKF publications. Despite the knowledge that the UKF can perform poorly when the parameters are improperly chosen, there exist no wide spread intuitive guidelines for how to tune them. With an application relevant example, this paper shows that standard parameter values can be far from optimal. By analyzing how each parameter affects the resulting UT estimate, guidelines for how the parameter values should be chosen are developed. The guidelines are verified both in simulations and on real data collected in an underground mine. A strategy to automatically tune the parameters in a state estimation setting is presented, resulting in parameter values in line with developed guidelines.

Selection of Tuning Parameters of the Unscented Kalman Filter using Analytical Truth Statistics

“…First, we consider the parameters α and κ and their effect on the estimation of the mean. We will follow the guidelines that typically we would use the unscaled UT (α = 1 and κ > 0), but when necessary to decrease the spread of the sigma-points we would use the scaled UT with (κ = 0 and α < 1) 10 . 9 () gz ()…”

Estimating States and Model Uncertainties Jointly by a Sparsity Promoting UKF

“…In Nielsen et al (2021) it has been shown that the choice of these is problem-dependent and has a significant influence on the filter performance. However, for the scope of this paper, we choose α = 10 −3 , β = 2 and κ = 0.…”

“…While the measurement covariance R ∈ R m×m often is easier to determine by taking a closer look at the plant's measurements, the initial square-root covariance S 0 and the process covariance Q ∈ R ñ×ñ remain a major challenge in filter design, see e.g. Chen et al (2021); Nielsen et al (2021). When promoting sparsity within the SQ-UKF even an additional covariance R pm ∈ R comes along which determines the pseudo measurements' performance.…”

Physics-Aware Tuning of Unscented Kalman Filter:Statistical Framework for Solving Inverse Problems Involving Nonlinear Dynamical Systems and Missing Data

“…In a similar vein, Theiler et al [32] used a multi-objective fitness function within the same framework, particularly targeting identification of states and parameters for lithium-ion batteries. As a more systematic approach, Scardua and Cruz [33,34] developed a surrogate model of the desired hyperparameters and tried to optimize the parameters by maximizing the probability of the measured data. In another approach, Graybill et al [35] defined a multi-objective loss function to find optimal hyperparameters that satisfy the desired objectives, such as optimizing computational time or specified error functions.…”