Double Exponential Cubature Kalman Filtering: Theory and Applications

Abstract

Gaussian filtering supports many estimation tasks, yet real systems present nonlinearity, outliers, and model mismatch. This thesis advances the methodology and practice of such filters in two parts. First, it develops the Double Exponential Cubature Kalman Filter (DECKF), which evaluates Gaussian-weighted moments using a double exponential cubature rule with positive weights and a scalable point set. The analysis clarifies accuracy and stability as the number of cubature points grows, observes positive-definiteness behavior in the prediction and update steps, and provides tuning guidance that accommodates cubature point count, process and measurement covariances, and numerical conditioning. An additional robust correction strategy, the Double Exponential Sliding Innovation Filter (DE-SIF), constrains the measurement update within a sliding boundary layer to limit the influence of abnormal innovations while preserving the standard Kalman structure and compatibility.

Second, the thesis studies performance in a demanding condition monitoring problem. The DECKF is combined with an interacting multiple model framework and is compared against the EKF and UKF on a mode-switching magnetorheological damper governed by Bouc-Wen dynamics. The study quantifies force-estimation accuracy, correlation with reference force, detection performance across operating modes, and statistical consistency via normalized innovations and related tests. Results show that the IMM-DECKF delivers strong force tracking and consistent innovations with competitive detection performance, and that its benefits grow with careful cubature point selection and covariance tuning.

Beyond the specific damper experiment, the proposed DE cubature rule and sliding innovation strategy apply to broader estimation tasks where Gaussian filters are standard, including target tracking, navigation, and control, and offer practical guidance on stability, tuning, and diagnostics.