State-Dependent Interacting Multiple Model-Unscented Kalman Filter for Real-Time Reconstruction of Unmeasured States

Abstract

This paper addresses the real-time reconstruction of unmeasured states in nonlinear systems operating across multiple dynamic regimes. A State-Dependent Interacting Multiple Model Unscented Kalman Filter (IMM-UKF) is proposed, in which mode-conditioned UKFs run in parallel within the standard IMM recursion, while the transition probability matrix is evaluated online from features derived from available measurements and state estimates. This allows operating-regime information to affect the interaction step and the prediction of mode probabilities before the likelihood-based correction is applied. The framework is instantiated for vehicle sideslip angle estimation under unknown tire-road friction conditions, using two candidate models and measurements compatible with low-cost onboard sensing. In this application, deviations of lateral acceleration and yaw rate measurements from dry-road reference maps are used to adapt the transition probabilities online. The estimator is assessed through a 200-run Monte Carlo campaign and compared with a fixed-TPM IMM-UKF and a single-model UKF. The proposed approach provides the most accurate and consistent sideslip-angle reconstruction among the considered estimators, with reduced estimation-error dispersion over the Monte Carlo campaign. The proposed formulation is methodological and targets applications in which key physical quantities must be reconstructed from available measurements under changing operating regimes.