The Gaussian multiplicative approximation for state‐space models

• DOI: 10.1002/stc.2904
• Publication Date: 2021-12-07T03:49:32Z
• Authors: Bhargob Deka; Luong Ha Nguyen; Saeid Amiri; James‐A. Goulet
• Keywords: State-space representation; State vector; Kernel (algebra)

Applications such as structural health monitoring (SHM) often rely on the analysis of time-series using methods state-space models (SSM). In this paper, we propose an analytical method called Gaussian multiplicative approximation (GMA) that is applicable to are encountered in practical SHM applications. The enables inference mean vector and covariance matrix for product two hidden states transition and/or observation linear estimation theory online model parameters states. potential combining GMA Bayesian dynamic (BDLM) illustrated through development (1) a generic component autoregressive can estimate both state variable parameter together; (2) trend seasonality identify non-harmonic periodic pattern whose amplitude changes linearly with time; (3) double kernel regression involves components. SHM-based case studies presented confirm exceeds performance existing nonlinear Kalman filter terms accuracy along computational cost.