Bayesian synergistic filter (BSF): Information fused model rectification and state-space estimation with uncertainty quantification

Bayesian synergistic filter (BSF), a novel generic filter for information fused model rectification and state-space estimation with uncertainty quantification, is proposed. Model discrepancy between the actual system and the computational model is a challenging issue for reliable state-space estimation. Due to the model discrepancy, the state-space estimation can be seriously distorted and misleading. To tackle this challenge, the proposed BSF evaluates the model discrepancy by fully exploiting the subtle information between the measurements and the corresponding predictions. By compensating for the evaluated model discrepancy, the computational model can be rectified to minimize its deviation from the actual system. Therefore, the computational model and the model rectification are synergized to develop a reliable state-space estimation. Moreover, the proposed BSF fuses the model rectification and the noise parameter estimation such that the stationarity constraint in conventional state-space filters can be released. Consequently, the proposed BSF achieves reliable state-space estimation for general linear/nonlinear systems under stationary/nonstationary situations. Furthermore, by taking the benefit of Bayesian inference, the estimation uncertainties of all estimates can be quantified accordingly. To demonstrate the efficacy and applicability of the proposed BSF, two simulated examples with various model discrepancies and stationary/nonstationary scenarios are discussed. Moreover, the performance of a conventional state-space filter and ablation tests are presented for comparison. Besides, a case study of a 600-meter-high television tower subjected to nonstationary earthquake excitation is presented.