Bayesian synergistic filter: Model rectification, noise parameter estimation and state-space estimation with uncertainty quantification

Bayesian synergistic filter (BSF), a novel generic filter for model rectification, noise parameter estimation and state-space estimation with uncertainty quantification, is proposed. Model discrepancy between the actual system and the computational model is one of the challenging issues for state-space estimation. Due to the model discrepancy, the state-space estimation can be seriously distorted and misleading. 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. Another challenging issue is the proper selections of the noise parameters. The proposed BSF estimates the noise parameters in an online manner to release the stationarity constraint in conventional state-space filters. Moreover, by recursively adopting the obtained information between the model rectification and noise parameter estimation, the updated adjustment can be incorporated as the filter evolves. 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. Besides, a case study of a 600-meter-high television tower subjected to nonstationary earthquake excitation is presented.