A Bayesian smoothing for input‐state estimation of structural systems

Instantaneous output‐only inversion of a system with delayed appearance of input influences on the measured outputs via filtering methods suffer from intensive amplification of the observation noise in the estimated quantities due to the ill‐conditionedness. To remedy this issue, in this paper, a new unbiased recursive Bayesian smoothing method is developed for input‐state estimation of linear systems without direct feedthrough to reduce estimation uncertainty through an extended observation equation. By minimizing input and state estimation error variance, the optimal smoothing input and state gain matrices are derived. Moreover, a new efficient method is proposed for the recursive calculation of correlation of state estimation error with modeling and observation noise vectors.