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.

中文翻译：

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用于结构系统输入状态估计的贝叶斯平滑

通过滤波方法对测量输出产生延迟影响的系统的瞬时仅输出反演由于病态性而遭受估计量中观察噪声的强烈放大。为了解决这个问题，在本文中，开发了一种新的无偏递归贝叶斯平滑方法，用于在没有直接馈通的情况下对线性系统进行输入状态估计，以通过扩展观察方程减少估计不确定性。通过最小化输入和状态估计误差方差，得到最优平滑输入和状态增益矩阵。此外，提出了一种新的有效方法，用于递归计算状态估计误差与建模和观测噪声向量的相关性。