College of Mathematics, Sichuan University, Chengdu 610064, Sichuan, China.
Sensors (Basel). 2018 Sep 6;18(9):2976. doi: 10.3390/s18092976.
In this paper, the state estimation for dynamic system with unknown inputs modeled as an autoregressive AR (1) process is considered. We propose an optimal algorithm in mean square error sense by using difference method to eliminate the unknown inputs. Moreover, we consider the state estimation for multisensor dynamic systems with unknown inputs. It is proved that the distributed fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurement; therefore, it achieves the best performance. The computation complexity of the traditional augmented state algorithm increases with the augmented state dimension. While, the new algorithm shows good performance with much less computations compared to that of the traditional augmented state algorithms. Moreover, numerical examples show that the performances of the traditional algorithms greatly depend on the initial value of the unknown inputs, if the estimation of initial value of the unknown input is largely biased, the performances of the traditional algorithms become quite worse. However, the new algorithm still works well because it is independent of the initial value of the unknown input.
本文针对具有未知输入的自回归 AR(1)过程模型的动态系统的状态估计问题进行了研究。我们提出了一种最优算法，该算法使用差分方法消除未知输入，在均方误差意义下达到最优。此外，我们还考虑了具有未知输入的多传感器动态系统的状态估计问题。证明了分布式融合状态估计等价于使用所有传感器测量值的集中卡尔曼滤波，因此它能够实现最佳性能。传统增广状态算法的计算复杂度随着增广状态维度的增加而增加。而新算法的计算复杂度相对较低，与传统增广状态算法相比，计算量大大减少。此外，数值例子表明，传统算法的性能在很大程度上取决于未知输入的初始值，如果对未知输入的初始值估计存在较大偏差，传统算法的性能会变得相当差。然而，新算法仍然能够很好地工作，因为它不依赖于未知输入的初始值。
