On the equivalence between the unbiased minimum-variance estimation and the infinity augmented Kalman filter

References

• Darouach, M., & Zasadzinski, M. (1997). Unbiased minimum variance estimation for systems with unknown exogenous inputs. Automatica, 33(4), 717–719. doi: 10.1016/S0005-1098(96)00217-8
   Web of Science ®Google Scholar
• Ding, B., & Fang, H. (2018). Fault estimation and prediction for nonlinear stochastic system with intermittent observations. International Journal of Robust & Nonlinear Control, 28(4), 1165–1181. doi: 10.1002/rnc.3925
   Web of Science ®Google Scholar
• Ding, J., Xiao, J., Zhang, Y., & Iqbal, M. N. (2014). Distributed state estimation for discrete-time nonlinear system with unknown inputs. Circuits, Systems, and Signal Processing, 33(11), 3421–3441. doi: 10.1007/s00034-014-9812-7
   Web of Science ®Google Scholar
• Fang, H., & De Callafon, R. A. (2012). On the asymptotic stability of minimum-variance unbiased input and state estimation. Automatica, 48(12), 3183–3186. doi: 10.1016/j.automatica.2012.08.039
   Web of Science ®Google Scholar
• Gao, Z. (2015). Fault estimation and fault tolerant control for discrete-time dynamic systems. IEEE Transactions on Industrial Electronics, 62(6), 3874–3884.
   Web of Science ®Google Scholar
• Gillijns, S., & De Moor, B. (2007). Unbiased minimum-variance input and state estimation for linear discrete-time systems. Automatica, 43(1), 111–116. doi: 10.1016/j.automatica.2006.08.002
   Web of Science ®Google Scholar
• Hsieh, C.-S. (2000). Robust two-stage kalman filters for systems with unknown inputs. IEEE Transactions on Automatic Control, 45(12), 2374–2378. doi: 10.1109/9.895577
   Web of Science ®Google Scholar
• Hu, L., Wang, Z., Han, Q. L., & Liu, X. (2018). Event-based input and state estimation for linear discrete time-varying systems. International Journal of Control, 91(1), 101–113. doi: 10.1080/00207179.2016.1269205
   Web of Science ®Google Scholar
• Keller, J., Darouach, M., & Caramelle, L. (1998). Kalman filter with unknown inputs and robust two-stage filter. International Journal of Systems Science, 29(1), 41–47. doi: 10.1080/00207729808929494
   Web of Science ®Google Scholar
• Kitanidis, P. K. (1987). Unbiased minimum-variance linear state estimation. Automatica, 23(6), 775–778. doi: 10.1016/0005-1098(87)90037-9
   Web of Science ®Google Scholar
• Li, B. (2013). State estimation with partially observed inputs: A unified kalman filtering approach. Automatica, 49(3), 816–820. doi: 10.1016/j.automatica.2012.12.007
   Web of Science ®Google Scholar
• Lourens, E., Reynders, E., Roeck, G. D., Degrande, G., & Lombaert, G. (2012). An augmented kalman filter for force identification in structural dynamics. Mechanical Systems & Signal Processing, 27(1), 446–460. doi: 10.1016/j.ymssp.2011.09.025
   Web of Science ®Google Scholar
• Ren, P., & Zhou, Z. (2017). Strain estimation of truss structures based on augmented kalman filtering and modal expansion. Advances in Mechanical Engineering, 9(11), 1–10. doi: 10.1177/1687814017735788
   Web of Science ®Google Scholar
• Simon, D. (2006). Optimal state estimation: Kalman, H infinity, and nonlinear approaches. New Jersey: John Wiley & Sons.
   Google Scholar
• Su, J., Li, B., & Chen, W.-H. (2015). On existence, optimality and asymptotic stability of the kalman filter with partially observed inputs. Automatica, 53, 149–154. doi: 10.1016/j.automatica.2014.12.044
   Web of Science ®Google Scholar
• Taha, A. F., Elmahdi, A., Panchal, J. H., & Sun, D. (2015). Unknown input observer design and analysis for networked control systems. International Journal of Control, 88(5), 920–934.
   Web of Science ®Google Scholar
• Wang, Z., Shi, P., & Lim, C.-C. (2017). Robust fault estimation observer in the finite frequency domain for descriptor systems. International Journal of Control. doi: 10.1080/00207179.2017.1403048
   Web of Science ®Google Scholar
• Zhang, K., Jiang, B., Shi, P., & Xu, J. (2014). Multi-constrained fault estimation observer design with finite frequency specifications for continuous-time systems. International Journal of Control, 87(8), 1635–1645. doi: 10.1080/00207179.2014.880950
   Web of Science ®Google Scholar