References
- Abooshahab, M. A., Alyaseen, M. M., Bitmead, R. R., & Hovd, M. (2022). Simultaneous input & state estimation, singular filtering and stability. Automatica, 137, Article ID 110017. https://doi.org/10.1016/j.automatica.2021.110017
- Anderson, B. D., & Moore, J. B. (2012). Optimal filtering. Courier Corporation.
- Basile, G., & Marro, G. (1969). On the observability of linear, time-invariant systems with unknown inputs. Journal of Optimization Theory and Applications, 3(6), 410–415. https://doi.org/10.1007/BF00929356
- Bitmead, R. R., Gevers, M. R., Petersen, I. R., & Kaye, R. J. (1985). Monotonicity and stabilizability-properties of solutions of the Riccati difference equation: Propositions, lemmas, theorems, fallacious conjectures and counterexamples. Systems & Control Letters, 5(5), 309–315. https://doi.org/10.1016/0167-6911(85)90027-1
- Bitmead, R. R., Hovd, M., & Abooshahab, M. A. (2019). A Kalman-filtering derivation of simultaneous input and state estimation. Automatica, 108, Article ID 108478. https://doi.org/10.1016/j.automatica.2019.06.030
- Buchstaller, D., Liu, J., & French, M. (2021). The deterministic interpretation of the Kalman filter. International Journal of Control, 94(11), 3226–3236. https://doi.org/10.1080/00207179.2020.1755895
- Chan, S., Goodwin, G., & Sin, K. (1984). Convergence properties of the Riccati difference equation in optimal filtering of nonstabilizable systems. IEEE Transactions on Automatic Control, 29(2), 110–118. https://doi.org/10.1109/TAC.1984.1103465
- Cheng, Y., Ye, H., Wang, Y., & Zhou, D. (2009). Unbiased minimum-variance state estimation for linear systems with unknown input. Automatica, 45(2), 485–491. https://doi.org/10.1016/j.automatica.2008.08.009
- Darouach, M., & Zasadzinski, M. (1997). Unbiased minimum variance estimation for systems with unknown exogenous inputs. Automatica, 33(4), 717–719. https://doi.org/10.1016/S0005-1098(96)00217-8
- Darouach, M., Zasadzinski, M., Onana, A. B., & Nowakowski, S. (1995). Kalman filtering with unknown inputs via optimal state estimation of singular systems. International Journal of Systems Science, 26(10), 2015–2028. https://doi.org/10.1080/00207729508929152
- Darouach, M., Zasadzinski, M., & Xu, S. J. (1994). Full-order observers for linear systems with unknown inputs. IEEE Transactions on Automatic Control, 39(3), 606–609. https://doi.org/10.1109/9.280770
- Deshpande, A. S. (2017). Bridging a gap in applied Kalman filtering: Estimating outputs when measurements are correlated with the process noise. IEEE Control Systems Magazine, 37(3), 87–93. https://doi.org/10.1109/MCS.5488303
- De Souza, C., Gevers, M., & Goodwin, G. (1986). Riccati equations in optimal filtering of nonstabilizable systems having singular state transition matrices. IEEE Transactions on Automatic Control, 31(9), 831–838. https://doi.org/10.1109/TAC.1986.1104415
- Gakis, G., & Smith, M. C. (2022). A deterministic least squares approach for simultaneous input and state estimation. IEEE Transactions on Automatic Control. https://doi.org/10.1109/TAC.2022.3209415
- Gillijns, S., & De Moor, B. (2007a). Unbiased minimum-variance input and state estimation for linear discrete-time systems. Automatica, 43(1), 111–116. https://doi.org/10.1016/j.automatica.2006.08.002
- Gillijns, S., & De Moor, B. (2007b). Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough. Automatica, 43(5), 934–937. https://doi.org/10.1016/j.automatica.2006.11.016
- Glover, J. (1969). The linear estimation of completely unknown signals. IEEE Transactions on Automatic Control, 14(6), 766–767. https://doi.org/10.1109/TAC.1969.1099329
- Hou, M., & Muller, P. C. (1992). Design of observers for linear systems with unknown inputs. IEEE Transactions on Automatic Control, 37(6), 871–875. https://doi.org/10.1109/9.256351
- Hou, M., & Muller, P. C. (1994). Disturbance decoupled observer design: A unified viewpoint. IEEE Transactions on Automatic Control, 39(6), 1338–1341. https://doi.org/10.1109/9.293209
- Hou, M., & Patton, R. J. (1998a). Input observability and input reconstruction. Automatica, 34(6), 789–794. https://doi.org/10.1016/S0005-1098(98)00021-1
- Hou, M., & Patton, R. J. (1998b). Optimal filtering for systems with unknown inputs. IEEE Transactions on Automatic Control, 43(3), 445–449. https://doi.org/10.1109/9.661621
- Hsieh, C.-S. (2000). Robust two-stage Kalman filters for systems with unknown inputs. IEEE Transactions on Automatic Control, 45(12), 2374–2378. https://doi.org/10.1109/9.895577
- Hsieh, C.-S., & Chen, F.-C. (1999). Optimal solution of the two-stage Kalman estimator. IEEE Transactions on Automatic Control, 44(1), 194–199. https://doi.org/10.1109/9.739135
- Kailath, T., Sayed, A. H., & Hassibi, B. (2000). Linear estimation. Prentice Hall.
- Keller, J.-Y., & Darouach, M. (1999). Two-stage Kalman estimator with unknown exogenous inputs. Automatica, 35(2), 339–342. https://doi.org/10.1016/S0005-1098(98)00194-0
- Kerwin, W. S., & Prince, J. L. (2000). On the optimality of recursive unbiased state estimation with unknown inputs. Automatica, 36(9), 1381–1383. https://doi.org/10.1016/S0005-1098(00)00046-7
- Kitanidis, P. K. (1987). Unbiased minimum-variance linear state estimation. Automatica, 23(6), 775–778. https://doi.org/10.1016/0005-1098(87)90037-9
- Kudva, P., Viswanadham, N., & Ramakrishna, A. (1980). Observers for linear systems with unknown inputs. IEEE Transactions on Automatic Control, 25(1), 113–115. https://doi.org/10.1109/TAC.1980.1102245
- Li, B. (2013). State estimation with partially observed inputs: A unified Kalman filtering approach. Automatica, 49(3), 816–820. https://doi.org/10.1016/j.automatica.2012.12.007
- Markovsky, I., & De Moor, B. (2005). Linear dynamic filtering with noisy input and output. Automatica, 41(1), 167–171. https://doi.org/10.1016/j.automatica.2004.08.014
- Mendel, J. (1977). White-noise estimators for seismic data processing in oil exploration. IEEE Transactions on Automatic Control, 22(5), 694–706. https://doi.org/10.1109/TAC.1977.1101597
- Moylan, P. (1974). A note on Kalman-Bucy filters with zero measurement noise. IEEE Transactions on Automatic Control, 19(3), 263–264. https://doi.org/10.1109/TAC.1974.1100570
- Murphy, K. P. (2012). Machine learning: A probabilistic perspective. MIT Press.
- Shaked, U. (1985). Explicit solution to the singular discrete-time stationary linear filtering problem. IEEE Transactions on Automatic Control, 30(1), 34–47. https://doi.org/10.1109/TAC.1985.1103784
- 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. https://doi.org/10.1016/j.automatica.2014.12.044
- Wang, S. H., Wang, E., & Dorato, P. (1975). Observing the states of systems with unmeasurable disturbances. IEEE Transactions on Automatic Control, 20(5), 716–717. https://doi.org/10.1109/TAC.1975.1101076
- Willems, J. C. (2004). Deterministic least squares filtering. Journal of Econometrics, 118(1-2), 341–373. https://doi.org/10.1016/S0304-4076(03)00146-5
- Yong, S. Z., Zhu, M., & Frazzoli, E. (2015). Simultaneous input and state estimation with a delay. In 2015 54th IEEE Conference on Decision and Control (CDC) (pp. 468–475). IEEE.
- Yong, S. Z., Zhu, M., & Frazzoli, E. (2016). A unified filter for simultaneous input and state estimation of linear discrete-time stochastic systems. Automatica, 63, 321–329. https://doi.org/10.1016/j.automatica.2015.10.040
- Zhou, K., Doyle, J. C., & Glover, K. (1996). Robust and optimal control. Prentice Hall.