RLS Wiener Fixed-Point Smoother and Filter with Randomly Delayed or Uncertain Observations in Linear Discrete-Time Stochastic Descriptor Systems
The purpose of this paper is to design the recursive least-squares (RLS) Wiener fixed-point smoother and filter in linear discrete-time descriptor systems. The signal process is observed with additional observation noise. The observed value is randomly delayed by multiple sampling intervals or has the possibility of uncertainty that the observed value does not include the signal and contains the observation noise only. It is assumed that the probability of the observation delay and the probability that the observation does not contain the signal are known. The delayed or uncertain measurements are characterized by the Bernoulli random variables. The characteristic of this paper is that the RLS Wiener estimators are proposed from the randomly delayed, by multiple sampling intervals, or uncertain observations particularly for the descriptor systems in linear discrete-time stochastic systems.
J. Feng, T. Wang and J. Guo, Recursive estimation for descriptor systems with multiple packet dropouts and correlated noises, Aerospace Science and Technology, 32(2014) 200-211.
M. H. Terra, J. Y. Ishihara and A. C. Padoan Jr., Information filtering and array algorithms for descriptor systems subject to parameter uncertainties, IEEE Trans. Signal Processing, 55(2002) 1-9.
J. Y. Ishihara, M. H. Terra and J. C. T. Campos, Robust Kalman filter for descriptor systems, IEEE Trans. Automatic Control, 31(2006) 1354-1358.
J. Y. Ishihara, M. H. Terra and J. C. T. Campos, Optimal recursive estimation for discrete-time descriptor systems, International Journal of Systems Science, 36(2005) 605-615.
J. Y. Ishihara and M. H. Terra, Robust state prediction for descriptor systems, Automatica, 44(2008) 2185-2190.
J. Sjöberg, Descriptor Systems and Control Theory, Division of Automatic Control Department of Electrical Engineering Linköpings universitet, SE-581 83 Linköping, 26th April 2005, Sweden,
B. Sahereha, J. Aliakbar and K, Sedigh Ali, H∞ filtering for descriptor systems with strict LMI conditions, Automatica 80 (2017) 88-94.
J.H. Kim, Delay-dependent robust H∞ filtering for uncertain discrete-time singular systems with interval time-varying delay, Automatica 46 (3) (2010), pp. 591-597.
M. D. Phung, T. V. Nguyen, T. H. Tran and Q. V. Tran, Localization of networked robot systems subject to random delay and packet loss, 2013 IEEE/ASME International Conference on Advanced Intelligent Mechatronics: Mechatronics for Human Wellbeing, AIM 2013 (2013) 1442-1447.
S. Sun, Linear minimum variance estimators for systems with bounded random measurement delays and packet dropouts, Signal Processing 89 (2009) 1457–1466.
S. Sun, L. Xie, W. Xiao, Y. C. Soh, Optimal linear estimation for systems with multiple packet dropouts, Automatica 44 (2008) 1333–1342.
S. Nakamori , R. Caballero-Aguila, A. Hermoso-Carazo and J. Linares-Perez, RLS Wiener estimators from observations with multiple and random delays in linear discrete-time stochastic systems, Applied Mathematics and Computation 225 (2013) 184–194.
N. Nahi, Optimal recursive estimation with uncertain observations, IEEE Trans. Inf. Theory, IT-15 (4) (1969) 457-462.
M. Hadidi, S. Schwartz, Linear recursive state estimators under uncertain observations, IEEE Trans. Automatic Control AC-24 (6) (1979) 944–948.
S. Nakamori, R. Caballero-A’ guilab, A. Hermoso-Carazo and J. Linares-P’erezc, Linear recursive discrete-time estimators using covariance information under uncertain observations, Signal Processing 83 (2003) 1553 –1559.
Y. Liu, B. Xu, L. Feng and S. Li, Optimal Filters with Multiple Packet Losses and its Application in Wireless Sensor Networks, Sensors 2010, 10, 3330-3350; doi:10.3390/s100403330
A. Hermoso-Carazo, J. Linares-P´erez and S.M. Valenzuela-Ruiz, Quadratic extended filtering in nonlinear systems with uncertain observations, Applied Mathematical Sciences 8 (4) (2014) 157–172.
S. Nakamori, RLS Wiener filter and fixed-point smoother with randomly delayed or uncertain observations in linear discrete-time stochastic systems, Computer Reviews Journal 1(1) (2018) 115-135.
S. Nakamori, RLS filter using covariance information and RLS Wiener type filter based on innovation theory for linear discrete-time stochastic descriptor systems, Computer Reviews Journal, 1(2) (2018), 136-147.
A. P. Sage and J. L. Melsa, Estimation Theory with Applications to Communications and Control, New York: McGraw-Hill, 1971.
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