Mean-square state and parameter estimation for stochastic linear systems with Poisson noise

Mean-square filter design for stochastic polynomial systems with Gaussian and Poisson noises

“…He serves as the editor-in-chief of the Journal of The Franklin Institute, an associate editor of Automatica, IET-Control Theory and Applications, International Journal of Systems Science, and other journals, as a session chairman at a series of the leading IEEE and IFAC conferences, and as a reviewer for a number of leading international journals and conferences in the area of automatic control. Systems 2010, 2012, 2014, World Automation Congress 2012, Mexican Automatic Control Conferences 2006, 2008 Basin was awarded the title of a highly cited researcher by Thomson Reuters (International Science Institute), the publisher of Science Citation Index, in 2009; he is a senior member of the IEEE Control Systems Society and a regular member of the Mexican Academy of Sciences. His research interests include optimal filtering and control problems, stochastic systems, time-delay systems, identification, sliding mode control and variable structure systems.…”

“…It is known that the mean-square filter for linear systems with Poisson white noises coincides with the Kalman-Bucy filter (Liptser and Shiryayev 1989;Pugachev and Sinitsyn 2001). Other results related to non-linear Poisson systems can be found in Lu, Liang, and Chen (2001), Kolmanovsky and Maizenberg (2002a), Hannequin and Mas (2002), Kolmanovsky and Maizenberg (2002b), Zhang, Fadili, Starck, and Dige (2008b), Dupé, Fadili, and Starck (2008), Zhang, Fadili, and Starck (2008a), , Basin, Maldonado, and Karimi (2011), Basin and Maldonado (2012). However, to the best of authors' knowledge, no filtering algorithms solving the mean-square filters * Corresponding author.…”

Mean-square filtering problem for stochastic polynomial systems with Gaussian and Poisson noises

“…Numerical simulation results are obtained solving the systems of filtering equations (21)-(24), (25)- (26), and (27)- (28). The obtained values of the estimates m 1G (t) + m 1P (t), m 2G (t)+m 2P (t), m l1 (t), m l2 (t), m k1 (t), and m k2 (t) satisfying the equations (21), (22), (25) and (27), respectively, are compared to the real values of the state variables x 1 (t) and x 2 (t) in (19).…”

“…The obtained values of the estimates m 1G (t) + m 1P (t), m 2G (t)+m 2P (t), m l1 (t), m l2 (t), m k1 (t), and m k2 (t) satisfying the equations (21), (22), (25) and (27), respectively, are compared to the real values of the state variables x 1 (t) and x 2 (t) in (19). For each of the two filters (21)-(24),(25)- (26) and (27)- (28), and the reference system (19)- (20), involved in simulation, the following initial values are assigned: x 10 = 1,…”

“…1 and 2, graphs of the state (19) x 1 (t), x 2 (t) and the filter (25), (26) estimates m k1 (t) and m k2 (t), are shown in Figs. 3 and 4, graphs of the state (19) x 1 (t), x 2 (t) and the filter (27), (28) estimates m l1 (t) and m l2 (t), are shown in Figs.…”