期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 63, 期 23, 页码 6245-6257出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2015.2465305
关键词
Hamilton-Jacobi inequality (HJI); linear matrix inequality (LMI); Poisson jump system; polytopic linear model (PLM) scheduling; robust scheduling filter
资金
- National Science Council [MOST-103-2745-E-007-001-ASP]
Nonlinear dynamic systems may suffer from both continuous Wiener noise and discontinuous Poisson noise. This paper studies a robust filter design for a class of nonlinear stochastic Poisson signal systems with external disturbances. Currently, there are no good filtering design methods to treat the discontinuous Poisson noise filter problem. Based on the Ito-Levy formula, a robust H-infinity filter design is proposed for nonlinear stochastic Poisson signal systems by solving a Hamilton-Jacobi inequality (HJI) for the robust filter design of a nonlinear stochastic Poisson signal system. However, such an HJI is difficult to solve. Hence, this study employs the Polytopic Linear Model(PLM) scheduling scheme to approximate this HJI by a set of linear matrix inequalities(LMIs) so that the H-infinity robust filter design problem for a nonlinear stochastic Poisson signal system can be simplified. The optimal H-infinity robust scheduling filter design problem for the nonlinear stochastic Poisson signal system is also discussed. Since the PLM interpolation method transforms the HJI-constrained optimization problem into an LMI-constrained optimization problem which can be efficiently solved using the LMI toolbox in MATLAB, an optimal filtering level gamma* (the minimum value of the filtering error-to-noise ratio in a mean square sense) can be achieved. Finally, a simulation example of a robust trajectory estimation problem in an anti-tactical ballistic missile radar system with discontinuous random maneuvering jets is given to illustrate the design procedure and to confirm the estimation performance of the proposed H-infinity robust scheduling filter.
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