Robust Scheduling Filter Design for a Class of Nonlinear Stochastic Poisson Signal Systems

摘要

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 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 robust filter design problem for a nonlinear stochastic Poisson signal system can be simplified. The optimal 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 (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 robus- scheduling filter.