Key result
A robust H∞ scheduling filter design using a Polytopic Linear Model scheme successfully approximated Hamilton-Jacobi inequalities to achieve an optimal filtering level for nonlinear stochastic Poisson signal systems.
Proposes a robust H∞ scheduling filter design for nonlinear stochastic Poisson signal systems using PLM and LMIs.
Simplifies robust H∞ filter design for nonlinear stochastic systems; leaves open empirical validation in applied settings.
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∞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∞robust filter design problem for a nonlinear stochastic Poisson signal system can be simplified. The optimal H∞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 γ* (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∞robust scheduling filter.
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Chen et al. (2015) studied this question. Robust H∞ scheduling filter design based on Polytopic Linear Model (PLM) was evaluated on Optimal filtering level γ* (minimum value of the filtering error-to-noise ratio in a mean square sense). A robust H∞ scheduling filter design using a Polytopic Linear Model scheme successfully approximated Hamilton-Jacobi inequalities to achieve an optimal filtering level for nonlinear stochastic Poisson signal systems.
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