Optimal‐switched extended H_∞ filter for nonlinear systems with stochastic uncertainties

Abstract

The extended H ∞ filter (EH ∞ F) is a conservative solution with infinite-horizon robustness for the state estimation problem regarding nonlinear systems with stochastic uncertainties, which leads to excessive costs in terms of filtering optimality and reduces the estimation precision, particularly when uncertainties related to external disturbances and noise appear intermittently. In order to restore the filtering optimality lost due to the conservativeness of the EH ∞ F design, we developed an optimal-switched (OS) filtering mechanism based on the standard EH ∞ F to obtain an optimal-switched extended H ∞ filter (OS-EH ∞ F). The OS mechanism has an error-tolerant switched (ETS) structure, which switches the filtering mode between optimal and H ∞ robust by setting a switching threshold with redundancy to uncertainties, and a robustness-optimality cost function (ROCF) is introduced to determine the threshold and optimize the ETS structure online. The ROCF is the weighted sum of the quantified filtering robustness and optimality. When a weight is given, the proposed OS-EH ∞ F can obtain the optimal state estimates while maintaining the filtering robustness at an invariant ratio. A simulation example of space target tracking has demonstrated the superior estimation performance of the OS-EH ∞ F compared with some other typical filters, thereby verifying the effectiveness of using the weight to evaluate the estimation result of the filters.

Robust estimation algorithm based on prior probability statistics

“…But these estimators are mostly suitable for linear systems or use linearization to deal with nonlinear estimation problems. Based on the standard extended filter and an optimal‐switched filtering mechanism, an optimal‐switched extended filter (OS‐EF) is proposed by Li et al 38 The OS‐EF has an error‐tolerant switched structure, which switches the filtering mode between optimal and robust by setting a switching threshold with redundancy to uncertainties, and a robustness‐optimality cost function is introduced to determine the threshold and optimize the error‐tolerant switched structure online. The OS‐EF algorithm has good applicability for nonlinear systems with uncertainties related to external disturbances and noise appeared intermittently.…”

The Sliding Innovation Filter

“…However, a trade-off exists between optimality and robustness. Other methods have extended the H ∞ filtering strategy further by combining it with the KF and its nonlinear variants [17], [18].…”