Probability-Guaranteed Envelope-Constrained Filtering for Nonlinear Systems Subject to Measurement Outliers

This article deals with the recursive filtering problem for nonlinear time-varying stochastic systems subject to possible measurement outliers. In order to mitigate the effects from possible abnormal measurements, we construct a filter with a saturation constraint imposed on the innovations where the saturation level is adaptively determined according to the estimation errors. Two performance indices, namely, the finite-horizon H-infinity specification and the envelope-constraint criterion with a prescribed probability, are put forward to describe the transient characteristics of the filtering error dynamics over a specified time interval. The purpose of the addressed problem is to design a filter capable of guaranteeing both the finite-horizon H-infinity performance index and the probability-guaranteed envelope-constraint. Sufficient conditions are derived for the existence of the desired filter via certain convex optimization algorithms. Finally, an illustrative numerical example is proposed to demonstrate the effectiveness of the developed algorithm.

Automated summary

This article addresses the recursive filtering problem for nonlinear time-varying stochastic systems with possible measurement outliers, proposing a filter design with saturation constraint to mitigate the effects of abnormal measurements. Performance indices such as finite-horizon H-infinity specification and envelope-constraint criterion are used to describe transient characteristics of filtering error dynamics, with sufficient conditions for the filter's existence derived through convex optimization algorithms. An illustrative numerical example is presented to demonstrate the effectiveness of the developed algorithm.