Linear set-membership state estimation with unknown but bounded disturbances

Abstract

In this article, we consider the problem of discrete-time linear state estimation when at every discrete instant Δ the Euclidean norm of the discrete-time disturbance ‖w(Δ)‖₂ is bounded within some known value. Specifically, given a hypersphere that contains the uncertain disturbance signal w(Δ) and an ellipsoid containing the uncertain system state x(Δ) at time step Δ, a sub-optimal approach to computing a linear minimax filter which constructs a minimal ellipsoid to contain x(Δ + 1) is derived. A distinct feature of our approach when compared to earlier solutions is that both the filter and the performance bound can be pre-computed off-line.

Keywords:

• Kalman filtering
• H _∞ estimation
• minimax filtering
• set-membership filter
• unknown but bounded noises
• bounded-power disturbances

Acknowledgement

The authors thank the reviewers for their helpful comments to improve the presentation and readability of this article.