On the use of low-pass filters in high-gain observers

• DOI: 10.1016/j.sysconle.2020.104856
• Publication Date: 2021-01-13T00:13:35Z
• Authors: Daniele Astolfi; Luca Zaccarian; Marc Jungers
• Keywords: Observability; High-gain antenna

To address the well-known noise sensitivity problems associated with high-gain observers, we insert a low-pass filter on the measurement channel. Considering nonlinear plants in observability canonical form, we first motivate an architecture where the output error is filtered by a linear system parametrized by its arbitrary order and a scalar positive gain. Our main result establishes an exponential finite gain bound for the estimation error, from the measurement noise, this gain being dependent on the high-gain and filter parameters. We also prove bounds depending on the filter parameters characterizing improved high-frequency gains from the measurement noise to the estimation error. The proposed construction is shown to behave desirably in numerical simulations.