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.

为了解决与高增益观测器相关的众所周知的噪声灵敏度问题，我们在测量通道上插入了一个低通滤波器。考虑可观察性典范形式的非线性植物，我们首先提出一种架构，在该架构中，输出误差由线性系统过滤，该线性系统由其任意阶数和标量正增益参数化。我们的主要结果是根据测量噪声建立一个估计误差的指数有限增益，该增益取决于高增益和滤波器参数。我们还根据滤波器参数证明了边界，这些滤波器参数表征了从测量噪声到估计误差的改善的高频增益。所提出的构造在数值模拟中表现出理想的性能。