Noise Sensitivity Reduction in Low-power Multi High Gain Observers Using Low-pass Filters

Abstract

Low-power multi high gain observers (LP MHGO) are proven to be effective in reducing the peaking of state estimation of nonlinear systems to an arbitrarily small magnitude. Moreover, they reduce the sensitivity of estimates to measurement noise. They also relax the numerical implementation problem of high gain observers by using gains powered up to the order of 2 instead of n. In this paper, we aim to further reduce the noise sensitivity of these observers by employing low-pass filters in the observer dynamics. The main results establish the convergence of the estimation error to zero with an arbitrarily small decay rate in the absence of noise, as well as an input to state stability feature when the noise is present. We also demonstrate in the linear case that the proposed observer improves the upper bound on the estimates. Simulation results compare the performance of the proposed observer with similar works and show the effectiveness of the proposed method.