IPG Observer: A Newton-Type Observer Robust to Measurement Noise

The previously proposed Newton observer for nonlinear systems has fast exponential convergence and applies to a wide class of problems. However, the Newton observer lacks robustness against measurement noise due to the computation of a matrix inverse. In this paper, we propose a novel observer for discrete-time system with sampled measurements to alleviate the impact of measurement noise. The key to the proposed observer is an iterative pre-conditioning technique for the gradient-descent method, used previously for solving general optimization problems. The proposed observer utilizes a non-symmetric pre-conditioner to approximate the observability mapping’s inverse Jacobian so that it asymptotically replicates the Newton observer with an additional benefit of enhanced robustness against measurement noise. Our observer applies to a wide class of nonlinear systems, as it is not contingent upon linearization or any specific structure in the plant nonlinearity. Its improved robustness compared to the prominent nonlinear observers is demonstrated through empirical results.