On Convergence of the Iteratively Preconditioned Gradient-Descent (IPG) Observer

This letter considers the observer design problem for discrete-time nonlinear dynamical systems with sampled measurements. The recently proposed Iteratively Preconditioned Gradient-Descent (IPG) observer, a Newton-type observer, has been empirically shown to have improved robustness against measurement noise than the prominent nonlinear observers, a property that other Newton-type observers lack. However, no theoretical guarantees on the convergence of the IPG observer were provided. This letter presents a rigorous convergence analysis of the IPG observer for a class of nonlinear systems in deterministic settings, proving its local linear convergence to the actual trajectory. The assumptions are standard in the existing literature of Newton-type observers, and the analysis further confirms the relation of IPG observer with Newton observer, which was only hypothesized earlier.