  This paper considers the observer design problem for discrete-time nonlinear
dynamical systems with sampled measurement data. Earlier, 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 paper 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. Our assumptions are standard in the existing literature of
Newton-type observers, and the analysis further confirms the relation of the
IPG observer with the Newton observer, which was only hypothesized earlier.
