Exponential stability of regularized moving horizon observer for N-detectable nonlinear systems

A moving horizon observer is analyzed for nonlinear N-detectable discrete-time systems. Conditions for global exponential stability are given. The algorithm can be implemented with regularization to ensure graceful degradation of performance when the data are not exciting. This regularization relies on monitoring an estimate of a Hessian-like matrix and conditions for local exponential convergence are given.