Regularized Nonlinear Moving Horizon Observer for Detectable Systems *

A moving horizon state observer is developed for nonlinear discrete-time systems. The new algorithm is proved to converge exponentially under a strong detectability assumption and the data being persistently exciting. However, in many practical estimation problems, such as combined state and parameter estimation, data may not be exciting for every period of time. The algorithm therefore has regularization mechanisms to ensure graceful degradation of performance in cases when data are not exciting and data are corrupted by noise. This includes the use of a priori estimates in the moving horizon cost function, and the use of thresholded singular value decomposition to avoid ill-conditioned or ill-posed inversion of the associated nonlinear algebraic equations that forms the basis of the moving horizon state estimate.