Numerical aspects of the inverse function theory

The state-estimation problem can be formulated as an inversion problem. From this point of view, we first review known results about the relationship between the existence of an unbiased estimate and the observability condition of a nonlinear system. The inversion relationship between the Fisher information matrix and the error covariance matrix, evaluated at the true state of an observable nonlinear System, is extended to an unobservable nonlinear system. A singular value decomposition technique solves the sensitivity question of a nonlinear inversion problem. The technique is applied to evaluate a radar calibration procedure.