5. Performance

When the state-dynamic model is non-linear, approximations are used to estimate the state of the system. The estimators are obtained either by analytic linearization of the state-dynamic system (EKF) or by statistical approximation (particle filters), making the estimators sub-optimal. To analyze the impact of the approximation, the covariance matrix of the estimation error is compared with the minimum bound called the Cramer-Rao a posteriori bound . This bound gives an indication of the estimator's performance limits. Widely used in parametric estimation, the Cramer-Rao inequality is also defined for random processes, as demonstrated by Van Trees