The inadequacy of the standard notions of detectability and observability to ascertain robust state estimation is shown. The notion of robust state estimation is defined, and for a class of processes the conditions under which the robust state estimation is possible, are given. A method of robust, nonlinear, multi-rate, state estimator design is presented. It can be used to improve robustness in an existing estimator or design a new robust estimator. Estimator tuning guidelines that ensure the asymptotic stability of the estimator error dynamics are given. To ensure that estimation error does not exceed a desired limit, the sampling period of infrequent measurements should be less than an upper bound that depends on factors such as the size of the process dominant time constant, the magnitude of measurement noise, and the level of process-model mismatch. An expression that can be used to calculate the upper bound on the sampling period of infrequent measurements, is presented. The upper bound is the latest time at which the next infrequent measurements should arrive to ensure that estimation error does not exceed a desired limit. The expression also allows one to calculate the highest quality of estimation achievable in a given process. A binary distillation flash tank and a free-radical polymerization reactor are considered to show the application and performance of the estimator.