This paper deals with robust state estimation when parametric uncertainties nonlinearly affect a plant state-space model. A new framework is suggested on the basis of simultaneous minimization of nominal estimation errors and the sensitivities of estimation errors to model uncertainties. Under the condition that plant parameters are differentiable with respect to modelling errors, an analytic solution is derived for the optimal estimator which can be recursively realized. The computational complexity of the derived filter is comparable to that of the Kalman filter. Numerical simulations show that the obtained filter may have smaller estimation variance than other methods.