State smoothing and filtering are treated for non-linear dynamic systems in the absence of observations in a considered observation interval. Models are taken to be non-linear functions of the states, disturbance noises, and observation noises, whereas the state estimation of these models cannot, in general, be performed by classical estimation schemes, such as the extended Kalman filter. State estimation is performed in blocks by estimating missing observations with interpolating functions. The resulting estimation scheme requires a constant memory for its implementation.