NMPC explicitly addresses constraints and nonlinearities during the feedback control of batch processes. This NMPC algorithm also explicitly takes parameter uncertainty into account in the state estimation and state feedback controller designs. An extended Kalman filter estimates the process noise covariance matrix from the parameter uncertainty description and employs a sequential integration and correction strategy to reduce biases in the state estimates due to parameter uncertainty. The shrinking horizon NMPC algorithm minimizes a weighted sum of the nominal performance objective, an estimate of the variance of the performance objective, and an integral of the deviation of the control trajectory from the nominal optimal control trajectory. The robust performance is quantified by estimates of the distribution of the performance index along the batch run obtained by a series expansion about the control trajectory. The control and analysis approaches are applied to a simulated batch crystallization process with a realistic uncertainty description. The proposed robust NMPC algorithm improves the robust performance by a factor of six compared to open loop optimal control, and a factor of two compared to nominal NMPC. Monte Carlo simulations support the results obtained by the distributional robustness analysis technique.