Here, we formulate robust state space models (SSMs) and develop inference tools in the context of fisheries science and management. Our prototype model concerns the maturity of fish by age over time, knowledge of which is fundamental to understanding the dynamics and productivity of fish stocks, a key component in fish stock assessment. Our SSM incorporates dynamics over time and yields robust estimates of the proportion of fish mature at various ages for a collection of cohorts of interest. The estimates are obtained using an iterative weighted likelihood where the high-dimensional unobserved dynamics of the SSM and the optimization over the fixed parameters are handled with the Automatic Differentiation Model Builder. The data used to both demonstrate and validate our new approach comes from the annual sampling program of Fisheries and Oceans Canada, the primary scientific and regulatory body responsible for stock assessments. In addition, we carried out a comprehensive simulation study to demonstrate the robustness of our approach to realistic contamination.