Ocean acidification monitoring and carbon accounting require accurate estimates of marine carbonate system variables, particularly in dynamic coastal regions where observations remain sparse. This study presents an approach to improving carbonate system state estimates in the California Current System through the assimilation of underwater glider observations with both dynamical and statistical models. We implement a 4D-Var data assimilation system that jointly assimilates physical variables, chlorophyll, and glider-based pH and alkalinity data into a regional coupled physical-biogeochemical model. Our results demonstrate that joint assimilation of carbonate system variables successfully improves pH and alkalinity estimates while maintaining the quality of physical and chlorophyll estimates. Cross-validation experiments reveal that pH data assimilation typically improves estimates near the observation network, although downstream advection of increments can occasionally degrade results. We also show that hybrid estimates that combine the output of the dynamical, physical ocean model with a statistical model produce accurate carbonate system estimates without requiring a biogeochemical model. This finding suggests that physical ocean models and data assimilation systems can obtain reasonable carbonate system estimates by combining statistical methods with model estimates of temperature and salinity.