The fast flowing ice stream of the Pine Island Glacier (PIG) in West Antarctica feeds the Pine Island Ice Shelf (PIIS). Its flow acceleration, thinning and mass loss has been associated with changes in sub-ice shelf ocean circulation. Several recent field and remote sensing programs focused on the Pine Island Embayment and PIG to study the local circulation, water mass properties, as well as bathymetry and cavity geometry. Observations of water mass properties entering and leaving the ice-cavity of the PIIS, as well as observations within the cavity are used to estimate a horizontal map of basal melt rates for the PIIS. For this purpose a regional ocean general circulation model that includes ice-ocean interactions is fitted to observations using optimal estimation methods. Hence, the estimates combine on both observations and the dynamical information about the circulation underneath the ice-shelf as resolved by the numerical model. The control variables, that are adjusted during the estimation process, are initial conditions, open boundary conditions, vertical mixing parameters, and melt rates. Data coverage, but also the choice of bathymetry and melt-rate parameterization, affect the state estimate and the net melt rate.