The singular evolutive extended Kalman (SEEK) filter has been proposed recently by \it Pham et al. \cite{seek} for data assimilation into numerical oceanic models. This filter has been applied in different realistic ocean frameworks and have provided satisfactory results \citegourdeau,seek,verron. However, the SEEK filter remains expensive in real operational assimilation. To reduce cost and obtain a better representativity, we introduce the idea «local correction basis». In this local analysis, the basis vectors support a small region of the model domain and vanish elsewhere. Such basis however can not be made to evolve according to the model without destroying its locality property. Therefore we shall keep this basis fixed and we argument it by a few global basis vectors which evolve. The resulting semi-evolutive partially local filter is much less costly to implement than the SEEK filter and yet can yield better results. In a first application, validation twin experiments are conducted in a realistic setting of the OPA model over the tropical pacific ocean.