A new data assimilation scheme derived from the singular evolutive extended Kalman (Seek) filter is introduced. The novel feature of the new filter is its correction basis which is partially local in the sense that it consists of "global" and "local" vectors, the later obtained from a local empirical orthogonal functions (Eof) analysis. Such an analysis was introduced in order to better represent the local variability of the ocean. This not only significantly reduces the implementation cost but may also improve the representativeness of the correction basis of the filter. The performance of this scheme is evaluated through twin experiments conducted in a realistic setting of the OPA model over the tropical Pacific zone. The results are compared against those of the Seek filter. The new filter is shown to perform better while it is up to six times faster. Adaptive tuning of the forgetting factor was also used, which enhances performance and improves the stability of the filter during model unstable periods.