We consider the problem of designing a stable adaptive filter (AF) for state estimation in a high-dimensional system when some parameters of the model and observation noise statistics are unknown. The procedure is essentially based on imposing additional constraints on the allocation of eigenvalues of the filter's transition matrix and on minimizing the prediction error. It is shown that under the detectability condition there exist simple stabilizing structures for the gain matrix with appropriate choices for adjusted parameters which satisfy the imposed constraints. Simple numerical examples are presented to illustrate the theory. A twin experiment on the assimilation of satellite data in the ocean model Miami Isopycnal Coordinate Ocean Model (MICOM) is described and implemented which shows the high efficiency of the proposed filter.