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Subspace-tracking algorithms have traditionally been unable to deal with a large number of sources and at the same timepreserve their computationally efficiency, since, typically, efficiency goes down as the cube of the signal subspace dimension. One solution to this problem, which is presented in this paper, is to use a newly developed algorithm for the design of spatial filters in matrix form, in order to spatially filter the incoming data snapshots. The result is that the signal subspaces are confined to small angular sectors and, thus, the effective number of signals present is reduced. A method is developed for designing spatial filters in an efficient manner by formulating the design procedure as a rank-deficient linear least-squares problem. The source-bearing estimation is done using the signal-covariance matrix, which is updated using a recently developed fast algorithm, which is necessary in situations where one or more sources are nonstationary. The combination of the subspace-based bearing-estimation and spatial filter algorithms is shown to give good performance in cases of medium signal-to-noise ratio and is capable of resolving sources that are below the resolution limit of both conventional and adaptive beamforming. In addition, the use of spatial filtering makes it possible to estimate bearings for more than N narrow-band sources, using an N-element array. An example illustrating this capability is given.