In an environment of spatially correlated additive noise, the direction estimation apparatus for coherent signals calculates (M−q−1) instantaneous cross-correlations between some array data, and selecting multiple pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations to form a Hankel correlation matrix, where a length of a spatial correlation in terms of antenna elements is assumed to be q. Next, the apparatus divides that Hankel matrix into an upper submatrix and a lower submatrix, and then calculates a linear operator at time n by using the adaptive LMS algorithm with a fixed or time-varying step-size parameter. Then a noise subspace is estimated from that linear operator. Finally the directions of incident signals at a predetermined time is estimated and tracked by using that noise subspace with Newton approximation.