The magnetotelluric method is increasingly being used to monitor electrical resistivity changes in the subsurface. One of the preferred parameters derived from the surface impedance is the strike direction, which is very sensitive to changes in the direction of the subsurface electrical current flow. The preferred method for estimating the strike changes is that provided by the phase tensor because it is immune to galvanic distortions. However, it is also a fact that the associated analytic formula is unstable for noisy data, something that limits its applicability for monitoring purposes, because in general this involves comparison of two or more very similar data sets. One of the issues is that the noise complicates the distribution of estimates between the four quadrants. This can be handled by sending all values to the same quadrant by adding or subtracting the appropriate amount. This is justified by showing that the analytic formula is also a least squares solution. This is equivalent to define penalty functions for the matrix of eigenvalues and then select the minima numerically. Contrary to the analytic formula this numerical approach can be generalized to compute strikes using windows of any number of periods, thus providing tradeoffs between variance and resolution. The performance of the proposed approach is illustrated by its application to synthetic data and to real data from a monitoring array in the Cerro Prieto geothermal field, México.