The problems of estimating the frequency parameter in a univariate noisy sinusoidal model, and deriving the asymptotic properties of the estimator, are well understood. In the multivariate context, there is very little known, apart from papers in the array processing literature, where the common frequency parameter is generally not estimated accurately. We present a method for estimating this frequency and show that the resulting estimator is strongly consistent and follows a central limit theorem. The performance of the estimator is demonstrated using the results of simulation studies.