Recently, optimal linearly constrained minimum variance (LCMV) filtering methods have been applied for fundamental frequency estimation. Like many other fundamental frequency estimators, these methods utilize the inverse covariance matrix. Therefore, the covariance matrix needs to be invertible which is typically ensured by using the sample covariance matrix involving data partitioning. The partitioning adversely affects the spectral resolution. We propose a novel optimal filtering method which utilizes the LCMV principle in conjunction with the iterative adaptive approach (IAA). The IAA enables us to estimate the covariance matrix from a single snapshot, i.e., without data partitioning. The experimental results show, that the performance of the proposed method is comparable or better than that of other competing methods in terms of spectral resolution.