Covariate Estimation & Unbiased Estimation

I work with a group that utilizes the Mahalanobis Distance to detect the health of a system, mostly electronics. Within this research, we are looking at the most efficient way to estimate the covariance matrix because degraded estimates effect the accuracy of outlier detection algorithms.

I'm not necessarily asking straight up what is the best method for covariance estimation, but where's a good place to get started?

Also, since I'm getting started, I would really appreciate any insight on what is known about covariance estimation. Thank you so much to anyone that takes some time on this.