Among the various covariance matrix estimators, the regularised Tyler estimator performs independently from the data distribution and is robust to data outlier corruption. However, the shrinkage parameter value selection depends on the target application and data configuration, and have a direct influence on the estimator performance results. Thus finding a generic rule optimal for every criterion is not straightforward. This paper proposes a new regularistaion parameter selection based on a subspace approach. The performances of this method are investigated both in simulation and application to the adaptive buried objects detection problem.