This letter considers the task of estimating the norm of an n-dimensional Gaussian random vector given a noisy/perturbed observation of it. In particular, the focus is on the case of additive Gaussian noise perturbation, which is assumed to be independent of the original vector. First, an expression for the optimal estimator is derived, and then the corresponding minimum mean square error (MMSE) is computed. The regime of large vector size is also analyzed, and it is shown that the MMSE normalized by n equals zero when n → ∞.
All Science Journal Classification (ASJC) codes
- Signal Processing
- Electrical and Electronic Engineering
- Applied Mathematics
- Gaussian noise
- MMSE estimator
- vector norm estimation