Rigorous statistical testing of deformation using a terrestrial laser scanner (TLS) can avoid events such as structure collapses. Such a procedure necessitates an accurate description of the TLS measurements' noise, which should include the correlations between angles. Unfortunately, these correlations are often unaccounted for due to a lack of knowledge. This contribution addresses this challenge. We combine (i) a least-square approximation to extract the geometry of the TLS point cloud with the aim to analyze the residuals of the fitting and (ii) a specific filtering coupled with a maximum likelihood estimation to quantify the amount of flicker noise versus white noise. This allows us to set up fully populated variance covariance matrices of the TLS noise as a result.