In this article, we borrow from the blind noise parameter estimation (BNPE) methodology early developed in the image processing field an original and innovative no-reference approach to estimate digital elevation model (DEM) vertical error parameters without resorting to a reference DEM. The challenges associated with the proposed approach related to the physical nature of the error and its multifactor structure in DEM are discussed in detail. A suitable multivariate method is then developed for estimating the error in gridded DEM. It is built on a recently proposed vectorial BNPE method for estimating spatially correlated noise using noise informative areas and fractal Brownian motion. The new multivariate method is derived to estimate the effect of the stacking procedure and that of the epipolar line error on local (fine-scale) standard deviation and autocorrelation function width of photogrammetric DEM measurement error. Applying the new estimator to Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) GDEM2 and Advanced Land Observing Satellite (ALOS) World 3D DEMs, good agreement of derived estimates with results available in the literature is evidenced. Adopted for TanDEM-X-DEM, estimates obtained agree well with the values provided in the height error map. In future works, the proposed no-reference method for analyzing DEM error can be extended to a larger number of predictors for accounting for other factors influencing remote sensing (RS) DEM accuracy.