This chapter addresses Gross Error Detection using uni-variate signal-based approaches and an algorithm for the peak noise level determination in measured signals. Gross Error Detection and Replacement (GEDR) may be carried out as a pre-processing step for various model-based or statistical methods. More specifically, this work presents developed algorithms and results using two uni-variate, signal-based approaches regarding performance, parameterization, commissioning, and on-line applicability. One approach is based on the Median Absolute Deviation (MAD) whereas the other algorithm is based on wavelets. In addition, an algorithm, which was developed for the parameterization of the MAD algorithm, is also utilized to determine an initial variance (or peak noise level) estimate of measured variables for other model-based or statistical methods. The MAD algorithm uses a wavelet approach to set the variance of the noise in order to initialize the algorithm. The findings and accomplishments of this investigation are: 1. Both GEDR algorithms, MAD based and wavelet based, show good robustness and sensitivity with respect to one type of Gross Errors (GEs), namely outliers. 2. The MAD based GEDR algorithm, however, performs better with respect to both robustness and sensitivity. 3. The algorithm developed to detect the peak noise level is accurate for a wide range of S/N ratios in the presence of outliers. © Springer-Verlag Berlin Heidelberg 2007.