## 1 Introduction  
The gross error detection and replacement (GEDR) for many methods based on models or statistics is an important issue in the control field. For instance, a parameter estimation (PE) and data reconciliation (DR) can be taken into consideration very often. At the present time, only a priori noise knowledge based techniques in GEDR are used in industrial applications to detect the outliers that are based on statistical methods. It should be noted that many techniques on the basis of statistical methods could be applied in this context. It becomes more and more essential to clean the data coming from a distributed control system (DCS) because applications in the field of production rely on a great quantity of raw data. Soft sensoring, data reconciliation and parameter estimation need \"clean data\" [1]. A denoising method based on techniques described in [2] is shown in [3]. This method presented in [4] is based on other methods considered in [2]. The above-mentioned method compares the information theory criterion. A robust version of the Hampel Filter has been developed in [5; 6; 7]. A new method of de-noising, which is based on methods already introduced in [2], is presented in [3]. It is based on the comparison of an information theory criterion that is the \"description length\" of the data. In [4; 8], this theoretical approach is applied. The description length is calculated for different subspaces of the basis and the method suggests choosing the noise variance and the subspace for which the description length of the data is at a minimum. In the work, based on [4], it is shown that the de-noising process can be done simultaneously. The approach presented in [4; 8] is based on \"minimum description length\" and that's why it seems to be unsuitable for online detection because it needs a relatively large amount of data. Simultaneous approaches often suffer from the fact that they are based on iterations, which, in turn, impose heavy CPU load requirements on the applications. As a consequence, these approaches often become infeasible for real-time applications, and, therefore, have not been widely used in industry. Real-time approaches dealing with outlier detection and/orde-noising, and featuring easy means of implementation, have also been developed as in [9]. In general, for removing the noise, a lower threshold should be set. This article intends to create an approach treating the outlier detection with denoising in real time without using an a priori noise knowledge technique. Reference [10] demonstrates a procedure that is median function-based, and it is applied in a wavelet-based algorithm. The wavelet-based algorithm proposed in this work is of particular quality due to the adopted a priori noise knowledge free technique. Nevertheless, some misclassifications that may occur are briefly shown at the end of this contribution. The advantage of the presented algorithm consists of its working independently, so no a priori knowledge of the noise level is necessary. Noise level algorithms are considered to be complex and need a great data volume (see [2; 3; 8]). The advantage of this technique shows that, using a limited stored data, a denoising and fault detection is possible. Figure 1 presents a block diagram of a GEDR package (PCK) interacting with gEST. This paper proposes an algorithm to differentiate discrete signals from their outlier observations using a library of Haar wavelet basis. The algorithm is totally general and can be used in many industrial applications. The effectiveness of the proposed method consists of applying the concept of Lipschitz for using as few samples as possible of the measured signal, and, in the meantime, highlighting the difference between the outliers and the desired signal. The goal is to extract coherent features from the measured signal that will be saved in terms of variance of the Lipschitz constant of the desired signal and outlier signals (or incoherent signal) of which the variance of the Lipschitz constant lies outside this confidential interval.