Data from the automatic monitoring of intensive care patients exhibits trends, outliers, and level changes as well as periods of relative constancy. All this is overlaid with a high level of noise and there are dependencies between the different items measured. Current monitoring systems tend to deliver too many false warnings which reduces their acceptability by medical staff. The challenge is to develop a method which allows a fast and reliable denoising of the data and which can separate artefacts from clinical relevant structural changes in the patients condition (Estadistica 53 (2001) 259). A simple median filter works well as long as there is no substantial trend in the data but improvements may be possible by approximating the data by a local linear trend. As a first step in this programme, the paper examines the relative merits of the L1 regression, the repeated median (Biometrika 68 (1982) 242) and the least median of squares (Bull. Internat. Statist. Inst. 46 (1975) 375; J. Amer. Statist. Assoc. 79 (1984) 871). The question of dependency between different items is a topic for future research.