Fast and Robust Filtering of Time Series with Trends

Fast and robust methods are needed for denoising time series data measured with high sampling frequencies. In intensive care e.g. physiological variables like the heart rate are observed in short time intervals. Systematic changes have to be detected quickly and distinguished from clinically irrelevant short term fluctuations and artifacts. Median filtering works well if there is no substantial trend in the data but improvements are possible by approximating the data by a local linear trend.