Robust signal extraction for on-line monitoring data

Abstract

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 artifacts from clinical relevant structural changes in the patients condition (Gather et al., 2002). 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 L 1 regression, the repeated median (Siegel, 1982) and the least median of squares (Hampel, 1975, Rousseeuw, 1984. The question of dependency between different items is a topic for future research.MSC: primary: 62G07; secondary: 62G35

Robust forecasting with exponential and Holt–Winters smoothing

“…. , m. The repeated median regression has been shown to have good properties for time series smoothing; see, for example, Davies et al (2004) and Fried (2004). A starting value of the recursive scale estimation in (12) is obtained by the MAD of the regression residuals in this startup period.…”

Modified repeated median filters

“…The resulting procedure would resemble the popular reweighted least squares (Rousseeuw andLeroy 1987, Gervini andYohai 2002). However, the instability of the LMS is dangerous in automatic applications (Davies et al 2004), and weighting the observations according to their distance from the LMS fit does not necessarily remove this instability when the observations in the window are located close to two or more straight lines. When using the repeated median for the initial fit as is done here we have not observed such instabilities in spite of the lack of continuity.…”

“…Similarly, MTM-filters rely on a location model for trimming. Instead, Davies et al (2004) suggest robust fitting of a linear trend µ t+i = µ t + iβ t , i = −k, . .…”

“…These filters are more efficient for Gaussian noise, they also remove spikes and may preserve steps even better than running medians (Himayat and Kassam 1993). Davies, Fried and Gather (2004) propose the repeated median, a robust regression estimator, to overcome the difficulties of the median during trends.…”

Effects of drift and noise on the optimal sliding window size for data stream regression models

“…Though the influence of the window size on the prediction is discussed in this work, nevertheless only heuristic methods for the choice of the widow size are used. Similar work is carried out in Davies et al (2004), also here the robust methods for on-line regression are applied to the time windows with fixed size without taking the possible non-stationarity and noisiness of the data into account. In Nadungodage et al (2011) not only the data from the current time window but also the previous data are used for prediction.…”