Multivariate Real-Time Signal Extraction by a Robust Adaptive Regression Filter

The Multivariate Linear Prediction Problem: Model-Based and Direct Filtering Solutions

“…It is common to approach real-time problems with linear filters, although there is a burgeoning literature on non-linear techniques. Borowski, Schettlinger, and Gather (2009) examine the multivariate real-time problem using regression techniques, with extensions in Schettlinger, Fried, and Gather (2010) that robustify the results. Nonparametric approaches to signal extraction may involve singular spectrum analysis (Golyandina, Nekrutkin, and Zhigljavski (2001) There exists a substantial literature addressing the issue of how to obtain a causal (or asymmetric) adaptation of a given symmetric filter.…”

“…First suppose that {X t } is weakly stationary with mean zero and spectral density F . The real-time estimation error is given in (6), which has mean zero and N × N variance matrix…”

Reducing False Alarms of Intensive Care Online‐Monitoring Systems: An Evaluation of Two Signal Extraction Algorithms

“…The estimate $\hat{\Sigma }(t)$ is utilised to detect residual vectors that are outliers regarding the local covariance structure, that is, residual vectors r( t − n * + s ), s = 1,…, n *, with $\text{r}{\left(t-n^{\ast }+s\right)}^{\text{T}}\widehat{\mathrm{normal\Sigma }}{0.75em0.75em(t0.75em0.75em)}^{-1}\text{r}\left(t-n^{\ast }+s\right)>d,$ where d > 0 is an adequate upper bound. (For more details see [16, 19] or [20]. ) Then, observation vectors y( t − n * + s ), which correspond to outlying residual vectors r( t − n * + s ), are removed from the window sample.…”

“…The adaptive online RM (aoRM) [ 15 ] chooses the window width for the RM automatically; as long as the data are “stable”, the window width gradually grows but when a structural change, for example, a level shift, occurs, the window width is set to a predetermined minimum value. The aoRM is enhanced to a filtering procedure for multivariate time series, namely, the adaptive online Trimmed Repeated Median-Least Squares (aoTRM-LS) filter [ 16 ]. This procedure factors in local cross-correlations (e.g., systolic and diastolic arterial pressure are highly correlated) in order to improve the filtering outcome.…”

Real‐time signal processing by adaptive repeated median filters

“…In [32] the proposed methodology of adaptive window width choice has been transferred to filters extracting signals from multivariate time series based on methods proposed in [33]. Applying such multivariate filters to highly correlated intensive-care time series, such as systolic, mean and diastolic blood pressures, seems a promising approach to an even stronger improvement of currently used threshold alarm systems.…”