  This paper presents a novel, closed-form, and data/computation efficient
online anomaly detection algorithm for time-series data. The proposed method,
dubbed RPE, is a window-based method and in sharp contrast to the existing
window-based methods, it is robust to the presence of anomalies in its window
and it can distinguish the anomalies in time-stamp level. RPE leverages the
linear structure of the trajectory matrix of the time-series and employs a
robust projection step which makes the algorithm able to handle the presence of
multiple arbitrarily large anomalies in its window. A closed-form/non-iterative
algorithm for the robust projection step is provided and it is proved that it
can identify the corrupted time-stamps. RPE is a great candidate for the
applications where a large training data is not available which is the common
scenario in the area of time-series. An extensive set of numerical experiments
show that RPE can outperform the existing approaches with a notable margin.
