  This work proposes a causal and recursive algorithm for solving the "robust"
principal components' analysis (PCA) problem. We primarily focus on robustness
to correlated outliers. In recent work, we proposed a new way to look at this
problem and showed how a key part of its solution strategy involves solving a
noisy compressive sensing(CS) problem. However, if the support size of the
outliers becomes too large, for a given dimension of the current PC space, then
the number of "measurements" available for CS may become too small. In this
work, we show how to address this issue by utilizing the correlation of the
outliers to predict their support at the current time; and using this as
"partial support knowledge" for solving Modified-CS instead of CS.
