  Security related questions for Cyber Physical Systems (CPS) have attracted
much research attention in searching for novel methods for attack-resilient
control and/or estimation. Specifically, false data injection attacks (FDIAs)
have been shown to be capable of bypassing bad data detection (BDD), while
arbitrarily compromising the integrity of state estimators and robust
controller even with very sparse measurements corruption. Moreover, based on
the inherent sparsity of pragmatic attack signals, $\ell_1$-minimization scheme
has been used extensively to improve the design of attack-resilient estimators.
For this, the theoretical maximum for the percentage of compromised nodes that
can be accommodated has been shown to be $50\%$. In order to guarantee correct
state recoveries for larger percentage of attacked nodes, researchers have
begun to incorporate prior information into the underlying resilient observer
design framework. For the most pragmatic cases, this prior information is often
obtained through some data-driven machine learning process. Existing results
have shown strong positive correlation between the tolerated attack percentages
and the precision of the prior information. In this paper, we present a pruning
method to improve the precision of the prior information, given corresponding
stochastic uncertainty characteristics of the underlying machine learning
model. Then a weighted $\ell_1$-minimization is proposed based on the pruned
prior. The theoretical and simulation results show that the pruning method
significantly improves the observer performance for much larger attack
percentages, even when moderately accurate machine learning model used.
