  We consider the problem of estimating the state of a linear Gaussian system
in the presence of integrity attacks. The attacker can compromise $p$ out of
$m$ sensors, the set of which is fixed and unknown to the system operator, and
manipulate the measurements arbitrarily. Under the assumption that all the
eigenvalues of system matrix $A$ have geometric multiplicity $1$ ($A$ is
non-derogatory), we propose a secure estimation scheme that is resilient to
integrity attack as long as the system is $2p$-sparse observable. In the
absence of attack, the proposed estimation coincides with Kalman estimation
with a certain probability that can be adjusted. Furthermore, our proposed
estimator is computational efficient during the security condition checking in
the designing phase and during the estimation computing in the online operating
phase. A numerical example is provided to corroborate the results and
illustrate the performance of the proposed estimator.
