  This paper proposes a secure state estimation scheme with non-periodic
asynchronous measurements for linear continuous-time systems under false data
attacks on the measurement transmit channel. After sampling the output of the
system, a sensor transmits the measurement information in a triple composed of
sensor index, time-stamp, and measurement value to the fusion center via
vulnerable communication channels. The malicious attacker can corrupt a subset
of the sensors through (i) manipulating the time-stamp and measurement value;
(ii) blocking transmitted measurement triples; or (iii) injecting fake
measurement triples. To deal with such attacks, we propose the design of local
estimators based on observability space decomposition, where each local
estimator updates the local state and sends it to the fusion center after
sampling a measurement. Whenever there is a local update, the fusion center
combines all the local states and generates a secure state estimate by adopting
the median operator. We prove that local estimators of benign sensors are
unbiased with stable covariance. Moreover, the fused central estimation error
has bounded expectation and covariance against at most $p$ corrupted sensors as
long as the system is $2p$-sparse observable. The efficacy of the proposed
scheme is demonstrated through an application on a benchmark example of the
IEEE 14-bus system.
