  This paper studies attack-resilient estimation of a class of switched
nonlinear systems subject to stochastic noises. The systems are threatened by
both of signal attacks and switching attacks. The problem is formulated as the
joint estimation of states, attack vectors and modes of hidden-mode switched
systems. We propose an estimation algorithm which is composed of a bank of
state and attack vector estimators and a mode estimator. The mode estimator
selects the most likely mode based on modes' posterior probabilities induced by
the discrepancies between obtained outputs and predicted outputs. We formally
analyze the stability of estimation errors in probability for the proposed
estimator associated with the true mode when the hidden mode is time-invariant
but remains unknown. For hidden-mode switched linear systems, we discuss a way
to reduce computational complexity which originates from unknown signal attack
locations. Lastly, we present numerical simulations on the IEEE 68-bus test
system to show the estimator performance for time-varying modes with a regular
mode set and a reduced mode set.
