  This paper discusses the problem of estimating a stochastic signal from
nonlinear uncertain observations with time-correlated additive noise described
by a first-order Markov process. Random deception attacks are assumed to be
launched by an adversary, and both this phenomenon and the uncertainty in the
observations are modelled by two sets of Bernoulli random variables. Under the
assumption that the evolution model generating the signal to be estimated is
unknown and only the mean and covariance functions of the processes involved in
the observation equation are available, recursive algorithms based on linear
approximations of the real observations are proposed for the least-squares
filtering and fixed-point smoothing problems. Finally, the feasibility and
effectiveness of the developed estimation algorithms are verified by a
numerical simulation example, where the impact of uncertain observation and
deception attack probabilities on estimation accuracy is evaluated.
