Filtering and smoothing estimation algorithms from uncertain nonlinear observations with time-correlated additive noise and random deception attacks

TL;DR

This paper develops recursive filtering and smoothing algorithms for estimating signals from nonlinear observations affected by time-correlated noise and deception attacks, with limited model knowledge, validated through simulations.

Contribution

It introduces novel recursive algorithms that handle uncertain nonlinear observations with adversarial deception attacks and limited model information.

Findings

Algorithms effectively estimate signals under attack conditions.

Estimation accuracy depends on attack and uncertainty probabilities.

Numerical simulations confirm the algorithms' robustness.

Abstract

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.