Windowing-based Gaussian approximation fusion filtering for multi-sensor nonlinear systems with false data injection attacks

This paper addresses the Gaussian approximation fusion filtering (GAFF) problem for a class of multi-sensor nonlinear systems subject to false data injection attacks (FDIAs), where the statistical properties of process and measurement noises are unknown. A local Gaussian approximation filtering framework is developed based on the joint Gaussian posterior prediction probability density function, explicitly incorporating the influence of the FDIAs. In order to estimate the unknown means and covariances of process and measurement noises, a moving window approximation technique is integrated with a random weighting estimation method, enabling the dynamic characterization of noise statistics. Subsequently, the cubature Kalman filtering method is adopted to implement local filtering process, which is transformed into the calculation of multi-dimensional integrals. Based on the diagonal covariance intersection fusion technique and combined with the sequential idea, a novel sequential diagonal covariance intersection fusion strategy is further proposed. Finally, the effectiveness of the proposed GAFF algorithm based on windowing is verified by a simulation example.