In this work, an observability Gramian (OG)-based Chernoff fusion (CF) rule is investigated for dealing with unknown correlated probability density functions (PDFs). Specifically, we introduce a generalised uniform observability (GUO) condition, which ensures that error covariances and estimate errors are bounded under nonlinear settings within the extended Kalman filter (EKF) framework. Leveraging the GUO condition, we develop an OG-centric weighting selection method that optimises fusion weights while guaranteeing non-divergent performance using an approximated Chernoff fusion (ACF) algorithm. The resulting OG-centric weights are then embedded to develop an OG-based approximated Chernoff fusion (OGBACF) algorithm that can compute fusion weights and error covariances in parallel. Finally, we conduct simulations to demonstrate the efficacy of our proposed fusion methodology.

In this chapter, the partial-neurons-based state estimation problem is studied for a class of delayed neural networks with state-dependent noises under redundant channels. For the purpose of improving the success rate of the data transmission from the sensor to the estimator, the redundant-channel-based transmission mechanism is considered. The main aim of the addressed problem is to design a state estimator to estimate the neurons&s; state by use of a small fraction of the sensor measurements. With the help of the Lyapunov stability theory, a sufficient condition is provided to ensure that the estimation error dynamics is exponentially mean-square bounded. The desired estimator gain is acquired by minimizing an asymptotic upper bound of the estimation error. Finally, a numerical simulation is carried out to demonstrate the usefulness of the presented estimator design scheme.