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.