This paper deals with a remote state estimation problem for a nonlinear system. In a typical networked control system (NCS) scenario, the estimator and controller are remotely located, and they are connected with the plant through a common communication network. Traditional Bayesian filters assume that the measurements are always available. However, that may not be the case in reality. As the sensor measurements are transmitted to the remotely located estimator through an unreliable communication channel, delay may be introduced. Similarly, the control signal is also applied remotely, and it reaches to the plant through a similar unreliable communication channel, and due to which here also delay may occur. In this paper, the authors develop a generalized framework of nonlinear filtering where the states can be estimated in presence of arbitrary random delay in (i) transmission of measurement from sensor to the estimator and (ii) transmission of input from the remotely located controller to the system. The filtering algorithm in such scenario is realized with deterministic sample points. The performance of the proposed method is tested experimentally on two simulation problems. With the help of the simulation results, it is shown that the developed method performs better than traditional non-delayed nonlinear filters in the presence of arbitrary delay in measurement and input.