  A networked system often uses a shared communication network to transmit the
measurements to a remotely located estimation center. Due to the limited
bandwidth of the channel, a delay may appear while receiving the measurements.
This delay can be arbitrary step random, and packets are sometimes dropped
during transmission as it exceeds a certain permissible number. In this paper,
such measurements are modeled with the Poisson distribution, which allows the
user to determine the maximum delay the system might suffer. When the
measurement delay exceeds the permissible number, the packet dropout happens.
Based on the proposed model, we solve the problem by assuming that the prior
and posterior densities of states are Gaussian and derive the expression of the
estimated state and the error covariance. Later, relaxing the Gaussian
assumption for densities, we propose a solution with the help of the sequential
Monte Carlo (SMC) approach. The proposed SMC method divides the set of
particles into several groups, where each group supports the possibility that
the received measurement is delayed by a certain number of steps. The strength
of an individual group is determined by the probability of a measurement being
delayed with the same number of steps that the group represents. This approach
estimates the states and also assesses the amount of delay from the received
measurements. Finally, the developed estimators are implemented on two
nonlinear estimation problems, and the simulation results are compared. The
proposed SMC approach shows better results compared to the designed Gaussian
delay filters and existing particle filters with delay.
