Modeling and estimation for networked systems with multiple random transmission delays and packet losses

Abstract

In networked systems, data packets are transmitted through networks from a sensor to a data processing center. Due to the unreliability of communication channels, a packet may be delayed even lost during the transmission. At each moment, the data processing center may receive one or multiple data packets or nothing at all. A novel model is developed to describe the possible multiple random transmission delays and data packet losses by employing a group of Bernoulli distributed random variables. It is transformed to a measurement model with multiple random delayed states and noises. Based on the model, an optimal linear filter in the linear minimum variance sense is proposed by using the orthogonal projection approach which is a universal tool to find the optimal linear estimate. It does not have a steady-state performance since it depends on the values of random variables that depict the phenomena of delays and losses at each moment. So it needs to be computed online. To reduce the online computational cost, a suboptimal linear filter dependent on the probabilities of random variables is also proposed. However, it is worth noting that it is linearly optimal among all the linear filters dependent on the probabilities. It can be computed offline since it has the steady-state performance. A sufficient condition of existence for the steady-state performance is given. A simulation example shows the effectiveness.