Theoretical Analysis of the Measurement Transportation Algorithm to Fuse Delayed Data in Distributed Sensor Networks

Distributed sensor networks are capable of robust dynamic system estimation. The shared information in the network can prevent significant degradation or the interruption of the estimation process when a particular network node fails. However, the estimation accuracy can be severely degraded if delayed information is navely fused. The classical algorithm to fuse delayed measurements in a distributed network is the reiterated Kalman filter (RKF), which provides the optimal estimate in linear and Gaussian systems. Nevertheless, this algorithm imposes a huge computational burden and requires considerable memory when the delay is large, thus precluding the use of RKF in embedded systems that lack the needed computational resources. Previously, we proposed a suboptimal algorithm called measurement transportation (MT) that greatly reduces both the memory requirement and computational burden and delivers accuracy comparable to that of the RKF in a simulated UAV network. However, MT was only tested with numerical simulations. Here, we extend the previous investigation with the detailed analysis of MT regarding its accuracy, memory necessity, and computational burden. Cases are shown when the analysis predicts that the accuracy delivered by MT is comparable to that of the RKF and the theoretical results are then validated with a simulated distributed sensor network.