Managing optimality in multi-sensor data fusion consistency using intersection and largest ellipsoid algorithms

Abstract

The purpose of this chapter is to provide a theoretical and practical framework to tackle the target tracking problem known as the track-to-track correlation problem. When static (e.g. radars) or dynamic (e.g. AWACs) sensors evolve in a network configuration to cover a surveillance area, the problem consists of fusing the collected observation data in order to get a coherent estimate. Many researchers have demonstrated the consistency by comparing the covariance errors matrix of the true value with the corresponding estimated value. Such approaches are mainly based on the well-known covariance intersection (CI) of Uhlmann et al. Despite of counter-examples given by some researchers, CI and its extended algorithms are still accurate to avoid the redundancy in a decentralised sensors network. In this chapter we present some fusing algorithms in cases where the sources are uncorrelated. We show the relationship between the Kalman's filter, the CI filter, and the Largest Ellipsoid algorithm. The properties of such algorithms are illustrated using graphics to compare their performance and the domain of solutions. Similarly, we introduce in the track-to-track correlation problem some notions of ellipsoid intersection to maintain consistency.