On optimal track-to-track fusion

Track-to-track fusion is an important part in multisensor fusion. Much research has been done in this area. Chong et al. (1979, 1986, 1990) among others, presented an optimal fusion formula under an arbitrary communication pattern. This formula is optimal when the underlying systems are deterministic, i.e., the process noise is zero, or when full-rate communication (two sensors exchange information each time they receive new measurements) is employed. However, in practice, the process noise is not negligible due to target maneuvering and sensors typically communicate infrequently to save communication bandwidth. In such situations, the measurements from two sensors are not conditionally (given the previous target state) independent due to the common process noise from the underlying system, and the fusion formula becomes an approximate one. This dependence phenomena was also observed by Bar-Shalom (1981) where a formula was derived to compute the cross-covariance of two track estimates obtained by different sensors. Based on this results a fusion formula was subsequently derived (1986) to combine the local estimates which took into account the dependency between the two estimates. Unfortunately, the Bayesian derivation made an assumption that is not met. This work points out the implicit approximation made and shows that the result turns out to be optimal only in the ML (maximum likelihood) sense. A performance evaluation technique is then proposed to study the performance of various track-to-track fusion techniques. The results provide performance bounds of different techniques under various operating conditions which can be used in designing a fusion system.