Covariance Reconstruction for Track Fusion with Legacy Track Sources

In multisensor target tracking, each sensor can have its own target state estimate based on the local sensor measurements. Most existing communication networks between local trackers/sensors transmit to a fusion center the local track estimates–sometimes without any estimation error covariances, sometimes with partial covariance information and only rarely with full covariance information. In order to form a global picture of the existing tracks, it is necessary to associate multiple local tracks and fuse them to obtain the global target state estimates. Under this tracking configuration, the fusion center can carry out this association and fusion of the (latest) local track estimates on demand, which, in general, is less frequent than the measurement rate at each local sensor. Another important reason that track fusion (TrkF) is a viable alternative to centralized tracking (CenT), which requires transmission of all the measurements to the fusion center, is that the performance of TrkF is very close to that of CenT [4]. The problem of associating tracks represented by their local state estimates and covariances from multiple sources has been studied extensively in literature. While different sensors typically have independent measurement errors, the local state estimation errors for the same target are dependent due to the common process noise (and the prior, if common). This dependence is characterized by the crosscovariances of the local estimation errors [3]. Methods have been proposed to fuse the local tracks that carry out decorrelation [11, 12, 13]. Other techniques include track fusion that explicitly utilizes the crosscovariance information in a Bayesian setting [7, 10], with asynchronous sensors [1], and more generally, with possible common priors [15, 16, 17]. The work of [20] dealt with simultaneous general track-totrack association and bias estimation. In addition, the “covariance intersection” method proposed in [14] can fuse two estimates with unknown correlation. However, it is a very conservative method that avoids the issue of crosscovariances but may yield a fused covariance with diagonal elements that indicate a degradation in each component from the best estimate before fusion [9]. A legacy sensor and tracking system is one that was built in the past under different requirements, specifically, with no requirements to support network fusion. Thus no hardware/software facilities (or inadequate facilities) were included in the system to support the kind of track fusion that is desired now. To get the relevant data that one would like out of the system (i.e., covariances) requires a significant hardware/software modification to the system, which is impractical. Concisely, legacy can be defined as “you are stuck with what you’ve got.” Before fusing local tracks, the fusion center has to decide whether they are from the same target. Track association is a hypothesis testing problem where local tracks are considered as having com-