The cross-covariance for heterogeneous track-to-track fusion

Track-to-track fusion (T2TF) has been studied widely for both homogeneous and heterogeneous cases, these cases denoting common and disparate state models. However, as opposed to homogeneous fusion, the cross-covariance for heterogeneous local tracks in different state spaces that accounts for the relationship between the process noises of the heterogeneous models seems not to be available in the literature. The present work provides the derivation of the cross-covariance for heterogeneous local tracks of different dimensions where the local states are related by a nonlinear transformation (with no inverse transformation). First, the relationship between the process noise covariances of the motion models in different state spaces is obtained. The cross-covariance of the local estimation errors is then derived in a recursive form by taking into account the relationship between the local state model process noises. In our simulations, linear minimum mean square (LMMSE) fusion is carried out for a scenario of two tracks of a target from two local trackers, one from an active sensor and one from a passive sensor.