Track-to-Track fusion with cross-covariances from radar and IR/EO sensor

The Track-to-track fusion (T2TF) problem for estimates from radar and infrared/electro-optical (IR/EO) sensor is studied in this work. For such a problem, the heterogeneous estimates from local trackers (LT) are in different state spaces with various dimensions and are related by a nonlinear relationship with no inverse transformation. For the homogeneous T2TF problem, where the common state model is shared by both LTs in the same state space, the cross-covariance between the local estimation errors, which has been known for some time, needs to be considered in the T2TF. However, such a cross-covariance for heterogeneous T2TF was not available in previous works. In the present work, the derivation of the cross-covariance for heterogeneous LTs of different dimension states is provided, yielding a recursion, by taking into account the relationship between the local state model process noises. A linear minimum mean square (LMMSE) estimator is used for the T2TF. With the cross-covariance involved, the fusion will generate the covariance of the fused estimation error which makes the system consistent as shown in the simulation through Monte-Carlo runs.