Asynchronous and Heterogeneous Track-to-Track Fusion with Mapped Process Noise and Cross-Covariance

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1 June 2020
Kaipei Yang, Yaakov Bar-Shalom, Peter Willett

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Track-to-track fusion has been studied extensively 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 (LTs) 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. This work provides the derivation of the cross-covariance for heterogeneous LTs 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. Both the synchronous and asynchronous systems are considered. A linear minimum mean square fusion is carried out for a scenario involving tracks from two LTs: one from an active sensor and one from a passive sensor.