Most existing track-to-track fusion (T2TF) algorithms for distributed tracking systems are given assuming that
the local trackers are synchronized. However, in the real world, synchronization can hardly be achieved and
local trackers usually work in an asynchronous fashion, where local measurements are obtained and local tracks
are updated at different times with different rates. Communication delays between local trackers and the fusion
center (FC) also cause delays in the arrival of the local tracks at the FC. This paper presents the optimal
asynchronous T2TF algorithm for distributed tracking systems under the linear Gaussian (LG) assumption,
which is also the linear minimum mean square error (LMMSE) fuser without the Gaussian assumption. The
information configuration of asynchronous T2TF with partial information feedback (AT2TFpf) is used. This is
the most practical configuration for AT2TF with time delays, since communication delays make full information
feedback very complicated. To illustrate the algorithm, a basic scenario of the fusion of two asynchronous local
tracks is used, where one is available at the FC with no delay and the other is transmitted from a local tracker
with a time delay. The algorithm can be extended to scenarios with more than two local trackers. The optimal
asynchronous T2TF algorithm is compared with the approximate algorithms proposed by Novoselsky (denoted
as AT2TFpfApprA-C) and is shown to have performance benefit in consistency as well as in fusion accuracy.
The drawback of the optimal fusion algorithm is that it has high communication and computational cost.
Two new approximate algorithms, AT2TFpfApprD and AT2TFpfApprE, are also proposed which significantly
reduce the cost of the optimal algorithm with little loss in fusion performance.