We consider long-haul sensor networks where sensors are remotely deployed over a large geographical area to perform certain tasks, such as tracking and/or monitoring of one or more dynamic targets. A remote fusion center fuses the information provided by these sensors to improve the accuracy of the final estimates of certain target characteristics. In this work, we pursue artificial neural network (ANN) learning-based approaches for estimation and fusion of target states in long-haul sensor networks. The joint effect of (1) imperfect communication condition, namely, link-level loss and delay, and (2) computation constraints, in the form of low-quality sensor estimates, on ANN-based estimation and fusion, is investigated by means of analytical and simulation studies.