Summary form only given. This paper presents a theoretical approach to the derivation of associations between two independent streams of data which take the form of bearing measurements or estimates on a set of objects in the real world relative to a common platform. The analysis is of particular relevance to the association of ESM tracks on a set of emitters with radar tracks on host platforms, and indeed is built upon a consideration of this problem: ESM sensors are subject to both noise and slowly varying bias. Detected emitters may be located on either detected or undetected platforms or locations. Several emitters may be located on a single platform. Some platforms detected by the radar may be radio silent. The main part of the analysis presented is a Bayesian technique to derive association probabilities, supplemented by a nominal decision logic.