Generalised Covariance Union: A Unified Approach to Hypothesis Merging in Tracking

Multi-hypothesis tracking (MHT) techniques can become prohibitively computationally expensive as the number of hypotheses increases. In order to maintain an estimate with bounded computational cost, multi-hypothesis methods often merge the estimates together. When the hypotheses are distributed according to a known probability then standard mixture reduction (SMR) methods exist for merging estimates. Also, covariance union (CU) has become a popular approach to merging hypotheses when their distribution is not known. This paper generalises CU to a new theory, which we refer to as generalised covariance union (GCU). GCU merges estimates when their distribution is not known precisely but is, instead, bounded above and below. We show that CU and the SMR approaches are limiting cases of GCU. We demonstrate the efficacy of the new approach via a Global Positioning System (GPS) tracking application with time delayed satellite signals.