A method for dealing with assignment ambiguity

Many landmark-based navigation systems suffer from the problem of assignment ambiguity: the navigation system receives a measurement from a landmark, but the identity of the landmark is not uniquely known. This uncertainty is frequently addressed by attempting to identify the landmark which caused the measurements. Two common approaches are the nearest neighbour and multiple hypothesis tracking methods. However, the nearest neighbour method is notoriously unreliable and the multiple hypothesis method can only be implemented in real time for a small number of hypotheses. We consider an alternative approach for assignment ambiguity which uses the covariance union (CU) algorithm. Every potential assignment is used to generate an estimate. CU is applied to the set of estimates. Providing the true assignment is included within the set, the unioned estimate is guaranteed to be consistent. We provide a theoretical development of CU, describe a method for computing its value, and illustrate its performance in a nonlinear navigation example.