A parallel algorithm for square root Kalman filtering is developed and implemented on the Connection Machine (CM). The algorithm makes efficient use of parallel prefix or scan operations which are primitive instructions in the CM. Performance measurements show that the CM filter runs in time linear in the state vector size. This represents a great improvement over serial implementations which run in cubic time. A specific multiple target tracking application is also considered, in which several targets (e.g., satellites, aircrafts and missiles) are to be tracked simultaneously, each requiring one or more filters. A parallel algorithm is developed which, for fixed size filters, runs in constant time, independent of the number of filters simultaneously processed.