Closed-Form Solution of a Recursive Tracking Filter with a Priori Velocity Initialization

A closed-form solution is presented for the transient gains and covariances of a two-state tracking filter which is initialized with a finite a priori velocity error variance. The formulas are applied to long-range tracking and fire control problems, and are shown to agree (in the limit) with classical formulas for a least-squares line estimator and a bias-in-noise estimator.