Methods are explored for estimating Range and Range-Rate from the geometry and kinematics of the air-air homing-missile combat situation rather than from direct measurements. The methods reported herein use the various signals available from the missile autopilot, plus the inertial rotation-rate of the Line of Sight provided by the seeker. It is shown that acceleration of the target in the radial direction, parallel to the Line of Sight, precludes successful estimation by the classical techniques such as adaptive parameter identification, Kalman filter estimation, or the various minimum-variance estimation methods. A nonlinear estimator is described which estimates the target acceleration and velocity components and can yield accurate range and range-rate estimates if correctly initialized at launch. This estimator is able to take advantage of the many inequalities which constrain the maneuvering of an air-air target. Errors and performance of this estimator are demonstrated by computer simulations.