A novel range estimator is proposed for unmanned aerial vehicles (UAVs) with a passive sensor which can measure both the line-of-sight (LOS) angle and rate. Apart from the previous passive ranging filters, our method is based on the linear kinematic relation; the relative velocity perpendicular to LOS vector is the multiplication of LOS rate and range. However, the LOS rate measurement noise forms the linear time-varying system model with stochastic parametric uncertainty. This motivates us to solve the range estimation problem within the context of the recently developed robust least squares (RLS) estimation scheme. Slight modification of the RLS filtering is made to prevent the range estimation performance degradation due to the non-stationary flight environment. Computer simulation results demonstrate the faster convergence property of the proposed method compared to the existing nonlinear estimators.