A practical time-varying line-of-sight (LOS) rate estimator is proposed for surface-to-air missile (SAM) homing guidance. The proposed filter is a pseudo-steady-state solution of the time-varying Kalman filtering problem which finds usage in on-board target tracking under ever-changing RF environments. The range-dependant LOS rate dynamics and variances of boresight error (BSE) measurements constitute the time-varying filtering problem. By employing the algebraic transformation method, an obstacle of real-time implementation involved with differential Riccati equation can be removed. Since, apart from the previous results, the explicit expression of time-varying Kalman gain is given in terms of range, range rate and modified target maneuvering index, one can effectively cope with unexpected situations in night. Analyzing stability and time-response in near-range allows insight into the operational condition of the proposed filter with mathematically rigorous manner.