Sample clock offset must be estimated in order to correctly demodulate an OFDM signal. Estimates are also required in passive radar processing, to produce a reference signal, which is properly matched to the transmission. A recently proposed clock offset estimation method for passive radar is found to be overly sensitive to measurement noise. However, the radar ambiguity surface is found to be unaffected by the specific errors engendered by this noise. The reasons for this are explored. An updated method based on state-space modeling and Kalman smoothing is proposed. This is found to restore clock offset estimation performance in cases of higher noise, achieving this with low processing latency. These improvements enable the method to be employed for other applications requiring high quality, time-critical clock offset estimation.