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Abstract Anthropogenic interference has been a long-standing problem for radio astronomy. In a previous paper, we presented a study of interference mitigation methods based on the concept of coherent time-domain canceling, which ideally allows one to “look through” interference, as opposed to avoiding the interference or deleting the afflicted data. The focus of that paper was on “reference antenna” methods, in which a separately acquired signal containing the interference waveform is used to identify the interference waveform in the primary signal. In this paper, we shift focus to methods in which the reference signal is instead a parametric model of the waveform, so that no additional antenna is needed. As in our previous paper, we present a rigorous theoretical analysis of performance. Findings are demonstrated using real-world interference from the Iridium system. We find that interference suppression is possible if the product of the interference-to-noise ratio and the number of statistically independent samples is greater than 1, and that suppression increases linearly with this product. However good performance is achieved only for interferers whose bandwidth is much less than the sample rate, and algorithm parameters must be carefully selected to avoid undesirable distortion of the noise spectral baseline.