In radio astronomy, reference signals from auxiliary antennae, receiving only the radio frequency interference (RFI), can be modified to model the RFI environment at the astronomy receivers. The RFI can then be cancelled from the astronomy signal paths. However, astronomers typically only require signal statistics. If the RFI statistics are changing slowly, the cancellation can be applied to the signal correlations at a much lower rate than required for standard adaptive filters. In this paper we describe five canceller setups; pre-and postcorrelation cancellers that use one or two reference signals in different ways. The theoretical residual RFI and added noise levels are examined, and demonstrated using microwave television RFI at the Australia Telescope Compact Array. The RFI is attenuated to below the system noise, a reduction of at least 20 dB. While dualreference cancellers add more reference noise than single-reference cancellers, this noise is zero-mean and only adds to the system noise, decreasing the sensitivity. The residual RFI that remains in the output of singlereference cancellers (but not dual-reference cancellers) sets a non-zero noise floor that does not act like random system noise and may limit the achievable sensitivity. Thus dual-reference cancellers often result in superior cancellation. Dual-reference pre-correlation cancellers require a double-canceller setup to be useful and to give equivalent results to dual-reference post-correlation cancellers.