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tokens: 5 per cent lower). This can be attributed to the same reason EPICal underperformed with the full sky model: EPICal only used a single pixel in the sky to form its solutions. When using the full sky model, it was under utilizing the information in the rest of the sky. But when the sky model only contains the bright point source, the single pixel used in EPICal is the location where this model is most accurate, effectively downweighting the pixels with incomplete sky model. In contrast, the visibility-based calibration method does not have any preference to a certain direction, and weights the sky equally (beyond the inherent response of the instrument). This results in a more harsh penalty for missing sources in the model. In the regime typical of HERA discussed above, EPICal's error floor was 10 per cent lower than that of visibility-based solutions. Any realistic sky model will lie somewhere between the two extremes explored here. In the case where the sky is modelled by a single source, as is often the case for an initial calibration, EPICal actually achieves smaller gain errors compared to the traditional visibility-based calibration. As the sky model improves, both visibility-based and EPICal gains improve, though the former quicker than the latter. In the limit of a perfect model, both calibration methods produce noise-like errors in their gains which scale down with more integration time. Comparing the two regimes of receiver noise levels (red versus black lines in Fig. 8 ), we see that the gains errors behave as one might expect given our above interpretations. In the case of a perfect sky model, the higher receiver noise results in larger gain errors for a given integration time, but follows the same t −1/2 noise trend. The imperfect model lines begin exhibit the same offset at low integration time because the errors are dominated by the thermal noise. But as integration time increases, they approach the same floor due to the same level of power from unmodelled sources. 5 APPLICATION TO LWA DATA We next demonstrate our calibration algorithm using an observation from the LWA station in New Mexico (Ellingson et al. 2013 ). The data are from the LWA narrow-band transient buffer, with time-domain voltage data from the 255 core antennas within a 110 m × 100 m ellipse. The central frequency is 74.03 MHz, with a total observing bandwidth of 100 kHz, analysed by a filter bank into 512 channels of bandwidth 195.3125 Hz each and with a post-channelization sampling period of 5.12 ms. For this demonstration, we limit ourselves to a single polarization. For the gridding step, we adopt a grid with extent 120 m to encompass the footprint of the array, and a grid spacing of half-wavelength (≈2 m). The result is a 64 × 64 pixel grid, making the MOFF computational complexity of N g log 2 N g on the same order as the N a 2 computations for a cross-correlator. Our gridding kernel is a square tophat function with sides of 3 m, corresponding to the size of