Interpolation

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Interpolation

The antenna offsets are derived from the Antenna Slow table together with other position values. Namely the 5 following elements have to be computed:

- lambda offset from reference position,
- beta offset,
- azimuth,
- elevation,
- local sidereal time.

All these elements are available in the ANTSLOW table, at a typical sampling rate of 1 Hz. Since the spectra dumps can be produced at different time sampling (no assumption is made on the rate or its variations), each spectrum positions are interpolated from the ANT table thanks to their respective Modified Julian Day values
(3.1)
where is the spectrum MJD value, and is the MJD value of the trace in the ANTSLOW table. is computed thanks to a dichotomic search in the table such as
(3.2)
being the interpolation fraction between the and trace, the positions are interpolated by
(3.3)
where and are the spectrum and antenna lambda offsets respectively. Same formula applies for the beta, azimuth, and elevation values.

If is found beyond the ANTSLOW table limits, the boundary values are applied without extrapolation. However, this is not expected to happen since such spectra should be rejected since they are out of the on-track range.