Other comments

5.8 Other comments

Another analysis scheme which is attractive in principle but does not seem useful in current-sensitivity Doppler data analysis is the Karhunen–Loéve expansion [58 , 40 ]. This is a signal-independent approach where the data themselves are used to construct a mathematical basis to express the data. Such representations may be useful for template-free analysis of time series dominated by a signal of unknown waveform. However, experiments with this analysis procedure on simulated noise-dominated Doppler data sets were disappointing; the modes discovered in the Karhunen-Loéve simulations were always the noise modes.

Editing flags developed, e.g., from spacecraft telemetry or from DSN tracking logs have not historically been useful⁸ as veto signals (the internal monitoring capabilities of the spacecraft and ground stations were, of course, not intended for this purpose). The Doppler itself is much more sensitive than the system monitors and also – being spatially distributed by cT₂ / 2 – has noise-signatures which often allow easier identification of specific disturbances affecting the time series (see, e.g., Section 4).

Even though each class of tracking antenna has a common design, there are low-level station-specific systematic differences. Getting data with different stations helps at least to identify these systematics (see, e.g., [5 ]). Also data taken at low elevation angle ( $∘ < 20$ ) with any antenna are statistically of poorer quality.

Finally, at current levels of sensitivity Doppler tracking observations are clearly search experiments. We are looking for signals with poorly-constrained waveforms which are “surprisingly” strong (thus expected to be rare). To maximize the chance that an unexpected real event will not be dismissed as due to a known noise process (or overlooked altogether), it is obviously useful to analyze the time series in different ways to bring out different aspects. Doppler tracking data sets are not impossibly large: It is practical for a person to actually look at all the data with varying time-frequency resolution – in addition to using formal and automated analysis procedures. (A potential difficulty is still actually recognizing unanticipated features if they are present. Reference [73 ] has interesting discussions of the problems of recognizing unexpected things.) As emphasized by Thorne [102 ], the largest events may be from unexpected sources so the data analysis scheme must be robust enough that unexpected signals are not preprocessed away.