$\tt{KOBEsim}$: a Bayesian observing strategy algorithm for planet detection in radial velocity blind-search surveys

Ground-based observing time is precious in the era of exoplanet follow-up and characterization, especially in high-precision radial velocity instruments. Blind-search radial velocity surveys thus require a dedicated observational strategy in order to optimize the observing time, which is particularly crucial for the detection of small rocky worlds at large orbital periods. We develop an algorithm with the purpose of improving the efficiency of radial velocity observations in the context of exoplanet searches, and we apply it to the K-dwarfs Orbited By habitable Exoplanets (KOBE) experiment. We aim at accelerating exoplanet confirmations or, alternatively, rejecting false signals as early as possible in order to save telescope time and increase the efficiency of both blind-search surveys and follow-up of transiting candidates. Once a minimum initial number of radial velocity datapoints is reached in such a way that a periodicity starts to emerge according to generalized Lomb-Scargle (GLS) periodograms, that period is targeted with the proposed algorithm, named $\texttt{KOBEsim}$. The algorithm selects the next observing date that maximizes the Bayesian evidence for such periodicity in comparison with a model with no Keplerian orbits. By means of simulated data, we prove that the algorithm accelerates the exoplanet detection, needing $29 - 33\,\%$ less observations and $41 - 47\,\%$ less timespan of the full dataset for low-mass planets ($m_{\rm p}\,<\,10\,M_{\oplus}$) in comparison with a conventional monotonic cadence strategy. The enhancement in the number of datapoints for $20\,M_{\oplus}$ planets is also appreciable, $16\,\%$. We also test $\texttt{KOBEsim}$ with real data for a particular KOBE target, and for the confirmed planet $HD~102365\,b$. Both of them demonstrate that the strategy is capable of speeding up the detection up to a factor of $2$.