  Protonated molecular species have been proven to be abundant in the
interstellar gas. This class of molecules is also pivotal for the determination
of important physical parameters for the ISM evolution (e.g. gas ionisation
fraction) or as tracers of non-polar, hence not directly observable, species.
The identification of these molecular species through radioastronomical
observations is directly linked to a precise laboratory spectral
characterisation. The goal of the present work is to extend the laboratory
measurements of the pure rotational spectrum of the ground electronic state of
protonated carbonyl sulfide (HSCO$^+$) and its deuterium substituted isotopomer
(DSCO$^+$). At the same time, we show how implementing different laboratory
techniques allows the determination of different spectroscopical properties of
asymmetric-top protonated species. Three different high-resolution experiments
were involved to detected for the first time the $b-$type rotational spectrum
of HSCO$^+$, and to extend, well into the sub-millimeter region, the $a-$type
spectrum of the same molecular species and DSCO$^+$. The electronic
ground-state of both ions have been investigated in the 273-405 GHz frequency
range, allowing the detection of 60 and 50 new rotational transitions for
HSCO$^+$ and DSCO$^+$, respectively. The combination of our new measurements
with the three rotational transitions previously observed in the microwave
region permits the rest frequencies of the astronomically most relevant
transitions to be predicted to better than 100 kHz for both HSCO$^+$ and
DSCO$^+$ up to 500 GHz, equivalent to better than 60 m/s in terms of equivalent
radial velocity. The present work illustrates the importance of using different
laboratory techniques to spectroscopically characterise a protonated species at
high frequency, and how a similar approach can be adopted when dealing with
reactive species.
