instrumentation: spectrographs, methods: data analysis, techniques: radial velocities, techniques: spectroscopic, planets and satellites: detection

Context. High-precision radial velocity (RV) measurements with slit spectrographs require the instrument profile (IP) and Earth's atmospheric spectrum to be known and to be incorporated into the RV calculation. Aims. We developed an RV pipeline, called Velocity and IP EstimatoR (viper), to achieve high-precision RVs in the near-infrared (NIR). The code is able to process observations taken with a gas cell and includes modelling of the IP and telluric lines. Methods. We utilised least-square fitting and telluric forward modelling to account for instrument instabilities and atmospheric absorption lines. As part of this process, we demonstrate the creation of telluric-free stellar spectra. Results. By applying viper to observations obtained with the upgraded CRyogenic high-resolution InfraRed Echelle Spectrograph (CRIRES+) and a gas absorption cell in the K band, we are able to reach an RV precision of around 3 m/s over a time span of 2.5 years. For observations using telluric lines for the wavelength reference, an RV precision of 10 m/s is achieved. Conclusions. We demonstrate that despite telluric contamination, a high RV precision is possible at NIR wavelengths, even for a slit spectrograph with varying IP. Furthermore, we show that CRIRES+ performs well and is an excellent choice for science studies requiring precise stellar RV measurements in the infrared.