As several large radio surveys begin operation within the coming decade, a wealth of radio data will become available and provide a new window to the Universe. In order to fully exploit the potential of these data sets, it is important to understand the systematic effects associated with the instrument and the analysis pipeline. A common approach to tackle this is to forward-model the entire system - from the hardware to the analysis of the data products. For this purpose, we introduce two newly developed, open-source Python packages: the HI Data Emulator (HIDE) and the Signal Extraction and Emission Kartographer (SEEK) for simulating and processing radio survey data. HIDE forward-models the process of collecting astronomical radio signals in a single dish radio telescope instrument and outputs pixel-level time-ordered-data. SEEK processes the time-ordered-data, removes artifacts from Radio Frequency Interference (RFI), automatically applies flux calibration, and aims to recover the astronomical radio signal. The two packages can be used separately or together depending on the application. Their modular and flexible nature allows easy adaptation to other instruments and data sets. We describe the basic architecture of the two packages and examine in detail the noise and RFI modeling in HIDE, as well as the implementation of gain calibration and RFI mitigation in SEEK. We then apply HIDE & SEEK to forward-model a Galactic survey based on data taken at the Bleien Observatory. For this survey, we forecast a sky coverage of 70% and a median signal-to-noise ratio of approximately 9 in the cleanest channels. However, we also point out the potential challenges of high RFI contamination and baseline removal when examining the early data from the Bleien Observatory. The fully documented HIDE & SEEK packages are published under the GPLv3 license on GitHub.
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