Microsatellites and drones are often equipped with digital cameras whose sensing system is based on color filter arrays (CFAs), which define a pattern of color filter overlaid over the focal plane. Recent commercial cameras have started implementing RGBW patterns, which include some filters with a wideband spectral response together with the more classical RGB ones. This allows for additional light energy to be captured by the relevant pixels and increases the overall SNR of the acquisition. Demosaicking defines reconstructing a multi-spectral image from the raw image and recovering the full color components for all pixels. However, this operation is often tailored for the most widespread patterns, such as the Bayer pattern. Consequently, less common patterns that are still employed in commercial cameras are often neglected. In this work, we present a generalized framework to represent the image formation model of such cameras. This model is then exploited by our proposed demosaicking algorithm to reconstruct the datacube of interest with a Bayesian approach, using a total variation regularizer as prior. Some preliminary experimental results are also presented, which apply to the reconstruction of acquisitions of various RGBW cameras.