The projection and localization functions of satellite images are often [1,2] represented by rational functions of degree 3 in 3 variables. This gives a very precise approximation of the physical model. The advantage of this representation is that it provides an universal and easy way to evaluate these functions, without needing to know the physical model of each particular satellite, that may be quite involved, and different between satellites. The algorithms that fit the parameters is easy but not trivial [3,4] because they must be robust to common degenerate cases. The goal of this project is to develop (and later, exploit) an algorithm that fits a RPC function to a given set of data points. This can be used, for example, to obtain the projection from the localization function, which is useful because some products only provide the latter. More interestingly, it can be used to merge several local corrections of the pointing error into a single, fixed, RPC model; or even to merge the RPC models of several overlapping images by a single model, for example in the case of Skysat tiles.

**Supervision**

Gabriele Facciolo, Carlo de Franchis, Enric Meinhardt

**Bibliographic References**

[1] Grodecki, Jacek, and Gene Dial. “Block adjustment of high-resolution satellite images described by rational polynomials.” *Photogrammetric Engineering & Remote Sensing* 69.1 (2003): 59-68.

[2] Habib, Ayman, et al. “Comprehensive analysis of sensor modeling alternatives for high resolution imaging satellites.” *Photogrammetric Engineering & Remote Sensing* 73.11 (2007): 1241-1251.

[3] Zhang, Yongjun, et al. “A new approach on optimization of the rational function model of high-resolution satellite imagery.” *IEEE Transactions on Geoscience and Remote Sensing* 50.7 (2012): 2758-2764.

[4] Yavari, Somayeh, et al. “Accuracy improvement of high resolution satellite image georeferencing using an optimized line-based rational function model.” *International Journal of Remote Sensing* 39.6 (2018): 1655-1670.