This paper investigates the problem of position estimation of unmanned surface vessels (USVs) operating in coastal areas or in the archipelago. We propose a position estimation method where the horizon line is extracted in a 360 degree panoramic image around the USV. We design a CNN architecture to determine an approximate horizon line in the image and implicitly determine the camera orientation (the pitch and roll angles). The panoramic image is warped to compensate for the camera orientation and to generate an image from an approximately level camera. A second CNN architecture is designed to extract the pixelwise horizon line in the warped image. The extracted horizon line is correlated with digital elevation model (DEM) data in the Fourier domain using a MOSSE correlation filter. Finally, we determine the location of the maximum correlation score over the search area to estimate the position of the USV. Comprehensive experiments are performed in a field trial in the archipelago. Our approach provides promising results by achieving position estimates with GPS-level accuracy.