Distributional loss for convolutional neural network regression and application to GNSS multi-path estimation

Convolutional Neural Network (CNN) have been widely used in image classification. Over the years, they have also benefited from various enhancements and they are now considered as state of the art techniques for image like data. However, when they are used for regression to estimate some function value from images, fewer recommendations are available. In this study, a novel CNN regression model is proposed. It combines convolutional neural layers to extract high level features representations from images with a soft labelling technique. More specifically, as the deep regression task is challenging, the idea is to account for some uncertainty in the targets that are seen as distributions around their mean. The estimations are carried out by the model in the form of distributions. Building from earlier work, a specific histogram loss function based on the Kullback-Leibler (KL) divergence is applied during training. The model takes advantage of the CNN feature representation and is able to carry out estimation from multi-channel input images. To assess and illustrate the technique, the model is applied to Global Navigation Satellite System (GNSS) multi-path estimation where multi-path signal parameters have to be estimated from correlator output images from the I and Q channels. The multi-path signal delay, magnitude, Doppler shift frequency and phase parameters are estimated from synthetically generated datasets of satellite signals. Experiments are conducted under various receiving conditions and various input images resolutions to test the estimation performances quality and robustness. The results show that the proposed soft labelling CNN technique using distributional loss outperforms classical CNN regression under all conditions. Furthermore, the extra learning performance achieved by the model allows the reduction of input image resolution from 80x80 down to 40x40 or sometimes 20x20.