Distributional loss for convolutional neural network regression and application to parameter estimation in satellite navigation signals

Abstract

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 state-of-the-art techniques for image-like data. However, when they are used for regression to estimate some function value from images, few recommendations are available to construct robust CNN regressor models. In this study, a robustness enforcing mechanism is proposed for CNN regression models. It combines convolutional neural layers to extract high level features representations from images with a soft labelling technique that helps generalization performance. 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. Building from earlier work (Imani and White, 2018), a specific histogram loss function based on the Kullback-Leibler (KL) divergence is applied during training. The prior distributions are selected according to the physical characteristics of the parameters to estimate. To assess and illustrate the technique, the model is applied to Global Navigation Satellite System (GNSS) multipath estimation where multipath signal parameters have to be estimated from correlator output images from the I and Q channels. The multipath 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.