High-integrity localization is a key element for safety-critical applications like autonomous driving. The navigation filter plays a crucial role in merging sensor data to estimate an accurate pose and calculate a confidence interval based on task requirements. This paper presents an end-to-end Student's t information filter for accurate data fusion and non-pessimistic confidence domain computation. The filter incorporates a Fault Detection and Exclusion stage based on the Kullback-Leibler Divergence. The degree of freedom of the t distribution shapes the heavy tail to make the estimation process more robust against non detected outliers. We show that the adjustment of the degree of freedom can be done in real time using measurement residuals which give an indirect vision of the environment complexity.The accuracy and integrity of the proposed approach are evaluated with real data acquired with an experimental vehicle using GPS and Galileo pseudoranges merged with camera measurements after a map matching step with a High-Definition map. A comparative study with other classical methods based on Kalman filtering is also reported.