Analytical planar wavefront reconstruction and error estimates for radio detection of extensive air showers

When performing radio detection of ultra-high energy astroparticles, the planar wavefront model is often used as a first step to evaluate the arrival direction of primary particles, by adjusting the wavefront orientation based on the peak of signal traces of individual antennas. The benefits of this approach are however limited by the lack of a good evaluation of its robustness. In order to mitigate this limitation, we derive in this work an analytical solution for the arrival direction as well as the corresponding analytical reconstruction uncertainty. Because it is fast and robust, this reconstruction method can be used as a proxy for more complex estimators, or implemented online for low-level triggering.