Solar-tracking methodology based on refraction-polarization in Snell's window for underwater navigation

Underwater navigation system is an indispensable part for autonomous underwater vehicles. Due to the indiscernibility of satellite signal, however, the underwater navigation problem is quite challenging, and a satellite-free navigation scheme should be looked for. Polarization navigation, inspired by insects’ capability of autonomous homing and foraging, is an alternative solution to satellite navigation with great application potential. Underwater polarization provides an indirect sun compass to animals for orientation determination. However, it is difficult to apply terrestrial solar-tracking methodologies in underwater situations due to the refraction of polarized skylight at the air–water interface. To resolve this issue, an underwater solar-tracking algorithm is developed based on the underwater refraction-polarization pattern inside the Snell's window. By employing Snell's law and Fresnel refraction formula to decouple the refractive ray bending and polarization deflection, the celestial polarization pattern is obtained based on underwater measurement. To further improve the accuracy, the degree of polarization is employed as a weight factor for E-vector. A long-lasting underwater experiment was conducted to validate the effectiveness of the proposed approach, and the results showed the root-mean-square errors of solar zenith and azimuth employing this algorithm were 0.3° and 1.3°, respectively. Our experimental results show that the refraction-polarization pattern inside the Snell's window exhibits immense potential to improve the solar-tracking accuracy for underwater navigation.