Orthogonal vector algorithm to obtain the solar vector using the single-scattering Rayleigh model.

Information obtained from a polarization pattern in the sky provides many animals like insects and birds with vital long-distance navigation cues. The solar vector can be derived from the polarization pattern using the single-scattering Rayleigh model. In this paper, an orthogonal vector algorithm, which utilizes the redundancy of the single-scattering Rayleigh model, is proposed. We use the intersection angles between the polarization vectors as the main criteria in our algorithm. The assumption that all polarization vectors can be considered coplanar is used to simplify the three-dimensional (3D) problem with respect to the polarization vectors in our simulation. The surface-normal vector of the plane, which is determined by the polarization vectors after translation, represents the solar vector. Unfortunately, the two-directionality of the polarization vectors makes the resulting solar vector ambiguous. One important result of this study is, however, that this apparent disadvantage has no effect on the complexity of the algorithm. Furthermore, two other universal least-squares algorithms were investigated and compared. A device was then constructed, which consists of five polarized-light sensors as well as a 3D attitude sensor. Both the simulation and experimental data indicate that the orthogonal vector algorithms, if used with a suitable threshold, perform equally well or better than the other two algorithms. Our experimental data reveal that if the intersection angles between the polarization vectors are close to 90°, the solar-vector angle deviations are small. The data also support the assumption of coplanarity. During the 51 min experiment, the mean of the measured solar-vector angle deviations was about 0.242°, as predicted by our theoretical model.