Limitation of Rayleigh sky model for bioinspired polarized skylight navigation in three-dimensional attitude determination

Abstract

Insects such as desert ants and drosophilae can sense polarized skylight for navigation. Inspired by insects, many researchers have begun to study how to use skylight polarization patterns for attitude determination. The Rayleigh sky model has become the most widely used skylight polarization model for bioinspired polarized skylight navigation due to its simplicity and practicality. However, this is an ideal model considering only single Rayleigh scatter events, and the limitation of this model in bio-inspired attitude determination has not been paid much attention and lacks strict inference proof. To address this problem, the rotational and plane symmetry of the Rayleigh sky model are analyzed in detail, and it is theoretically proved that this model contains only single solar vector information, which contains only two independent scalar pieces of attitude information, so it is impossible to determine three Euler angles simultaneously in real-time. To further verify this conclusion, based on a designed hypothetical polarization camera, we discuss what conditions different three-dimensional attitudes must satisfy so that the polarization images taken at different 3D attitudes are the same; this indicates that multiple solutions will appear when only using the Rayleigh sky model to determine 3D attitude. In conclusion, due to its single solar vector information and the existence of multiple solutions, it is fully proved that 3D attitude cannot be determined in real time based only upon the Rayleigh sky model. Code is available at: https://github.com/HuajuLiang/HypotheticalPolarizationCamera

Impact of sensor tilt on bio-inspired polarized skylight orientation determination

“…In order to construct a comprehensive and perfect simulation system, not only skylight polarization model, but also polarization imaging sensor need to be constructed [34]. In this section, a hypothetical polarization imager is designed and described in detail.…”

“…Polarization E-vector of Rayleigh sky model is consistently perpendicular to the solar vector, so the orientation can be determined by total least square method, which is then named Least-square approach [30][31][32][33]. However, all most of these heading determination approaches require the polarization sensor point toward the zenith of sky dome [34]: Zenith approach needs to directly capture the polarization information at the sky zenith; SM-ASM and Symmetry approaches require that reference direction of AOP is converted to the local meridian using the sky zenith as a reference point; Least-square approach requires a known sky zenith dependent coordinate system to accurately determine orientation.…”

Polarized light-aided visual-inertial navigation system: global heading measurements and graph optimization-based multi-sensor fusion

“…The drift-free polarized light compass (PLcompass) does not accumulate measuring error [8,9], which favorably leads to a long-term high positioning accuracy. Another main concern with the polarized light-aided VINS (with LC detection thread) scheme lies in the fact that conventional VINS is subject to divergent heading angles [4,10], which doe not allow for absolute heading references and necessary pose corrections. An outdoors-applicable, full-time and environmental disturbance-free atmospheric polarization pattern is the answer to this challenging issue.…”

A bio-inspired polarization navigation sensor based on artificial compound eyes

“…In recent years, scholars have conducted a great deal of research on bio-inspired polarization navigation sensors [11][12][13][14][15], which are mainly divided into two categories. One is based on photodiodes and the other is based on a camera.…”