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

Insects such as desert ants, 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. Rayleigh sky model has become the most widely used skylight polarization model for bio-inspired polarized skylight navigation, due to its simplicity and practicality. However, this model is an ideal model considering only single Rayleigh scatter event, whose limitation in bio-inspired attitude determination has not been paid much attention and lacks strict inference proof. Aiming at this problem, the rotational symmetry and plane symmetry of 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 discussed what conditions different three-dimensional attitudes must satisfy so that the polarization images taken at different 3D attitudes are the same, which indicates multiple solutions will appear when only using Rayleigh sky model to determine 3D attitude. In conclusion, according to 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 Rayleigh sky model. Code is available at: https://github.com/HuajuLiang/HypotheticalPolarizationCamera.

[1]  Alireza Khosravian,et al.  Rigid Body Attitude Control Using a Single Vector Measurement and Gyro , 2012, IEEE Transactions on Automatic Control.

[2]  Andrew A. Lacis,et al.  Scattering, Absorption, and Emission of Light by Small Particles , 2002 .

[3]  Alexander A. Kokhanovsky,et al.  Aerosol Optics: Light Absorption and Scattering by Particles in the Atmosphere , 2008 .

[4]  Gábor Horváth,et al.  How well does the Rayleigh model describe the E-vector distribution of skylight in clear and cloudy conditions? A full-sky polarimetric study. , 2004, Journal of the Optical Society of America. A, Optics, image science, and vision.

[5]  Jinkui Chu,et al.  A Novel Attitude Determination System Aided by Polarization Sensor , 2018, Sensors.

[6]  Xiaofeng He,et al.  Performance improvement of visual-inertial navigation system by using polarized light compass , 2016, Ind. Robot.

[7]  Eric J. Warrant,et al.  Neural coding underlying the cue preference for celestial orientation , 2015, Proceedings of the National Academy of Sciences.

[8]  Peter T Weir,et al.  Flying Drosophila melanogaster maintain arbitrary but stable headings relative to the angle of polarized light , 2018, Journal of Experimental Biology.

[9]  Taeyoung Lee,et al.  Global Attitude Estimation using Single Direction Measurements , 2007, 2007 American Control Conference.

[10]  Chingiz Hajiyev,et al.  Review on gyroless attitude determination methods for small satellites , 2017 .

[11]  Xue Chenyang,et al.  Attitude Determination Based on Location of Astronomical Markers With Skylight Polarization Pattern , 2015, IEEE Sensors Journal.

[12]  Xin Wang,et al.  Empirical corroboration of an earlier theoretical resolution to the UV paradox of insect polarized skylight orientation , 2013, Naturwissenschaften.

[13]  Moshe Hamaoui,et al.  Polarized skylight navigation. , 2017, Applied optics.

[14]  Zheng You,et al.  Angle algorithm based on Hough transform for imaging polarization navigation sensor. , 2015, Optics express.

[15]  Huijie Zhao,et al.  Polarization patterns under different sky conditions and a navigation method based on the symmetry of the AOP map of skylight. , 2018, Optics express.

[16]  Tang Jun,et al.  Polarized Skylight Pattern-Based Approach to Attitude Determination , 2015, IEEE Sensors Journal.

[17]  范之国 Fan Zhi-guo,et al.  Three-dimensional attitude information obtained by the skylight polarization pattern , 2016 .

[18]  Steven M. Reppert,et al.  Polarized Light Helps Monarch Butterflies Navigate , 2004, Current Biology.

[19]  Stéphane Viollet,et al.  Polarized skylight-based heading measurements: a bio-inspired approach , 2019, Journal of the Royal Society Interface.

[20]  M. Berry,et al.  Polarization singularities in the clear sky , 2004 .

[21]  H. J. Strutt,et al.  LVIII. On the scattering of light by small particles , 1871 .

[22]  Stéphane Viollet,et al.  AntBot: A six-legged walking robot able to home like desert ants in outdoor environments , 2019, Science Robotics.

[23]  Xiaofeng He,et al.  Multicamera polarized vision for the orientation with the skylight polarization patterns , 2018 .

[24]  R. Wehner.  Desert ant navigation: how miniature brains solve complex tasks , 2003, Journal of Comparative Physiology A.

[25]  Nadav Shashar,et al.  Light polarization under water near sunrise. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[26]  Xianlin Huang,et al.  Principles and Applications of Polarized-light-aided Attitude Determination in Integrated Navigation , 2006, 2006 Chinese Control Conference.

[27]  Thor I. Fossen,et al.  Robust Navigation System for UAVs in GNSS-and Magnetometer-Denied Environments , 2019, 2019 International Conference on Unmanned Aircraft Systems (ICUAS).

[28]  F. Landis Markley,et al.  Attitude Determination Using Two Vector Measurements , 1998 .

[29]  Tao Ma,et al.  An Evaluation of Skylight Polarization Patterns for Navigation , 2015, Sensors.

[30]  Claudia Emde,et al.  A 3-D polarized reversed Monte Carlo radiative transfer model for Millimeter and submillimeter passive remote sensing in cloudy atmospheres , 2005, IEEE Transactions on Geoscience and Remote Sensing.

[31]  Zheng You,et al.  Real-time Imaging Orientation Determination System to Verify Imaging Polarization Navigation Algorithm , 2016, Sensors.

[32]  F. Landis Markley,et al.  Optimal Attitude Matrix from Two Vector Measurements , 2008 .

[33]  Steven M Reppert,et al.  Neurobiology of Monarch Butterfly Migration. , 2016, Annual review of entomology.

[34]  Roman Garnett,et al.  Bioinspired polarization vision enables underwater geolocalization , 2018, Science Advances.

[35]  Basil el Jundi,et al.  Night sky orientation with diurnal and nocturnal eyes: dim-light adaptations are critical when the moon is out of sight , 2016, Animal Behaviour.

[36]  Gábor Horváth,et al.  First observation of the fourth neutral polarization point in the atmosphere. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[37]  Art Lompado,et al.  Passive optical sensing of atmospheric polarization for GPS denied operations , 2016, SPIE Defense + Security.

[38]  Basil el Jundi,et al.  The role of the sun in the celestial compass of dung beetles , 2014, Philosophical Transactions of the Royal Society B: Biological Sciences.

[39]  Gábor Horváth,et al.  Polarized Light and Polarization Vision in Animal Sciences , 2014, Springer Series in Vision Research.

[40]  Birgit Greiner,et al.  Celestial polarization patterns during twilight. , 2006, Applied optics.

[41]  Jing Chen,et al.  A Novel Stability Parameters Calculating Method for Container Ship Based on Attitude Sensor , 2018, 2018 International Symposium in Sensing and Instrumentation in IoT Era (ISSI).

[42]  Alexander A. Kokhanovsky,et al.  Light Scattering Reviews , 2006 .

[43]  Mehrzad Namvar,et al.  Adaptive Compensation of Gyro Bias in Rigid-Body Attitude Estimation Using a Single Vector Measurement , 2013, IEEE Transactions on Automatic Control.

[44]  Stéphane Viollet,et al.  Insect-inspired vision for autonomous vehicles. , 2018, Current opinion in insect science.

[45]  Bernhard Mayer,et al.  The impact of aerosols on polarized sky radiance: model development, validation, and applications , 2009 .

[46]  G. Horváth,et al.  How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation. , 2001, The Journal of experimental biology.

[47]  Abd El Rahman Shabayek.  Combining omnidirectional vision with polarization vision for robot navigation. (Apports combinés de la vision omnidirectionnelle et polarimétrique pour la navigation de robots) , 2012 .

[48]  O. Graydon.  Global position by polarization , 2018, Nature Photonics.

[49]  James Richard Forbes,et al.  Nonlinear Estimator Design on the Special Orthogonal Group Using Vector Measurements Directly , 2017, IEEE Transactions on Automatic Control.

[50]  Joseph L. Cox,et al.  Sensors and Systems for Space Applications III , 2009 .

[51]  Xiaofeng He,et al.  Integrated Polarized Skylight Sensor and MIMU With a Metric Map for Urban Ground Navigation , 2018, IEEE Sensors Journal.

[52]  Bernhard Ronacher,et al.  Transfer of directional information between the polarization compass and the sun compass in desert ants , 2014, Journal of Comparative Physiology A.

[53]  John William Strutt,et al.  Scientific Papers: On the Scattering of Light by small Particles , 2009 .

[54]  G. Wahba.  A Least Squares Estimate of Satellite Attitude , 1965 .

[55]  M. V. Berry,et al.  Nature’s optics and our understanding of light , 2014, مجلة جامعة فلسطين التقنية خضوري للأبحاث.

[56]  Jun Zhou,et al.  Microsatellite attitude determination based on skylight polarization and geomagnetic measurement , 2019, Optik.

[57]  Xin Wang,et al.  An analytical model for the celestial distribution of polarized light, accounting for polarization singularities, wavelength and atmospheric turbidity , 2016 .

[58]  Daniel Mathiot,et al.  Diffusion of indium in GaSb , 1980 .

[59]  Stéphane Viollet,et al.  An ant-inspired celestial compass applied to autonomous outdoor robot navigation , 2019, Robotics Auton. Syst..

[60]  Shuai Zhang,et al.  A Bionic Camera-Based Polarization Navigation Sensor , 2014, Sensors.

[61]  F. Markley,et al.  Fast Quaternion Attitude Estimation from Two Vector Measurements , 2002 .

[62]  Art Lompado,et al.  Using Atmospheric Polarization Patterns for Azimuth Sensing , 2014, Defense + Security Symposium.

[63]  Joseph A Shaw,et al.  Effects of surface reflectance on skylight polarization measurements at the Mauna Loa Observatory. , 2011, Optics express.

[64]  J. Hannay,et al.  Polarization of sky light from a canopy atmosphere , 2004 .

[65]  Nan Zhang,et al.  Novel robust skylight compass method based on full-sky polarization imaging under harsh conditions. , 2016, Optics express.

[66]  Eli Shlizerman,et al.  Neural Integration Underlying a Time-Compensated Sun Compass in the Migratory Monarch Butterfly. , 2016, Cell reports.

[67]  Jakob N. Foerster,et al.  Three-dimensional head-direction coding in the bat brain , 2014, Nature.

[68]  Jun Liu,et al.  Attitude calculation method based on full-sky atmospheric polarization mode. , 2019, The Review of scientific instruments.

[69]  Michael H. Dickinson,et al.  Celestial navigation in Drosophila , 2019, Journal of Experimental Biology.

[70]  James Richard Forbes,et al.  Exponential convergence of a nonlinear attitude estimator , 2016, Autom..

[71]  Xinyan Deng,et al.  Attitude Stabilization of a Biologically Inspired Robotic Housefly via Dynamic Multimodal Attitude Estimation , 2009, Adv. Robotics.

[72]  Jinkui Chu,et al.  Orthogonal vector algorithm to obtain the solar vector using the single-scattering Rayleigh model. , 2018, Applied optics.

[73]  James K. Hall,et al.  Quaternion attitude estimation for miniature air vehicles using a multiplicative extended Kalman filter , 2008, 2008 IEEE/ION Position, Location and Navigation Symposium.