1.2　Bioinspired polarization orientation method

There are many organisms in nature that can use atmospheric polarization for orientation,such as bees,sand ants,and dragonflies.They can return to their nests hundreds of meters away in a nearly straight path after a complex and tortuous foraging process in the absence of a significant reference.The compound eye is the main visual organ of insects,and its dorsal edge region (DRA) is a small area facing the sky,as shown in Fig.1.2.It is this part of the area where the small eye is highly sensitive to atmospheric polarization distribution patterns.

In terms of the research on the distribution characteristics and characterization methods of atmospheric polarization,relevant research work was carried out abroad as early as the 16th century.In 1669,the Danish physicist B.Erasmus discovered the polarization of light for the first time in an experiment,which opened up a new field of light research ^[1] .Thereafter,French scholar J.Babinet,K.Coulson,British physicist D.Brewster et al.on the basis of F.Arago'research,a large number of in-depth experiments have been carried out to further develop and improve the basic theory of atmospheric polarization through a large number of in-depth experiments on the causes and characterization methods of atmospheric polarization ^[2] .In 1871,the British scientist Rayleigh deeply studied the scattering effect of small particles in the air on light,and proposed the classical Rayleigh scattering theory,Rayleigh scattering theory,on the premise of ignoring the multiple scattering of complex particles,which provided important theoretical support for the later study of the distribution pattern of atmospheric polarization in clear sky ^[3] .In 1908,the German physicist G.Mie proposed a multi-scattering model of light based on spherical particles,namely the Mie scattering theory,the Mie scattering theory,which pushed the study of single scattering of atmospheric polarization to a multi-scattering study that is more similar to the real scattering model ^[4] .In 1982,Professor Wehner of the University of Zurich in Switzerland proposed the Rayleigh model to describe the distribution pattern of atmospheric polarization in clear weather based on Rayleigh's single scattering theory ^[5] .In 2017,the University of Amsterdam in the Netherlands proposed a three-dimensional Monte Carlo radiative transfer program (ARTES) for simulating scattered light from planetary atmospheres,which is used to study how three-dimensional atmospheric asymmetry affects polarization signals,and will evaluate the application of infrared polarization method in direct imaging to observe planetary masses ^[6] .In 2021,the California Institute of Technology (Caltech) used polarization spectroscopy and O-2 near-infrared radiometry to measure the information content of aerosol profiles and evaluate the uncertainty,and the results showed that the addition of hyperspectral resolution radiometry and polarization measurement not only reduced the number of required viewing angles,but also effectively improved the polarization and radiation signal-to-noise ratio and detection sensitivity ^[7] .

The research on the distribution and characterization of atmospheric polarization by domestic scholars started late.In 2011,Gao Jun's team from Hefei University of Technology characterized and analyzed the atmospheric polarization pattern based on the complex spherical map and E-vector description,and modeled and simulated the atmospheric polarization pattern under microscopic Rayleigh scattering,and proposed an analytical model of the polarization pattern in the sky under the influence of multiple scattering factors ^[8] .In 2013,Professor Zhao Kaichun of Tsinghua University and others designed an automatic detection device for polarization patterns in the sky ^[9] .In the same year,Professor Chu Jinkui's team from Dalian University of Technology conducted a study on the influence of sunlight and moonlight on the polarization pattern of twilight,and proved that the polarization pattern of sunlight plays a major role in the formation of the polarization pattern of the sky at twilight ^[10] .In 2014,Zhang Zhongshun of Hefei University of Technology proposed a full-Stokes vector-Stokes vector atmospheric polarization pattern measurement system with a field of view of nearly 180° ^[11] .In 2015,Wang Ziqian of Hefei University of Technology studied a modeling simulation of the atmospheric polarization pattern Stokes vector based on the Rayleigh scattering model,and found that the atmospheric polarization pattern Stokes vector has a zigzag distribution ^[12] .In 2015,the team of Professor Liu Jun of North University of China carried out research on atmospheric polarization pattern detection and model reconstruction based on the Rayleigh scattering model,which laid a foundation for subsequent research on the application and algorithm of polarization navigation ^[13] .In 2018,Fan Zhiguo et al.from Hefei University of Technology analyzed the macroscopic variation law of the atmospheric polarization pattern and clarified the modeling method of the"∞"character characteristics of the atmospheric polarization pattern,which improved the feasibility of the course information of polarization navigation ^[14] .Based on the relative relationship between the oblique attitude coordinate system and the horizontal coordinate system,a modeling method for the atmospheric polarization pattern in the oblique attitude was proposed ^[15] .In 2021,the Key Laboratory of the National Meteorological Satellite Center used remote sensing multi-angle technology to combine the polarization and anisotropy of atmospheric reflection with the observations of lidar and directional polarization cameras,respectively,and analyzed and studied the aerosol characteristics as multi-angle pure intensity signals and multi-angle polarization signals ^[16] .These theoretical studies provide a basis for the application of atmospheric polarization pattern.

The above research status at home and abroad shows that the distribution characteristics and characterization methods of atmospheric polarization light have received extensive attention from researchers at home and abroad,and atmospheric polarization pattern detection devices have also been applied.The distribution characteristics and characterization methods of accurate atmospheric polarization in complex environments have become a research hotspot,which has opened the prelude to the research on autonomous navigation using sky polarization information.Characteristics and characterization methods of atmospheric polarization,as shown in the Fig.1.3.

In 1982 and 1989,Wehner et al.at the University of Zurich in Switzerland studied how to derive bee celestial maps and special parts of the retina from the E-vector model in the sky,as shown in Fig.1.4,simulate the directional distribution of the E-vector in the sky to use the polarization pattern in the sky as a compass for navigation ^[17,18] .Subsequently,scientists have done a lot of research on the visual perception,flight guidance,navigation,learning and memory of various organisms in nature using their visual/brain polarization-sensitive neurons in complex and unfamiliar environmental conditions such as day/night and mist/clouds.In 2001,Labhart et al.at the University of Zurich in Switzerland discovered that polarization-sensitive neurons (POL neurons) in the cricket visual system can integrate large-area information in the sky,improve the quality of atmospheric polarization signals,and enhance the sensitivity of navigation information by filtering out local perturbations of polarization patterns caused by clouds ^[19] .In 2011,the University of Marburg,Germany,further studied the response of two descending neurons and the anterior thoracic ganglion of the locust brain to polarization and the mechanism of navigation using the atmospheric polarization E-vector pattern ^[20] .Honeybee POL neurons and navigation using atmospheric polerization pattern,as shown in Fig.1.4.

In 2015,the University of Bristol in the United Kingdom carried out research on the characterization of the polarization sensitivity of the human eye and developed a new method for measuring the lower limit of human perceived polarization light detection by gratings with only polarization contrast at different degrees of polarization ^[21] .In 2019,the Institute of Biological Neuroscience in Berlin,Germany,conducted research on the heading selection mechanism of flying Drosophila under different polarization angles,and found that these behavioral responses are wavelength-specific.That is,they can be selected under polarized ultraviolet stimulus,but not under polarized green light,which provides further evidence for Drosophila to use celestial cues for visual navigation and course correction ^[22] .In 2020,a study by the University of Maryland State discovered that mantis shrimp can navigate based on the hierarchical path integration of the sun,overhead polarization patterns,and internal unique orientation cues when foraging,which became the first fully underwater animal path integration method discovered so far,which opens up a new way to study the neural basis of navigation behavior and improve navigation methods in arthropods and other diving animals ^[23] .In 2021,Dron University in Sweden and Simon Fraser University in Canada conducted a detailed analysis of the beetle's use of polarization for navigation,and the study showed that the beetle used the polarization patterns generated by the Sun,the Milky Way and the Moon to move in a fixed direction during the day and night:in the morning and afternoon,the sun was used to determine the direction,but at noon,the wind was used to determine the direction,and at night or in the forest,the polarization was mainly relied on to maintain a straight path ^[24,25] .

The good application prospect of polarization orientation has also attracted extensive attention from domestic scholars.In 2009,the team of Professor Chu Jinkui of Dalian University of Technology designed a new bionic polarization angle sensor based on the principle of Bioinspired Polarization orientation,proposed an angle error compensation algorithm,and carried out the navigation test of the navigation sensor prototype for outdoor mobile robots.Subsequently,in 2015,the team proposed a heading angle measurement system based on polarization and MEMS gyroscopes,which can provide accurate heading information for flight control ^[26,27] .In 2013,the team of Professor Gao Jun of Hefei University of Technology also carried out sensor design research based on the principle of bionics,solved the ambiguity problem of polarization navigation angle measurement,and proposed a heading angle calculation method based on the symmetry detection method of atmospheric polarization pattern and the POLneuron model of imitation sand ants ^[28] .In 2014,Professor Hu Xiaoping's team at the National University of Defense Technology proposed an angular error calibration method and analyzed the polarization orientation algorithm and error ^[29] .From 2016 to 2019,the team proposed a bionic navigation algorithm based on the grid cell model/positional cell model and biological navigation mechanism,a multi-eye polarization visual navigation method,a navigation topology map construction method,and a bionic polarization light orientation method based on the animal hippocampus navigation mechanism and the RatSLAM algorithm,as well as for the ground unmanned platform ^[31-34] .In 2020,the team proposed a model and method for building atmospheric polarization orientation for any pixel based on known information under cloudy weather conditions ^[35] .In 2015,the team of Professor Liu Jun of North University of China proposed a heading angle solution method based on full-sky atmospheric polarization detection and a method for extracting the pitch angle and roll angle of an aircraft based on the stability distribution characteristics of the atmospheric polarization pattern,and carried out experimental verification ^[30] .In 2021,in order to improve the fitting accuracy of the solar meridian,the team proposed a method of coarse extraction of the axis of symmetry and then accurate extraction of the solar meridian after continuous rotation,which finally improved the accuracy of the polarization orientation system ^[36] .Bioinspired Polarization sensor and its navigation test results,as shown in Fig.1.5.

It can be seen from the above research status at home and abroad that the directional measurement based on bioinspired polarization sensor has achieved good results under laboratory conditions.On the basis of the above research,how to further improve the orientation accuracy in the practical application process has become an important research direction of bioinspired polarization compass.Therefore,it is necessary to carry out the research on the processing method of bioinspired polarization compass orientation error.