Sunlight during its propagation in the atmosphere due to air molecules reflection, scattering of aerosol particles and the like, as well as vegetation, water and other polarized light is generated. While the human visual perception can not be directly polarized, but many organisms such as sand ants, bees, grasshoppers and other insects, and even big ear bat, was able to take advantage of its unique visual structure, perception and use of the phenomenon of polarization of light to obtain information in order to navigate , foraging, communication, migration and other activities. Anatomical studies have shown that a series of biological, biological polarized light having navigation capabilities which is depends on the particular structure of the compound eye polarization photosensitive neural process can be detected and the atmosphere rapidly changing polarization mode information, so as to extract reliable compass navigation information. The results of the study polarized bionic navigation provides the biological basis, it has opened up a research-based navigation bionic polarized light is.
Atmospheric polarization mode polarization distribution is a regular pattern in the sky the finally formed polarized light, which contains important information direction. Biological studies have shown that insect navigation sand ants, bees and other atmospheric polarization mode information instead of applying a single point of the sky, but to use the entire or partial information having stable atmospheric polarization mode distribution, and the angle between the sun and the body axis meridian extract, enabling navigation. Therefore, the use of atmospheric polarization mode effective access to information as the position of the sun in the sky, a significant point, that navigation can provide a reference datum is to achieve polarized light to navigate the premise and key technologies, but also to track the position of the sun and take advantage of great significance.
Characterization atmospheric Rayleigh polarization modes: under clear weather conditions, light scattering particles in the atmosphere, Rayleigh scattering satisfy the conditions, the atmosphere can therefore be characterized by polarization mode Rayleigh scattering theory obtained. Characterized that the Rayleigh scattering of sunlight after a position of each point on the surface of the celestial sphere occurs with atmospheric particles, i.e. the observer receives, which accurately describes the distribution of the optical fiber under atmospheric conditions over the presentation of the most widely used is a kind of characterization methods. Polarization mode and the atmosphere can be regarded as a set of air at various points of the scattering effect. Rayleigh scattering model is described conventional atmospheric conditions over the most classic polarization mode of characterization, the real atmosphere polarization mode having high similarity, the degree of polarization is generally used (DOP) and polarization angle (the AOP, also known as E - Vector direction) will be described, the figure shows the polarization mode Rayleigh characterized atmospheric modeling coordinate system. Drawing the observer as an origin 
, the position of the sun 
, for the designated days 
, the direction of the zenith 
axis, east direction 
axis, the direction of true north 
axis. Any point spherical surface 
of the zenith angle 
, azimuth angle 
, 
to the true north direction is 0, a positive value for the north east. Expressed as the spatial position of the sun 
, wherein, 
for the sun zenith angle, 
for the sun azimuth, elevation angle of the sun 
, the sun position in a radial coordinate system to the geographic azimuth 
expressed.
Polarization orientation angle 
is defined as a point measured 
at E - where the radial direction of the vector with the angle, according to the law of Rayleigh scattering, any one measured point 
at E - vector:
Among 
them, 
, .
When expressed as a coordinate position of the sun in three-dimensional coordinates 
, which is the elevation angle 
, azimuth angle 
can be obtained when any point in the sky 
, as the elevation angle 
, azimuth angle of the polarization direction of the angle of the theoretical value:
The figure below shows the relationship between the coordinate system of several Rayleigh model, including the geographic coordinate system, camera coordinate system, the incident coordinate system. Drawing, 
showing geographic north, 
represents a geographic coordinate system, 
represents the camera coordinate system 
represents a coordinate system of the incident light, 
the 
horizontal and vertical axes of the image are parallel 
to the plane perpendicular to the camera, point to point days; 
represents a position of the sun 
represents observation point , 
and respectively, the position of the sun zenith angle and azimuth angle in a geographic coordinate system, 
and 
are observation points in the camera coordinates zenith and azimuth angle; 
as the incident coordinate system E - vector, the vector 
, 
, 
perpendicular to the plane formed of three points, by the vector 
and the vector 
cross product obtained; incident coordinate system 
axes and E - is the angle between the polarization vector of the direction where the angle (polarization angle for short) 
.
Incident coordinate system E - angle of polarization vector 
function for solving E - vector should first solve the polarization angle 
, the polarization angle solving step is as follows: First, an image is obtained under a clear sky, weather, using the imaging camera NiKon-D850 
, 
, 
and 
four polarization angle atmospheric polarized image, the camera apparatus as shown, is mounted in front of the camera lens fisheye lens, and a polarizing plate disposed in front of the fisheye lens, and rotating the polarizer to different angles to obtain different polarization shooting atmospheric polarized image angle.
Atmospheric four different polarization angles of captured image obtained as follows, a recording time at 5:03 on May 22, 2019, the angle of the polarization of the image from left to right, respectively , , and .
Provided four polarized image light intensity, respectively 
, 
, 
and 
, thereby calculating Stokes vector component in the polarization state 
, 
, 
:
A , , calculated for each pixel a 
polarization angle is at:
Redraw the 
map, so that the central and symmetric along a meridian sun ∞-shaped distribution was calculated as:
Coordinates provided two pixels in the sky at different positions corresponding to the observation points, respectively 
and 
, corresponding to the coordinates of the two zenith and azimuth angles are:
Which 
is the position coordinates of the center of the image, 
the focal length of the camera.
偏振角图像中
，
处的像素灰度值
，
为该两观测点处的散射光的偏振角的值，则在入射光坐标系中表示E-矢量为：
在三维空间的坐标系为
，绕三个坐标轴其中一轴旋转得到新的坐标系，则原先坐标系中的点用旋转后的坐标系表示时，点的坐标转换关系如下：
为了计算太阳矢量，需要将E-矢量从入射光坐标系转换到相机坐标系。若要将入射光坐标系转化到相机坐标系，需要将入射光坐标系旋转两次：将入射光坐标系绕
轴向上旋转
角度，得到新的坐标系
；将坐标系
绕
轴（
轴与
轴重合）向右旋转
角度，得到相机坐标系
。每旋转一次坐标系，左乘对应的旋转矩阵，旋转矩阵中的角度对应于坐标轴旋转的角度，由此可得入射光坐标系到相机坐标系的坐标转换矩阵为：
则将，处的E-矢量在相机坐标系中表示为：
由任意两个E-矢量叉乘得到太阳矢量的规律，可表示太阳矢量为：
取太阳矢量中的前两个元素，可得太阳的方位角为：
在实验拍摄大气偏振图像时，将相机坐标系的
轴放置与地理北极
重合的位置，则计算航向角为
或者
。