Polarization compass sun tracking method based on atmospheric polarization distribution characteristics of non-ideal Rayleigh scattering

Abstract

The present invention discloses a sun tracking method based on the polarization distribution characteristics of the non-ideal Rayleigh scattering atmosphere. First, a sky polarization sensor is used to receive sky polarization image information. This polarization information is then converted into the polarized light E vector direction, and the possible range of the neutral point is set between [0, 2π]. This is used to establish a Hough space grid. The E vector direction is then converted into Hough space weights using an elliptical Hough transform. After all data undergoes the Hough transform, the point with the highest weight in the Hough space is the neutral point location. At this point, the neutral point accuracy is determined to meet the set accuracy. If so, the neutral point information is used to achieve polarization compass orientation. The proposed sun compass orientation method based on the elliptical Hough transform has good environmental adaptability and high robustness, enabling fully autonomous, long-duration compass orientation.

Description

Technical Field

[0001] The present invention relates to an improvement to a polarization compass navigation algorithm, and more particularly, to a polarization compass sun tracking method based on the non-ideal Rayleigh scattering atmospheric polarization distribution characteristics. The method can improve the environmental adaptability of sky polarization compass orientation and can also serve as the basis for polarization compass orientation. Background Art

[0002] Heading information is crucial in autonomous navigation technology. Inertial navigation can provide highly accurate and interference-resistant heading information in the short term, but this will result in gradually increasing cumulative errors over time. The polarization compass carried by the gyroscope carrier is a heading instrument that can independently measure the aircraft's heading while also exhibiting excellent stability and high sensitivity. However, the polarization compass is susceptible to interference from the magnetic field in the environment, causing compass errors and reducing the accuracy of heading measurements. Directional compass technology based on the position of the sun has existed since ancient times. Its principle is to use the Earth's rotation and revolution orbit to calculate the position relationship between the sun and the Earth, and then calculate heading information based on the position of the sun in the sky. The Earth's rotation and revolution orbit is only affected by the sun, the Earth, and the moon, and its calculation error is less than 1 arc second.

[0003] The error in positioning calculations by navigation satellites is determined solely by the accuracy of the measurements of the sun's position in the sky. While magnetic sensors (polarization compasses) can provide highly accurate heading information, their observation range is limited and susceptible to obstructions such as clouds.

[0004] Existing polarization navigation technologies, such as the "Adaptive method for estimating information from a polarized skylight" published in Applied Optics in 2021, use the Rayleigh single scattering model to implement a polarization compass. However, due to certain differences between the actual atmosphere and the ideal Rayleigh scattering model, this approximation reduces the accuracy of the polarization compass's orientation.

[0005] Bionic polarization compass orientation technology uses the polarization pattern of scattered light from the atmosphere to determine the sun's position and calculate heading information. Even if the sun is obscured, the sun's position can be determined by measuring the polarization distribution of scattered light from the sky, resulting in greater environmental adaptability and robustness. Consequently, many organisms, including sand ants and scarab beetles, use sky polarization information for navigation, and in recent years, scholars have also begun to pay extensive attention to this technology. The current mainstream polarization compass orientation method is to solve for the sun vector based on the E-vector perpendicularity relationship of the Rayleigh single scattering model. However, in actual applications, there are certain differences between the atmosphere and the ideal Rayleigh scattering model, which can reduce the accuracy of inertial navigation orientation. Summary of the Invention

[0006] To improve the accuracy of polarized compass heading in conditions of poor air quality and cloud cover, the present invention proposes a polarized compass sun tracking method based on the polarization distribution characteristics of a non-ideal Rayleigh scattering atmosphere. This method uses the Hannay model, referred to as a non-ideal Rayleigh scattering model, instead of the Rayleigh single scattering model. Polarization information is first converted into the E vector direction of polarized light, and the possible range of the neutral point is set between [0, 2π]. A Hough space grid is then established, and the E vector direction is converted into Hough space weights using the elliptical Hough transform. After all data are Hough transformed, the point with the highest weight in the Hough space is the neutral point location. At this point, the accuracy of the neutral point calculation is determined. If sufficient, the neutral point information is used to perform polarized compass heading. Otherwise, the neutral point range is used to improve accuracy, and the neutral point range is calculated again using the Hough transform until the result is sufficiently accurate. The Hannay multiple scattering elliptical model used in this invention is closer to the real atmosphere than the ideal Rayleigh scattering model. The elliptical Hough transform can extract elliptical information from the image. Therefore, the elliptical Hough transform can be used to process data from the sky polarization sensor based on the Hannay multiple scattering ellipse model, further improving the environmental adaptability of polarized sun compass orientation and reducing the errors introduced by the single scattering model. Furthermore, the sun compass orientation method using the elliptical Hough transform has good environmental adaptability and high robustness, enabling fully autonomous and long-duration compass orientation.

[0007] The present invention provides a polarization compass sun tracking method based on non-ideal Rayleigh scattering atmospheric polarization distribution characteristics, which comprises the following steps:

[0008] Step 1: information acquisition based on polarization sensor;

[0009] The corresponding data of the sky polarization sensor is the micro-array polarization sensing information of 4 pixels as a group, wherein the polarizer directions of these 4 pixels are 90 degrees, 45 degrees, 135 degrees and 0 degrees respectively, and the light intensities corresponding to 90 degrees, 45 degrees, 135 degrees and 0 degrees are 1 respectively. 90 , I 45 , I 135 、I0;Calculate the Stokes vector based on the sky polarization data and record it as S(I,Q,U,V):

[0010] I=I0+I 90 (1)

[0011] Q=I0-I 90

[0012] U=I 45 +I 135

[0013] V=0

[0014] The polarization angle is calculated based on the Stokes vector. The formula is:

[0015]

[0016] The formula for inferring the direction of the E vector in three-dimensional space using the polarization angle is:

[0017] P 2d =[sin(AOP), cos(AOP), 0] (3)

[0018] P 3dE =P 2d ·L(θ1)·L(θ2) (4)

[0019] Step 2: Construct Hough space;

[0020] The neutral point Hough space is denoted as H(n 11 , n 12 , n 21 , n 22 ), for Hough space H(n 11 , n 12 , n 21 , n 22 ) is recorded as H ζ (n 11 , n 12 , n 21 , n 22 ), the subscript ζ represents the number of Hough transforms; the Hough space H ζ (n 11 , n 12 , n 21 , n 22 ) is divided into a discrete grid of 20×20×20×20;

[0021] Step 3: Calculate the zenith angle and azimuth angle represented by the Hough space grid point;

[0022] The calculated zenith angle and azimuth angle represented by the Hough space grid point:

[0023]

[0024]

[0025]

[0026]

[0027]

[0028] Step 4: Solid angle coordinates of the neutral point;

[0029] The coordinates of the neutral point solid angle are marked as [Zen1, Azi1, Zen2, Azi2], and the [Zen1, Azi1, Zen2, Azi2] corresponds to the point [n 11 , n 12 , n 21 , n 22 ] is represented by:

[0030] P N1 =[sin(Zen1)·cos(Azi1), sin(Zen1)·sin(Azi1), cos(Zen1)] (1O)

[0031] P N2 =[sin(Zen2).cos(Azi2),sin(Zen2)·sin(Azi2),cos(Zen2)] (11)

[0032] Step 5: Calculate the weight of the neutral point;

[0033] The coordinate of any pixel point in the navigation image corresponding to the three-dimensional space is called data pixel point P pixel (x p ,y p , z p );

[0034] Use E vector direction P 3dE , the neutral points N1 and N2 correspond to the coordinates P in three-dimensional space N1 With P N2 , and the image pixel coordinates P pixel (k p ,y p , z p ) Calculate the weight corresponding to the Hough space point:

[0035]

[0036] Traverse each P of the sky polarization image sensor pixel (x p ,y p , z p ), and let each P pixel (x p ,y p , z p ) traverses every grid point in the Hough space, thereby completing the Hough transform and obtaining the Hough space data set MMH 霍夫 ; From the MMH 霍夫 Select the grid point with the highest weight, denoted as described Is the result of the operation; according to The grid coordinates [n 11 , n 12 , n 21 , n 22 ] to calculate the next Hough space H ζ+1 (n 11 , n 12 , n 21 , n 22 ) in the Babinet neutral point N1 and Brewster neutral point N2:

[0037]

[0038]

[0039]

[0040]

[0041] Step 6: Determine the neutral point accuracy;

[0042] The neutral point accuracy threshold is denoted as δ 阈值 ; The current neutral point calculation accuracy is recorded as δ ζ , and δ ζ =Zen′ max1 -Zen′ min1 ;

[0043] When δ ζ ≤δ 阈值 When H ζ (n 11 , n 12 , n 21 , n 22 ) Return to step 3;

[0044] When δ ζ >δ 阈值 When , execute step 7;

[0045] Step 7, calculate the sun's zenith angle and azimuth angle;

[0046] According to the Hannay neutral point model, the midpoint of the neutral point is the sun's position, which can be used as navigation information; the sun's zenith angle and azimuth angle are calculated using the neutral point zenith angle and azimuth angle [Zen1, Azi1, Zen2, Azi2]:

[0047]

[0048]

[0049] Zenith angle of the sun sun and azimuth Azisun Together with the zenith angle and azimuth angle [Zen1, Azi1, Zen2, Azi2] of the neutral point constitute the orientation information of the polarized compass based on sun tracking.

[0050] The advantages of the method of the present invention compared with the prior art are:

[0051] (1) In the method of the present invention, the Hannay model is used instead of the Rayleigh scattering model, which reduces the impact of multiple scattering interference on navigation accuracy and improves environmental adaptability under cloudy skies.

[0052] (2) In the method of the present invention, the Hough transform algorithm is used to extract navigation information from damaged images, thereby avoiding the influence of clouds in the sky or obstructions on the navigation accuracy.

[0053] (3) In the method of the present invention, navigation information is obtained by extracting the neutral point in the sky, and no external equipment is required, so that long-duration passive autonomous navigation can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 The present invention is a flow chart of a polarization compass sun tracking method based on the polarization distribution characteristics of the non-ideal Rayleigh scattering atmosphere.

[0055] Figure 2 Schematic diagram of polarization direction distribution of the array analyzer of the sky polarization sensor of the present invention.

[0056] Figure 3 Schematic diagram of the neutral point and E vector in the three-dimensional space coordinate system of the present invention.

[0057] Figure 4 Schematic diagram of the weight calculation principle of Hough space voting.

[0058] Figure 5 This is an error comparison diagram processed by the method of the present invention. DETAILED DESCRIPTION

[0059] The present invention will be described in further detail below with reference to the accompanying drawings.

[0060] The method of the present invention is a compass error correction method for a gyro polarization compass in an inertial navigation system. After correction by the method of the present invention, the measurement accuracy of the inertial navigation can be improved on the one hand, and the orientation accuracy of the polarization compass can be improved on the other hand.

[0061] In the present invention, the Hannay model is used instead of the Rayleigh single scattering model, which is called a non-ideal Rayleigh scattering model.

[0062] In the present invention, in order to facilitate the explanation of the coordinate transformation of the polarization direction data, the sky polarization sensor coordinate system Oxc y c and the device coordinate system O b -x b y b z b ,like Figure 2 、 Figure 3 The polarization direction angle and the E vector direction are defined by the two coordinate systems.

[0063] See also Figure 1 As shown, the present invention provides a polarization compass sun tracking method based on non-ideal Rayleigh scattering atmospheric polarization distribution characteristics, comprising the following steps:

[0064] Step 1: information acquisition based on polarization sensor;

[0065] In the present invention, the corresponding data of the sky polarization sensor is the micro-array polarization sensing information of 4 pixels as a group, wherein the polarizer directions of the 4 pixels are 90 degrees, 45 degrees, 135 degrees and 0 degrees respectively, and the light intensities corresponding to 90 degrees, 45 degrees, 135 degrees and 0 degrees are 1 respectively. 90 , I 4s , I 135 、I0. The Stokes vector is calculated based on the sky polarization data and is recorded as S(I, Q, U, V):

[0066]

[0067] I represents light intensity.

[0068] Q represents the second term of the Stokes vector.

[0069] U represents the third term of the Stokes vector.

[0070] V represents the fourth term of the Stokes vector.

[0071] The polarization angle is calculated based on the Stokes vector, and the formula is:

[0072]

[0073] Since the polarization angle is the angle between the projection of the polarization direction on the polarization sensor and the Y-axis of the polarization image, the polarization direction in three-dimensional space, that is, the direction of the E vector, can be inferred from the polarization angle. The formula is:

[0074] P 2d =[sin(AOP), cos(AOP), 0] (3)

[0075] P 3dE =P 2d ·L(θ1)·L(θ2) (4)

[0076] P2d It is the projection of the polarization direction on the polarization image.

[0077] P 3dE It is the polarization direction in three-dimensional space, that is, the direction of the E vector.

[0078] θ1 is the direction of the data pixel corresponding to y c The angle between the axes.

[0079] θ2 is the altitude angle represented by the image data pixel.

[0080] L(θ) is the rotation matrix.

[0081] L(θ1) is the rotation matrix of the angle.

[0082] L(θ2) is the rotation matrix of the altitude angle.

[0083] Step 2: Construct Hough space;

[0084] See also Figure 3 As shown, the neutral point Hough space is denoted as H(n 11 , n 12 , n 21 , n 22 ), where n 11 represents the zenith angle of the Babinet neutral point N1, n 12 represents the azimuth of the Babinet neutral point N1, n 21 represents the zenith angle of the Brewster neutral point N2, n 22 Represents the azimuth of the Brewster neutral point N2.

[0085] In the present invention, for the variable n in the Hough space 11 , n 12 , n 21 , n 22 , its initial range should be [0, 2π].

[0086] In the present invention, the Hough transform performed on the Hough space is denoted as H ζ (n 11 , n 12 , n 21 , n 22 ). The Hough space H ζ (n 11 , n 12 , n 21 , n 22 ) is divided into a discrete grid of 20 × 20 × 20 × 20. The subscript ζ represents the number of Hough transforms, and ζ = 1, 2, 3, 4, 5, with a maximum of 5 Hough transforms.

[0087] In the present invention, the Hough space at the time of initialization is denoted as H 霍夫 (n 11 , n 12 , n 21 , n 22 ).

[0088] The Hough space after Hough transform with ζ=1 is denoted as H ζ＝1 (n 11 , n 12 , n 21 , n 22 ), referred to as the first Hough transform. The Hough space of the first Hough transform

[0089] The Hough space after the Hough transform with ζ = 2 is denoted as H ζ＝2 (n 11 , n 12 , n 21 , n 22 ), referred to as the second Hough transform. The Hough space of the second Hough transform

[0090]

[0091] The Hough space after the Hough transform of ζ=3 is recorded as Hζ=3(n 11 , n 12 , n 21 , n 22 ), referred to as the third Hough transform. The Hough space of the third Hough transform is

[0092]

[0093] The Hough space after the Hough transform with ζ=4 is denoted as H ζ＝4 (n 11 , n 12 , n 21 , n 22 ), referred to as the fourth Hough transform. The Hough space of the fourth Hough transform is

[0094]

[0095] The Hough space after the Hough transform with ζ=5 is denoted as H ζ＝5 (n 11 ,n 12 ,n 21 ,n 22 ), referred to as the fifth Hough transform. The Hough space of the fifth Hough transform is

[0096]

[0097] In the present invention, the Hough space H 霍夫 (n 11 ,n 12 ,n 21 ,n 22 ) After Hough transformation ζ times, the range of its variable Hough space will be reduced to the original It is helpful to approach the true zenith angle and azimuth angle of the neutral point (N1, N2).

[0098] In the present invention, in order to distinguish the Hough space formed after the Hough transform, the current Hough space is recorded as H ζ (n 11 ,n 12 ,n 21 ,n 22 ), the next Hough space is denoted as H ζ+1 (n 11 ,n 12 ,n 21 ,n 22 ).

[0099] Step 3: Calculate the zenith angle and azimuth angle represented by the Hough space grid point;

[0100] Because the polarization image of the sky is flat, performing a two-dimensional Fourier transform on the polarization image yields very low high-frequency values ​​in the resulting spectrum. Low-frequency signals can be approximately considered linear near each grid point in Hough space, allowing the azimuth and zenith angle represented by each grid point to be calculated using linear interpolation.

[0101] The calculated zenith angle and azimuth angle represented by the Hough space grid point:

[0102]

[0103]

[0104]

[0105]

[0106]

[0107] step zen1 is the step size of the zenith angle axis of the Babinet neutral point N1 corresponding to the Hough space.

[0108] Zen max1 is the maximum value of the zenith angle of the Babinet neutral point N1.

[0109] Zen min1 is the minimum value of the zenith angle of the Babinet neutral point N1.

[0110] Zen1 is the zenith angle of the Babinet neutral point N1 in Hough space.

[0111] n 11 is the zenith angle of the Babinet neutral point N1.

[0112] step azi1 is the step size of the azimuth axis of the Babinet neutral point N1 corresponding to the Hough space.

[0113] Azi max1 is the maximum value of the azimuth angle of the Babinet neutral point N1.

[0114] Azi min1 is the minimum value of the azimuth of the Babinet neutral point N1.

[0115] Azi1 is the azimuth of the Babinet neutral point N1 in Hough space.

[0116] n 12 is the azimuth of the Babinet neutral point N1.

[0117] step zen2 is the step size of the zenith angle axis of the Brewster neutral point N2 corresponding to the Hough space.

[0118] Zen max2 is the maximum value of the zenith angle of the Brewster neutral point N2.

[0119] Zen min2 is the minimum zenith angle of BrewSter neutral point N2.

[0120] Zen2 is the zenith angle of the Babinet neutral point N2 in Hough space.

[0121] n 21 is the zenith angle of the Brewster neutral point N2.

[0122] step zen2 is the step size of the zenith angle axis of the Brewster neutral point N2 corresponding to the Hough space.

[0123] Azi max2 is the maximum value of the azimuth angle of the Brewster neutral point N2.

[0124] Azi min2 is the minimum azimuth angle of the Brewster neutral point N2.

[0125] Azi2 is the azimuth of the Babinet neutral point N2 in Hough space.

[0126] n 22 is the azimuth of the Brewster neutral point N2.

[0127] Step 4: Solid angle coordinates of the neutral point;

[0128] The coordinates of the three-dimensional space corresponding to the neutral point can be calculated based on the zenith angle and azimuth angle.

[0129] In the present invention, the neutral point solid angle coordinates are marked as [Zen1, Azi1, Zen2, Azi2], and the [Zen1, Azi1, Zen2, Azi2] correspond to the neutral point in the Hough space [n 11 , n 12 , n 21 , n 22 ] is represented by:

[0130] P N1 =[sin(Zen1)·cos(Azi1), sin(Zen1)·sin(Azi1), cos(Zen1)] (1O)

[0131] P N2 =[sin(Zen2)·cos(Azi2), sin(Zen2)·sin(Azi2), cos(Zen2)] (11)

[0132] P N1 is the coordinate of the neutral point N1 in three-dimensional space.

[0133] P N2 is the coordinate of the neutral point N2 in three-dimensional space.

[0134] Zen1 is the zenith angle of the Babinet neutral point N1 in Hough space.

[0135] Azi1 is the azimuth of the Babinet neutral point N1 in Hough space.

[0136] Zen2 is the zenith angle of the Brewster neutral point N2 in Hough space.

[0137] Azi2 is the azimuth of the Brewster neutral point N2 in Hough space.

[0138] Step 5: Calculate the weight of the neutral point;

[0139] See also Figure 4 As shown, the coordinate of any pixel point in the navigation image corresponding to the three-dimensional space is marked as data pixel point P pixel (x p ,y p , z p). The acquisition accuracy of the navigation image is determined by the acquisition equipment.

[0140] In the present invention, the E vector direction P is used 3dE , the neutral points N1 and N2 correspond to the coordinates P in three-dimensional space N1 With P N2 , and the image pixel coordinates P pixel (x p ,y p , z p ) Calculate the weight corresponding to the Hough space point:

[0141]

[0142] A p1 It is the line connecting the Babinet neutral point N1 to the pixel point.

[0143] A p2 It is the line connecting Brewster neutral point N2 to the pixel point.

[0144] P 3dE is the line connecting the directions of the E vector.

[0145] A bs A p1 and A p2 The angle bisector of p1 )、N(A p2 )accomplish.

[0146] N(A p1 ) is the neutral point N1 on the line A p1 Normalized function on .

[0147] N(A p2 ) is the neutral point N2 on the line A p2 Normalized function on .

[0148] W is the weight of the pixel to the Hough space grid.

[0149] The weight W is Figure 4 It is calculated based on the angle between .

[0150] In the present invention, each P of the sky polarization image sensor is traversed. pixel (x p ,y p , z p ), and let each P pixel (x p ,y p , z p ) traverses every grid point in the Hough space, thereby completing the Hough transform and obtaining the Hough space data set MMH霍夫 From the MMH 霍夫 Select the grid point with the highest weight, denoted as described This is the result of the operation. The grid coordinates [n 11 , n 12 , n 21 , n 22 ] to calculate the next Hough space H ζ+1 (n 11 , n 12 , n 21 , n 22 ) in the Babinet neutral point N1 and Brewster neutral point N2:

[0151]

[0152]

[0153]

[0154]

[0155] Zen′ min1 For the next Hough space H ζ+1 (n 11 , n 12 , n 21 , n 22 ) is the minimum value of the zenith angle of the Babinet neutral point N1 in .

[0156] Zen′ max1 For the next Hough space H ζ+1 (n 11 , n 12 , n 21 , n 22 ) is the maximum value of the zenith angle of the Babinet neutral point N1 in .

[0157] Azi′ min1 For the next Hough space H ζ+1 (n 11 , n 12 , n 21 , n 22 ) is the minimum value of the azimuth of the Babinet neutral point N1 in .

[0158] Azi′ max1 For the next Hough space H ζ+1 (n 11 , n 12 , n 21 , n22 ) is the maximum value of the azimuth angle of the Babinet neutral point N1 in .

[0159] Zen′ min2 For the next Hough space H ζ+1 (n 11 , n 12 , n 21 , n 22 ) is the minimum value of the zenith angle of the Brewster neutral point N2 in.

[0160] Zen′ max2 For the next Hough space H ζ+1 (n 11 , n 12 , n 21 , n 22 ) is the maximum value of the zenith angle of the Brewster neutral point N2 in .

[0161] Azi′ min2 For the next Hough space H ζ+1 (n 11 , n 12 , n 21 , n 22 ) is the minimum azimuth angle of the Brewster neutral point N2 in .

[0162] Azi′ max2 For the next Hough space H ζ+1 (n 11 , n 12 , n 21 , n 22 ) is the maximum value of the zenith angle of the Brewster neutral point N2 in .

[0163] Step 6: Determine the neutral point accuracy;

[0164] In the present invention, the neutral point accuracy threshold is denoted as δ 阈值 The current neutral point calculation accuracy is recorded as δ ζ , and δ ζ =Zen′ max1 -Zen′ min1 .

[0165] When δ ζ ≤δ 阈值 When H ζ (n 11 , n 12 , n 21 , n 22 ) Return to step 3;

[0166] When δ ζ >δ 阈值When , execute step 7;

[0167] Due to the time complexity problem of direct Hough transform calculation, the present invention uses the zenith angle to process the neutral point accuracy, which can calculate the neutral point position with high accuracy in a shorter time.

[0168] Step 7, calculate the sun's zenith angle and azimuth angle;

[0169] According to the Hannay neutral point model, the midpoint of the neutral point is the sun's position, and the sun's position can be used as navigation information. In the present invention, the sun's zenith angle and azimuth angle are calculated by the neutral point zenith angle and azimuth angle [Zen1, Azi1, Zen2, Azi2]:

[0170]

[0171]

[0172] Zen sun is the sun's zenith angle.

[0173] Azi sun is the solar azimuth.

[0174] Zen1 is the zenith angle of the Babinet neutral point N1 in Hough space.

[0175] Zen2 is the zenith angle of the Babinet neutral point N2 in Hough space.

[0176] Azi1 is the azimuth of the Babinet neutral point N1 in Hough space.

[0177] Azi2 is the azimuth of the Babinet neutral point N2 in Hough space.

[0178] In the present invention, the zenith angle of the sun is sun and azimuth Azi sun Together with the zenith angle and azimuth angle [Zen1, Azi1, Zen2, Azi2] of the neutral point constitute the orientation information of the polarized compass based on sun tracking.

[0179] Based on deep space navigation technology, the present invention inserts an E-vector acquisition module for the polarization direction and a Hough transform module based on neutral point extraction, converts image data into neutral point information data, transmits it to the autonomous navigation algorithm, and improves the orientation accuracy of the polarization compass.

[0180] Example 1

[0181] On a certain aircraft, the imaging equipment was a PHXO50S-P polarization camera and a FE185CO57HA-1 fisheye lens. At the geographical location of Haidian District, Beijing (116.352°N, 39.986°E), polarization images of the sky were captured from 2:30 PM to 5:00 PM Beijing time. Navigation was performed using both the traditional Rayleigh scattering method (VR) and the proposed method (EHT). The navigation accuracy was compared. Figure 5 In the figure, the horizontal axis represents the navigation time and the vertical axis represents the error. Figure 5 The comparison of navigation accuracy under different image damage ratios is shown in Figure 2. It can be seen that the error of the EHT method is generally smaller than that of the VR method.

Claims

1. A polarization compass sun tracking method based on non-ideal Rayleigh scattering atmospheric polarization distribution characteristics, comprising the following steps: Step 1: Acquisition of information based on sky polarization sensor; Step 7, calculate the sun's zenith angle and azimuth angle; Between step 1 to step 7 is the elliptical Hough space transformation step; The Hannay model is used instead of the Rayleigh single scattering model, known as the non-ideal Rayleigh scattering model. A compass correction method is applied to the polarization compass based on the atmospheric polarization distribution characteristics of non-ideal Rayleigh scattering. The polarization compass, after compass correction, collects polarization information in the sky under conditions of poor air quality and cloud cover. Elliptical Hough transforms are used to process data from the sky polarization sensor based on the Hannay multiple scattering ellipse model. Specifically, the steps of elliptical Hough space transformation are: Step 2: construct the elliptical Hough space; Step 3: Calculate the zenith angle and azimuth angle represented by the elliptical Hough space grid points; Step 4: Solid angle coordinates of the neutral point; Step 5: Calculate the weight of the neutral point; Step 6: Determine the neutral point accuracy; In step 1, the sky polarization sensor is used to obtain information. The corresponding data of the sky polarization sensor is the micro-array polarization sensing information of 4 pixels as a group, wherein the polarizer directions of these 4 pixels are 90 degrees, 45 degrees, 135 degrees and 0 degrees respectively, and the light intensities corresponding to 90 degrees, 45 degrees, 135 degrees and 0 degrees are respectively 、 、 、 ; The Stokes vector is calculated based on the sky polarization data and recorded as ; Indicates light intensity; represents the second term of the Stokes vector; represents the third term of the Stokes vector; represents the fourth term of the Stokes vector; The polarization angle is calculated based on the Stokes vector. The formula is: The formula for inferring the direction of the E vector in three-dimensional space using the polarization angle is: is the projection of the polarization direction on the polarization image; is the polarization direction in three-dimensional space, that is, the direction of the E vector; The data pixel corresponds to the direction and The angle between the axes; is the altitude angle represented by the image data pixel; is the rotation matrix; is the rotation matrix of the angle; is the rotation matrix of the altitude angle; In the second step of constructing the elliptical Hough space, the neutral point elliptical Hough space is recorded as ,in, represents the zenith angle of the Babinet neutral point N1, represents the azimuth of the Babinet neutral point N1, represents the zenith angle of the Brewster neutral point N2, represents the azimuth of Brewster’s neutral point N2; For the variables of the elliptic Hough space , its initial range should be ; The Hough transform of the elliptical Hough space is denoted as , subscript Represents the number of Hough transforms; the elliptical Hough space Divided into discrete grid points; The maximum number of Hough transforms in elliptical Hough space is 5; In the step 3 of calculating the zenith angle and azimuth angle represented by the elliptical Hough space grid point, the calculated zenith angle and azimuth angle represented by the elliptical Hough space grid point are: is the step size of the zenith angle axis of the Babinet neutral point N1 corresponding to the elliptical Hough space; is the maximum value of the zenith angle of the Babinet neutral point N1; is the minimum value of the zenith angle of the Babinet neutral point N1; is the zenith angle of the Babinet neutral point N1 in the elliptical Hough space; is the zenith angle of the Babinet neutral point N1; is the step size of the azimuth axis of the Babinet neutral point N1 corresponding to the elliptical Hough space; is the maximum value of the azimuth of the Babinet neutral point N1; is the minimum value of the azimuth of the Babinet neutral point N1; is the azimuth of the Babinet neutral point N1 in the elliptical Hough space; is the azimuth of the Babinet neutral point N1; is the step size of the zenith angle axis of the Brewster neutral point N2 corresponding to the elliptical Hough space; is the maximum value of the zenith angle of Brewster neutral point N2; is the minimum value of the zenith angle of the Brewster neutral point N2; is the zenith angle of the Babinet neutral point N2 in the elliptical Hough space; is the zenith angle of Brewster neutral point N2; is the step size of the zenith angle axis of the Brewster neutral point N2 corresponding to the elliptical Hough space; is the maximum value of the azimuth angle of Brewster neutral point N2; is the minimum value of the azimuth angle of the Brewster neutral point N2; is the azimuth of the Babinet neutral point N2 in the elliptical Hough space; is the azimuth of Brewster neutral point N2; In the solid angle coordinates of the neutral point in step 4, the solid angle coordinates of the neutral point are marked as , Corresponding to the point in elliptical Hough space The coordinates below are expressed as: is the coordinate of the neutral point N1 in three-dimensional space; is the coordinate of the neutral point N2 in three-dimensional space; is the zenith angle of the Babinet neutral point N1 in the elliptical Hough space; is the azimuth of the Babinet neutral point N1 in the elliptical Hough space; is the zenith angle of the Brewster neutral point N2 in the elliptical Hough space; is the azimuth of the Brewster neutral point N2 in the elliptical Hough space; In the calculation of the neutral point weight in step 5, the coordinates of any pixel point in the navigation image corresponding to the three-dimensional space are marked as data pixels. ; Use E vector direction , the coordinates of the neutral points N1 and N2 corresponding to the three-dimensional space and , and the image pixel coordinates Calculate the weight corresponding to the elliptical Hough space point: It is the line connecting the Babinet neutral point N1 to the pixel point; It is the line connecting Brewster neutral point N2 to the pixel point; is the line connecting the direction of E vector; for and The angle bisector of 、 accomplish; The neutral point N1 is connected to the Normalized function on ; The neutral point N2 is connected to the Normalized function on ; W is the weight of the pixel to the elliptical Hough space grid; Traverse each of the sky polarization image sensors , and let each Traverse every grid point of the elliptical Hough space to complete the Hough transform and obtain the elliptical Hough space data set ; From the Select the grid point with the highest weight, denoted as , Is the result of the operation; according to Grid coordinates of To calculate the next elliptic Hough space The value range of Babinet neutral point N1 and Brewster neutral point N2; Compute the next elliptic Hough space The value range of Babinet neutral point N1 and Brewster neutral point N2 is; For the next elliptic Hough space The minimum value of the zenith angle of the Babinet neutral point N1 in; For the next elliptic Hough space The maximum value of the zenith angle of the Babinet neutral point N1 in; For the next elliptic Hough space The minimum value of the azimuth of the Babinet neutral point N1 in; For the next elliptic Hough space The maximum value of the azimuth angle of the Babinet neutral point N1 in; For the next elliptic Hough space The minimum value of the zenith angle of the Brewster neutral point N2; For the next elliptic Hough space The maximum value of the zenith angle of the Brewster neutral point N2; For the next elliptic Hough space The minimum azimuth of the Brewster neutral point N2 in ; For the next elliptic Hough space The maximum value of the zenith angle of the Brewster neutral point N2; In step 6 of judging the neutral point accuracy, the neutral point accuracy threshold is recorded as ; The current neutral point calculation accuracy is recorded as ,and = - ; when When Bring back step three; when When , execute step 7; In step 7, when calculating the sun's zenith angle and azimuth, according to the Hannay neutral point model, the midpoint of the neutral point is the sun's position, and the sun's position can be used as navigation information; through the neutral point zenith angle and azimuth To calculate the sun's zenith angle and azimuth angle is; is the sun's zenith angle; is the solar azimuth; is the zenith angle of the Babinet neutral point N1 in the elliptical Hough space; is the zenith angle of the Babinet neutral point N2 in the elliptical Hough space; is the azimuth of the Babinet neutral point N1 in the elliptical Hough space; is the azimuth of the Babinet neutral point N2 in the elliptical Hough space; Sun's zenith angle and azimuth Zenith angle and azimuth angle to the neutral point Together they form the orientation information for a polarized compass based on sun tracking.

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