CN111220150B - Sun vector calculation method based on underwater polarization distribution mode - Google Patents

Sun vector calculation method based on underwater polarization distribution mode Download PDF

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CN111220150B
CN111220150B CN201911252040.4A CN201911252040A CN111220150B CN 111220150 B CN111220150 B CN 111220150B CN 201911252040 A CN201911252040 A CN 201911252040A CN 111220150 B CN111220150 B CN 111220150B
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郭雷
胡鹏伟
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Beihang University
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Abstract

The invention relates to a sun vector calculation method based on an underwater polarization distribution mode. Firstly, acquiring underwater polarization azimuth angle information in at least two arbitrary observation directions under an underwater celestial coordinate system; then, inverting the atmospheric incident light propagation direction in the underwater observation direction based on the light refraction law; then, determining an atmospheric polarization E-vector corresponding to the polarization E-vector observed underwater by utilizing a Fresnel refraction formula; and finally, obtaining a solar vector by utilizing the vertical relation between the atmospheric polarization E-vector and the solar vector according to the Rayleigh scattering model. The invention establishes a solar vector calculation basic model based on the polarization distribution mode in the underwater Snell window under the horizontal attitude, and can be popularized and applied to underwater application scenes of point source type and image type polarization sensors.

Description

Sun vector calculation method based on underwater polarization distribution mode
Technical Field
The invention relates to a method for calculating a solar vector based on an underwater polarization distribution mode, which considers the change of refraction on an underwater E-vector, realizes the calculation of the solar vector by utilizing the polarization distribution mode in an underwater Snell window and belongs to the field of underwater polarized light navigation.
Background
At present, the information available for underwater autonomous navigation is very deficient. Inertial navigation is a navigation mode widely applied at present, has the advantages of full autonomy, strong anti-interference performance and the like, but errors of the inertial navigation can be accumulated over time, so that other navigation modes are needed for assisting correction. Because electromagnetic waves are seriously attenuated in water, the traditional radio and satellite navigation cannot be applied underwater; on the one hand, in unknown unfamiliar sea areas, prior geophysical field information is lacked, so that navigation based on the geophysical field, such as geomagnetism and terrain matching, is difficult to realize; on the other hand, no preset underwater transponder is arranged in a strange sea area, so that the underwater sound positioning and other means cannot be applied. The outstanding requirement of current underwater navigation is to realize auxiliary correction of inertial navigation by means of error-free accumulation and independent of prior information.
Biological studies have shown that organisms such as solenopsis invicta, honeybees, bats, rainbow trout, etc. can navigate through sensitive atmospheric polarization distribution patterns. The sunlight generates Rayleigh scattering with particles such as atmospheric molecules in the process of passing through the atmosphere, and a stable and regular polarized light distribution mode is presented on the celestial sphere. Spatial information is contained in the optical field, and the position information of the sun can be calculated through sensing of atmospheric polarization distribution, so that functions of navigation positioning and the like are realized. The method for acquiring the navigation information by sensing the natural environment has the advantages of autonomy, stability, no error accumulation and the like.
The current bionic polarization navigation research mainly focuses on the application scene of the atmosphere, the polarization degree and the polarization E-vector are two parameters of the atmospheric polarization distribution mode, and the key point of the polarization navigation research is how to extract spatial information from the perceived polarization distribution mode, namely the polarization degree or the polarization E-vector distribution mode. For example, chinese patent CN201410652332.8 and chinese patent CN201510303533.1 respectively propose a method for resolving a sun vector based on atmospheric polarization degree distribution characteristics, and chinese patent CN201710027484.2 propose a method for obtaining a sun azimuth by using an atmospheric polarization E-vector. The intrinsic models of the methods are all based on a single Rayleigh scattering model, and the solar vector is solved by utilizing the geometric relationship of the polarization E-vector, the solar perpendicularity and the like. In the above patent, the calculation of the solar vector is a model established only based on the atmospheric scattering effect, and the change of the water body refraction effect on the polarization E-vector direction is not considered, so the underwater polarization distribution does not completely conform to the single Rayleigh scattering model, and therefore, the above patent method is not suitable for the calculation of the solar vector based on the underwater polarization distribution.
Disclosure of Invention
In order to solve the technical problem, the invention provides a solar vector calculation method based on a polarization distribution mode in an underwater Snell window on the basis of the research on the underwater distribution mode of a single Rayleigh scattering model under the refraction action. The underwater polarized light mainly has two sources, namely, a polarized distribution mode formed in a Snell window after the atmospheric polarized light is refracted; the other source is the polarization distribution formed by the sunlight under the scattering action of the water medium after penetrating into the water, and exists inside and outside the Snell window, but the polarized light intensity of the source is weaker, and can be ignored compared with the polarized light after refraction in the Snell window, and only the polarized light of the source exists outside the Snell window. Because the Snell window is transmitted light, the light intensity is stronger, so the polarization distribution mode of the part is more added to the acquisition of navigation information from the perspective of the sensor. The influence of the refraction effect of water on the underwater distribution of atmospheric polarized light mainly has two aspects, namely the refraction changes the propagation direction of non-vertical incident light, and the refraction effect can influence the polarization E-vector angle. Therefore, in the method, the acquired polarization distribution mode in the underwater Snell window can be used for resolving the sun vector so as to obtain navigation information.
The technical scheme adopted by the invention for solving the technical problems is as follows: a sun vector resolving method based on an underwater polarization distribution mode comprises the following implementation steps:
firstly, acquiring any n observation directions under an underwater celestial coordinate system through a horizontally placed polarization sensor
Figure GDA0003150763870000021
Underwater polarization E-vector information on
Figure GDA0003150763870000022
Wherein k is 1, 2.., n; n is more than or equal to 2;
step (2) combining the underwater observation direction of the step (1)
Figure GDA0003150763870000023
Reflecting the incident angle i of the light in the underwater observation direction based on the law of refractionk；
And (3) combining a Fresnel refraction formula, and obtaining the polarization E-vector of the underwater observation obtained in the step (1)
Figure GDA0003150763870000024
And the light incidence angle i calculated in the step (2)kInverting its corresponding atmospheric polarization E-vector
Figure GDA0003150763870000025
Step (4) according to the atmospheric polarization E-vector
Figure GDA0003150763870000026
Orthogonal relation to sun vector, using multiple atmospheric polarization E-vectors
Figure GDA0003150763870000027
And resolving to obtain a sun vector s.
Further, the underwater observation direction of the step (1)
Figure GDA0003150763870000028
The specific requirements are as follows:
for any observation direction
Figure GDA0003150763870000029
The angle from zenith to observation, i.e. zenith angle, is ζk(ii) a Determining zenith angle according to Snell window visual angle theta
Figure GDA00031507638700000210
Under the coordinate system of the northeast China,
Figure GDA00031507638700000211
expressed as:
Figure GDA00031507638700000212
wherein,
Figure GDA00031507638700000213
to observe the direction
Figure GDA00031507638700000214
And defining the north direction as the azimuth angle zero position and the north east as the positive direction of the corresponding azimuth angle.
Further, the step (2) is based onThe law of refraction of light is inverted to the incident angle i of light in the underwater observation directionkThe method is concretely realized as follows:
observing direction under water
Figure GDA0003150763870000031
Angle of refraction r of lightkThe incident angle i of the incident light on water is obtained by the law of refraction of lightkComprises the following steps:
Figure GDA0003150763870000032
wherein n isair,nwaterRefractive indices of air and water, respectively; angle of refraction r of refracted rays in underwater observation directionkZenith angle zeta with observation directionkEqual, while the surface refraction does not change the azimuth of the ray propagation.
Further, the combination of Fresnel refraction formula in the step (3) and the polarization E-vector of the underwater observation obtained in the step (1)
Figure GDA0003150763870000033
And the light incidence angle i calculated in the step (2)kInverting its corresponding atmospheric polarization E-vector
Figure GDA0003150763870000034
Setting the included angle between a certain underwater polarization E-vector and the local meridian, namely the underwater polarization azimuth angle is chiwater(ii) a The underwater E-vector is formed by refracting a polarized light in the atmosphere, and the polarization azimuth angle of the polarized E-vector in the atmosphere is Xair(ii) a Then there is the following relationship:
Figure GDA0003150763870000035
wherein σ⊥,σ||Refractive indices representing a pair of orthogonal components of the E-vector normal and parallel to the plane of incidence, respectively, from FresnelThe equation for the molar refraction yields:
Figure GDA0003150763870000036
therefore, the method comprises the following steps:
Figure GDA0003150763870000037
the E-vector is then expressed in the northeast coordinate system as:
eair＝vcosχair+usinχair
wherein v, u respectively represent the tangential unit vectors of the longitude direction and the latitude direction of the observation point, namely:
Figure GDA0003150763870000038
Figure GDA0003150763870000039
so that any underwater observation direction
Figure GDA00031507638700000310
The waterborne polarization E-vector corresponding to the upper light ray is as follows:
Figure GDA0003150763870000041
further, the step (4) utilizes the atmospheric polarization E-vector
Figure GDA0003150763870000042
Perpendicular to the sun vector, using n atmospheric polarization E-vectors
Figure GDA0003150763870000043
The sun vector s is obtained by resolving, and the specific method is as follows:
the sun vector can be obtained by randomly selecting two of n atmospheric polarization E-vectors:
Figure GDA0003150763870000044
namely, it is
Figure GDA0003150763870000045
Wherein,
Figure GDA0003150763870000046
representing the E-vector obtained at n inversions
Figure GDA0003150763870000047
Any two different amounts of; wherein k is 1,2, 3.., n; to fully utilize the acquired n polarization E-vectors, let:
Figure GDA0003150763870000048
Figure GDA0003150763870000049
where m ∈ {1,2, 3.,. n-1} then:
E1×E2＝(λ1m+1+λ1m+2+…+λmn)s'
therefore, the method comprises the following steps:
Figure GDA00031507638700000410
in the above formula, s' is the ambiguous sun vector, and since the z direction of the sun vector is positive in the northeast sky coordinate system, the zenith vector z is introduced as [ 001 ═ c]TAnd eliminating ambiguity through the following formula to obtain the sun vector under the northeast coordinate system as:
s＝sign[s'·z]s'
wherein sign [ a · b ] represents the sign of the inner product of vectors a and b.
Has the advantages that:
compared with the prior art, the invention has the following advantages: the existing solar vector calculating method based on the polarization distribution mode is used in an atmospheric scene, and the solar vector calculating method based on the underwater polarization distribution is not available. The underwater polarization distribution is different from an atmospheric polarization distribution mode under the refraction action of water, the method can realize the solar vector calculation based on the polarization distribution mode in the underwater Snell window, and the application scene of the bionic polarized light navigation is expanded from the atmosphere to the underwater.
Drawings
FIG. 1 is a flow chart of a solar vector calculation method based on an underwater polarization distribution mode according to the present invention;
FIG. 2 is an underwater polarization distribution three-dimensional spatial coordinate system according to the present invention;
FIG. 3 is a diagram of the principle of refraction of polarized light on water.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments, and all other embodiments obtained by a person skilled in the art based on the embodiments of the present invention belong to the protection scope of the present invention without creative efforts.
According to an embodiment of the present invention, as shown in fig. 1, a solar vector solution method based on an underwater polarization distribution mode of the present invention includes the following steps:
step 1, obtaining any n observation directions under an underwater celestial coordinate system by utilizing a polarization sensor
Figure GDA0003150763870000051
Underwater polarization E-vector information on
Figure GDA0003150763870000052
Wherein k is 1, 2.., n; n.gtoreq.2, e.g.FIG. 2 shows a unit hemisphere as an underwater celestial coordinate system, which represents an upward observation field from an observation point O under water; the circle shown by the dot-dash line in FIG. 2 is the Snell window, and if the view angle of the Snell window is θ, the zenith angle is determined
Figure GDA0003150763870000053
Therefore, under the coordinate system of the northeast China,
Figure GDA0003150763870000054
expressed as:
Figure GDA0003150763870000055
wherein,
Figure GDA0003150763870000056
to observe the direction
Figure GDA0003150763870000057
And defining the north direction as the azimuth angle zero position and the north east as the positive direction of the corresponding azimuth angle.
Step 2, inverting the incident angle i of the light in the underwater observation direction based on the light refraction lawkUnderwater observation direction
Figure GDA0003150763870000058
Angle of refraction r of lightkAngle of incidence i of incident light on water from the law of refraction of lightkComprises the following steps:
Figure GDA0003150763870000059
wherein n isair,nwaterRefractive indices of air and water, respectively; angle of refraction r of refracted rays in underwater observation directionkZenith angle zeta with observation directionkEqual, while the water surface refraction does not change the azimuth of the light propagation.
Step 3, combining with a Fresnel refraction formula,polarization E-vector observed from underwater
Figure GDA00031507638700000510
And the light incidence angle i calculated in the step (2)kInverting its corresponding atmospheric polarization E-vector
Figure GDA00031507638700000511
As shown in FIG. 2, the P point is any observed point in the celestial coordinate system, and a right-hand rectangular coordinate system is established by passing the P point, wherein x isPAxis down the meridian tangent, yPAxial direction is positive east along tangential direction of latitude, zPThe axis is upward along the normal direction of the spherical surface of the point P; the thick line segment of the double arrows passing through the P point represents an E-vector in the underwater observation direction, the vector is a spherical tangent, and the included angle between the vector and the local meridian is the polarization azimuth angle chi of the E-vectorwater(ii) a As shown in FIG. 3, the atmospheric polarization E-vector can be decomposed into two orthogonal components, E, perpendicular and parallel to the plane of incidence⊥And E||(ii) a Atmospheric polarization E-vector EairPolarization E-vector E formed underwater after refractionwater(ii) a Since the refractive action of water is not uniform for the refractive indices of the two orthogonal components, the following relationship holds:
Figure GDA0003150763870000061
T⊥,T||respectively representing underwater polarization E-vector EwaterOrthogonal components at right angles, parallel to the plane of incidence; sigma⊥,σ||Respectively represents the refractive indexes of orthogonal components of the E-vector which are vertical to and parallel to the incident surface, and the refractive indexes are respectively shown as follows according to a Fresnel refractive formula:
Figure GDA0003150763870000062
Figure GDA0003150763870000063
let the polarization azimuth angle of the polarization E-vector in the atmosphere be chiairThen, the following relationship exists:
Figure GDA0003150763870000064
and because the zenith angle is geometrically equal to the refraction angle, namely ζ ═ r knows:
Figure GDA0003150763870000065
therefore, the method comprises the following steps:
Figure GDA0003150763870000066
the E-vector is then expressed in the northeast coordinate system as:
eair＝vcosχair+usinχair
wherein v, u respectively represent the tangential unit vector passing through the observation point in the warp direction and the weft direction, namely:
Figure GDA0003150763870000067
Figure GDA0003150763870000068
so that the direction is observed underwater
Figure GDA0003150763870000069
The waterborne polarization E-vector corresponding to the upper light ray is as follows:
Figure GDA00031507638700000610
step 4, the specific method for obtaining the sun vector by utilizing the vertical relation between the atmospheric polarization E-vector and the sun vector is as follows:
the sun vector can be obtained by randomly selecting two of n atmospheric polarization E-vectors:
Figure GDA0003150763870000071
namely, it is
Figure GDA0003150763870000072
Wherein
Figure GDA0003150763870000073
Representing the E-vector obtained at n inversions
Figure GDA0003150763870000074
Two different E-vectors are arbitrarily selected;
to fully utilize the n polarization E-vectors obtained by the polarization sensor, let:
Figure GDA0003150763870000075
Figure GDA0003150763870000076
where m ∈ {1,2,3,.., n-1}, then:
E1×E2＝(λ1m+1+λ1m+2+…+λmn)s'
therefore, the method comprises the following steps:
Figure GDA0003150763870000077
in the above formula, s' is the ambiguous sun vector, and since the z direction of the sun vector is positive in the northeast sky coordinate system, the zenith vector z is introduced as [ 001 ═ c]TAnd disambiguation by the following equationAnd obtaining the sun vector under the northeast coordinate system as follows:
s＝sign[s'·z]s'
wherein sign [ a · b ] represents the sign of the inner product of vectors a and b.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, but various changes may be apparent to those skilled in the art, and it is intended that all inventive concepts utilizing the inventive concepts set forth herein be protected without departing from the spirit and scope of the present invention as defined and limited by the appended claims.

Claims (4)

1. A sun vector resolving method based on an underwater polarization distribution mode is characterized by comprising the following steps:
firstly, acquiring any n observation directions under an underwater celestial coordinate system through a horizontally placed polarization sensor
Figure FDA0003150763860000011
Underwater polarization E-vector of
Figure FDA0003150763860000012
Wherein k is 1, 2.., n; n is more than or equal to 2;
step (2) combining the underwater observation direction of the step (1)
Figure FDA0003150763860000013
Reflecting the incident angle i of the light in the underwater observation direction based on the law of refractionk；
And (3) combining a Fresnel refraction formula, and obtaining the polarization E-vector of the underwater observation obtained in the step (1)
Figure FDA0003150763860000014
And the light incidence angle i calculated in the step (2)kInverting its corresponding atmospheric polarization E-vector
Figure FDA0003150763860000015
The polarization E-vector of the underwater observation obtained in the step (1) is combined with the Fresnel refraction formula in the step (3)
Figure FDA0003150763860000016
And the light incidence angle i calculated in the step (2)kInverting its corresponding atmospheric polarization E-vector
Figure FDA0003150763860000017
Setting the included angle between a certain underwater polarization E-vector and the local meridian, namely the underwater polarization azimuth angle is chiwater(ii) a The underwater polarization E-vector is formed by refracting a certain polarized light in the atmosphere, and the polarization azimuth angle of the atmospheric polarization E-vector is Xair(ii) a Then there is the following relationship:
Figure FDA0003150763860000018
wherein σ⊥,σ||The refractive indices, which represent a pair of orthogonal components of the E-vector, perpendicular and parallel to the plane of incidence, respectively, are given by the Fresnel refractive equation:
Figure FDA0003150763860000019
therefore, the method comprises the following steps:
Figure FDA00031507638600000110
the E-vector is then expressed in the northeast coordinate system as:
eair＝v cosχair+u sinχair
wherein v, u respectively represent the tangential unit vector passing through the observation point in the warp direction and the weft direction, namely:
Figure FDA00031507638600000111
Figure FDA00031507638600000112
so that any underwater observation direction
Figure FDA00031507638600000113
The corresponding polarization E-vector of the upper ray is:
Figure FDA0003150763860000021
step (4) according to the atmospheric polarization E-vector
Figure FDA0003150763860000022
Orthogonal relation to sun vector, using multiple atmospheric polarization E-vectors
Figure FDA0003150763860000023
And resolving to obtain a sun vector s.
2. The underwater polarization distribution mode-based solar vector calculation method according to claim 1, wherein:
the underwater observation direction of the step (1)
Figure FDA0003150763860000024
The specific requirements are as follows:
for any observation direction
Figure FDA0003150763860000025
From zenith to observerThe angle of the direction, i.e. zenith angle, being ζk(ii) a Determining zenith angle according to Snell window visual angle theta
Figure FDA0003150763860000026
Under the coordinate system of the northeast China,
Figure FDA0003150763860000027
expressed as:
Figure FDA0003150763860000028
wherein,
Figure FDA0003150763860000029
to observe the direction
Figure FDA00031507638600000210
And defining the north direction as the azimuth angle zero position and the north east as the positive direction of the corresponding azimuth angle.
3. The underwater polarization distribution mode-based solar vector calculation method according to claim 1, wherein:
the step (2) is used for inverting the incident angle i of the light in the underwater observation direction based on the light refraction lawkThe method is concretely realized as follows:
observing direction under water
Figure FDA00031507638600000211
Angle of refraction r of refracted raykThe incident angle i of the incident light on water is obtained by the law of refraction of lightkComprises the following steps:
Figure FDA00031507638600000212
wherein n isair,nwaterRefractive indices of air and water, respectively;angle of refraction r of refracted rays in underwater observation directionkZenith angle zeta with observation directionkEqual, while the surface refraction does not change the azimuth of the ray propagation.
4. The underwater polarization distribution mode-based solar vector calculation method according to claim 1, wherein:
the step (4) of utilizing the atmospheric polarization E-vector
Figure FDA00031507638600000213
Perpendicular to the sun vector, using n atmospheric polarization E-vectors
Figure FDA00031507638600000214
The sun vector s is obtained by resolving, and the specific method is as follows:
the sun vector can be obtained by randomly selecting two of n atmospheric polarization E-vectors:
Figure FDA0003150763860000031
namely, it is
Figure FDA0003150763860000032
Wherein,
Figure FDA0003150763860000033
representing the E-vector obtained at n inversions
Figure FDA0003150763860000034
Any two different amounts of; wherein k is 1,2, 3.., n; to fully utilize the acquired n polarization E-vectors, let:
Figure FDA0003150763860000035
Figure FDA0003150763860000036
where m ∈ {1,2, 3.,. n-1} then:
E1×E2＝(λ1m+1+λ1m+2+…+λmn)s'
therefore, the method comprises the following steps:
Figure FDA0003150763860000037
in the above formula, s' is the ambiguous sun vector, and since the z direction of the sun vector is positive in the northeast sky coordinate system, the zenith vector z is introduced as [ 001 ═ c]TAnd eliminating ambiguity through the following formula to obtain the sun vector under the northeast coordinate system as:
s＝sign[s'·z]s'
wherein sign [ a · b ] represents the sign of the inner product of vectors a and b.
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