Method for determining temporal invariances of the degree of linear polarisation in the sky for a navigation system

Abstract

The invention relates to a method for determining temporal invariances of the degree of linear polarisation DOLP of the light from a celestial body in a visible celestial hemisphere, which method is implemented in a system for determining positioning and navigation information, the visible celestial hemisphere being centred on the geographical position of the system. The method comprises the following steps of: acquiring (102) a plurality of successive polarised images of the visible celestial hemisphere; determining (104), for each acquired image, a representation of the degrees of linear polarisation, DOLP; determining (106) at least one grouping of DOLP invariances from a pair of representations selected from among the DOLP representations; determining (110) a measurement point P from the grouping of invariances, the point P corresponding to the celestial pole in the visible celestial hemisphere. The method further comprises a step of determining the altitude and / or the azimuth of the celestial pole from the point P, the azimuth corresponding to the direction of the geographical pole.

Description

DESCRIPTION Title of the invention: METHOD FOR DETERMINING THE TEMPORAL INVARIANCES OF THE DEGREE OF LINEAR POLARIZATION IN THE SKY FOR A NAVIGATION SYSTEM Technical field

[0001] The present invention relates generally to geolocation, and in particular to a method for determining the temporal invariances of the degree of linear polarization in the sky for determining the celestial pole.

[0002] Geolocation systems, such as GNSS, are traditionally used to determine the position of an object in the Earth system.

[0003] A GNSS (Global Navigation Satellite Systems) system is a satellite positioning system configured to provide the position of an object (device or system) with good accuracy, across the entire Earth and in real time. Such a system is today considered one of the most accurate geolocation systems. However, such a system is susceptible to multiple signal reflections introduced by urban canyons (e.g. skyscrapers, buildings, foliage, etc.), jamming and identity theft.

[0004] To improve satellite positioning systems, it is known to combine them with devices using geopositioning approaches based on measurements of polarized light from the sky. These approaches are called biomimetic approaches or bioinspired approaches. For example, in the article “Desert navigator: the journey of an ant” by Rudiger Wehner, Harvard University Press, 2020, the proposed biomimetic approach is inspired by the navigation mechanism implemented by desert ants that are sensitive to the sky polarization pattern. It should be noted that known bioinspired approaches require the use of conventional localization modalities (e.g., the solar astronomical calendar or solar ephemeris) combined with an estimation of the sun's position obtained via the sky polarization pattern.Estimating the sun's position involves calculating the angles of polarization (AoLP) and degrees of linear polarization (DoLP). This solution is for example addressed in the article “Global autonomous positioning in GNSS challenged environments: A bioinspired strategy by polarization pattern” by J. Yang et al., IEEE Trans, on Industrial Electronics, 68(7), pages 6308-6317, 2020. However,. the use of conventional localization modalities in combination with measurements of polarized light from the sky can generate a significant memory cost as well as a computational cost for the system and the heading determination method.

[0005] There is thus a need for an improved method based solely on measurements of polarized light from the sky to determine the positioning and heading of a system relative to the geographic pole. Summary of the invention

[0006] The present invention improves the situation by proposing a method for determining the temporal invariances of the degree of linear polarization of light coming from a star in a celestial vault, implemented in a system for determining positioning and navigation information, the celestial vault being centered on the geographical position of the system. The method comprises at least the following steps consisting of: - acquire a plurality of polarized images I n successive of at least part of the celestial vault; - determine, for each image I n acquired, a representation of the degrees of linear polarization Id n ; - determining at least one grouping of temporal invariances of degrees of linear polarization of the light coming from the star, a grouping of invariances being determined from a pair of representations selected from the plurality of representations of the degrees of linear polarization Id n ; - determine a measurement point P from at least one group of invariances, the measurement point P corresponding to the celestial pole in the celestial vault of the system.

[0007] The method further comprises a step of determining the altitude and / or azimuth of the celestial pole from the obtained measurement point P. The azimuth corresponds to the direction of the geographic pole associated with the geographic position of the system.

[0008] Advantageously, the positioning and navigation information determination system may be geographically positioned at a coordinate latitude <f> o , and the method may further comprise a step consisting of determining the coordinate c|) o of latitude of the system from the determined altitude.

[0009] Each polarized image I n can be acquired at a time t n , the minimum time difference between two acquisition times of two successive polarized images being predefined.

[0010] According to some embodiments, each polarized image I n can include a set of pixels p xy , each pixel being associated with coordinates (x,y) and a set of detection intensities according to distinct polarization angles such that p xy = (l0», l 90 », 1 45 ", I 135 o) xy . Each representation Id n can include a set of degrees of linear polarization d xy , each degree of xy being calculated from the Stokes vector, such that: 0135°)xy ■

[0013] Advantageously, each grouping of invariances can be determined from a differential representation D m comprising a set of differences A xy calculated from the pair of representations of the degrees of linear polarization Id n selected.

[0014] Each grouping of invariances can be determined from a binary representation B m determined from the differential representation D m and a predetermined binarization threshold s p of the difference in degrees of linear polarization A xv .

[0015] In embodiments, the plurality of polarized images I n can comprise at least three images. At least two groupings of invariances of degrees of linear polarization of the light coming from the star can be determined. The measurement point P can be determined from the intersection between the at least two groupings of invariances.

[0016] The intersection between the at least two invariance groups can be performed from the determination of an intersection representation H comprising a set of overlapping values ​​h xy calculated from at least two of the binary representations B m . The measuring point P can correspond to the coordinates for which the superposition value h xy is maximum.

[0017] In embodiments, the plurality of polarized images I n may comprise at least two images, the grouping of invariances comprising a radial invariance, by radial symmetry, and a plane invariance, by plane symmetry, of degrees of linear polarization of the light coming from the star. The measurement point P may be determined from a point p, of intersection between the radial invariance and the plane invariance, and from information on the offset of the celestial pole relative to the intersection point pj.

[0018] Advantageously, the method may comprise a step consisting of determining at least one simulation Id® of the pattern of degrees of linear polarization of the light coming from the star over the entire celestial vault, each simulation Id® being determined from one of the images of the plurality of polarized images I n of at least part of the celestial vault.

[0019] The method may further comprise a step of acquiring displacement and rotation data of the operated system between the successive acquisition of at least two of the polarized images I n . Determining the at least one invariance grouping may include consideration of displacement and rotation data.

[0020] The geographical position of the system can be further associated with a coordinate longitude £ o The method may comprise a step of determining the coordinate £ o of longitude of the system from data from a referenced clock and the direction of polarization at the measurement point P of the system positioned successively at at least two distinct geographical positions.

[0021] The invention also provides a system for determining positioning and navigation information. The system comprises:

[0022] - a polarized light acquisition module, the light coming from a star in the celestial vault centered on the geographical position of the system, the acquisition module being configured to carry out the acquisition of a plurality of polarized images I n successive of at least part of the celestial vault;

[0023] - a processing module configured to determine, for each image I n acquired, a representation of the degrees of linear polarization Id n , the processing module being further configured to determine at least one grouping of temporal invariances of degrees of linear polarization of the light coming from the star, each grouping of invariances being determined from a pair of representations Id n selected from the plurality of representations of the degrees of linear polarization Id n , the processing module being further configured to determine a measurement point P from the at least one grouping of invariances, the measurement point P corresponding to the celestial pole in the celestial vault of the system.

[0024] The system further comprising a positioning and navigation module configured to determine the altitude and / or the azimuth of the celestial pole from the measurement point P obtained, the azimuth corresponding to the direction of the geographic pole associated with the geographic position of the system.

[0025] The method and system according to the embodiments of the invention make it possible to detect a celestial pole solely from the polarized light of the sky and more precisely from the degree of linear polarization (DoLP) pattern, without requiring the use of other conventional localization modalities.

[0026] They thus make it possible to determine the direction of geographic north and the latitude of the system from the estimation of the position of the celestial pole, i.e. positioning and heading information relevant to the improvement of geopositioning and navigation systems. Description of figures

[0027] Other characteristics, details and advantages of the invention will emerge from reading the description given with reference to the appended drawings given by way of example.

[0028] [Fig.1] Figure 1 is a diagram showing a system for determining positioning and navigation information, according to embodiments of the invention.

[0029] Figures [Fig. 2(a)], and

[0030] [Fig. 2(b)] are schematic representations of the geographic position of the celestial pole determination system, according to embodiments of the invention.

[0031] [Fig.3] Figure 3 is a flowchart representing the method of determining the time invariances of the degree of linear polarization of light coming from a star in the sky, according to embodiments of the invention.

[0032] Figure [Fig.4(a)] is a schematic representation of the pixels of a sensor of a polarized light acquisition module of the celestial pole determination system, according to embodiments of the invention.

[0033] Figure [Fig.4(b)] is a schematic representation of a polarized light acquisition module, according to embodiments of the invention.

[0034] [Fig.5] Figure 5 illustrates the results of steps of the method for determining the temporal invariances of the degree of linear polarization of light coming from a star in the sky, according to embodiments of the invention.

[0035] [Fig.6] Figure 6 is a flowchart representing sub-steps of the method for determining invariance groups, according to embodiments of the invention.

[0036] [Fig.7] Figure 7 is a diagram representing the axes of plane and radial invariance, via a half-sphere visualization of a differential representation of two representations of the degree of linear polarization, according to embodiments of the invention.

[0037] Figures [Fig.8(a)],

[0038] [Fig.8(b)], and

[0039] [Fig.8(c)] are flowcharts representing sub-steps of the method for determining invariance groups, according to embodiments of the invention.

[0040] [Fig.9] Figure 9 is a schematic representation of the geographical position of the celestial pole determination system in a reference frame (E,N,Z), according to embodiments of the invention.

[0041] [Fig.10] Figure 10 is a flowchart showing substeps of determining longitude coordinates of the celestial pole determination system, according to embodiments of the invention.

[0042] [Fig.11] Figure 11 is a diagram showing a celestial pole determination system, according to embodiments of the invention.

[0043] [Fig.12] Figure 12 illustrates the results of steps of binarization and intersection of the differences in degrees of linear polarization, according to exemplary embodiments of the invention.

[0044] [Fig.13] Figure 13 is a graph illustrating the results of the geographic pole direction values ​​and latitude values ​​determined by the method for determining the time invariances of the degree of linear polarization of light from a star in the sky, according to embodiments of the invention.

[0045] Identical references are used in figures to designate identical or similar elements. For clarity, the elements shown are not to scale. Detailed description

[0046] Figure 1 represents a system for determining positioning and navigation information 1, according to embodiments of the invention.

[0047] The system for determining positioning and navigation information 1 comprises a device 10 for determining the temporal invariances of the degree of linear polarization of light coming from a star in the sky, also called hereinafter a celestial pole determination device, according to certain embodiments of the invention.

[0048] As used herein, the term "light" refers to one or more optical waves, for example and without limitation, in the ultraviolet, visible and / or infrared ranges. Such optical waves may for example be associated with a spectral (or multi-spectral) band predefined by the system 1.

[0049] The celestial pole determination device 10 is configured to determine the coordinates of a celestial pole relative to the system 1, on the surface of a planet such as Earth. The information determination system The positioning and navigation system 1 further comprises a positioning and navigation information determination unit 20 configured to determine the coordinate (p0) of the latitude of the system 1 and the direction of the geographic pole, from the determination of the coordinates of the celestial pole. The positioning and navigation information determination system 1 can then use the coordinate (p0) of the latitude of the system 1 and the direction of the geographic pole for geopositioning and / or navigation of the system 1.

[0050] As used herein, the term "celestial pole" refers to a virtual point on the celestial vault of a planet, such as Earth, corresponding to the intersection between the planet's rotational axis and its associated celestial sphere. A celestial pole thus corresponds to a projection onto the celestial sphere of a geographic pole (also called a 'true pole' in opposition to the magnetic pole). In other words, a celestial pole refers to a virtual point on the celestial vault around which the stars rotate from the point of view of an observer on the surface of the Earth, for example, due to the rotation of the Earth on its axis.

[0051] Figure 2(a) schematically represents the Earth, in the form of a circle with center C composed of two hemispheres including the Northern Hemisphere and the Southern Hemisphere. There are two celestial poles as shown in Figure 2(a): the North Celestial Pole (or NCP for "North Celestial Pole") associated with the Northern Hemisphere, and the South Celestial Pole (or SCP for "South Celestial Pole") associated with the Southern Hemisphere. The system for determining positioning and navigation information 1 is characterized by its geographical position, noted O, on the surface of the Earth for example. In particular, the geographical position of the system 1 , for example in the Northern Hemisphere, includes the coordinate longitude (not shown in Figure 2(a)) and the coordinate latitude (p0 defined from the Zenith axis Z passing through the center C of the earth and point O. In Figure 2(a), the angle (p' o corresponds to the coordinate of the colatitude of the geographical position of system 1. The celestial vault, represented in Figure 2(b), is centered at point O and is also called 'sky'. In Figure 2(b), the angle y called 'scattering angle' corresponds to the angle between the vector 'observer-sun' and the vector 'observer-observation point'.

[0052] Figure 3 shows a method for determining positioning and navigation information, according to embodiments of the invention. The method for determining positioning and navigation information can be implemented by the system 1. Steps 102 to 108 correspond more specifically to the method for determining the temporal invariances of the degree of linear polarization of the light coming from a star in the sky (or method for determining the celestial pole), implemented by the celestial pole determination device 1.

[0053] As shown in Figure 3, the method comprises a step 102 of acquisition by the system 1 of a number N of successive polarized images, denoted I n The index 'ri associated with different polarized images is an integer between 1 and N, and the value of N is an integer greater than or equal to 2.

[0054] Each polarized image I n represents at least a part of the celestial vault. For the N different successive polarized images, the acquired light comes from the same star. For example and without limitation, for a system positioned on Earth, this star can be the sun or the moon, while for a system positioned on Mars, this star can be the sun. Thus, the N successive polarized images I n can be acquired during the day. Alternatively, the N successive polarized images I n can be acquired at night. In particular, each polarized image I n is acquired at an instant (or acquisition time) t n . The minimum time gap ôt min between two moments t n and t n+1 image acquisition can be defined according to the technological capabilities of the polarized light acquisition module used to acquire the plurality of images I n . For example and without limitations, the minimum time gap min can be between a few milliseconds and a few minutes. The maximum time difference max between two moments t n and t n+1 image acquisition time can advantageously be several hours, for example.

[0055] In addition, each image I n acquired can be characterized by a set of acquisition points noted p xy , such that each acquisition point (also called pixel or photosensor in the following description) is associated with coordinates (%, y). For example and without limitation, a set of pixels of an image I n can be distributed according to a circular distribution, as shown in figure [Fig.4(a)], Each coordinate (%, y) then represents a projection of a point of the celestial vault in an XY plane perpendicular to the U axis of system 1 (XY plane shown in figure [Fig.4(b)]). The U axis shown in figure [Fig.4(b)] corresponds to the optical axis associated with system 1 during the acquisition of an image I n . Such an axis U can be for example equivalent to the Zenith axis Z.

[0056] Since the images are polarized, each pixel is associated with a plurality of detection intensities according to distinct polarization angles. For example and without limitation, each pixel p xy can be associated with 4 detection intensity values ​​corresponding respectively to distinct polarization angles according to the following equation (01):

[0058] It should be noted that according to the Rayleigh scattering model of light coming from a star propagating in the atmosphere (especially terrestrial), the interactions between the photons of light and the molecules of the atmosphere lead to a partial linear polarization of this light from the celestial vault according to a pattern called a "polarization pattern". This polarization pattern depends on the relative position of the star with respect to the position O of the system 1, on the surface of the Earth, for example.This polarization pattern can be mathematically described from two quantities: the angle between the direction of linear polarization of light and an axis of a predefined reference frame (i.e. the angle of linear polarization or AoLP) and the degree of linear polarization of light (or DoLP) as described for example in the article "Polarization and Intensity of Light in the Atmosphere” by KL Coulson et al., Deepak Pub., 1988. In particular, the DoLP (or "DoLP pattern") can be mathematically modeled as a function of the scattering angle y shown in Figure [Fig.2(b)]. The DoLP can be described according to the following equation (02):.

[0060] In step 104, for each image I n acquired, a representation Id n of the DoLP pattern of at least one part of the sky is determined (or calculated).

[0061] Each DoLP representation Id n determined can be characterized by a set of calculated degrees of linear polarization noted d xy associated with the coordinates (%, y) of the pixels p xy .

[0062] In embodiments, for each coordinate (%, y), the degree of linear polarization d xy can be calculated from the Stokes vector defined from the Rayleigh scattering model and described according to the following equation (03):

[0064] In the previous equation (03), the coefficients (s0) xy , (sl) xy and (s2) xy are defined according to the values ​​of the plurality of detection intensities of each pixel p xy of image I n , and can be described respectively according to the following equations (04), (05) and (06):

[0068] A set of calculated linear polarization degrees of xy of a DoLP Id representation n can be distributed, according to a circular distribution, as illustrated by the set of pixels in figure [Fig.4(a)],

[0069] Note that the values ​​a xy of linear polarization angles AoLP can also be calculated from the Stokes vector, according to the following equation (07):

[0071] In other embodiments, for each coordinate (%, y), the degree of linear polarization d xy can be calculated from Malus's law for example.

[0072] Figure 5 represents an example of implementation of steps of the method for determining positioning and navigation information, according to certain embodiments of the invention.

[0073] In particular, in Figure 5, the DoLP Id representations l t Id2, Id3 and Id4 (representing the result of the application of step 104) come from the polarized images, respectively I2, I3 and / 4, acquired at the acquisition times t2, t3 and t4. In this example, the time differences δ between two polarized image acquisition times I n are between 30 minutes and 60 minutes. In addition, the DoLP ld representations n are illustrated according to a gray level, such that for each coordinate (%, y), a value of xy can be between a minimum value of degrees of linear polarization DoLP min and a maximum value of degrees of linear polarization DoLP max .

[0074] According to equation (02), the minimum DoLP value min is equal to 0. According to the Rayleigh scattering model, the minimum DoLP value min corresponds to a diffusion angle y equal to 0, associated with the light rays coming from the projection of the star (i.e. the sun or the moon for example) on the celestial vault, i.e. point A in figure 2(b). Thus, the coordinates (%, y) associated with the minimum DoLP value min correspond to the position of the projection of the star on the celestial vault on the XY plane perpendicular to the U axis of system 1. According to equation (02), the maximum DoLP value max is equal to 1. According to the Rayleigh scattering model, the maximum DoLP value max corresponds to a scattering angle y equal to TT / 2, associated with the light rays coming from point A' in Figure 2(b). It should be noted that due to the phenomenon of Mie scattering and multiple scattering for example, the maximum DoLP value max is in practice significantly less than 1. As illustrated in Figure 5, a DoLP Id representation n includes a first radial symmetry with respect to this projection of the star (i.e. with respect to the center of the black circles on the DoLP Id representations n ), as well as a second so-called plane (or axial) symmetry. Such a plane symmetry of the DoLP pattern is defined on the celestial vault as a function of the plane perpendicular to a vector OA passing through point A associated with the star and point O (i.e. position of system 1). On the DoLP representation Id n , such a plane symmetry is represented by a curve passing through the maximum DoLP values mnx .

[0075] In step 106, at least one grouping of temporal invariances of degrees of linear polarization of light coming from a celestial body are determined. Each grouping of invariances is determined from a pair of representations Id n of the DoLP determined in step 104.

[0076] A grouping of invariances includes a time invariance by radial symmetry (called radial invariance) and a time invariance by plane symmetry (called plane invariance) of the degree of linear polarization of the light between the two representations Id n of the pair.

[0077] Figure 6 represents sub-steps of step 106 of determining one or more groups of invariances of the method of determining positioning and navigation information, represented in Figure 5, according to certain embodiments of the invention.

[0078] In substep 1062, at least one pair (or couple) of DoLP representations may be selected. Referring to the example of FIG. 5, a first pair C of DoLP representations may be C^Id^Id^, a second pair C2 of DoLP representations may be, for example, C2( / d2^ d 3)> et un third pair C3 of DoLP representations can be selected as for example C3( / d3, / d4).

[0079] Those skilled in the art will easily understand that other pairs of DoLP representations can be selected from representations having non-successive acquisition times such as for example C4( / d1, / d3).

[0080] Referring again to Figure 6, at substep 1064, for each pair C m distinct, a differential representation D m of the two selected DoLP representations can be determined. The index 'm' associated with the different pairs of selected DoLP representations (and therefore with different determined differential representations) is an integer between 1 and M, and the value of M is an integer greater than or equal to 1.

[0081] In particular, each differential representation D m determined can be characterized by a set of calculated polarization degree differences, noted A xy , associated with the coordinates (%, y). For each coordinate (%, y), the difference A xy can be determined between the degrees of polarization d xy of the two selected DoLP representations. For example, for a couple C m Id n , Id n+1 ), the differential representation D m can thus be defined according to the following equations (08):

[0083] A set of calculated polarization degree differences A xy of a differential representation D m can be distributed, according to a circular distribution, as for example the set of pixels in figure [Fig.4(a)] and the set of calculated linear polarization degrees d xy .

[0084] Advantageously, step 104 of determining the representation ld n of the DoLP pattern may comprise a sub-step of applying a filter to limit the noise inherent in the acquisition of the images. For example and without limitation, such a filter may be a low-pass spatial filter and / or a temporal filter applied to an element n taking into account the elements n - 1 of the previous acquisitions.

[0085] In particular, in Figure 5, the differential representations D l t D2 and D3 represent the result of the application of sub-steps 1062 and 1064 and are derived respectively from the DoLP representations of the pairs C^Id^Id^, C2( / d2^ d 3) et C3( / d3, / d4) selected. The differential representations D m are illustrated according to a gray level such that, for each coordinate (%, y), a value A xy can be understood, in absolute value, between a minimum value of difference in degrees of linear polarization A min and a maximum value of difference in degrees of linear polarization A max .

[0086] In the case where the maximum and minimum values ​​of the calculated degree of linear polarization are respectively 1 and 0, the maximum value of difference A max can be equal to or can tend towards 1 and the minimum difference value A min can be equal or can tend towards 0. These maximum and minimum difference values ​​depend on the time difference ø between the two acquisition times of the images associated with the pair C m . Thus, the different coordinates (%, y) associated with a set of values ​​equal to or close to the minimum difference value A min correspond to the projections of points of the celestial vault where the degrees of linear polarization between the two DoLP representations of the couple C m selected are equal or approximate values. Such a set of values ​​corresponds to the point projections where the DoLP pattern remains invariant or approximately invariant. Thus, for a differential representation D m , the set of values ​​equal to or close to the minimum difference value A min then corresponds to the grouping of invariances of the degree of linear polarization of light coming from a star in the celestial vault.

[0087] As illustrated by the two black bands on the images in the middle row of Figure 5, each grouping of invariances of a differential representation D m can schematically comprise a first axis of invariance and a second axis of invariance. As illustrated in Figure 5, the first axis, denoted i p (Or then corresponds to an axis called the "plane invariance axis". The second axis, noted i r (Yes rm ), corresponds to an axis called the “radial invariance axis” positioned equidistant between the two projections of the star of the two DoLP representations, noted respectively A1 and A2, corresponding to a half-sphere visualization of a differential representation D m as shown in Figure 7.

[0088] In substep 1066 of Figure 6, a binarization of each calculated polarization degree difference A xy associated with the coordinates (%, y) can be applied to obtain a binary representation B m of the differential representation D m , which makes it possible to improve the highlighting of the grouping of invariances, and in particular the highlighting of the plane invariance axis i p and the radial invariance axis i r associated with couple C m .

[0089] As used herein, the term "binarization" refers to the conversion of each difference value A xy associated with the coordinates (%, y) in binary values. Thus, the binary representation B m can be characterized by a set of determined binary values, noted / 3 xy and associated with the coordinates (%, y). For each coordinate (%, y), the binary value / 3 xy can take one of two possible values, such as 0 or 1 . Also, the binary value / 3 xy can be chosen from the absolute value of the difference value A xy and a predetermined binarization threshold of the difference in degrees of linear polarization. For example and without limitation, a binary representation B m can thus be defined according to the following equations (09):

[0091] A set of differences of determined binary values ​​ / 3 xy of a binary representation B m can be distributed, according to a circular distribution, such as for example the set of pixels in figure [Fig.4(a)],

[0092] As illustrated in Figure 5, the binary representations B lt B2 and B3 represent the result of the application of sub-step 1066 and are derived respectively from the differential images D lt D2 and D3. The grouping of invariances of each binary representation (represented by two white bands according to equations (09)) schematically includes the first axis (or curve) of invariance radial (respectively i rl , i r2 and i r3 ) and the second axis (or curve) of plane invariance (respectively i pl , i p2 and i p3 ).

[0093] Reference is again made to the method of Figure 3. After step 106, the method for determining positioning and navigation information may comprise a step 108, in which a measurement point P is determined between one or more determined invariance groupings each associated with a pair C m of selected DoLP representations. The coordinates (%, y) of the measurement point P correspond to the projection of the celestial pole (NCP or SCP) of the celestial vault on the plane perpendicular to the U axis of system 1.

[0094] In fact, the measuring point P corresponds to a calculated value of difference in degrees of polarization A xy equal to or close to the minimum value A min , for each couple C m considered. The measurement point P then corresponds to an invariant or approximately invariant DoLP pattern (and therefore a constant scattering angle value y) for each pair C m considered, that is, for each DoLP representation ld n calculated.

[0095] In embodiments, the determination of the measurement point P can be carried out from an addition operation, applied to each coordinate (%, ), of the different binary values ​​p xy associated with at least two binary representations B m couples C m . In this case, the plurality of polarized images I n includes at least three images used to determine at least two binary representations B m and obtain at least two invariance groupings. The determination of the measurement point P can then comprise a sub-step corresponding to the determination of an intersection representation H illustrated in Figure 8(a). Such an intersection representation H is characterized by a set of superposition values ​​denoted h xy associated with the coordinates (%, y) and defined according to the following equation (10):

[0097] A set of overlapping values ​​h xy of an intersection representation H can be distributed, like the set of pixels in figure [Fig.4(a)], according to a circular distribution.

[0098] For example, in Figure 8(a), the intersection representation H is derived from the binary representations B lt B2 and B3, and a binary representation B4 not shown in Figure 8(a). The invariance groupings of each binary representation, represented by the different white bands, then intersect at an intersection point corresponding to the measurement point P.

[0099] Determining the coordinates (%, y) associated with the measurement point P may also include a sub-step consisting of applying a predetermined intersection threshold s h to the superposition values ​​h xy of the intersection representation H. In this case, the intersection point p a can then correspond to a set of coordinates (%, y) defined according to the following equation (11):

[0101] For example and without limitation, for an intersection representation H determined from binary values ​​ / 3 xy associated with two binary representations B m , the predetermined intersection threshold s h can be equal to 1.

[0102] Alternatively, determining the coordinates (%, y) associated with the measurement point P may also include a sub-step of determining superposition values ​​h xy maximums of the intersection representation H. In this case, the measurement point P can then correspond to a set of coordinates (%, y) defined according to the following equation (12):

[0103] p a = {xy]|(max h xy ) (12)

[0104] In other embodiments, the intersection representation H may be generated directly from the differential representations D m couples C m . The set of superposition values ​​h xy can thus be determined from the calculated polarization degree differences A xy as defined by the following equation (13):

[0106] In this case, the application of a predetermined intersection threshold s h to the superposition values ​​h xy of the intersection representation H to determine the coordinates (%, y) associated with the measurement point P can be defined according to the following equation (14):

[0108] For example and without limitation, for an intersection representation H determined from binary values ​​p xy , associated with two differential representations D m , the predetermined intersection threshold s h can be a value significantly greater than 0.

[0109] Alternatively, determining the superposition values ​​h xy minimums of the intersection representation H to determine the coordinates (x,y) associated with the measurement point P can be defined according to the following equation (15):

[0110] p a = {xy}|(min h xy ) (15)

[0111] It should be noted that the superposition point is positioned at the intersection of the radial invariance axes (or curves) i rm . Thus, the determination of the measurement point P as a function of an intersection representation H can be carried out from a prior operation of determining the radial invariance axis i rm of at least two groupings among the plurality of generated invariance groupings.

[0112] In this case, the intersection representation H comes from the superposition (i.e. an addition operation for example) of the axes (or curves) of radial invariance i rm of each invariance grouping, which then intersect at an intersection point corresponding to the measurement point P. In Figure 8(b), the radial invariance curves i rm of each invariance grouping on the intersection representation H are represented by the black curves.

[0113] In particular, the determination of the radial invariance axis i rm of an invariance group associated with a pair of DoLP C representations m (Jd n , ld n+1 ) may include a prior sub-step of modeling a first curve defined in the XY plane and a second curve defined in the XY plane, distinct from the first curve. For example and without limitation, the first and second curves C(x,y) may be modeled from the maximum binary values ​​p xy of the binary representation B m associated with couple C m , or minimum values ​​of the differences, in absolute value, of calculated degrees of polarization A xy differential representations D m associated with couple C m For example.

[0114] Furthermore, determining the radial invariance axis of an invariance grouping may include a substep of evaluating the (x,y) coordinate points of the two minimum DoLP values min corresponding respectively to the position of A n and A n+i on the XY plane (i.e. position of the projection of the star on the celestial vault of the representations ld n and ld n+1 ). In this case, for time differences ø between two polarized image acquisition times l n relatively small (i.e. deviations of a few hours maximum, such as two hours), the curve of the radial invariance axis i r (x,y) (curve representing radial invariance) corresponds to the curve C(x,y) intersecting (i.e. crossing or intercepting) perpendicularly the line ® n (n+i)( >y) formed by the coordinates (x,y) of the points A n and A n+ i.

[0115] Determining the radial invariance axis of a group of invariances may also include a sub-step of evaluating one or more curves called 'plane symmetry curves', with coordinates (x,y), each plane symmetry curve being relative to the maximum DoLP values max of one of the two DoLP representations (in particular Id n and / or Id n+1 ) and corresponding to the associated plane symmetry. In this case, the determination of the radial invariance axis may comprise a sub-step of distance measurement (for example Euclidean distance) of a first distance value between the first curve C(x,y) and the one or two plane symmetry curves, and of a second distance value between the second curve C(x,y) and the one or two plane symmetry curves. Thus, for time differences δ between two polarized image acquisition times I n relatively small (i.e. deviations of a few hours maximum, such as two hours), the curve of the radial invariance axis i r (x,y) can correspond to the curve C(x,y) associated with the highest distance value.

[0116] In some embodiments, the determination of the measurement point P can be carried out from the point p t of intersection between the curve of the radial invariance axis i r (x,y) and the curve of the plane invariance axis i p (x,y) (curve representing the plane invariance) of a group of invariances from a couple C m , as illustrated in Figure 8(c). In this case, the determination of the measurement point P can then include a step of applying drift corresponding to the shift of the coordinates (x,y) of the intersection point p t on the radial invariance axis i r (x,y) according to a drift value r. The drift value r can for example be predefined depending on the calendar date (i.e. the declination of the star) of the acquisition of the images associated with the pair C m .

[0117] The positioning and navigation method further comprises a step 110 consisting of determining the altitude of the celestial pole and / or the azimuth of the celestial pole from the measurement point P obtained. In particular, step 110 may consist of determining the coordinate (p0) of latitude and / or the direction of the geographic pole of the system 1 from the measurement point P obtained. This step may be implemented by the positioning and navigation information determination unit 20 of FIG. 1.

[0118] The elevation angle or altitude of the celestial pole (NCP or SCP) on the celestial vault centered at point O is equivalent to angle 0 o defined with respect to the XY plane perpendicular to the U axis of system 1. In the case where the U axis is equivalent to the Zenith Z axis, as illustrated in figure 9 where the point O is represented at the center of a reference (E,N,Z) (meaning East, North, Zenith according to the English name), the altitude of the celestial pole corresponds to the coordinate (p0) of latitude of the geographical position of system 1.

[0119] Furthermore, the direction axis passing through point O and the projection of the celestial pole onto the XY plane perpendicular to the U axis of system 1 corresponds to the direction of the geographic pole (e.g., the North Pole, NP, or the South Pole, SP). As shown in Figure 9, the direction of the geographic pole can be described by the angle a p relative to the reference direction of the acquisition module used to acquire the plurality of images I n . It should be noted that a p is also called the azimuth of the celestial pole. The projection of the celestial pole in the plane (EN) is located on the N axis of the (E,N,Z) reference frame as illustrated in Figure 9 (in Figure 9, a p is the angle between the N axis and the X axis in the (EN) plane).

[0120] For example and without limitation, determining the coordinate (p0) of latitude of system 1 may include a substep of determining the length L xy between the coordinates (%, y) associated with the measurement point P and the coordinates (%, y) of the center of the image I n , as well as the application of a calculation function to the length L xy associated with the measurement point P. The celestial vault being considered as a half-sphere, the coordinate (p0) of latitude of system 1 can then be defined according to the following equation (16): [O121] o = (L xy ) (16)

[0122] The calculation function can be predefined according to the parameters associated with step 102 of acquiring polarized images I n . For example and without limitations, in the case of using an equidistant fisheye lens of focal length f in this acquisition step, as shown in figure [Fig.4(b)], the function for calculating the coordinate (p0) of latitude of system 1 can be defined according to the following equation (17):

[0124] In embodiments, a step of determining one or more simulations Id^ of the pattern of degrees of linear polarization of the light of the entire celestial vault centered at point O can be carried out from the DoLP representation Id n of only a part of the sky and equation (02) of the DoLP pattern according to the Rayleigh scattering model. In this case, step 106 of determining the grouping of invariances can be applied directly to the simulations Id^ of the DoLP pattern.

[0125] Such Id^ simulations are useful when one or more I images n include weather and environmental obstacles (such as clouds, buildings, etc.). Such Id^ simulations can be used to complement DoLP Id representations n truncated by these obstacles, the truncated parts potentially including the desired celestial pole position. Such obstacles can also significantly modify the degree of linear polarization of the surrounding light, with Id^ simulations then making it possible to correct the deviations due to these modifications.

[0126] Such Id^ simulations are useful when one or more I images n are acquired from a localized sensor. Advantageously, an image Id^ can also be produced from image I n including few acquisition points p xy , that is to say an image I n comprising two to a few dozen pixels.

[0127] In embodiments where the U axis is not equivalent to the Zenith Z axis, determining the coordinate (p0) of latitude of system 1 may include a substep of correcting the length L xy to take into account the inclination of the plane associated with the pixels of image I n relative to the surface of the Earth. In particular, the method may comprise implementing a calibration of the orientation of the system 1 . Such a calibration may be implemented from the measurement of the gravity vector at the geographical position of the system 1 , for example. Such a calibration may also be implemented beforehand at a position of known latitude and heading to determine the celestial pole and deduce the orientation of the U axis. Finally, such a calibration may further be implemented from the use of ephemerides.

[0128] In embodiments, a step of acquiring displacement data, i.e. rotation and translation, of the system 1, can be implemented, during the acquisition of the polarized images I n successive. In this case, step 106 of determining the invariance groups and / or step 108 of determining the measurement point P can be applied by taking into account these rotation data and these translation data according to a maximum value of a few kilometers. For example and without limitation, for two selected DoLP representations of the same pair C m Id n , Id n+1 ), if system 1 has undergone a rotation of +90° relative to the U axis between the acquisition times t n and t n+1 , sub-step 1064 of determining a differential representation D m can be performed after applying a -90° rotation of the DoLP Id representation n+1 in the plane associated with the pixels of image I n .

[0129] In embodiments, the method for determining positioning and navigation information may further comprise a step of determining the longitude of the system 1 from the data of a referenced clock and determining the coordinates (%, y) of the measurement point P for a system 1 positioned successively at at least two distinct geographical positions Oi and O2, on the surface of the Earth.

[0130] Figure 10 represents sub-steps of the step of determining the longitude of the system 1, according to certain embodiments.

[0131] The referenced clock may be a “Polar Wheatstone Clock” type clock. In this case, the step of determining the longitude may comprise, in sub-steps 124 and 128 respectively, the calculation of the value of the direction of linear polarization of light (AoLP) at the celestial pole (coordinates (%, ) of the measurement point P) then the determination of the solar time a> 01 for the system 1 at geographic position Oi (positioning carried out in step 122) and solar time M O2 for system 1 at geographic position O2 (positioning performed in step 126). Note that solar time corresponds to the angle between the arcs of the great circles connecting the star to the celestial pole and the celestial pole to the zenith (i.e. the 'zenith-celestial pole' vector), which is equivalent to the angle between the polarization vector at the celestial pole and the great circle arc connecting the celestial pole and the zenith.

[0132] The sub-step 124 of determining the longitude may also comprise the initialization of an internal clock in the system 1, in the step of determining the coordinates of the measurement point P, for a system 1 positioned at the geographical position O1. Such an internal clock makes it possible to determine the time difference tx between the determination of the coordinates of the measurement point P, for a system 1 positioned at the geographical position O1, and the determination of the coordinates of the measurement point P, for a system 1 positioned at the geographical position O2.

[0133] In response to the movement of system 1 from geographic position O1 to geographic position O2 and the determination of the hour angle) o2 , the longitude determination step may further include a comparison value Aa> of the solar hours M 01 And <z> o2 respectively at geographical positions O1 and O2. The comparison value can be, for example, the difference between solar time <z> o2 determined at the geographical position O2 and the sum between the time difference tx and the solar time M 01 , determined at the geographical position O1. The comparison value Aa> can then be defined according to the following equation (18):

[0134] Ao) = o) o2 — ( <D 01 + tx) (18)

[0135] In embodiments, the time difference tx may be, for example and without limitation, less than or substantially equal to one week. In this case, the variations in the equation of time are small and the solar hours a> 01 and M O2 can be compared according to equation (18) without taking into account the variation in duration between the two measurements.

[0136] In other embodiments, the maximum time difference between coordinate determinations of the measuring point P does not verify the approximation of small variations of the equation of time. In this case, the solar hours a> 01 And ) o2 can be transformed into mean solar hours M' O1 and M' O2 from the equation of time given by the ephemeris. Thus, the mean solar hours M' O1 and >' o2 can be compared according to equation (18).

[0137] In sub-step 130, the difference in longitude M between the coordinate longitude ol of system 1 of the geographical position Oi and the coordinate longitude £ 02 of system 1 of the geographical position O2 can be determined based on the comparison value Aa> of the hour angles.

[0138] In sub-step 132, in the case where the coordinate longitude ol from system 1 to geographic position O1 is a known datum of system 1, the longitude of coordinate £ 02 from system 1 to geographic position O2 can be determined based on the longitude value ol and the difference in longitude M.

[0139] Figure 11 shows an example of the structure of the system 1 for determining positioning and navigation information positioned at the coordinate longitude and at the coordinate latitude O , according to certain embodiments of the invention.

[0140] The system 1 for determining positioning and navigation information, shown in FIG. 11, may comprise a polarized light acquisition module 210 configured to carry out the acquisition of successive polarized images l n . The polarized light acquisition module 210 comprises in particular a mathematical model called 'camera optical model' associated with the projection of the celestial sphere in the 2D plane, that is to say in the XY plane perpendicular to the optical axis of the system 1. The polarized light acquisition module 210 may for example and without limitation be a digital single-lens reflex camera comprising a so-called "fisheye" lens making it possible to ensure acquisition over a 180° viewing angle. In this case, the polarized light acquisition module 210 may comprise a lens 212 and a detector 214 such that the optical model for determining the coordinate (%, y) of a projection point of the vault on the detector corresponds to the ratio between the focal length of the lens and the angle of the projection point with the optical axis. Furthermore, the detector 214 of the polarized light acquisition module 210 may have a generally rectangular or square geometry.However, for such a so-called circular "fisheye" lens, the. useful area of ​​the detector 214 generally forms a circular area as shown in Figure [Fig.4(a)]. In addition, each pixel of the sensor of the digital camera may comprise an array of 4 pixels sensitive to a specific polarization at 0°, 90°, 45° and 135° for example. Alternatively, the camera may comprise a polarizing filter and the acquisition of each polarized image I n corresponds to the acquisition of 4 images taken for 4 different polarizer angles at 0°, 90°, 45° and 135° for example.

[0141] The celestial pole determination device 10 may comprise a processing module 220 configured to perform the calculation and determination of the coordinates (%, y) of the measurement point P and the various representations necessary during the process, comprising the DoLP Id representations n , differential representations D m , binary representations B m , intersection representation H.

[0142] The unit 20 for determining the positioning and navigation information may comprise a module 230-1 for determining the latitude coordinate (geographic position O of the system 1) and a module 230-2 for determining the azimuth of the celestial pole.

[0143] In embodiments, the system 1 for determining positioning and navigation information may also comprise a correction module 240 configured to generate simulations Id^ of the pattern of degrees of linear polarization of the light of the entire celestial vault centered at point O from representations DoLP Id n of only part of the sky and equation (02) of the DoLP pattern according to the Rayleigh scattering model.

[0144] The correction module 240 can also be configured to detect an offset between the optical axis U associated with the polarized light acquisition module 210 and the Zenith axis Z. In the case of the detection of such an offset, the correction module 240 can be configured to apply a correction of the lengths L xy and L to take into account the inclination of the plane associated with the pixels of the image l n relative to the Earth's surface.

[0145] In embodiments, the system 1 for determining positioning and navigation information may also comprise a module of displacement and displacement acquisition 250 configured to move the system 1 to different geographic positions on Earth.

[0146] The displacement and displacement acquisition module 250 can thus be configured to carry out the acquisition of translation and rotation data of the system 1 during and / or after the displacement of the system 1. For this, the module 250 can comprise physical measurement units such as accelerometers, a gyroscope, a gravity sensor, etc.

[0147] Advantageously, the system 1 can be used to perform geopositioning in civil or military applications of autonomous navigation on unmanned platforms such as terrestrial drones, aerial drones positioned at high altitude or low altitude, or submarines positioned at a maximum depth defined by the spectral band predefined by the system 1. Such unmanned platforms can have automatic or remote-controlled piloting. Such use in an application of the invention to geopositioning combining an inertial navigation system and celestial pole determination (or heading determination) makes it possible to compensate for positioning and orientation errors of the unmanned platforms generated over time by exclusive inertial navigation. Furthermore, the system 1 can be used to measure the orientation of an object on earth relative to the geographic pole.

[0148] In embodiments, the system 1 for determining positioning and navigation information may also comprise a memory module 260 configured to save all of the acquisitions, measurements, and calculations performed. The memory module 260 may also comprise the referenced clock enabling the determination of the longitude of the system 1.

[0149] In embodiments, the system 1 may include one or more data input / output interfaces, such as human-machine interfaces 270 (HMIs). These human-machine interfaces may include one or more information acquisition means or information transmission means, such as input and control devices (e.g., microphone, speaker, keyboard) and / or one or more display devices (e.g., video screen, touch screen, etc.). For example and without limitation, the system 1 may include a human-machine interface 270 configured to generate a display longitude coordinates H o and latitude O at point O, to an operator of system 1.

[0150] Figures 12 and 13 illustrate the results obtained by implementing the method for determining positioning and navigation information, according to certain embodiments of the invention.

[0151] In particular, Figure 12 illustrates results of step 1066 of binarizing the differences in degrees of polarization calculated to obtain the binary representations B m and highlight the groupings of invariances of degrees of linear polarization between the DoLP representations of couple C m . Figure 12 also illustrates the results of step 108 of determining the measurement point P carried out from the generation of an intersection representation H by operation of adding the binary representations B m .

[0152] Figure 13 is an example of graphs illustrating the results of the direction values ​​of the geographic pole a p and latitude values ​​(p0 determined by the method of figure 3 for a system 1 positioned at point O, as a function of the rotation of system 1 around the optical axis U.

[0153] Those skilled in the art will understand that the method, according to the embodiments of the invention, can be implemented in various ways by hardware, software, or a combination of hardware and software, in particular in the form of program code that can be distributed as a program product, in various forms. The program code can be distributed using computer-readable media, which can include computer-readable storage media and communication media. The methods described in the present disclosure can be implemented in particular in the form of computer program instructions executable by one or more processors in a computer computing device. These computer program instructions can also be stored in a computer-readable medium.

[0154] The invention is not limited to the embodiments described above as a non-limiting example. It encompasses all variant embodiments that may be envisaged by those skilled in the art. In particular, those skilled in the art Tl will understand that the invention is not limited to the different steps of the method and the different modules of the system described as non-limiting examples.< / z> < / z> < / f>

Claims

Claims 1. Method for determining the temporal invariances of the degree of linear polarization of light coming from a star in a celestial vault, implemented in a system for determining positioning and navigation information, said celestial vault being centered on the geographical position of said system, characterized in that the method comprises at least the following steps consisting of: o acquiring (102) a plurality of polarized images I n successive images of at least part of said celestial vault; o determine (104), for each image I n acquired, a representation of the degrees of linear polarization ld n; o determine (106) at least one grouping of temporal invariances of degrees of linear polarization of the light coming from said star, a grouping of invariances being determined from a pair of representations selected from said plurality of representations of the degrees of linear polarization ld n ; o determining (108) a measurement point P from said at least one grouping of invariances, the measurement point P corresponding to the celestial pole in the celestial vault of said system; the method further comprising a step of determining the altitude and / or the azimuth of said celestial pole from the measurement point P obtained, said azimuth corresponding to the direction of the geographic pole associated with the geographic position of said system.

2. The method of claim 1, wherein said positioning and navigation information determination system is geographically positioned at a coordinate latitude O, and wherein the method further comprises a step of determining the coordinate O latitude of said system from said determined altitude.

3. Method according to one of the preceding claims, in which each polarized image l n is acquired at a time t n , the minimum time difference between two acquisition times of two successive polarized images being predefined.

4. Method according to one of the preceding claims, in which each polarized image I n includes a set of pixels p xy , each pixel being associated with coordinates (%, y) and a set of detection intensities according to distinct polarization angles such that p xy = (I o ° 9o°>l45°>Ii35°)xy> et in which each representation ld n includes a set of degrees of linear polarization d xy , each degree of xybeing calculated from the Stokes vector, such that:

5. Method according to one of the preceding claims, in which each grouping of invariances is determined from a differential representation D m comprising a set of differences A xy calculated from said pair of representations of the degrees of linear polarization Id n selected.

6. Method according to claim 5, in which each grouping of invariances is determined from a binary representation B m determined from said differential representation D m and a predetermined threshold for binarization of the difference in degrees of linear polarization A xy .

7. Method according to one of claims 1 to 6, in which said plurality of polarized images I ncomprises at least three images, in which at least two groupings of invariances of degrees of linear polarization of the light coming from said star are determined, and in which said measurement point P is determined from the intersection between said at least two groupings of invariances.

8. Method according to claims 6 and 7, in which the intersection between said at least two groups of invariances is carried out from the determination of an intersection representation H characterized by a set of superposition values h xy calculated from at least two of said binary representations B m , and in which said measuring point P corresponds to the coordinates for which the superposition value h xy is maximum.

9. Method according to one of claims 1 to 6, wherein said plurality of polarized images l ncomprises at least two images, said grouping of invariances comprising a radial invariance, by radial symmetry, and a plane invariance, by plane symmetry, of degrees of linear polarization of the light coming from said star, and in which said measurement point P is determined from a point p L of intersection between said radial invariance and said plane invariance, and of information on the offset of said celestial pole relative to said point of intersection Pi- 10. Method according to one of the preceding claims, in which the method comprises a step consisting of determining at least one simulation Id^ of the pattern of degrees of linear polarization of the light coming from said star over the whole of said celestial vault, each simulation Id^ being determined from one of the images of said plurality of polarized images I n of at least part of said celestial vault.

11. Method according to one of the preceding claims, in which the method comprises a step consisting of carrying out the acquisition of displacement and rotation data of said operated system between the successive acquisition of at least two of said polarized images I n , and wherein determining said at least one grouping of invariances comprises taking into account said displacement and rotation data.

12. Method according to one of the preceding claims, in which said geographic position of said system is further associated with a coordinate longitude o , and wherein the method comprises a step of determining the coordinate £ o of longitude of said system from data from a referenced clock, and of the direction of polarization at the level of the measurement point P of said system positioned successively at the level of at least two distinct geographical positions.

13. System (10) for determining positioning and navigation information, characterized in that the system comprises: o a polarized light acquisition module (210), said light coming from a star in the celestial vault centered on the geographical position of said system, said module (210) being configured to carry out the acquisition of a plurality of polarized images I n successive images of at least part of said celestial vault; o a processing module (220) configured to determine, for each image I n acquired, a representation of the degrees of linear polarization Id n , said module (220) being further configured to determine at least one grouping of temporal invariances of degrees of linear polarization of the light coming from said star, each grouping of invariances being determined from a pair of representations Id nselected from said plurality of representations of the degrees of linear polarization Id n , said module (220) being further configured to determine a measurement point P from said at least one grouping of invariances, the measurement point P corresponding to the celestial pole in the celestial vault of said system; the system further comprising a positioning and navigation module (230) configured to determine the altitude and / or the azimuth of said celestial pole from the measurement point P obtained, said azimuth corresponding to the direction of the geographic pole associated with the geographic position of the system.

Images