A navigation device for observing polarized light characteristics in the sky area with maximum polarization degree

Abstract

The invention discloses a navigation device for observing polarized light characteristics of a sky region with a maximum polarization degree, belonging to the field of navigation, and comprising a sun sensor, two polarization sensors, a triangular prism and a three-axis rotating platform. The sun is found through the sun sensor, so that the center of mass of the sun imaged in the sun sensor is located at the origin of its coordinate system; the solar zenith meridian is found through the symmetry of the two polarization sensors imaging the sky region with a maximum polarization degree, the direction cosine matrix and its inverse matrix from the carrier coordinate system to the platform coordinate system at the position are calculated, the solar azimuth and altitude angle of the observation point at that time are queried through the solar ephemeris, the direction cosine matrix from the geographic coordinate system to the platform coordinate system at the current position is calculated, and the direction cosine matrix from the navigation coordinate system to the carrier coordinate system is calculated to obtain the yaw angle, pitch angle and roll angle of the carrier and the heading of the carrier. The invention can observe the maximum polarization degree region in real time for orientation and attitude determination, thereby improving the anti-interference ability of the navigation device.

Description

Technical Field

[0001] The invention belongs to the field of navigation, and in particular relates to a navigation device for observing polarized light characteristics of a sky region with a maximum polarization degree. Background Art

[0002] Sensors that provide azimuth or heading measurements are key components in navigation systems. In practice, two solutions are often given for situations where satellite navigation is denied: one is to use a relative heading sensor, such as a ring laser gyroscope. However, this method has a drift over time that causes performance degradation, and an external absolute heading must be used for long-term use. The second is to use an absolute heading sensor digital magnetic compass. A good magnetic compass can provide an accuracy of 5-10mil. However, due to unpredictable local changes in the Earth's magnetic field, the anti-interference ability of the magnetic compass needs to be further improved.

[0003] Bionic polarized light navigation is a new autonomous navigation method based on the natural properties of the earth. It is based on the highly sensitive polarized vision of organisms and the regular distribution pattern of polarized light in the sky as the basis for navigation. It has the characteristics of no error accumulation over time, strong anti-interference ability and anti-deception, and can be used as a favorable supplement to existing navigation technology. It provides heading and attitude information for the carrier under the condition of satellite navigation failure, effectively improves the accuracy and reliability of the navigation system, and has important scientific significance and broad application prospects.

[0004] The orientation system using polarized light orientation navigation method can be divided into two categories based on the sampling mechanism: point source and imaging. The point source orientation system consists of a polarizer, a photodiode, and a logarithmic amplifier. It performs orientation by measuring the polarization degree of a certain point in the sky. It has the characteristics of good real-time performance and high robustness. The imaging orientation system consists of an optical lens, a polarizer, and an image sensor. It performs orientation by measuring the polarization information of the entire sky or part of the sky. It is resistant to disturbances in some areas of the sky.

[0005] Whether it is a point source polarization sensor or an imaging polarization sensor, it is currently not possible to actively select the sky area to measure. When the polarization degree of the measured sky area decreases as the solar altitude angle increases, the measurement accuracy of the sensor is seriously affected, and the navigation performance is reduced or even fails. Summary of the invention

[0006] In view of the deficiency of existing polarized light sensors that the directional performance decreases when the polarization degree decreases as the solar altitude angle increases, the present invention provides a navigation device for observing the polarization light characteristics of the sky area with the maximum polarization degree based on the full-sky atmospheric polarization characteristics and the directional characteristics of the polarized light sensor. The measurement accuracy and navigation performance are not affected by the solar altitude angle and the sensor tilt.

[0007] The technical scheme adopted by the present invention is as follows: a navigation device for observing polarized light characteristics of a sky region with a maximum polarization degree, comprising a sun sensor, two polarization sensors, a triangular prism and a three-axis rotating platform, wherein the two bottom surfaces of the triangular prism are isosceles right triangles, the triangular prism is mounted on the platform of the three-axis rotating platform, the pixels of the sun sensor are 2048×2048, and the field of view is 185°×185°; the field of view of the two polarization sensors is 119°×95°; the sun sensor is mounted on the bottom surface of the triangular prism, the first polarization sensor is mounted on the first side surface of the triangular prism, and the second polarization sensor is mounted on the second side surface of the triangular prism, and the optical axes of the first polarization sensor, the second polarization sensor and the sun sensor are all perpendicular to each other, so as to ensure that when the sun sensor is aimed at the sun, the polarization sensor can capture the sky region with a maximum polarization degree;

[0008] Assume that the sun sensor coordinate system is X0S0Y0Z0, the first polarization sensor coordinate system is X1P1Y1Z1, the second polarization sensor coordinate system is X2P2Y2Z2, and the three-axis rotation platform coordinate system is X p OY p Z p , the carrier coordinate system takes the upper right front as X b OY b Z b , select the northeastern sky geographic coordinate system X of the observation point g OY g Z g As the navigation coordinate system, each coordinate system adopts the right-hand coordinate system, and the initial position of the three-axis rotating platform coordinate system coincides with the carrier coordinate system; the attitude transformation matrices between the sun sensor coordinate system to the first polarized light sensor coordinate system, the second polarized light sensor coordinate system, and the three-axis rotating platform coordinate system are respectively:

[0009]

[0010] The sun is found by the sun sensor, so that the center of mass of the sun image in the sun sensor is located at the origin of its coordinate system; the solar zenith meridian is found by the symmetry of the imaging of the sky area with the maximum polarization degree by two polarization sensors, and the direction cosine matrix of the three-axis rotating platform coordinate system from the carrier coordinate system to the position is calculated. and its inverse matrix The solar azimuth and altitude angle of the observation point are queried through the solar ephemeris, and the direction cosine matrix of the three-axis rotating platform coordinate system from the geographic coordinate system to the current position is calculated. Calculate the direction cosine matrix from the navigation coordinate system to the vehicle coordinate system Thus, the yaw angle, pitch angle, roll angle and heading of the carrier are obtained.

[0011] Furthermore, the solar sensor photoelectric detector adopts a 1-inch CMOS photoelectric detector.

[0012] Furthermore, the two polarization sensors are both 2 / 3 inch polarization image sensors.

[0013] Another object of the present invention is to provide a navigation orientation and attitude determination method for observing polarized light characteristics of the sky region with maximum polarization degree by means of the above navigation device, the method steps are as follows:

[0014] S1: Starting position: The initial position of the three-axis rotating platform coordinate system coincides with the carrier coordinate system;

[0015] S2: The sun sensor captures the image in the sky, extracts the centroid of the largest bright spot, and determines whether the sun is in the field of view. If the sun is in the field of view, proceed to the next step. Otherwise, the three-axis rotating platform rotates around Z p The axis rotates 180 degrees and repeats this step. The rotation transformation matrix is ​​R z (γ1), γ1 = 0° or 180°;

[0016] S3: Calculate the horizontal and vertical field of view angles (γ2, α) according to the centroid coordinates (x, y) of the solar image point; the solar sensor photodetector has a pixel of 2048x2048 and a field of view of 185°×185°, so

[0017] S4: Three-axis rotating platform around Z p The axis is rotated by an angle of γ2, so that the center of mass of the solar image point is located on the Y0 axis of the image plane of the solar sensor coordinate system. The rotation transformation matrix is ​​R z (γ2); then the three-axis rotating platform rotates around X p The axis rotates by an angle α, so that the mass center of the solar image point is located at the origin of the image plane of the solar sensor coordinate system, that is, the optical axis of the solar sensor points to the sun. The rotation transformation matrix is ​​denoted by R x (α);

[0018] S5: Use two polarization sensors to image the sky area with the maximum polarization degree, and determine whether the polarization images obtained by the two polarization sensors are symmetrical. If yes, proceed to the next step. Otherwise, judge by the degree of symmetry of the two images, and then rotate the three-axis rotating platform around Y p The axis is rotated by an angle β until the polarization images captured by the two polarization sensors are symmetrical. The rotation transformation matrix is ​​R y (β);

[0019] S6: At this time, the optical axis of the sun sensor points to the sun, and the polarization images taken by the two polarization sensors are about Y p Axially symmetric, with the solar zenith meridian at Y p OZ pIn the plane, the direction cosine matrix from the carrier coordinate system to the three-axis rotating platform coordinate system is Then the direction cosine matrix from the three-axis rotating platform coordinate system to the carrier coordinate system is According to the time, longitude and latitude of the observation point, query the solar ephemeris to obtain the solar altitude angle h s and azimuth A s ; Then the direction cosine matrix from the local geographic coordinate system to the three-axis rotating platform coordinate system is

[0020] S7: Then the direction cosine matrix from the local geographic coordinate system to the carrier coordinate system is Conclusion

[0021] S8: Calculate the three attitude angles and yaw angle of the carrier according to the direction cosine array Pitch angle θ = arcsin(A 23 ), Roll Angle

[0022] S9: Determination of the carrier heading: Since the geographic coordinate system is northeast and the carrier coordinate system is right front and up, the yaw angle in the attitude angle is opposite to the rotation direction of the corresponding axis, so the heading needs to be determined by converting the yaw angle. Since the yaw angle is usually defined as north-east as positive, the yaw angle of the attitude in the right front and up carrier coordinate system is converted to the carrier heading. The formula is: ψ b =2π-ψ.

[0023] Advantages and beneficial effects of the present invention:

[0024] First: Compared with other polarization observation methods, the present invention is based on the analysis of atmospheric polarization characteristics, combined with the respective characteristics of solar sensors and polarized light sensors, to design a polarization navigation system that can observe the sky area with the maximum polarization degree. The present invention is not affected by the solar altitude angle, and can observe the maximum polarization degree area in real time for orientation and attitude determination, thereby improving the anti-interference ability of the equipment.

[0025] Second: when the present invention determines the heading and attitude, the maximum polarization area is observed in real time for orientation. Even if the sensor is tilted, effective polarization information can be observed, thereby improving the effectiveness of the system heading determination.

[0026] Third: before the present invention uses the observation of atmospheric polarization characteristics to determine the heading, the position of the sun has been found, and there is no ambiguity in the determined heading, which improves the reliability of the system polarization orientation.

[0027] Fourth: The vertical field of view of the solar sensor is 185°. Even when the horizontal tilt angle of the carrier is 90°, it can still cover the entire sky area by rotating 180°, thereby finding the sun. This enables the use of atmospheric polarization orientation even when the carrier is at a large tilt angle, and has strong robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 Schematic diagram of atmospheric polarization in celestial coordinate system;

[0029] Figure 2 Degree of polarization DoLP projection diagram on a two-dimensional plane;

[0030] Figure 3 Polarization angle Aop projection on a two-dimensional plane;

[0031] Figure 4 Installation relationship diagram between various coordinate systems for polarization orientation and attitude determination;

[0032] Figure 5 Schematic diagram of the relationship between the coordinate systems of the polarized light navigation system;

[0033] Figure 6 Flowchart of the method for observing the maximum polarization orientation and attitude determination. DETAILED DESCRIPTION

[0034] The following is a clear and complete description of the technical solutions in the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. It should be pointed out that, unless otherwise specified, all technical and scientific terms used in this application have the same meanings as those commonly understood by ordinary technicians in the technical field to which this application belongs.

[0035] Example 1

[0036] Atmospheric polarization model and characteristics:

[0037] When sunlight propagates in the atmosphere, unpolarized sunlight will form polarized light with certain polarization characteristics after being scattered by particles and dust in the atmosphere. The polarization caused by molecular scattering in the atmosphere is well described using Rayleigh scattering theory, a subset of Mie theory. Rayleigh scattering theory requires that these scattering media are very small compared to the incident wavelength, and that the scattered light undergoes a single scattering effect before measurement. Although the conditions prescribed by Rayleigh scattering may be limited, Rayleigh scattering theory generally fully describes atmospheric scattering. Especially when the sky is clear, the use of first-order Rayleigh scattering theory can be a good approximation to describe the scattering of sunlight in the sky. In addition, the resulting polarization pattern can infer the azimuth and attitude information of the polarimeter used to measure and analyze the sky polarization pattern.

[0038] According to the Rayleigh scattering model, the vibration direction of the electric vector at the observation point P is perpendicular to the plane formed by the observer position O, the observation point P and the sun position S, as shown in Figure 1 According to the Rayleigh scattering model, the degree of polarization (DoLp) and polarization angle (Aop) at any point P can be expressed as:

[0039]

[0040]

[0041] Where DoLP max is the maximum polarization degree, and θ is the angle between point P and the sun's position S, that is, the scattering angle.

[0042] The relevant polarization properties for navigation purposes include the degree of linear polarization (DoLP) and the angle of polarization (AoP) of the scattered light observed by the sensor. A single-point polarimeter with a very small field of view in the sky dome can measure the polarization response of that part of the sky, and by translating and tilting the sensor for each point on the hemisphere, a polarization map of the sky can be constructed. And, the projection of the degree of polarization (DoLP) and the angle of polarization (AoP) onto a two-dimensional plane is represented by a polar plot obtained by stereographic projection of the hemisphere down onto a two-dimensional plane. Figure 2-Figure 3 As shown, the projections of the degree of polarization and polarization angle on the horizontal plane of the geographic coordinate system at longitude 41.12° and latitude 123.10° at 9:00 on October 26, 2023 are respectively.

[0043] A scheme is designed to determine the heading and attitude by observing the polarization characteristics of the maximum polarization degree: from the polarization degree (DoLp) diagram, it can be seen that the polarization degree is the largest in the sky area where the scattering angle θ with the sun is 90 degrees; from the polarization angle (Aop) diagram, it can be seen that the distribution of polarization angles is antisymmetric about the projections of the solar meridian and the anti-solar meridian, and the solar zenith meridian is the symmetry axis.

[0044] According to the distribution characteristics of polarization degree and polarization angle, and in view of the problem that polarization orientation is affected by the solar altitude angle, this embodiment provides a navigation device for observing polarized light characteristics of the sky area with maximum polarization degree, including a solar sensor S0, two polarization sensors P1.P2, a triangular prism and a three-axis rotating platform, wherein the triangular prism is installed on the platform of the three-axis turntable, and the two bottom surfaces of the triangular prism are isosceles right triangles. The height of the triangular prism is determined according to the size of the solar sensor and polarization light sensor to be installed, the solar sensor S0 adopts a 1-inch CMOS photodetector CMV4000, with a focal length of 2.7mm, a pixel of 2048×2048, a field of view of 185°×185°, and a 1 / 100,000 dimming film at the rear end of the lens; the two polarization sensors P1.P2 both adopt a 2 / 3-inch polarization image sensor IMX250MZR, with a field of view of 119°×95°; Figure 4 As shown, the sun sensor S0 is mounted on the bottom surface A1 of the triangular prism, the first polarized light sensor P1 is mounted on the first side surface A2 of the triangular prism, and the second polarized light sensor P2 is mounted on the second side surface A3 of the triangular prism. The relationship between the sun sensor S0 and the two polarized light sensors P1 and P2 after being mounted on the regular triangular prism and the three-axis rotating platform coordinate system and the carrier coordinate system is as shown in FIG. Figure 4-5 As shown, the initial position of the three-axis rotating platform coordinate system coincides with the carrier coordinate system; and the optical axis of the first polarized light sensor P1, the optical axis of the second polarized light sensor P2 and the optical axis of the sun sensor S0 are perpendicular to each other, ensuring that when the sun sensor S0 is aimed at the sun, the polarized light sensor can capture the sky area with the maximum polarization degree; assuming that the sun sensor coordinate system is X0S0Y0Z0, the first polarized light sensor coordinate system is X1P1Y1Z1, the second polarized light sensor coordinate system is X2P2Y2Z2, and the three-axis rotating platform coordinate system is X p OY p Z p , the carrier coordinate system takes the upper right front as X b OY b Z b , select the northeastern sky geographic coordinate system X of the observation point g OY g Z g As the navigation coordinate system, each coordinate system adopts the right-hand coordinate system; among them, the attitude transformation matrices between the sun sensor coordinate system to the first polarized light sensor coordinate system, the second polarized light sensor coordinate system, and the three-axis rotating platform coordinate system are respectively:

[0045]

[0046] The sun is found by the sun sensor, so that the center of mass of the sun image in the sun sensor S0 is located at the origin of its coordinate system; the solar zenith meridian is found by the symmetry of the imaging of the sky area with the maximum polarization degree by the two polarization sensors P1.P2, and the direction cosine matrix of the three-axis rotating platform coordinate system from the carrier coordinate system to the position is calculated. and its inverse matrix The solar azimuth and altitude angle of the observation point are queried through the solar ephemeris, and the direction cosine matrix of the three-axis rotating platform coordinate system from the geographic coordinate system to the current position is calculated. Calculate the direction cosine matrix from the navigation coordinate system to the vehicle coordinate system Thus, the yaw angle, pitch angle, roll angle and heading of the carrier are obtained.

[0047] Example 2

[0048] like Figure 6 As shown, this embodiment provides a navigation orientation and attitude determination method for observing polarized light characteristics of the sky area with the maximum polarization degree. The method uses the navigation device recorded in Example 1, and the method steps are as follows:

[0049] S1: Starting position: The initial position of the three-axis rotating platform coordinate system coincides with the carrier coordinate system;

[0050] S2: The sun sensor captures the image in the sky, extracts the centroid of the largest bright spot, and determines whether the sun is in the field of view. If the sun is in the field of view, proceed to the next step. Otherwise, the three-axis rotating platform rotates around Z p The axis rotates 180 degrees and repeats this step. The rotation transformation matrix is ​​R z (γ1), γ1 = 0° or 180°;

[0051] S3: Calculate the horizontal and vertical field of view angles (γ2, α) according to the centroid coordinates (x, y) of the solar image point; the solar sensor photodetector has a pixel of 2048x2048 and a field of view of 185°×185°, so

[0052] S4: Three-axis rotating platform around Z p The axis is rotated by an angle of γ2, so that the center of mass of the solar image point is located on the Y0 axis of the image plane of the solar sensor coordinate system. The rotation transformation matrix is ​​R z (γ2); then the three-axis rotating platform rotates around X p The axis rotates by an angle α, so that the mass center of the solar image point is located at the origin of the image plane of the solar sensor coordinate system, that is, the optical axis of the solar sensor points to the sun. The rotation transformation matrix is ​​denoted by R x (α);

[0053] S5: Use two polarization sensors to image the sky area with the maximum polarization degree, and determine whether the polarization images obtained by the two polarization sensors are symmetrical. If yes, proceed to the next step. Otherwise, judge by the degree of symmetry of the two images, and then rotate the three-axis rotating platform around Y p The axis is rotated by an angle β until the polarization images captured by the two polarization sensors are symmetrical. The rotation transformation matrix is ​​R y (β);

[0054] S6: At this time, the optical axis of the sun sensor points to the sun, and the polarization images taken by the two polarization sensors are about Y p Axially symmetric, with the solar zenith meridian at Y p OZ p In the plane, the direction cosine matrix from the carrier coordinate system to the three-axis rotating platform coordinate system is Then the direction cosine matrix from the three-axis rotating platform coordinate system to the carrier coordinate system is According to the time, longitude and latitude of the observation point, query the solar ephemeris to obtain the solar altitude angle h s and azimuth A s ; Then the direction cosine matrix from the local geographic coordinate system to the three-axis rotating platform coordinate system is

[0055] S7: Then the direction cosine matrix from the local geographic coordinate system to the carrier coordinate system is Conclusion

[0056] S8: Calculate the three attitude angles and yaw angle of the carrier according to the direction cosine array Pitch angle θ = arcsin(A 23 ), Roll Angle

[0057] S9: Determination of the carrier heading: Since the geographic coordinate system is northeast and the carrier coordinate system is right front and up, the yaw angle in the attitude angle is opposite to the rotation direction of the corresponding axis, so the heading needs to be determined by converting the yaw angle. Since the yaw angle is usually defined as north-east as positive, the yaw angle of the attitude in the right front and up carrier coordinate system is converted to the carrier heading. The formula is: ψ b =2π-ψ.

Claims

1. A navigation device for observing polarized light characteristics in a sky region with a maximum polarization degree, characterized in that: The invention comprises a sun sensor, two polarization sensors, a triangular prism and a three-axis rotating platform, wherein the two bottom surfaces of the triangular prism are isosceles right triangles, the triangular prism is mounted on the three-axis rotating platform, the pixels of the sun sensor are 2048×2048, and the field of view is 185°×185°; the field of view of the two polarization sensors is 119°×95°; the sun sensor is mounted on the bottom surface of the triangular prism, the first polarization sensor is mounted on the first side surface of the triangular prism, and the second polarization sensor is mounted on the second side surface of the triangular prism, and the optical axes of the first polarization sensor, the second polarization sensor and the sun sensor are all perpendicular to each other, so as to ensure that when the sun sensor is aimed at the sun, the polarization sensor can capture the sky area with the maximum polarization degree; Assume that the sun sensor coordinate system is X0S0Y0Z0, the first polarization sensor coordinate system is X1P1Y1Z1, the second polarization sensor coordinate system is X2P2Y2Z2, and the three-axis rotation platform coordinate system is X p OY p Z p , the carrier coordinate system takes the upper right front as X b OY b Z b , select the northeastern sky geographic coordinate system X of the observation point g OY g Z g As the navigation coordinate system, each coordinate system adopts the right-hand coordinate system, and the initial position of the three-axis rotating platform coordinate system coincides with the carrier coordinate system; the attitude transformation matrices between the sun sensor coordinate system to the first polarized light sensor coordinate system, the second polarized light sensor coordinate system, and the three-axis rotating platform coordinate system are respectively: The sun is found by the sun sensor, so that the center of mass of the sun image in the sun sensor is located at the origin of its coordinate system; the solar zenith meridian is found by the symmetry of the imaging of the sky area with the maximum polarization degree by the two polarization sensors, and the position of the carrier when the polarization images taken by the two polarization sensors are symmetric about the solar zenith meridian is obtained, and the direction cosine matrix of the three-axis rotating platform coordinate system from the carrier coordinate system to the position is calculated. and its inverse matrix The solar azimuth and altitude angle of the observation point are queried through the solar ephemeris, and the direction cosine matrix of the three-axis rotating platform coordinate system from the geographic coordinate system to the current position is calculated. Calculate the direction cosine matrix from the navigation coordinate system to the vehicle coordinate system Thus, the yaw angle, pitch angle, roll angle and heading of the carrier are obtained.

2. A navigation device for observing polarized light characteristics of a sky region with a maximum polarization degree according to claim 1, characterized in that: The solar sensor photoelectric detector adopts a 1-inch CMOS photoelectric detector.

3. The navigation device for observing polarized light characteristics of the sky region with the maximum polarization degree according to claim 1, characterized in that: The two polarization sensors described above both use 2 / 3 inch polarization image sensors.

4. A navigation orientation and attitude determination method for observing polarization characteristics of sky area with maximum polarization degree obtained by a navigation device for observing polarization characteristics of sky area with maximum polarization degree according to any one of claims 1 to 3, characterized in that: The steps are as follows: S1: Starting position: The initial position of the three-axis rotating platform coordinate system coincides with the carrier coordinate system; S2: The sun sensor captures the image in the sky, extracts the centroid of the largest bright spot, and determines whether the sun is in the field of view. If the sun is in the field of view, proceed to the next step. Otherwise, the three-axis rotating platform rotates around Z p The axis rotates 180 degrees and repeats this step. The rotation transformation matrix is ​​R z (γ1), γ1 = 0° or 180°; S3: Calculate the horizontal and vertical field of view angles (γ2, α) according to the centroid coordinates (x, y) of the solar image point; the solar sensor photodetector has a pixel of 2048x2048 and a field of view of 185°×185°, so S4: Three-axis rotating platform around Z p The axis is rotated by an angle of γ2, so that the center of mass of the solar image point is located on the Y0 axis of the image plane of the solar sensor coordinate system. The rotation transformation matrix is ​​R z (γ2); then the three-axis rotating platform rotates around X p The axis rotates by an angle α, so that the mass center of the solar image point is located at the origin of the image plane of the solar sensor coordinate system, that is, the optical axis of the solar sensor points to the sun. The rotation transformation matrix is ​​denoted by R x (α); S5: Use two polarization sensors to image the sky area with the maximum polarization degree, and determine whether the polarization images obtained by the two polarization sensors are symmetrical. If yes, proceed to the next step. Otherwise, judge by the degree of symmetry of the two images, and then rotate the three-axis rotating platform around Y p The axis is rotated by an angle β until the polarization images captured by the two polarization sensors are symmetrical. The rotation transformation matrix is ​​R y (β); S6: At this time, the optical axis of the sun sensor points to the sun, and the polarization images taken by the two polarization sensors are about Y p Axially symmetric, with the solar zenith meridian at Y p OZ p In the plane, the direction cosine matrix from the carrier coordinate system to the three-axis rotating platform coordinate system is Then the direction cosine matrix from the three-axis rotating platform coordinate system to the carrier coordinate system is According to the time, longitude and latitude of the observation point, query the solar ephemeris to obtain the solar altitude angle h s and azimuth A s ; Then the direction cosine matrix from the local geographic coordinate system to the three-axis rotating platform coordinate system is S7: Then the direction cosine matrix from the local geographic coordinate system to the carrier coordinate system is Conclusion S8: Calculate the three attitude angles and yaw angle of the carrier according to the direction cosine array Pitch angle θ = arcsin(A 23 ), Roll Angle S9: Determination of the carrier heading: Since the geographic coordinate system is northeast and the carrier coordinate system is right front and up, the yaw angle in the attitude angle is opposite to the rotation direction of the corresponding axis, so the heading needs to be determined by converting the yaw angle. Since the yaw angle is usually defined as north-east as positive, the yaw angle of the attitude in the right front and up carrier coordinate system is converted to the carrier heading. The formula is: ψ b =2π-ψ.

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