star sensors installed on near⁃space vehicles are susceptible to earth⁃atmosphere radiation. As a result, the accuracy of star extraction and the performance of celestial system is significantly degraded. Aiming at this problem, a high precision star image pre⁃processing method to eliminate earth⁃atmosphere radiation is proposed. By analyzing the propagation mechanism of earth⁃atmosphere radiation, the atmospheric scattering model and ground reflection model are established, and an accurate earth⁃atmosphere radiation intensity model is constructed. Subsequently, the radiation intensity model is transformed into the background grayscale model in local ranges with the analysis of the relationship between the transmission path of the earth⁃atmosphere radiation received in the local ranges of the star sensor image plane and the pixel coordinates. Furthermore, the background estimation method is used to accurately estimate and compensate the stray light background under the influence of the earth⁃atmosphere radiation. Eventually, the performance of the proposed method is verified by simulated and real star images. The results show that the proposed method can effectively improve the SNR of star images and the accuracy of star extraction, and has good anti⁃interference performance.
Star sensor is a celestial sensor that uses stars as observation objects. It has advantages such as good autonomy, high measurement accuracy, no accumulated error, small volume and mass, and is widely used in aerospace vehicles. When star sensors work, in addition to receiving the radiation energy of the target star, they are also affected by stray radiation such as sunlight, moonlight, terrestrial light, and terrestrial heat. Among them, terrestrial light is formed by the complex atmospheric scattering and surface reflection of sunlight, which forms non-uniform background grayscale on the image plane of the star sensor, thereby reducing the contrast of the image plane and the signal-to-noise ratio of the star, affecting the accuracy of star centroid extraction and astronomical navigation. Therefore, for star sensors carried by near-Earth space vehicles, how to eliminate the influence of atmospheric light on star maps is a key technology that urgently needs to be solved in astronomical navigation.
At present, there are three types of methods to eliminate the impact of terrestrial light on star maps: frequency domain feature elimination, spatial domain feature elimination, and background estimation elimination. The frequency domain feature elimination method utilizes the high-frequency characteristics of star points in the frequency domain to distinguish them from low-frequency backgrounds, thereby removing the background grayscale caused by atmospheric light. However, due to the wide spectral range of the Earth’s atmospheric light background in the star map, there is aliasing between the star points and the Earth’s atmospheric light background in the frequency domain, which makes this method ineffective in removing Earth’s atmospheric light; Due to the “protruding” characteristics of star points in the spatial domain, and the relatively gentle changes of the Earth’s atmospheric light background in the spatial domain, the spatial domain feature elimination method utilizes the differences between star points and the Earth’s atmospheric light background in the spatial domain, and uses morphological filtering or grayscale forward difference algorithms to remove the Earth’s atmospheric light background. However, for low signal-to-noise ratio star maps under the influence of terrestrial light, star points are usually submerged by the background, resulting in insignificant morphological characteristics. This method will remove some areas of star points as background, thereby damaging the energy distribution of star points and affecting the accuracy of centroid extraction; The background estimation and elimination method is based on the correlation of the atmospheric background grayscale values in a local area. The background grayscale is modeled as a plane, and then the adjacent pixel grayscale values are used to estimate and compensate for the background grayscale at the star point, thereby eliminating the influence of atmospheric light on the star map. Due to the concentrated geometric position of star point imaging, the algorithm can avoid star points during background estimation by designing templates, resulting in less damage to the energy distribution of star points and better preprocessing performance. However, the actual terrestrial light is formed through complex scattering and reflection, and its distribution pattern on the image plane is complex and variable, making it difficult to accurately describe it using a planar background model, resulting in poor estimation accuracy of the terrestrial light background and restricting its removal effect.
This article analyzes the scattering and reflection of sunlight through the Earth atmosphere system, constructs an accurate model of the radiation intensity of the Earth atmosphere light, and analyzes the distribution pattern of the background grayscale of the Earth atmosphere light in the star map. Furthermore, a preprocessing algorithm based on the cubic surface model for anti Earth atmosphere light star maps is designed.
The atmospheric light will form non-uniform background grayscale on the image plane of the star sensor, which affects the accuracy of star point centroid extraction and astronomical navigation. To quantitatively analyze its distribution pattern on the image plane of the star sensor, it is necessary to establish a radiation intensity model of terrestrial light to analyze the radiation intensity of terrestrial light received by each pixel on the image plane.
The sunlight is scattered by the Earth’s atmosphere and reflected by the Earth’s surface, resulting in the formation of atmospheric light. In fact, due to the significant variation of atmospheric density with altitude and temperature, light propagates along the curve under the refraction of non-uniform atmosphere. However, the deflection angle of light caused by atmospheric refraction is less than 38 ‘, which has little effect on the radiation intensity and distribution pattern of light. Therefore, to simplify the analysis process, the assumption of a straight line was adopted for the path of light reaching the pupil plane of the star sensor, and its propagation path is shown in Figure 1.
In the figure, path ① is the propagation path of atmospheric scattered light. Sunlight enters from point C in the atmosphere, undergoes scattering in point P, and then passes out of the atmosphere from point A to reach the star sensor’s pupil plane S. Path ② is the propagation path of surface reflected light, where sunlight enters through the atmosphere C and passes through the atmosphere to reach the Earth’s surface G. After surface reflection, it exits the atmosphere and reaches the star sensor’s pupil plane S. The superposition of atmospheric scattered light and surface scattered light forms terrestrial light. To establish a radiation intensity model for terrestrial light, radiation intensity models for atmospheric scattered light and surface scattered light can be established separately.
To establish a radiation intensity model for atmospheric scattered light, taking a beam of atmospheric scattered light as an example, its propagation path in the atmosphere is shown in Figure 2.
The sunlight enters the atmosphere from point C and scatters at an angle of P θ Scattering occurs, and the scattered light shoots out of the atmosphere from point A.
Light travels in the atmosphere and undergoes attenuation due to absorption and scattering by the atmosphere. According to Lambert Beer’s law, the radiation intensity of light at point P can be calculated; Light scattering occurs at point P, and the scattered light propagates along the path PA, attenuated by atmospheric influence, and then exits the atmosphere at point A; In the actual process, sunlight is scattered at various points on path AB, and based on the atmospheric scattered light radiation intensity at point A, the radiation intensity of light scattered at different scattering angles can be calculated.
The sun shines on the surface of the Earth to form a sunlit area, where the surface elements reflect sunlight outward and form surface reflected light after passing through the atmosphere. Analyze the surface pixel i at point G, and the reflected light path at that pixel is shown in Figure 3.
After the reflected light is attenuated by the atmosphere, it is emitted from point A into the atmosphere. Taking into account the atmospheric scattering effect and surface reflection effect, a model of the intensity of terrestrial light radiation emitted from point A is obtained. Based on the terrestrial light radiation intensity model, the factors affecting the intensity of terrestrial light radiation can be explored, and the distribution pattern of terrestrial light background on the image plane of the star sensor can be analyzed.
Geoatmospheric light is composed of both surface reflected light and atmospheric scattered light. However, due to the blocking effect of the Earth on navigation stars, there are no star image points in the star map area affected by surface reflected light, so surface reflected light will not affect the imaging of star points. The background grayscale of star image points in the star map is mainly caused by atmospheric scattered light, which is the main factor affecting star imaging. It is necessary to analyze their radiation intensity characteristics. Due to the fact that the thickness of the atmosphere is much smaller than the radius of the Earth and the curvature of the atmosphere is smaller, the length of the incident path CP of sunlight is much smaller than the length of the outgoing path PA. In addition, the altitude at which sunlight is incident is relatively high, and the atmosphere is thin. Therefore, the optical distance D (CP) of the light transmission process is much smaller than D (PA). As shown in Figure 4, based on the geometric relationship, the relationship between the differential dl of the scattering path length and the differential dh of the scattering point height can be obtained
Due to the fact that the length of the light transmission path is much smaller than the radius of the Earth, the corresponding points on the scattering path φ The amplitude of change is relatively small, not exceeding 5 °, and can be considered as a constant value. From the above equation, it can be seen that the radiation intensity of atmospheric scattered light can be expressed as the wavelength of light rays λ、 Scattering angle θ And the function of scattering height hs. Considering the Earth and atmosphere as ideal spheres, based on geometric relationships, the relationship between scattering height hs and scattering path length l can be obtained. For star sensors, the wavelength of the light they can be sensitive to is fixed, i.e β （ λ） Is a constant. Due to the constant intensity of solar radiation, it can be inferred that the radiation intensity of atmospheric scattered light is only related to the scattering angle and the length of the scattering path, which means that the radiation intensity of ground air light that affects star imaging is affected by the scattering angle and the length of the scattering path.
Based on the above analysis of the radiation intensity characteristics of terrestrial light, the distribution pattern of terrestrial light background in the star map was explored, and a local grayscale model of terrestrial light background was constructed. Based on this model, a star map preprocessing algorithm resistant to terrestrial light was designed, as shown in Figure 5.
The navigation starlight height used in astronomical navigation is usually higher than 20km, and the relationship between the scattering path length l of atmospheric scattered light in the corresponding area and the transmission coefficient T (l) is shown in Figure 6.
During the background estimation process, the range of pixel neighborhoods is taken to be 10 pixels × 10 pixels. For near-Earth space vehicles, their flight altitude is usually less than 200 km, and the variation in the length of the scattering path of the received ground-air light in the atmosphere within the local pixel neighborhood range does not exceed 300 km. Therefore, the transmission coefficient in Figure 6 can be piecewise fitted using a cubic function. In addition, according to the geometric relationship, within the local pixel neighborhood range, the length of the scattering path of the received ground-air light in the atmosphere continuously and monotonically changes, As shown in Figure 7. Due to its amplitude of change being much smaller than the length of the scattering path, it can be considered that the scattering path varies linearly along the x-direction and y-direction of the length star map. The slope model is used to approximate the length of the scattering path of light in the atmosphere in a local area,
Based on the linear relationship between the incident light intensity of the star sensor and the pixel imaging grayscale, a local background grayscale model can be established; The background grayscale of the local area’s atmospheric light is distributed along a cubic surface.
In order to reduce the interference of random imaging noise on the estimation of the ground air light background, the least squares method is used to estimate the parameters of the ground air light background grayscale model using the grayscale of the pixels around the star points. By using the least squares method, the sum of squared residuals is minimized, and the derivative of the sum of squared residuals with respect to each parameter is 0. The equation system can be obtained, and the various parameters of the Gaussian function can be obtained by solving this linear equation system. The elements in matrix A can be calculated offline based on the size of the filtering template; The elements in matrix Y can be obtained by filtering the images in the local region. Therefore, when using the algorithm proposed in this article for preprocessing, only the corresponding filtering template needs to be constructed, and unknown parameters are estimated through image filtering processing. Finally, the background estimation value of the central pixel can be obtained based on the fitting parameters, and the ground atmosphere light background at the star point can be obtained. Then, subtract the background estimate from the denoised star map to obtain the preprocessed star map.
Using stars with a magnitude less than 6 Mv from the SAO J2000 catalog to create a simulated star map catalog. The simulated star map under the influence of terrestrial light is shown in Figure 8.
The red box in the image represents the position of the star point, the purple horizontal line represents the position of the Earth’s edge in the map, and the star light at the bottom of the map is obscured by the Earth. By analyzing the images, it can be seen that the ground air light forms a background with a continuous gradient distribution of grayscale on the image plane, covering an area from the ground to a height of about 60 km from the surface. The uneven distribution of background grayscale caused by it increases first and then decreases with the increase of ground distance, making it difficult to describe it with a simple plane. If threshold segmentation and centroid extraction are directly performed on the star map, low signal-to-noise ratio star points in the lower region of the star map are prone to missed detection, while a large number of false alarms will appear in the upper region, making it difficult to accurately complete the centroid extraction task.
The star map was preprocessed using the algorithm proposed in this article, and the results obtained are shown in Figure 9.
By analyzing the pre processed star map, it can be seen that the algorithm proposed in this paper can effectively remove the background grayscale caused by the atmospheric light. To verify the performance of the algorithm, the maximum background estimation method based on the plane model and the morphological filtering method based on the improved Top Hat transform were selected to preprocess the star map with the algorithm proposed in this paper. Taking the star point on the far left side of the star map that is heavily affected by the Earth’s atmosphere as an example, the standard star map, the star map under the influence of the Earth’s atmosphere, and the pre processed local star map are shown in Figure 10.
By comparing the standard star map with the preprocessed local star map, it can be seen that the maximum background estimation method can maintain the grayscale distribution characteristics of the star points after preprocessing. However, due to the algorithm modeling the grayscale of the stray light background as an isosurface, which does not match the actual distribution pattern of the earth’s atmospheric light, the algorithm can only estimate and compensate for the evenly distributed parts of the earth’s atmospheric light background, and the removal effect of the earth’s atmospheric light background is not good; The morphological filtering method based on the improved Top Hat transform can effectively remove the background in the star map. However, due to the influence of ground light, the star points are submerged in the background, and the morphological relationship between them and the background is not obvious. This algorithm treats the edge part of the star points as the background gray level to remove, severely damaging the distribution characteristics of the star point gray level; The algorithm in this article can effectively protect the grayscale distribution characteristics of star points by designing filtering templates to avoid them. In addition, the algorithm in this article adopts a more accurate background model that conforms to the variation pattern of background grayscale, thus effectively removing the non-uniform background grayscale caused by atmospheric light.
To further analyze the performance of each algorithm, the background average gray level, single star signal-to-noise ratio, signal-to-noise ratio improvement factor, and centroid extraction accuracy before and after star image preprocessing were compared, as shown in Table 1.
From Table 1, it can be seen that the pre processed star map using the maximum background estimation method has a relatively high background gray level, which leads to insufficient removal of the earth atmosphere background. The residual earth atmosphere background gray level in the star map will affect the accuracy of centroid extraction, resulting in low extraction accuracy; After preprocessing with morphological filtering, the signal-to-noise ratio of star images is low, and the grayscale distribution characteristics of star points are destroyed, resulting in low success rate and extraction accuracy of centroid extraction; The algorithm proposed in this paper can accurately remove non-uniform background grayscale while preserving star features, significantly improving the signal-to-noise ratio of star images, and can improve the centroid extraction accuracy by about 40% compared to the maximum background estimation method, with good preprocessing effects.
Further experiments were conducted on observing stars under the influence of Earth’s atmospheric light, and real-life star maps were obtained under the influence of Earth’s atmospheric light. Using the maximum background estimation method based on the planar model and the morphological filtering method based on the improved Top Hat transform, the star map was preprocessed using the algorithm proposed in this paper. A typical star map was used as an example for comparison, as shown in Figure 11.
As shown in Figure 11 (a), in the actual star map, in addition to the background grayscale caused by atmospheric light, it may also be affected by other interference sources such as clouds and space debris, forming local highlight areas in the star map. In the locally highlighted area, the background grayscale changes sharply, making it difficult to describe its change pattern with a simple planar model. Therefore, the maximum background estimation method based on the planar model has poor removal effect on the background grayscale in the actual star map, retaining the highlighted parts in the background, which leads to misrecognition; The morphological filtering method severely damages the energy distribution of star points, resulting in the failure of star point extraction; The algorithm designed in this article is based on a cubic surface model to estimate the background of a star image. For bright areas with drastic changes in background grayscale, the established cubic surface model can still accurately reflect the distribution of background grayscale in local areas. By fitting the parameters of the surface model, the background grayscale can be effectively estimated and compensated, solving the problem of mistakenly identifying stray light backgrounds as stars, Has strong anti-interference ability and a wide range of applications.
Using the above three algorithms to preprocess 20 actual star maps, the star detection rate, star misdetection rate, and signal-to-noise ratio improvement factor obtained are shown in Table 2.
By analyzing the preprocessing results, it can be seen that the algorithm proposed in this paper can more effectively improve the signal-to-noise ratio of star maps, thereby improving the star detection rate. In addition, this algorithm also has a good removal effect on complex backgrounds, reducing the false stars caused by the background, reducing the false detection rate of star points, and having strong anti-interference ability.
To eliminate the influence of terrestrial light on star maps, this paper proposes a star map preprocessing algorithm based on the background grayscale model of terrestrial light. By analyzing the propagation mechanism of ground-air light, an accurate model of ground-air light radiation intensity was constructed, and the relationship between the radiation intensity of ground-air light and the scattering angle and scattering path length was revealed. Based on this, a local range grayscale model of the ground air light background is constructed for estimation and compensation of the ground air light background. The background grayscale model used in the algorithm in this article can accurately reflect the complex distribution pattern of the ground air light background. By fitting the parameters in the model, accurate estimation and compensation of the complex scattered light background can be achieved. In addition, for the stray light caused by other interference sources, the established background model can still accurately describe its variation pattern in local areas, and can accurately estimate and compensate for it. It has strong anti-interference ability and can effectively eliminate the influence of ground gas light on the star map, ensuring the accuracy of star image point centroid positioning under ground gas light interference.
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