Star Map Preprocessing for Star Sensors

After shooting the star map of Star Sensors, the primary task is to extract and determine the centroid of the star map, in order to identify the star map and determine the attitude of the star sensor’s line of sight. In order to minimize the influence of factors such as star map distortion and atmospheric disturbances, the centroid method was used to extract the centroid of stars in the center area of the actual star map. The output of the centroid calculation results was achieved through programming, which is used as input for star map recognition and attitude determination software.

Due to the influence of factors such as Earth rotation, atmospheric disturbances, and map distortion in the actual star map, this will inevitably affect the accuracy of determining the center of mass of the observed star. In addition, the errors in the center of mass calculation algorithm itself will ultimately affect the accuracy of attitude calculation. In order to separately estimate the accuracy of the attitude calculation algorithm, it is necessary to conduct star map simulation. Therefore, based on the Kenneth Daniel Diaz camera simulator, an ideal star camera model was constructed, and the catalog stars were transformed from the celestial coordinate system to the image plane coordinate system through coordinate translation and conversion. Star map simulation was conducted for simulating star map recognition, attitude determination algorithm accuracy analysis, and analysis of factors affecting attitude determination accuracy.

1. Workflow for centroid determination

The process of determining the centroid of a star map is divided into two parts: first, traverse the entire star map to determine the threshold of the star map; Traverse the star map again, search for pixels within a certain threshold range that meet the conditions of the candidate region. After searching for the candidate region, calculate the noise reference value of the candidate region, perform denoising processing, and then calculate the light intensity center of the candidate region. Extract the centroid of the star and determine the centroid of the sub pixel of the star based on the centroid equivalent.

The specific information flow is shown in Figure 4.2.

After obtaining the star map, the first thing to do is to extract the observed stars from the image data, that is, to extract the centroid of the stars

Under initial conditions, as long as the pixel values of the coordinate points (xi, yi) on the COMS/CCD detector of the camera are within the range of [ValMax ValMin], the point is considered the center of the candidate region, with each region having a size of 5 × 5 pixels. The principle for selecting the threshold is to conduct statistical analysis on the entire star map, in order to determine the upper threshold limit ValMax and lower threshold limit ValMin of the star map.

In order to determine the center of light intensity (xc, yc), the first step is to determine the noise reference value, which will be used as the offset of the observed star signal. The noise reference value can be achieved by calculating the average value of the B region. So when determining the center of the observation star, the first step is to use the above method for denoising.

Once the observation star extraction is successful, the next step is to determine the center of each star. The general method is to calculate the centroid equivalent to determine the “center of light intensity”, and use the light intensity level as the “distribution quality”. Due to the highly close relationship between optical systems, detectors, and centroid determination, the selection of centroid determination algorithms and hardware components is closely related.

In order to accurately determine the position of stars on the detector, it is crucial to understand the shape of the image of stars on the detector. For an optical system, the position and direction of the detector relative to the focal plane are different, and the images of stars on the detector are also different. Due to the fact that a star can be regarded as a point light source, its image on the detector conforms to the PSF function of the optical system. For different optical devices, their PSF varies due to their physical characteristics and refractive methods.

The sensitivity of a pixel is a function of its internal position, the shape of a single pixel’s photosensitive area, and wavelength. After knowing that the coordinates of the center of light intensity on the detector are a function of the actual center of the observed star, the center of mass of the observed star can be determined by the detected center of light intensity. The reason for the difference in accuracy in determining xc and yc for observing the center of mass of a star is the non-uniformity of star imaging, which depends on the optical system and the imaging position of the star on the detector. In order to obtain the sub pixel level coordinates of the center position of a star, an optical system defocusing technique is used to spread the star image to several pixels.

When using ordinary civilian optical lenses, the assumption of Gaussian light intensity distribution is only satisfied when observing stars in the direction of the line of sight. In order to minimize factors such as star map distortion, atmospheric refraction, and disturbances that are detrimental to the determination of the camera’s optical system’s axis of view attitude, only the centroid of the central area of the image is determined.

After processing a series of star maps, the results showed that the algorithm sometimes causes “loss” of stars, especially when multiple pixels at the center of the star reach saturation (such as the brightest star in the image, which has been proven to be a very bright planet – Jupiter), but hardly introduces “pseudo stars”. This is better than being able to detect all stars but introducing ‘pseudo stars’. The reason is that as long as there are 5 correctly identified stars, a 98% recognition reliability can be achieved, and the introduction of “pseudo stars” will lead to a high false recognition rate.

2. Star Map Simulation

For actual star maps, the centroid errors of observed stars caused by factors such as atmospheric refraction, star map distortion, errors in the centroid determination algorithm itself, and Earth rotation will ultimately affect the accuracy of attitude calculation as input errors. In order to estimate the accuracy of attitude calculation algorithms, star map simulation is necessary. According to the needs of this study, an ideal star camera simulation suitable for this study was conducted based on the camera simulator described in the literature. The coordinate transformations involved were analyzed in detail, and the coordinate transformations used in the star camera simulator were shown in detail, and the corresponding attitude transformation matrix was derived; Improvements have been made to the accuracy of the centroid position, extending the accuracy of the navigation star’s centroid position in the image plane to sub pixels instead of rounding to integer pixels; And adaptive modifications have been made to the coordinate axis definition of the image plane based on the actual situation of CCD cameras.

The configuration parameters of the star camera simulator mainly include: CCD size 1024 pixels × 1024 pixels, field of view 15 ° ×  15 °, magnitude threshold taken as 6.5. The epoch time is the epoch of the Hipparcos catalog, which is J1991.25.

After determining the stars in the field of view, the next step is to project them onto the image plane. The origin of ECI coordinates is at the center of the Earth, while the origin of the satellite camera coordinate system is at the center of the optical system of the satellite camera (i.e. the center of the image plane). The two coordinate systems have different origins. Therefore, the transformation from ECI to the image plane requires the use of coordinate translation and rotation around the coordinate axis. Due to the fact that stars are very far away from Earth, the transformation from ECI to the camera coordinate system can ignore the errors introduced by coordinate translation for star orientation, so only coordinate rotation transformation needs to be considered.

The main process of star map simulation is: a random line of sight generator provides random line of sight direction (right ascension, right latitude and rotation angle of line of sight) of the star camera simulator, and then calls the CreatTestFOV module to generate a simulated star map data. This cycle is 1000 times to generate a simulated star map determined by 1000 onboard line of sight.

The main process of star map simulation is shown in Figure 4.13.

The function of the CreatTestFOV module is to extract all navigation stars located at the center of the visual axis and capable of falling within the imaging plane from the navigation star catalog based on the size of the field of view and focal length, thereby generating a simulated star map. Due to the high accuracy of the centroid determination of bright stars in the actual star map, the “observed stars” in the simulated star map are also sorted in ascending order of their magnitude, with bright stars ranking first.

The output of the star camera simulator includes the navigation star number of the star in the field of view, the coordinates of the image plane, and the parameters that generate the simulated star map (the right ascension and right ascension of the random axis of view, as well as the rotation angle of the axis of view). As shown in Table 4.2, it will serve as input data for simulating star map recognition and attitude calculation accuracy analysis.