In order to realize the error analysis and functional testing of star tracker on the ground，a dynamic simulation algorithm for star map based on improved celestial sphere was proposed． This algorithm can complete simulation of star map in － orbit whenever the aircraft launched and at any attitude． A new method of space district dividing was also presented in order to improve the traditional method of space district divided by ascension and declination，and fully considered declination arc length was gradually shortened with latitude increasing． It can avoid leakage of the navigation star selection，and also can improve the efficiency of searching． Mathematical model of star spot was analyzed，and it can make the simulation image more realistic． In addition，mop － up phenomenon of dynamical star image was simulated，which can well simulate the actual work case of star tracker in － orbit with high dynamic．
Star sensor is a high-precision attitude sensor that uses stars as reference objects to assist the attitude control system in determining the spacecraft’s attitude. For error calibration and functional testing of star sensors, ground testing can only be used for star sensor detection. One is the field observation test on the ground, which means conducting field observation tests in a real ground environment with relatively good atmospheric environment and relatively weak stray light. This method is greatly affected by the weather and cannot simulate the on-orbit state of the star sensor. The second is indoor dynamic star simulator testing, which simulates the sky star map on the ground and can form a closed-loop testing system with the tested star sensor.
Through star map simulation, star simulators can achieve testing of star sensor star point extraction, star map recognition, attitude calculation, and other functions. However, how to achieve dynamic star map simulation, improve the frequency of star map updates, meet the real-time requirements of star sensor detection, and how to avoid navigation star selection issues caused by traditional retrieval methods are the difficulties and keys in design. In response to the above issues, this article proposes to use an orbit generator to provide real-time attitude information to calculate the axis of view direction, achieving dynamic simulation of star maps. At the same time, fully considering the situation where the arc length of the right ascension on the celestial sphere gradually decreases with the increase of latitude, a new celestial sphere partition retrieval algorithm is proposed to address the phenomenon of missing navigation stars caused by traditional partition retrieval algorithms based on right ascension and right ascension. This solves the problem of missing navigation stars and increases the update frequency of star maps, which increases with the decrease of the field of view of the star simulator, with an update frequency of milliseconds, It can meet the real-time requirements of dynamic simulation. In addition, simulations were conducted on the tail sweeping phenomenon caused by high dynamics in the star pattern.
The basic working principle of a dynamic star simulator is: the star simulator controls the computer to calculate the field of view direction of the optical axis of the star sensor on the missile body based on the launch point information and the real-time orbit and attitude parameters provided by the orbit simulation computer, and extracts the navigation star map within the field of view of the star sensor at that time. The implementation of dynamic simulation and the rapid search of navigation stars are the difficulties and key points in the design of star simulators. Star simulators mainly provide simulated star maps for testing and calibration of star sensors under laboratory conditions. Firstly, set the missile launch time, launch point information, and missile body attitude. Then, the direction of the line of sight is determined through coordinate transformation, and the navigation star library is searched based on the direction of the line of sight. The precise coordinates of the navigation star in the image plane are obtained through coordinate transformation of the navigation star in the field of view. Finally, transform the magnitude into the corresponding image grayscale. The schematic diagram of the software algorithm is shown in Figure 1.
According to the algorithm principle in Figure 1, it can be seen that the simulation process of the star simulator algorithm is mainly divided into the following parts: calculating the direction of the line of sight, searching the navigation star library in zones, and displaying the star map.
The SKYMAP standard star library used in this article records a total of 299485 stars with brightness less than 10 magnitudes. After processing the SKY2000 catalog, a magnitude of 2-5 was left behind A total of 1432 navigation stars from 7 constitute the navigation star library.
(1) Calculate the orientation of the visual axis
In the literature “Research on the Algorithm of the All Sky Ground Dynamic Star Simulator”, the direction of the line of sight is directly given. However, in order to be more in line with the actual situation, the direction of the line of sight should be determined based on the flight attitude of the aircraft in orbit. The specific solution process is shown in Figure 2.
From Figure 2, it can be seen that in the process of obtaining information such as launch time, launch point information, and missile attitude, and solving the direction of the line of sight, the most important thing is to obtain the transfer matrix Cic from the launch inertia coordinate system to the equatorial Cartesian coordinate system, Cib from the launch inertia coordinate system to the missile body coordinate system, and Cbs from the missile body coordinate system to the star sensor coordinate system.
(2) Partition search navigation star library
To improve the search speed of navigation stars, the celestial sphere can be divided into regions. The literature proposes a method of evenly dividing the right ascension and right ascension zones, requiring each search 9 sub regions, but this method has the problem of missing navigation stars. The literature “Design and Implementation of Dynamic Star Map Display Algorithm” proposes a non-uniform partitioning method to solve this problem. The declination is at (-60 °, 60 °), and the declination is uniformly partitioned. The declination is at (-90 °, -60 °) and (60 °, 90 °), and global search is used, but to some extent, the search efficiency is reduced. So this article proposes a new partitioning method. Similar to the latitude coil, imagine that there are many circles in the east-west direction of the celestial sphere, defined as a meridian like coil. Similar to declination, the degree corresponding to a warp like coil can be defined as declination like, as shown in Figure 5.
After the axis of view is determined, a maximum of 9 sub regions need to be searched to determine the star map within the field of view. When the axis of view points to certain regions, only 7 or 8 sub regions need to be searched. If both declination and declination are equally divided by 10 degrees, the entire celestial sphere is divided into a total of 18 degrees × 18=324 sub intervals, so the retrieval efficiency is greater than or equal to 9/324=1/36, which is much better than the 1/12 of global retrieval. And this algorithm will improve its retrieval efficiency as the field of view shrinks, assuming that the field of view of the star simulator is 12 ° × 12 °, then in this algorithm, both declination and declination will be equally divided by 6 °, and the entire celestial sphere will be divided into a total of 30 × 30=900 sub intervals, with a retrieval efficiency greater than or equal to 9/900=1/100, which is higher than the 1/80 in the literature.
In summary, using the algorithm proposed in this article greatly improves the update rate of the star map, meets the real-time requirements of dynamic simulation, and also solves the problem of missed selection of navigation stars.
(3) Star map display
After solving for the direction of the line of view and retrieving the navigation stars within the field of view based on this partition, it is necessary to map the navigation star to the CCD image plane coordinate system, transform the magnitude into the corresponding gray value, and establish a mathematical model of the star spot. The imaging system convolves the brightness distribution of star targets multiple times, and using Gaussian point spread function to simulate the light intensity distribution of star images has good authenticity. The magnitude range is a floating-point number between -1 and 11, but the magnitude of the navigation star used in this simulator is between 2 and 5 Between 7, therefore, when the magnitude is 2, the corresponding grayscale is 255. By using the linear magnitude simulation method and substituting it into the formula transformation, the required star point grayscale map can be obtained.
The experimental software platform adopts Microsoft Visual Studio 2008 version, with a field of view size of 20 ° × 20 °, CCD resolution of 512 × 512, pixel size 25 μ M × twenty-five μ M. Based on the algorithm analysis of the star simulator above, the simulation experiment mainly consists of two parts: one is the basic star map simulation, and the other is the simulation of the dynamic tail sweeping phenomenon of stars.
The simulation shows that the algorithm proposed in this article meets the real-time requirements and can avoid the problem of missing navigation stars.
Based on Figure 9, assuming a pitch angle change rate of 0.1 °/s in the aircraft attitude angle and an exposure time of 3.5 seconds, the simulated star map shown in Figure 10 is obtained.
By simulating the motion sweeping phenomenon shown in Figure 10, the phenomenon of “motion blur” can be simulated when there is a sufficiently fast relative motion between the star sensor and the captured star map. Thus, the correctness of the motion compensation algorithm in star sensor star point extraction can be verified.
This article addresses the shortcomings of traditional navigation star retrieval algorithms and proposes a method of partitioning based on quasi declination and declination, which solves the problem of star leakage, improves the update rate of star maps, and meets the real-time requirements of star sensor dynamic testing. Finally, simulation was conducted on the sweeping phenomenon of the star map caused by dynamics. However, the article did not consider the conversion between apparent magnitude and instrumental magnitude, as well as star color simulation. Further research will be conducted on this topic.
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