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Real-Time On-Orbit Calibration of Angles Between Star Sensor and Earth Observation Camera for Optical Surveying and Mapping Satellites

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Real-Time On-Orbit Calibration of Angles Between Star Sensor and Earth Observation Camera for Optical Surveying and Mapping Satellites ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume IV-2/W5, 2019 ISPRS Geospatial Week 2019, 10–14 June 2019, Enschede, The Netherlands REAL-TIME ON-ORBIT CALIBRATION OF ANGLES BETWEEN STAR SENSOR AND EARTH OBSERVATION CAMERA FOR OPTICAL SURVEYING AND MAPPING SATELLITES Wei Liu 1*, Hui Wang 2, Weijiao Jiang 2, Fangming Qian 3, Leiming Zhu 4 1 Xi’an Research Institute of Surveying and Mapping, No.1 Middle Yanta Road, Xi’an, China - [email protected] 2 State Key Laboratory of Integrated Service Network, Xidian University, Xi’an, China - [email protected] 2 State Key Laboratory of Integrated Service Network, Xidian University, Xi’an, China - [email protected] 3 Information Engineering University, Zhengzhou, China - [email protected] 4 Centre of TH-Satellite of China, Beijing, China - [email protected] Commission I, WG I/4 KEY WORDS: Star Sensor, Attitude Measurement, Error Analysis, On-Orbit Calibration, Angle between Cameras, On-orbit Monitoring Device ABSTRACT: On space remote sensing stereo mapping field, the angle variation between the star sensor’s optical axis and the earth observation camera’s optical axis on-orbit affects the positioning accuracy, when optical mapping is without ground control points (GCPs). This work analyses the formation factors and elimination methods for both the star sensor’s error and the angles error between the star sensor’s optical axis and the earth observation camera’s optical axis. Based on that, to improve the low attitude stability and long calibration time necessary of current satellite cameras, a method is then proposed for real-time on-orbit calibration of the angles between star sensor’s optical axis and the earth observation camera’s optical axis based on the principle of auto-collimation. This method is experimentally verified to realize real-time on-orbit autonomous calibration of the angles between the star sensor’s optical axis and the earth observation camera’s optical axis. 1. INTRODUCTION high-precision real-time calibration method for the angles between the star sensor’s optical axis and the earth observation Exterior orientation elements are a key factor influencing the camera’s optical axis is needed. positioning accuracy, when performing satellite photogrammetry Therefore, this paper presents a real-time calibration method of without ground control points (GCPs) (Wang, 2004). Exterior the angles between the star sensor’s optical axis and the earth orientation elements are commonly determined by converting the observation camera’s optical axis. The method can be realized on star sensor’s measured attitude, using the angle conversion the optical mapping satellite on-orbit by installing an optical relationship between the star sensor’s optical axis and the earth autocollimator inside the star sensor and earth observation observation camera’s optical axis. However, the accuracy of the camera optical systems. The change of the main optical axis of exterior orientation elements is affected by systematic or random each camera can be reflected by the change of the spot image errors in both the star sensor and the angles between the star position, using the original optical path of the camera. sensor’s optical axis and the earth observation camera’s optical Subsequently, we calculate the angular variation between the star axis contain, caused by various on-orbit factors, such as pressure, sensor’s optical axis and the earth observation camera’s optical vibration and temperature. Based on previous research results axis, allowing for real-time calibration on the satellite. and a large amount of measured data we’ve accumulated in the long-term, the paper analyses the measurement error and on-orbit 2. ATTITUDE MEASUREMENT PRINCIPLE calibration results of the star sensor, and finds that the thermo elastic error is the main factor to cause the angle variation 2.1 Attitude Measurement Principle of Star Sensor between the star sensor’s optical axis and the earth observation camera’s optical axis, which limits the positioning accuracy. The star sensor is a high-precision space attitude measuring Currently, two methods are used to address the angles error. In device used to determine the three-axis attitude of a satellite, one, the structure is optimized and the heat-resistant material is which uses stars as reference objects. The instantaneous pointing used during load development (Blarre et al., 2006). However, due of the star sensor in the inertial coordinate system is calculated to factors such as temperature control level and technological using a photographed stellar image. Then, the exterior orientation level, this method has only offered a limited improvement on elements of the earth observation camera are calculated positioning accuracy. In the other, a photographic calibration according to the angles between the star sensor’s optical axis and method based on the ground calibration field is used after the the earth observation camera’s optical axis. The working satellite is on-orbit (Radhadevi et al., 2011), (Chen et al., 2015). principle of the star sensor can be divided into star extraction However, the calibration period of the existing calibration (Delabie, Schutter and Vandenbussche, 2014), star identification method will not be able to meet the needs of future high-precision (Padgett, Kreutz-Delgado and Udomkesmalee, 2012), and surveying and mapping capabilities. Therefore, an efficient and * Corresponding author This contribution has been peer-reviewed. The double-blind peer-review was conducted on the basis of the full paper. https://doi.org/10.5194/isprs-annals-IV-2-W5-583-2019 | © Authors 2019. CC BY 4.0 License. 583 ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume IV-2/W5, 2019 ISPRS Geospatial Week 2019, 10–14 June 2019, Enschede, The Netherlands attitude calculation (Psiaki and Mark, 2000), as shown in Figure 1. cos 0− sin 1 0 0 cos sin 0 M t = 0 1 0 0 cos sin − sin cos 0 s sin 0 cos 0− sin cos 0 0 1 Guide star database cos cos− sin sin sin cos sin+ sin sin cos− sin cos =− cos sin cos cos sin Star sensor sin cos + cos sin sin sin sin− cos sin cos cos cos Stellar Star Star attitude image extraction identification calculation (2) Star sensor Then: Figure 1. Working principle of star sensor AAA11 12 13 The attitude parameters of the satellite have various expressions, −1 (3) MMMAAAg== g t such as direction cosine, Euler angles (attitude angles), and t s() s 21 22 23 quaternion. Quaternion is always used to avoid singularity in the AAA31 32 33 attitude calculation. However, as the attitude angles are more intuitive and easier to understand, it is commonly used to give Where M g = transformation matrix of the star sensor’s research indicators and rules. The conversion relationship of the s coordinate system in the inertial coordinate system calculated by attitude quaternion q0, q1, q2, q3 (q0 is a scalar) to the attitude the star sensor’s attitude (rotating around Z-axis, angles , and (roll, pitch, and yaw) (rotating around Z-axis, ()s,, s s then X-axis, at last Y-axis) is: then X-axis, at last Y-axis) g = transformation matrix of the earth observation M t −1 2()q1 q 3− q 0 q 2 camera’s coordinate system in the inertial coordinate system tan 22 calculated by the earth observation camera’s attitude 12−+()qq03 (1) −1 (rotating around Z-axis, then X-axis, at last Y-axis) = sin 2 q q+ q q ()t,, t t ()2 3 0 1 = the elements of the i-th row and the j-th column of 2()q q− q q Aij tan−1 1 2 0 3 12−+qq22 ()02 the matrix Therefore, the exterior orientation elements of the 2.2 Calculation of the exterior orientation elements of the earth observation camera can be calculated as: earth observation camera A The star sensor measures the attitude of the star sensor’s -arctan(13 ) coordinate system relative to the inertial coordinate system. Here, A t 33 (4) the angles between the star sensor’s optical axis and the earth t = arcsin(A23 ) observation camera’s optical axis is used to establish a A relationship between the star sensor’s coordinate system and the t -arctan(21 ) A earth observation camera’s coordination system to then calculate 22 the attitude of the earth observation camera relative to the inertial coordinate system. 3. ANALYSIS OF THE ANGLES ERROR BETWEEN THE STAR SENSOR’S OPTICAL AXIS AND THE EARTH OBSERVATION CAMERA’S OPTICAL AXIS The stable star sensor data of the TH-1 02 satellite (Wang and HU, 2012) and calibration result of angles between the star sensor’s optical axis and the earth observation camera’s optical axis based on the ground calibration field was selected for statistical analysis. 3.1 Error Statistics of Star Sensor Measurement The single-star sensor attitude difference method (WANG and LI, 2012), (LI and LI, 2012) was performed on fourteen randomly selected data sets of star sensor A and B in the period of 2012- 2016. The resulting standard deviation and total error curve is shown in Table 1 and Figure 3, respectively. The actual on-orbit measurement error of the star sensor was Figure 2. Angles between the star sensor’s optical axis and the between 4.83″ and 9.02″ (X/Y axis overall), higher than the earth observation camera’s optical axis nominal value of 5″, basically. This was likely caused because Figure 2 shows the angles between the star sensor’s optical axis the star sensor is also subject to error factors other than the and the earth observation camera’s optical axis. The nominal error when running on orbit. We will discuss the error transformation matrix of the star sensor’s coordinate system in factors in section 3.3.
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