In order to calibrate the star sensors installation matrix of GRACE-FO satellite in orbit, this paper realizes the calibration of star sensor from two aspects, relative installation matrix calibration and absolute installation matrix calibr ation of SCA/ACC. By counting the quaternion observations between star sensors since launch, the relative installation matrix deviation between star sensors is estimated. The relative installation matrix deviation is applied to the calculation of interboresight angles of star sensors and the fusion attitude, which shows that the relative installation matrix estimation algori thm adopted in this paper is correct. Using the pitch and yaw maneuvering signals of the satellite during KBR antenna phase center calibration, the angular acceleration calculated by the star sensors are taken as the observed value and the angular accelera tion of the accelerometer is taken as the reference value. The absolute installation matrix deviation of the SCA/ACC is estimated based on the least square algorithm, and the non-orthogonal factor between the accelerometer axis is considered in the estimation. The absolute deviation of the installation matrix of the SCA/ACC is 0.07, 0.19 and -0.07 degrees in the three directions of roll, pitch and yaw, respectively, and the estimated accuracy is 0.01, 0.04 and 0.04 degrees. At the same time,there is a strong coupling property between the deviation of the SCA/ACC installation matrix and the axis non-orthogonal factor of the accelerometer, and the coupling effect can be avoided by estimating two parameters at the same time.
The static star simulator belongs to the calibration type star simulator, which provides relatively static star point images. It mainly consists of a control circuit, a light source, a star point reticle, a filter, and a collimating optical system, as shown in Figure 1
Figure 1 Schematic diagram of the composition of the static star simulator
Place a star point dividing plate with several small holes on the focal plane of the collimating optical system, and the light source corrects the spectrum to illuminate the star point dividing plate through a filter. After being imaged by the collimating optical system to simulate the position of the star at infinity, a complete star map is formed at the entrance pupil of the star sensor. The simulation of magnitude is achieved by adjusting the brightness of the light source through a control circuit.
Determine the design indicators of the static star simulator based on the usage requirements of the star sensor to be tested, as shown in Table 1.
Table 1 Optical System Design Indicators
The collimating optical system is an important component of the static star simulator, which directly affects the simulation accuracy of the star map. Therefore, the designed optical system must have high imaging quality. In order to ensure that the outgoing light flux of the star simulator is equal to the incoming light flux of the star sensor, the outgoing pupil of the collimating optical system should coincide with the incoming pupil of the star sensor, which conforms to the principle of pupil connection. Due to the high accuracy requirements for star point position simulation in star simulators, the optical system should have high imaging position accuracy. The main factor affecting imaging position accuracy is system distortion, so the relative distortion of the system should be strictly controlled; At the same time, considering that the star map reading method of the star sensor is to capture the energy center of each star point, it is also important to focus on controlling the deviation between the energy center of the optical system and the main light.
This article adopts a transmission design. The transmission system has a simple structure, low light energy loss, and is easy to install and adjust. The optimized optical system has good image quality, and the optical path is shown in Figure 2.
Figure 2 Optical System Optical Path Diagram
(1) Optical Transfer Function (MTF)
The modulation transfer function is the most comprehensive evaluation index in image quality evaluation, which can intuitively reflect the excellence of optical systems.
(2) Distortion
Distortion has no impact on the imaging clarity of the optical system, but it directly affects the positional accuracy of the star points. Therefore, eliminating system distortion is the focus of design.
(3) Point plot
In practical design of optical systems, scattered patterns are formed due to aberrations and lack of concentration in imaging, known as point plots, which can reflect the energy distribution of the system.
(4) Wavefront aberration
According to the Rayleigh criterion, the maximum wave aberration does not exceed λ/ At 4 o’clock, the system can be considered flawless.
This article estimates the relative installation matrix of star sensors based on the SCA1A data of three in orbit star sensors of GRACE-FO satellite since its launch, and obtains the QSA corrected by the relative installation matrix. By calculating the angle between the main optical axes of the star sensors and comparing it with the angle obtained from the in orbit star sensor observation data, the difference between the main optical axes of the star sensors after using the corrected QSA approaches 0, verifying the accuracy of the relative installation matrix calibration algorithm used in this paper; By performing star sensitive fusion pose determination, the jump in pose determination results after updating the relative installation matrix is effectively eliminated, indicating that the relative installation matrix calibration algorithm proposed in this paper can be applied to update the installation matrix before pose determination. The absolute installation matrix calibration algorithm for star sensors/accelerometers based on simultaneous estimation of non orthogonal factors between ACC axes can effectively absorb the influence of non orthogonal factors between ACC axes on the estimated parameters, and obtain more reasonable calibration values for the absolute installation matrix of star sensors/accelerometers. Based on the KBR calibration maneuver signal, the absolute deviation of the star sensor/accelerometer installation matrix obtained in the roll, pitch, and yaw directions is 0.07 degrees, 0.19 degrees, and -0.07 degrees, respectively, with estimated accuracy of 0.01 degrees, 0.04 degrees, and 0.04 degrees. The impact of this absolute installation matrix on the inversion of time-varying gravity fields is worth further in-depth research.
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