The calibration of star sensors is a prerequisite for high-precision attitude information output, including laboratory calibration and in orbit calibration. Laboratory calibration uses cooperative objectives and based on object image transformation relationships to calibrate the internal and external orientation elements of the star sensor. The internal orientation elements include focal length, main point, and distortion, while the external orientation elements include installation matrix. Due to the higher calibration accuracy requirements of star sensors compared to general cameras, two-dimensional differentiation plates will not be used as the calibration reference, and instead, turntables and light tubes are used to simulate light or theodolites. The mechanical impact of the aircraft launch process and changes in the in orbit photothermal environment will inevitably have a serious impact on the calibrated star sensors, resulting in a certain deviation from the laboratory calibration results. When the internal and external orientation elements of the star sensor have deviated from the laboratory calibration values, further in orbit compensation is needed to prevent the accuracy of the star sensor’s attitude determination from decreasing. Therefore, in orbit calibration is crucial for high-precision star sensors.
At present, there are two methods for in orbit calibration of star sensors: attitude dependent and attitude independent. The in orbit calibration method based on attitude correlation requires the attitude information of the star sensor, which comes from stars, inertial gyroscopes, or landmarks. The attitude measurement error is coupled with the orientation element error inside the star sensor, inevitably affecting the calibration parameters of the star sensor. The attitude independent in orbit calibration method only utilizes the constant angular distance between the object and image light rays of the star sensor, and does not rely on the attitude information of the star sensor, reducing complex attitude calculation and avoiding coupling between attitude measurement errors and orientation element errors within the star sensor.
The method based on attitude independence is divided into batch processing algorithm and sequential processing algorithm according to the input data method. The former requires storing the image plane coordinates of multiple star frames and corresponding celestial coordinate information, and the information used is comprehensive and not prone to parameter overfitting. The latter adopts the extended Kalman filtering algorithm, which only uses one frame of star sensitive data information to update the star sensor parameters at a time, and has low data storage requirements. However, the sequential processing algorithm is sensitive to the setting of filtering parameters and is prone to overfitting.
Another partitioning method based on attitude independence is based on distortion models, including zero order distortion compensation models and high order distortion compensation models. The zero order distortion model is commonly used in early in orbit calibration models, which only calibrate the main point and focal length. In the unit pointing expression of the navigation star in the star sensor coordinate system, due to the symmetry between the main point and coordinates, its numerical estimation of the main point is not the optical main point, but rather the compensation for the zero order distortion of the star sensor. The zero order distortion model does not consider higher-order distortion and is generally only used as a model for estimating the initial values of the orientation elements within the star sensor. A large amount of research now focuses on high-order model compensation for star sensors, including using theoretical distortion models or smooth functions to compensate for the coordinates of star image points on the image plane to compensate for the deviation of image light rays. In the traditional model of distortion calibration independent of the attitude of star sensors, the high-order distortion coefficients in the direction of 𝑌 and 𝑌 on the image plane will have serious mutual effects, requiring a large amount of training data to obtain stable high-order distortion coefficients, posing a great challenge to the limited computing resources and storage space of in orbit star sensors.
On the one hand, due to the reasons of optical machining and assembly, the actual distortion will deviate from the theoretical distortion formula, causing the theoretical distortion model to be unsuitable. According to Taylor’s theorem, polynomials can represent any complex smooth surface. On the other hand, research has found that in traditional high-order distortion calibration models, compensation terms for focal length can be generated by merging high-order distortion coefficients to eliminate the mutual influence of high-order distortion coefficients and achieve more stable high-order distortion compensation effects. Therefore, this article proposes to use focal length polynomials to compensate for higher-order distortion, while coordinate constants compensate for zero-order distortion. In order to prevent overfitting or underfitting of calibration parameters, a cross validation regression method was proposed to determine the order of the focal length polynomial. Simulation experiments and analysis show that the algorithm introduced in this article can achieve better calibration results compared to traditional attitude independent in orbit calibration algorithms.
The main purpose of in orbit calibration methods that are independent of the attitude of star sensors is to reduce inter star angular distance errors, which is consistent with the need for star sensors to use angular distance as recognition features. The undistorted coordinates of star image points on the image plane are not the main focus of this type of calibration method, which is very different from general camera calibration methods.
The traditional attitude independent in orbit calibration algorithm for star sensors has certain problems. When the star sensor is in orbit, the system error of the main point will become a part of the attitude measurement system error of the star sensor. After the star sensor is installed in the aircraft, additional attitude information is needed to assist in correction.
Send us a message,we will answer your email shortly!
TY-Space Technology (Beijing) Ltd. is professional focusing on advanced attitude optical sensors, especially Star Trackers for space industry.
