Centroiding Algorithms Compared for Star Tracker Performance with Gaussian Noise

Autonomous navigation relies on accurately determining a spacecraft’s orientation, and star trackers are crucial components for achieving this, identifying stars to provide positional reference points. Márcio Afonso Arimura Fialho, from the Division of Electrical and Electronics Engineering at Brazil’s National Institute for Space Research (INPE), and colleagues investigate the performance of several algorithms designed to precisely pinpoint the centre of starlight captured by these trackers. The team’s simulations, which incorporate realistic noise and image blurring, demonstrate how lightweight, computationally efficient algorithms can achieve comparable accuracy to more complex methods, offering a pathway to robust and reliable autonomous navigation systems. This research is significant because it provides valuable insights into optimising star tracker performance, potentially reducing the computational burden on spacecraft and enabling more agile and responsive space missions.

Algorithms with low computational costs are crucial for many applications, and these were compared to a shape fitting algorithm based on a method for finding the best fit to a set of data points. These algorithms are also applicable for astrometry and adaptive optics, fields requiring precise measurements of celestial objects. A star tracker represents one of the most accurate attitude sensors used aboard spacecraft, utilising observed stars as references for determining attitude, or spatial orientation. The overall accuracy of a star tracker fundamentally depends on its ability to precisely determine the centroid, or centre, of each star’s image, a process known as centroiding. This research focuses on improving the efficiency and accuracy of centroiding algorithms, which are essential for reliable spacecraft navigation and control

Simulating Star Tracker Image Centroiding Algorithms

The algorithms were evaluated through Monte Carlo simulations, creating synthetic 7×7 pixel images with a single star near the center, using parameters derived from the Brazilian Autonomous Star Tracker (AST-INPE). The star’s image, known as the Point Spread Function (PSF), was modeled as a Gaussian distribution, providing a reasonable approximation for well-focused images. To improve accuracy, the Gaussian PSF was sampled in a 10×10 sub-grid for each synthetic image, and the results summed. The background level and threshold were estimated from the 24 edge pixels of each image, using a 5×5 internal window for centroiding.

The simulations modeled various sources of error, including random noise, read-out noise, and errors in converting light to digital signals. Six centroiding algorithms, labeled ALG-1 to ALG-6, were tested. ALG-1 is based on the Center of Gravity (CoG) algorithm, subtracting a background level and considering only pixels above a threshold, similar to the algorithm currently implemented in AST-INPE. ALG-2 is similar to ALG-1, but considers all pixels without thresholding. ALG-3 is based on the Iteratively Weighted Center of Gravity (IWCoG) algorithm, using a weighting function following a normal distribution at each iteration, with a weighting function width of 0.
ALG-4 is based on Intensity Weighted Centroiding (IWC), raising the corrected pixel intensity to the power of 2. 0. ALG-5 combines the exponent of IWC with the thresholding of ALG-1. ALG-6 is a shape fitting algorithm using the least squares method to fit a Gaussian shape to the star image, sampled in a 4×4 sub-grid.

For each synthetic image, the true centroid position was randomly located within the central pixel. The estimated brightness, computed by each algorithm, was used to calculate the magnitude, which was then compared to the true magnitude to compute errors. Results show a large increase in centroiding and magnitude estimation errors for stars brighter than magnitude 1, due to saturation. For intermediate magnitudes (1. 4 to 4.
ALG-3 performed poorly, similar to ALG-4 and ALG-5. For dim stars (mag 4), ALG-2 performed the worst, followed by ALG-1, with the large increase in magnitude errors for ALG-1 due to thresholding. ALG-6, the shape fitting algorithm, was the most accurate in both centroiding and magnitude estimation, but had the highest computational cost.

Centroiding Algorithms for Spacecraft Star Trackers

The research presents a comprehensive evaluation of six algorithms designed to accurately determine the center of starlight within images, a critical process for star trackers used in spacecraft navigation. These trackers rely on precisely identifying star positions, and the accuracy of this identification is directly linked to the performance of the centroiding algorithm employed. The study focused on algorithms suitable for implementation in a new star tracker currently under development, prioritizing both accuracy and computational efficiency. The simulations generated synthetic images of stars, mimicking the conditions expected from the star tracker’s sensor, including realistic noise and distortions.

These images were then processed by each algorithm to determine how accurately the center of the star could be identified. The results demonstrate that even relatively simple algorithms can achieve high accuracy, with some performing surprisingly well compared to the more complex shape-fitting method. Specifically, the research highlights the importance of weighting pixels appropriately during the centroiding process, with algorithms that consider the intensity of each pixel achieving better results. The iterative weighting approach proved particularly effective. While the shape-fitting algorithm offered a potentially more precise solution, its computational demands are significantly higher, making it less practical for real-time applications.

The study also carefully modeled various sources of noise that affect star tracker images, including electronic noise from the sensor and variations in light intensity. By incorporating these realistic effects into the simulations, the researchers were able to assess the robustness of each algorithm under challenging conditions. The findings suggest that even with significant noise, the tested algorithms can consistently achieve sub-pixel accuracy, essential for maintaining accurate spacecraft orientation and navigation.

Centroiding Algorithms Compared For Star Tracker Accuracy

The research presents a comparative analysis of six centroiding algorithms designed for a new star tracker. These algorithms, five lightweight options and one shape-fitting method, were tested through numerical simulations incorporating realistic noise and a Gaussian distribution.