Predicting the Expected Amount of Observable Space Debris with an SSA Capable Star Tracker

The Earth's space environment is becoming increasingly congested. To aid in the effort of space situational awareness (SSA), a comprehensive sensor network is required to accurately map the spatial distribution of resident space objects (RSOs). Star trackers, typically used for optical attitude determination, are ideal candidates for dual-use as opportunistic SSA sensors due to their inherent capabilities. A fast and reliable methodology to estimate the amount of debris an optical sensor can detect is crucial. However, the vastness and variability of the space environment complicate this task. Given the scale and diversity of space-based objects, simulations are often employed but are computationally intensive and limited in scope, with a strong stochastic component. This paper presents a novel method for reliably predicting the expected RSO signal detectable within the field of view of a generalized optical sensor. By leveraging the governing radiometric equations and key geometrical constraints, individual particles are modeled to determine the photoelectron flux on the sensor's detector plane. These particles, weighted by their spatial density, are integrated over the conical volume defined by the sensor field of view. Using importance-sampled Monte Carlo integration, this method achieves comprehensive and accurate representations of the debris environment with relatively few samples. Additionally, a reliable estimate is formed for the precision of this approach. This customizable algorithm offers valuable insights during the preliminary design of new missions and serves as a robust tool for cross-validation of real-world data. Its features are demonstrated for both a space-based and ground-based scenario.