A smarter way to track satellites beyond Earth's orbit

Purdue University engineer Keith LeGrand is developing advanced methods to track the location and movement of objects in cislunar space, the region surrounding Earth that extends beyond the moon's orbit. As more satellites and infrastructure venture into this challenging environment, maintaining situational awareness becomes increasingly critical for securing and defending U.S. national and economic interests.

LeGrand's research focuses on characterizing when objects in cislunar space may have altered course and understanding how uncertainty about their positions evolves over time.

The cislunar environment presents unique challenges, such as poor visibility, extreme distances, and the sun–Earth–moon system's complex gravitational interactions. These factors make it difficult to operate and maintain awareness of objects in this region. LeGrand's team develops algorithms that determine how uncertainty about an object's position grows over time, employing a technique called Gaussian mixture approximation.

While traditional Gaussian models work well for linear systems, the nonlinear nature of engineering systems like orbital mechanics and satellite motion requires a more sophisticated approach.

LeGrand's new method splits Gaussian distributions into smaller, more manageable pieces when they become too inaccurate to track effectively. This approach, called Higher-Order Tensor-Based Deferral of Gaussian Splitting (HOTDOGS), ensures that computational resources are used efficiently while maintaining accuracy. By only splitting distributions when necessary, HOTDOGS minimizes the number of smaller distributions and reduces computational complexity.

This framework allows for faster and more accurate predictions in the complex and chaotic cislunar environment, enabling safer and more efficient operations for smaller satellites.