![\"Keith](\"https:\/\/www.purdue.edu\/newsroom\/wp-content\/uploads\/2026\/08\/LeGrand-secondary.jpg\" "\\"\\"")
The challenge is ensuring that the distribution is split as efficiently as possible while retaining accuracy. Efficient splitting and minimizing the number of smaller distributions are critical as too many mixture components can make computation slow or impossible.<\/p>\n\n\n\n
\u201cThink of splitting as adding detail only where needed,\u201d LeGrand said. \u201cAs uncertainty evolves in chaotic environments, it gets stretched and distorted. By splitting one distribution into smaller Gaussian pieces, each piece can be tracked more accurately, and simpler equations that take less computational power work much better on those smaller parts.\u201d<\/p>\n\n\n\n
Modeling uncertainty with efficiency and accuracy<\/h2>\n\n\n\n
LeGrand has developed a framework<\/a> for splitting these distributions to ensure that the results are more accurate and faster to compute.<\/p>\n\n\n\n First, the framework includes a splitting method that preserves the overall average and spread of uncertainty. In other words, the method ensures that, even after the distribution is broken into smaller pieces, the big picture doesn\u2019t change. It also introduces new methods for choosing the best way to split based on how the system behaves.<\/p>\n\n\n\n Additionally, LeGrand has created an algorithm<\/a>, Higher-Order Tensor-Based Deferral of Gaussian Splitting (HOTDOGS), which takes that framework into account and creates rules for when to split a distribution.<\/p>\n\n\n\n Instead of immediately breaking up a distribution into many small pieces, HOTDOGS starts with only a few splits and watches how they change over time. It will then only split when it starts to stretch or distort too intensely. In other words, the algorithm waits until splitting is necessary and then follows each smaller piece separately to stay accurate while remaining efficient.<\/p>\n\n\n\n \u201cThe key idea behind HOTDOGS is not doing more work than necessary,\u201d LeGrand said. \u201cBy letting uncertainty evolve and the algorithm only stepping in when it truly starts to break down, we get the same level of accuracy with far less computation. That balance is essential if we want reliable predictions without slowing everything down.\u201d<\/p>\n\n\n\n Rather than treating uncertainty as a static problem, LeGrand\u2019s approaches adapt as conditions change, adding detail only where it is truly needed and directly supporting safer space navigation, improved situational awareness and better decision-making.<\/p>\n\n\n\n \u201cThe goal of our work is to make uncertainty prediction both smarter and more efficient,\u201d LeGrand said. \u201cAs cislunar space grows more crowded and complex, we hope we can provide a clearer picture of all the activities happening throughout the region.\u201d<\/p>\n\n\n\n LeGrand\u2019s research is sponsored by the Air Force Research Laboratory (AFRL) Regional Network \u2014 Midwest<\/a>, a science and technology ecosystem in which partners from universities, industry and government help the AFRL drive innovation, and the Air Force Office of Scientific Research\u2019s Young Investigator Program.<\/p>\n\n\n\n Purdue University is a research institution ranked among the top 10 public universities in the United States. More than 106,000 students study at Purdue across multiple campuses, including more than 57,000 at our main campus locations in West Lafayette and Indianapolis. As a land-grant university committed to affordability and accessibility, Purdue\u2019s main campus has frozen tuition 14 years in a row, enabling more students than ever to graduate debt-free.<\/p>\n\n\n\n Nonlinearity- and Uncertainty-Informed Moment-Matching Gaussian Mixture Splitting Higher-Order Tensor-Based Deferral of Gaussian Splitting for Orbit Uncertainty PropagationAbout Purdue University<\/h2>\n\n\n\n
Papers<\/h2>\n\n\n\n
<\/em>IEEE Transactions on Aerospace and Electronic Systems
DOI: 10.1109\/TAES.2025.3632242<\/a><\/p>\n\n\n\n
<\/em>IEEE Transactions on Aerospace and Electronic Systems
DOI: 10.1109\/TAES.2026.3662318<\/a><\/p>\n\n\n