Mathematical Sciences and Systems Engineering

Project Summary

As the numbers of cooperative and non-cooperative spacecraft in orbit increase, they have created interest in the development of autonomous chaser satellites for on-orbit servicing, active debris removal, and satellite inspections. Performing these operations requires accurate estimation and identification of satellite geometry. This project depicts an implementation of 3D Gaussian Splatting for mapping satellite geometries. We share training methods and the 3D rendering capabilities of the model using a realistic satellite mock-up that is tested across several realistic lighting conditions. We present training and rendering metrics, along with comparisons to past 3D reconstruction methods. Our model is capable of training on board and produces high-quality renders of novel views of an unknown satellite. We achieve a rendering speed nearly two orders of magnitude faster than previous neural radiance field (NeRF) based methods. These abilities play a crucial role in subsequent machine intelligence tasks involving autonomous navigation and control tasks.

Project Objective

Our goal is to identify and reconstruct the geometry of an unknown satellite using a single video feed of data with a low-compute algorithm that will have the capability to be implemented onboard a spacecraft.

Analysis

We analyze the performance of the model based on standard metrics for generative modeling. These include Structural Similarity Index (SSIM), Peak Signal to Noise Ratio (PSNR), and Learned Perceptual Image Patch Similarity (LPIPS), which we evaluate on images of the satellite mock-up not used during training. SSIM measures the perceived difference between the two images for qualities like luminance and contrast. High SSIM indicates high performance. PSNR is a measurement of image quality at the pixel level. High PSNR indicates good performance. LPIPS is a more complicated tool that aims to calculate the human-perceived similarity between the two images. This metric uses a VGG neural network to compute the distance between a real and synthetic image patch. Low LPIPS indicates that the two images are more similar to one another. For rendering performance and computational requirements, we also analyze training time, rendering frame rates, and VRAM for both training and rendering. All metrics are measured on a single NVIDIA GTX 3080Ti GPU.

Future Works

Future plans for this 3D reconstruction model involve incorporating novel rendered views into a YOLOv5 object detector for more accurate, reliable, and precise detections of satellite components.

Project Summary

In relation to the United Nation's Sustainable Development Goals (SDGs) for global prosperity, this project investigates inflation's influence, intensified by the COVID-19 pandemic, on the progression towards these goals. From eliminating poverty to establishing clean energy and resilient infrastructure, the UN has laid out 17 SDG's for humanity to aim for by 2030. Each of these goals can be broken into components where data is gathered on each of these sub-targets. This project shows a statistical exploration of data pertaining to these goals and their relationship with inflation. We present the process and findings of this exploration, as well as, the eventual method used to model inflation using SDG relevant predictors. The outcome of which demonstrates the nuanced relationship between economic indicators, like inflation, and the status of SDGs.

Project Objective

The objective of this project is to identify which components of the UN's Sustainable Development Goals illustrate dependence on inflation by leveraging statistical and machine learning methods to uncover the relationship between inflation and various predictors.

Analysis

We used data primarily from the UN and World Bank, including metrics like Consumer Price Index (CPI) and COVID-19-related statistics. The initial statistical exploration, focused on the correlation between CPI changes and SDG sub-targets, which identified a link with real and lending interest rates. Subsequent methods (distance correlation and mutual information) were applied to refine the selection of predictors for inflation, leading to the pivotal incorporation of the Fisher Equation. This known equation relates nominal interest rate, real interest rate, and the inflation rate, which would come to guide the following phases of analysis. Several methods were used to distill feature significance, like principal component analysis (PCA). Further machine learning techniques, notably XGBoost and Lasso regression, were leveraged to discern resilient features. The culmination of this study involved deploying ML methods (decision tree regressors and XGBoost) within the PCA-reduced feature space to predict real and lending interest rates. The findings facilitated the modeling of inflation via proxy variables derived from PCA components, culminating in an inflation estimation model framed by the Fisher Equation.

Future Works

Future work for this data exploration involve further investigating the cause and effect relationship between the predictors used in this model and inflation, as well as, using a refined model to develop an outlook and timeline for the SDG's progression.