数学科学与系统工程

项目总结

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, 主动清除碎屑, 卫星检查. 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.

项目目标

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.

分析

We analyze the performance of the model based on standard metrics for generative modeling. 其中包括结构相似指数(SSIM), 峰值信噪比(PSNR), 和学习感知图像斑块相似度(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. SSIM越大，性能越好. PSNR is a measurement of image quality at the pixel level. PSNR高，性能好. 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, 我们还分析了训练时间, 渲染帧率, 以及用于训练和渲染的VRAM. All metrics are measured on a single NVIDIA GTX 3080Ti GPU.

未来的工作

Future plans for this 3D reconstruction model involve incorporating novel rendered views into a YOLOv5 object detector for more accurate, 可靠的, 以及对卫星部件的精确探测.

项目总结

In relation to the United Nation's Sustainable Development Goals (SDGs) for global prosperity, 这个项目调查通货膨胀的影响, COVID-19大流行加剧了这种情况, 关于实现这些目标的进展. 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. 我们将介绍这一探索的过程和发现, 以及, the eventual method used to model inflation using SDG relevant predictors. The outcome of which demonstrates the nuanced relationship between economic indicators, 像通货膨胀, 以及可持续发展目标的现状.

项目目标

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.

分析

我们使用的数据主要来自联合国和世界银行, including metrics like Consumer Price Index (CPI) and COVID-19-related statistics. 初步的统计探索, 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. 这个已知方程与名义利率有关, 实际利率, 通货膨胀率, which would come to guide the following phases of analysis. Several methods were used to distill feature significance, like principal component analysis (PCA). 进一步的机器学习技术, 特别是XGBoost和Lasso回归, 是用来辨别弹性特征的吗. 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.

未来的工作

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