About

Grace Gao is an Associate Professor of Aeronautics and Astronautics at Stanford University and is also a courtesy faculty member of Electrical Engineering. Her research focuses on autonomous systems, controls, and related aerospace technologies. She is involved in advancing the understanding and development of autonomous systems and controls within the field of aeronautics and astronautics, contributing to the academic and practical progress in these areas.

Research topics

• Computer Science
• Discrete mathematics
• Combinatorics
• Algorithm
• Pure mathematics
• Geometry
• Geology
• Environmental science
• Remote sensing
• Ecology
• Geography
• Mathematics
• Agronomy

Selected publications

• Ellipsotopes: Uniting Ellipsoids and Zonotopes for Reachability Analysis and Fault Detection

  IEEE Transactions on Automatic Control · 2022 · 46 citations

  Senior authorCorresponding
  • Computer Science
  • Mathematics
  • Computer Science

  Ellipsoids are a common representation for reachability analysis, because they can be transformed efficiently under affine maps, and they allow conservative approximation of Minkowski sums, which let one incorporate uncertainty and linearization error in a dynamical system by expanding the size of the reachable set. Zonotopes, a type of symmetric, convex polytope, are similarly frequently used, because they allow efficient numerical implementations of affine maps and exact Minkowski sums. Both of these representations also enable efficient, convex collision detection for fault detection or formal verification tasks, wherein one checks if the reachable set of a system collides (i.e., intersects) with an unsafe set. However, both representations often result in conservative representations for reachable sets of arbitrary systems, and neither is closed under intersection. Recently, representations, such as constrained zonotopes and constrained polynomial zonotopes, have been shown to overcome some of these conservativeness challenges, and are closed under intersection. However, constrained zonotopes cannot represent shapes with smooth boundaries, such as ellipsoids, and constrained polynomial zonotopes can require solving a nonconvex program for collision checking or fault detection. This article introduces <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ellipsotopes</i> , a set representation that is closed under affine maps, Minkowski sums, and intersections. Ellipsotopes combine the advantages of ellipsoids and zonotopes while ensuring convex collision checking. The utility of this representation is demonstrated on several examples.

  DOI

• The influence of surface canopy water on the relationship between L-band backscatter and biophysical variables in agricultural monitoring

  Remote Sensing of Environment · 2021 · 67 citations

  Senior authorCorresponding
  • Environmental science
  • Remote sensing
  • Agronomy

  The presence of surface water on the canopy affects radar backscatter. However, its influence on the relationship between radar backscatter and crop biophysical parameters has not been investigated. The aim of this study was to quantify the influence of surface canopy water (SCW) on the relationship between L-band radar backscatter and biophysical variables of interest in agricultural monitoring. In this study, we investigated the effect of SCW on the relationship between co- and cross-polarized radar backscatter, cross ratios (VH/VV and HV/HH), and radar vegetation index (RVI) and dry biomass, vegetation water content (VWC), plant height and leaf area index (LAI). In addition, the effect of SCW on estimated vegetation optical depth (VOD) and its relationship with internal VWC was investigated. The analysis was based on data collected during a field experiment in Florida, USA in 2018. A corn field was scanned with a truck-mounted, fully polarimetric, L-band radar along with continuous monitoring of SCW (dew, interception) and soil moisture every 15 min for 58 days. In addition, pre-dawn destructive sampling was conducted to measure internal vegetation water content and dry biomass. Results showed that the presence of SCW can increase the radar backscatter up to 2 dB and this effect was lower for cross ratios (CRs) and RVI. The Spearman's rank correlations between radar observables and biophysical parameters were, on average, 0.2 higher for dry vegetation compared to wet vegetation. The estimated VOD from wet vegetation was generally higher than those from dry vegetation, which led to different fitting parameter (so-called b) values in the linear fit between VOD and VWC. The results presented here underscore the importance of considering the influence of SCW on the retrieval of biophysical variables of interest in agricultural monitoring. In particular, they highlight the importance of overpass time, and the impact that daily patterns in dew and interception can have on the retrieval of biophysical variables of interest.

  DOI

Recent grants

• CAREER: High Integrity Navigation for Autonomous Vehicles

  NSF · $517k · 2019–2024

Frequent coauthors

• Sriramya Bhamidipati

  Jet Propulsion Laboratory

  56 shared

• Shubh Gupta

  46 shared

• Adyasha Mohanty

  Stanford University

  39 shared

• Akshay Shetty

  39 shared

• Tara Mina

  Stanford University

  34 shared

• Liang Heng

  Dà-Jiāng Innovations Science and Technology (China)

  31 shared

• Per Enge

  31 shared

• Todd Walter

  29 shared

Education

• Ph.D., Aeronautics and Astronautics

  Stanford University

  2010

• M.S., Aeronautics and Astronautics

  Stanford University

  2006

• B.S., Aerospace Engineering

  University of California, Berkeley

  2004

Awards & honors

• NSF CAREER Award
• Institute of Navigation Early Achievement Award
• RTCA William E. Jackson Award
• Inspiring Early Academic Career Award from Stanford Universi…
• Distinguished Promotion Award from University of Illinois at…

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