GEDI Waveform Fitting (Cubic B-Splines)

Author: Brandon J. Woodard
Institution: Brown University

This script fits modeled laser return waveforms to NASA GEDI full-waveform LiDAR data using cubic B-splines and nonlinear least squares.

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What is GEDI?

GEDI (Global Ecosystem Dynamics Investigation) is a NASA full-waveform LiDAR instrument aboard the International Space Station.
It measures forest vertical structure by recording transmitted and returned laser pulse energy over nanoseconds.

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What This Script Does

• Loads GEDI waveform CSV data\
• Builds cubic B-spline models of signals (scipy.interpolate.splrep, k=3)\
• Convolves transmit pulse with a Gaussian\
• Fits modeled signal to GEDI return waveform\
• Estimates:
  • Vertical & horizontal shifts
  • Scaling parameters
  • Peak locations
  • Goodness-of-fit (Chi-square)

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Requirements

Install dependencies:

pip install numpy scipy matplotlib pandas scikit-learn numba

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How to Run

1. Place your GEDI waveform CSV in the same directory.
2. Set filename in the script:

filename = "your_file.csv"

3. Run:

python script_name.py

The script will:

• Plot the GEDI return waveform
• Plot the fitted model
• Print fitted parameters and chi-square error

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Core Modeling Idea

The modeled return signal:

R(t) = vs + vsc · Spline(hsc · t + hs)

Where parameters control vertical shift, horizontal shift, and scaling.

The transmit pulse is convolved with a Gaussian to approximate system broadening.

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Notes

• Uses cubic B-splines (not raw waveforms).
• Designed for GEDI-like CSV waveform exports.
• Intended for research / signal analysis experimentation.

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