Map Matching Thought Exercise

ION MagNav Workshop, PLANS 2023, Monterey, CA

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Distribution A: Authorized for public release. Distribution is unlimited. Case No. 2023-0427.

Crumpled paper demo

Fold a sheet of paper in thirds.

Crumple and unfold

Code

from matplotlib import pylab as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator
import numpy as np

plt.ion();

Self-similarity of magnetic anomaly maps

Imagine a surface that is actually periodic in all directions:

2-D example

Code

fig, ax = plt.subplots(subplot_kw={"projection": "3d"})
# Make data.
X = np.arange(-2*np.pi, 2*np.pi, 0.1)
Y = np.arange(-2*np.pi, 2*np.pi, 0.1)
X, Y = np.meshgrid(X, Y)
Z = np.sin(X) * np.sin(Y)

# Plot the surface.
surf = ax.plot_surface(X, Y, Z, cmap=cm.cubehelix,
                       linewidth=0, antialiased=False)

# Customize the z axis.
ax.set_zlim(-1.01, 1.01)
ax.zaxis.set_major_locator(LinearLocator(10))
# A StrMethodFormatter is used automatically
ax.zaxis.set_major_formatter('{x:.02f}')

# Add a color bar which maps values to colors.
fig.colorbar(surf, shrink=0.5, aspect=5)

plt.show()

modified from https://matplotlib.org/stable/gallery/mplot3d/surface3d.html

1-D example

Code

fig, ax = plt.subplots()

x = np.arange(-2*np.pi, 2*np.pi, 0.1)
y = np.sin(x)

ax.plot(x,y)
ax.grid()
ax.set_xlabel('x')
ax.set_ylabel('y')

plt.show(); 

1-D with linear bias

Code

fig, ax = plt.subplots()

x = np.arange(-2*np.pi, 2*np.pi, 0.1)
y = np.sin(x) + -0.1 * x

ax.plot(x,y)
ax.grid()
ax.set_xlabel('x')
ax.set_ylabel('y')

plt.show(); 

Discuss impact of bias on map-matching