satvis 0.1.1

Satellite LOS visibility calculator

satvis: A satellite visibility calculator.

Description

satvis is a small library of functions used to calculate line-of-sight (LOS) visibility between spacecraft and plot access windows. The core functions that the library is based on are implementations of algorithms developed by J. A. Lawton and Salvatore Alfano et. al. Visibility windows are represented as IntervalTrees. Access windows are plotted using matplotlib.

Install

pip install satvis

Examples

Example 1

To calculate the visibility between two Earth-centered-inertial (ECI) points:

earth_radius = 6378 # km
extra_height = 0 # km
r1 = array([[earth_radius + 400, 0, 0]]).transpose() # position of object 1
r2 = array([[earth_radius, 0, 0]]).transpose() # position of object 2

[vis, phi, a1, a2] = visibilityFunc(r1, r2, earth_radius, extra_height)
print(vis)
print(phi)
print(a1)
print(a2)

# Prints:
# 0.3451182504723773
# 0.00014753614577624565
# 0.34526578661815355
# 0.0

where vis is the value of the visibility function, phi is the angle (in radians) drawn between the two Earth-centered-inertial points, and a1 and a2 are intermediate construction angles. A value of vis>0 means that the two points have a direct LOS to each other.

Example 2

If you just want to know if two points are visible to each other in a binary fashion, use isVis:

[vis_bool] = isVis(r1, r2, earth_radius, extra_height)
print(vis_bool)
# True

Example 3

A series of visibility function values can be represented as a couple of ndarrays or an IntervalTree via the zeroCrossingFit function. This is handy if you want to calculate visibility windows between two objects.

t = array([0, 1, 2, 3, 4]) # time vector
vis = array([-1, -0.1, 0.5, 4, 2]) # objects become visible to each other between t[1] and t[2]
[crossings, rise_set, vis_tree] = zeroCrossingFit(vis, t)
print(crossings)
print(rise_set)
print(vis_tree)

# Prints:
# [1.40896106] 
# [1.]
# tree=IntervalTree([Interval(1.4089610649024726, 4)])

Where crossings is a list of times at which the visibility function value crosses zero, rise_set indicates the direction of the crossing (1=rise, -1=set), and tree is an IntervalTree indicating time windows during which the visibility function value is positive. See the IntervalTree package on GitHub for details on its structure.

Example 4

If the two objects never see each other, the returned arrays and IntervalTree are empty.

vis = array([-1, -0.1, -0.5, -4, -2]) 
[crossings, rise_set, vis_tree] = zeroCrossingFit(vis, t)
print(crossings)
print(rise_set)
print(vis_tree)
# []
# []
# IntervalTree()

Example 5

You can assign an identifier to Intervals within an IntervalTree. This is useful if you combine multiple IntervalTrees representing more than two objects.

vis1 = array([-1, -0.1, 0.5, 4, 2])
vis2 = array([-2, -1, -0.5, 1, 1.1]) 
[_, _, vis_tree1] = zeroCrossingFit(vis1, t, "pair1")
[_, _, vis_tree2] = zeroCrossingFit(vis2, t, "pair2")
combined_tree = vis_tree1 | vis_tree2
print(vis_tree1)
print(vis_tree2)
print(combined_tree)
# tree=IntervalTree([Interval(1.4089610649024726, 4, 'pair1)])
# tree=IntervalTree([Interval(2.328702338492417, 4, 'pair2')])
# IntervalTree([Interval(1.4089610649024726, 4, 'pair1'), Interval(2.328702338492417, 4, 'pair2')])

Citations:

• Alfano, Salvatore & Jr, Negron, & Moore, Jennifer. (1992). Rapid Determination of Satellite Visibility Periods. Journal of The Astronautical Sciences. Vol. 40, April-June, pp 281-296.
• Lawton, J. A.. (1987). Numerical Method for Rapidly Determining Satellite-Satellite and Satellite-Ground Station In-View Periods. Journal of Guidance, Navigation and Control. Vol. 10, January-February, pp. 32-36
• Chaim Leib Halbert's IntervalTree package on GitHub, https://pypi.org/project/intervaltree/#description