Satellite Ecosystem Entropy

Table of Contents


Access the Satellite Ecosystem Entropy (SEE) tool here.


The Satellite Ecosystem Entropy (SEE) visual analytics webapp is a Space Domain Awareness (SDA) capability that provides strategic and operational space operators an “ecosystem” perspective for space objects of interest. SEE identifies ecosystem activity transitions which represent fleeting opportunities to compete below the level of armed conflict. The SEE webapp does this by measuring space ecosystem and resident satellite entropies continually in order to make decisions which advantage one player over another.

Origins and Adaptation

The SEE tool relies on identifying satellite maneuvers. We did this by adapting an algorithm developed six decades ago.

In the aftermath of Sputnik, a frequently cited 1963 paper by Southworth and Hawkins proposed a distance function between two orbits — Statistics of Meteor Streams. The paper ended up being heavily cited because it allowed (back in 1963) the clustering of asteroids and meteors from their two line elements (TLE), in order to determine their origin from different ancient parent bodies that had fragmented eons ago. The paper asserts that a much better distance function would be a delta-v, which was hard to compute in the early 1960s:

“An excellent measure of the difference between orbits, if it can be found, is the amount of perturbation that will transform one of the orbits into the other. A perturbation of an orbit arises from an accelerating force applied for a period of time; hence the velocity change so arising is the natural measure of the perturbation. In general, no single perturbation can suffice because the two orbits will not intersect; we may expect that an appreciable difference between a pair of orbits that were once the same will normally be the result of many perturbations. Since D comprehends all orbital elements, it appears possible that D is a measure of total perturbation; we must determine, however, whether the different elements may be so combined. We consider an idealized model for orbit change, postulating random vectorial increments dV to the vectorial orbital velocity Vh of a meteor.”

Southworth and Hawkins derive a trigonometric-based Euclidean distance between meteor TLEs. Rather than looking at meteor streams, we adapted the technique to examine perturbations between satellite TLE observations. We use this algorithm to examine single objects in a time series; changes in the abstract orbital distance measure between observations suggest the addition of power (aka delta-v). After adjusting for time differences between observations and converting the results into a logarithmic scale, we observe orbital power differentials between 10^-6 to 10^1.

What does “Fast Power” Mean?

We call the metric “Fast Power” because:

  1. It is a computationally efficient (fast) and a rigorous calculation, and
  2. It represents the “power” (energy over time) required to close the distance between two single satellite observations in an abstract energy or approximate fuel space over time.

Lower measures imply “closeness,” but it is closeness in abstract energy/fuel space, not physical space.

When examining two separate objects, the early 1960s algorithm estimates orbital similarity between the two objects in terms of energy distance. An energy distance measure may be thought of as a way to estimate how much energy it would take to place the two objects in a similar orbit. So, two objects may be relatively distant from one another in a Cartesian coordinate system, but relatively close in terms of energy distance.

A terrestrial example might help. Imagine two cars. One is five miles from home, and the other is ten miles from home. The first car is on an unimproved back road; the other is on an interstate. Compared to 5 miles on a dirt road, 10 miles on an interstate may actually be “closer” in energy space or fuel (power) space. We are examining ways to compute the close “energy neighborhood” around objects of interest in order to examine the processes of approaching objects.

Because there are very few measures less than 10^-5 and greater than 10^-2, we binned the each “Fast Power” measure according to the exponent values as follows:

Original Measure Label Power Change Interpretation from previous TLE
Less than 10^-5 FP -5 or Less Negligible; very close to zero
Between 10^-4 & 10^-5 FP -4 Station keeping likely
Between 10^-3 & 10^-4 FP -3 Small maneuver
Greater than 10^-2 FP -2 or More Large maneuver


Our methodology combines TLE data from, satellite metadata characteristics, and the adapted Southworth/Hawkins “Fast Power” algorithm.

TLEs are collected daily. Although they are not the most accurate, there are massive amounts of historical data readily available, which is critical to creating ecosystem patterns of life, since these patterns can emerge across varying time scales.

Critical to the ecosystem approach is building a satellite meta catalog which contains various analysis contexts. There are over 1600 objects in the GEO belt. Data for the satellite meta catalog are collected and compiled as follows:

  1. Basic Satellite Data: Satellite name, number, country of origin, and mission are all collected from the website. These data are updated at least monthly.
  2. Geosynchronous Orbital Slot (Longitude): The orbital slot for each satellite is derived using the calculated longitude for each TLE observation. Satellites with relatively stable longitudes are assigned to one of eighteen 20 degree global slots; objects which traverse slots are assigned to the “Various” orbital slot.

Process event logs are created which combine these data. The figure below contains an excerpt of the GEO belt satellite meta catalog. The “Country,” “Mission,” and “Slot” contexts enable additional analyses other than a single satellite pattern of life. Not only do these contexts provide more data which in turn increases statistical confidence for decision-makers, they also deliver insights which would otherwise be unavailable. For example, country-level analyses may reveal unique or emerging tactics, techniques, and procedures (TTP). Likewise, orbital slot analyses may identify different tempos unique to certain slots. Orbital slot pattern of life models may also be used to identify objects with POLs statistically different from the majority of objects in the slot.

Entropy Calculations

Satellite Ecosystem Time Series Entropy

Satellite Ecosystem Time Series Entropy represents the variability of categorical process activities within an ecosystem at a particular moment in time. Also characterized as the average level of “information”, “surprise”, or “uncertainty” inherent to possible outcomes.

All recent ecosystem process activities are counted and normalized as a percentage of the total. If a process activity did not occur in the time period, the last process activity performed is used. Daily ecosystem entropy derived; last observed maneuver is considered active for the purposes of calculating entropy on any given day. If appropriate, different time intervals may be used: ie monthly or hourly window.

Entropy is calculated and stored as a time series: H(P) = -∑ p(i) log2p(i) 

where p(i) is the normalized statistical percentage of a process activity (i) at a given time interval (ie month, day, or hour)

Individual Satellite Entropy