# Mechanisms of Exploration — Probe Scanning

Po Huit, Explorer
Fitting Director, Signal Cartel
Seyllin Conference YC 120
http://po8.org/seycon-yc120-probe-scanning.html

## Abstract

This document is a report on work in understanding and modeling probe scanning, with the goal of discovering optimal probe formations. The basics of probe scanning and probe formations are described. A review of Capsuleer research on probe scanning models is given. Models for and experiments with one-probe and two-probe scanning are given. Finally, analysis of the possibilities of computer-aided search for optimal formations is discussed.

## Introduction: Perfect Probe Formations

This document is a report on work in understanding and modeling probe scanning. The research reported here is quite preliminary. A primary purpose of this document is to solicit questions, suggestions and advice in tackling this problem.

The ultimate goal of this research is to discover perfect probe formations.

The Probe Scanner is a key piece of equipment on many ships in New Eden. Capsuleers use scanners for finding other Capsuleers to fight, for finding other hostiles to fight, and especially for finding ancient sites to explore for valuable relics and data."

The default scanner probe ‘formation’ presented to the Capsuleer is an interesting thing. There are a couple of potential questions to be answered about it:

• Why is the default formation not symmetric in three dimensions?

• Why does the default formation work well?

• What could be done to improve the default formation?

Many Capsuleers have discovered probe formations that work slightly better in certain situations. These formations allow the resolution of some signatures the standard formation cannot. However, formations like the “cube” or “face-centered tetrahedron” do not seem to perform as well as one would expect.

There is a well-documented “official” history of probe scanning. Capsuleers have also posed and answered questions similar to these on Galnet."

Constructing new probe formations with better performance seems to be a real possibility. Such probe scanner formations should be engineered from first principles. To accomplish this, a fuller understanding of the operation of scanner probes is needed. Ultimately, Capsuleers may be able to engineer optimal formations for various needs, using the computing power at their disposal to analyze and optimize formations.

## Probe Scanning Basics

The basic operation of scanners is well-understood by most Capsuleers. Nonetheless, a review is merited: some of the arcana published by official sources is a bit confusing.

A probe launcher can launch and manage up to eight probes. The basic principle of probing is signal-strength quadrilateration. The simultaneous strength of the signals returned from a target by four or more probes can be compared with their known locations. This gives an estimate of the target’s location.

At any given time a given probe has a defined radius of operation. Targets outside a probe’s radius will not be sensed by that probe. Targets inside will be. When a target is sensed by less than four probes, the scanning system will still give an estimate. This estimate will be a pair of points (3 probes), a ring (2 probes) or a sphere (1 probe).

The probe scanner does not attempt to reason “by exclusion”, although this can be done manually: if a portion of an ambiguous estimate could not have been produced by the failure of one or more probes to detect the target, this portion can be ruled out. For example, if one of two points is within the radii of four probes, the other point must be the true estimate.

The maximum and minimum probe radius are common to all probes of a given type. Within these limits, a probe’s radius can be set only to power-of-two steps.

• Combat probes can be set to radii between 0.5 and 32 AU. The allowable radii are 32, 16, 8, 4, 2, 1, and 0.5 AU.

• Core probes can be set to radii between 0.25 and 16 AU. The allowable radii are 16, 8, 4, 2, 1, 0.5 and 0.25 AU.

A target’s position estimated quality is reflected by the probe scanner interface as a percentage between 0 and 100%. When the estimated quality reaches 100%, the target is considered to be fully located. A fully-located target’s position is made available to other ship systems for navigation, bookmarking, etc. When the quality is less than 100%, the target’s estimated position contains uncertainty. This uncertainty shows up as deviation of the estimated position from the true position.

Estimation quality and deviation are a linear function of several factors. Deviation is largely a linearly-inverse function of return quality.

• Probe radius: The target return quality is inversely proportional to the probe radius.

• Probe strength: The target return quality isn linearly proportional to the probe strength. The probe strength is governed by:

• The type of probe chosen.

• The type of probe scanner chosen.

• Bonuses from standard modules and rigs attached to the ship.

• Bonuses given by the ship itself.

• The level of training of various skills achieved by the Capsuleer operating the system.

All of these bonuses to probe strength are linear, and are easy to understand and account for. They will be largely neglected in what follows.

• Target strength: The target return quality is a function of the target, which varies by target type and parameters. The Capsuleer usually has no control of target strength.

The basic operation of combat scanners and probes looks to be identical to that of core scanners and probes. This work considers only combat probing. Combat probing makes it easier to set up experiments, since the experimenter has full control of the target. Future work is needed to check that results obtained by this approach. hold in other situations.

## Probe Formation Basics

Probe formations were introduced into probe scanners in a major system upgrade in YC 115. Prior to this, Capsuleers had to set the position and radius of each probe individually for each scan. Manual per-probe position and radius setting is still possible. Formations set manually can be saved for later reuse.

Default “spread” and “pinpoint” formations are provided by the probe system hardware. These formations are geometrically similar, but not identical.

• The spread formation (Figure 1) consists of a spread hexagon of probes in the plane of the solar system. The two remaining probes are placed in the center of the hexagon just above and below plane. This formation is effectively a hexagonal tiling of the plane with extra probe strength in the center.

• The pinpoint formation (Figure 2) consists of a dense pentagon of overlapping probes in the plane of the solar system, The three remaining probes are placed in the center of the pentagon above, on, and below the plane. This formation is more space-filling, although it still has high planarity.

Scaling a probe formation scales both the formation itself and the radius of the individual probes. The scaling of a probe formation goes in the same power-of-two steps as the probe radii.

Scaling is a linear expansion/contraction around the centroid of the formation, with all probes given equal weight. The centroid $$\bar{c}$$ of a set of $$n$$ equally-weighted three-dimensional points specified with Cartesian coordinates $$\bar{x_i}$$ is simply the average of their positions.

$\bar{c} = \frac{\sum \bar{x_i}}{n}$

It would be convenient for the Capsuleer to be able to set the center for asymmetric formations, but this is not currently possible.

Custom formations are achieved by manually manipulating individual probes and saving the result. Custom formations are scaled using the same mechanics as the default formations.

An official manufacturer note at the time of the release of probe formations states that:

These [default formations] are not intended to be the absolute best possible formations, but rather a solid starting point for budding explorers.

## Gaps In Knowledge

While the official details of probe scanning are well-understood, there are quite a few gaps in that knowledge. A great deal of the detail remains unknown and unconfirmed.

Let us define the probe system state as the positions and radii of all probes relative to the target.

• *Question: What functions of the probe system state mathematically describe the target estimate quality and deviation?"

This is an important question, because there is no theoretical way to evaluate the quality of a formation without it. Without a formation quality model, optimization becomes impossible.

## Prior Research

A number of Capsuleers and Capsuleer corporations have investigated the mathematics of probe scanning. This section summarizes an attempt to find that research, with references as appropriate. The author has also archived copies of relevant documents to preserve this work.

• Scanning on the EvEinfo wiki, date unknown

This is a superficially quite credible account of the probe strength calculation. The account is marred only by its extreme age. Some things are clearly outdated.

For example, it appears that currently any scannable target hit by at least one probe will always appear in the results.

The funny \xE2\x80\x93 sequence in the formulas is a miscoded en-dash, that is, a minus sign.

This appears to be a copy of an old Goonwiki document. As the author is no longer in Goons, he cannot verify whether it has ever been edited there. Recalling the state of their wiki, he is skeptical.

• Apocrypha Probe Scanning by Space Wanderer YC 111

This is a superficially quite credible account of how multiple probes are combined. Again, it is elderly. Probe hardware may have changed.

• Probe Multiplier by Elisa Fir YC 114

This is an empirical formula describing how to combine the strengths of multiple probes. This formula is quoted without attribution on the EVE University wiki link below.

• Manufacturer Notes YC 115

This is when probe formations are introduced by manufacturers." There do not seem to be any manufacturer-reported changes to the actual probe scan mechanics.

• Probe scan strength for combat probing and exploration by Pilgrim In Exile, last edited YC 116

These are a much newer and much more casual account of the calculations.

Some details seem to be incorrect: for example, the suggestion that probe placement on top of the target guarantees a best scan. This author has experimentally verified that this is not the case for more than one probe.

• Signal Strength and Base Signature Strength on the Backstage Lore Wiki, last edited YC 117

These pages give an alternate account of probe scanning, which may or may not be more accurate than the older ones. The formulas were reportedly derived empirically: I am suspicious that the older ones are actually closer to right.

• Scanning on the EvE University Wiki, last edited YC 119

This is a mostly qualititative account. A scan deviation calculation is included.

Finally, I also have been given a report of a recent piece of relevant work which I have not yet had time to investigate.

## Models and Experiments

For now, let us assume that the detailed reports we have are mostly correct. It is reasonable to start by enumerating the general things everyone seems to agree on about the probe scan process.

1. The scan quality is a deterministic function of several variables, most of which are well understood.

2. Core and combat probe scanning are closely related. The same general formulas apply to both. There are factor-of-two modifications in some cases, but that’s about it. The specific formulas for target strength differ between combat signatures (ships and structures) and cosmic signatures.

3. At least up to some threshold, more probes on a signature is better than fewer. At least up to some threshold, probes closer to a signature are better than farther away. Smaller probe radii that hit a signature are linearly better than larger. The probe strength is a well-understood function (described below) of attributes of the ship, probe scanner, probes and pilot.

Let us develop a couple of models based on the historical reports. We can then evaluate these models empirically on a validated simulator.

• Effective Probe Strength ($$S_p$$): The effective strength of an individual probe can be computed by the formula

$S_p = S_b \cdot (1 + 0.05 (A + A_r)) \cdot (1 + L) \cdot (1 + H) \cdot \Pi (1 + \rho_i F_i))$

where $$S_b$$ is the probe base sensor strength, $$A$$ and $$A_r$$ are the pilot skill levels in Astrometrics and Astrometric Rangefinding, $$L$$ is the launcher bonus, $$H$$ is the hull bonus, $$F_i$$ are the fitting bonuses for the various relevant fittings, and $$\rho_i$$ is the “stacking penalty” for multiple fittings, with the fittings ordered best-to-worst. Specifically

$\rho_i = e^{-(3(i - 1)/8)^2}$

All of this is a bit irrelevant, as the effective probe strength can be easily looked up either in the ship’s fitting display or in a fitting tool. We will use $$S_p$$ as a fundamental value in what follows.

• Effective Target Strength ($$S_t$$): This is the ease with which a given target can be scanned. For anomalies, this is essentially tabular: each type of anomaly has a characteristic strength. For ships and structures, the signature strength is the ratio of effective signature radius of the target to its effective sensor strength. Both signature radius and sensor strength can be changed: the former in all the obvious ways, the latter with Signal Boosters loaded with ECCM Scripts.

• Probe Radius ($$N_R$$): This reflects the distance from the probe to the target as well as the radius of the probe. The radius $$R$$ of the probe is usually given in AU, but for our purposes it is best thought of in steps $$N_R$$ above the minimum radius $$R_b$$ (0.25 AU for core probes, 0.5 AU for combat probes), such that

$R = R_b \cdot 2^{N_R - 1}$

Combat probes have a base signal strength half that of core probes, but since they have a minimum radius that is twice that of core probes, their effect strength at a given probe radius is the same.

## Single Probe Scanning

The simplest case to start with is scanning with a single probe. This removes a number of complications in experiment and evaluation.

The Goonwiki Formula is a good candidate for single-probe scan strength. This model says that quality will vary as the 3/2 power of probe-target distance.

$Q = S_p \cdot S_t \cdot \left (1 - 0.65 \left ( \frac{D}{R} \right )^{3/2} \right )$

Here D/R is the fractional distance from the target to the probe, ranging from 0 to 1.

I have performed simulator experiments to check this model. Scanning was performed by a Helios positioned at the origin, fitted with four Scan Rangefinding Array II, a Gravity Capacitor II, and an Expanded Probe Launcher II with a single Sisters Combat Scanner probe. Pilot was at max scanning skills, except Covert Ops IV. The ship fitting display indicated 66 points of sensor strength.

The experimental setup was:

1. Build a line of eight bookmarks about 20 AU in length, separated by roughly log spacing. Actual bookmark / Depot distances from the scan position:
1: 0 AU
2: 1.57 AU
3: 3.5 AU
4: 5.27 AU
5: 7.5 AU
6: 10.6 AU
7: 15.33 AU
8: 21.33 AU


These distances were taken from the “old map” display.

1. Anchor a Mobile Depot at each of these bookmarks. The line of Mobile Depots allows a single scan to return multiple quality measurements. Makes the experiments go faster.

2. Scan with a single probe at the near end of the line, varying probe radius.

3. Gather return percentages.

The following table shows the results of Run 1.1 of this experiment. The table indicates test point number, test point signature, test point distance from probe, then test point percent signal strength as function of probe radius.

                     32   64   16    8    16   16   8     4     2     4

1  CFC  0       2.6  1.3  5.2  10.5  5.2  5.2  9.9  16.8  17.1  21.8
2  ZLM  1.57    2.6  1.3  5.2  10.2  5.1  5.1  9.8  15.8        17.8
3  WOD  3.5     2.6  1.3  5.0   8.8  4.8  5.0  8.7  10.0         9.8
4  KVL  5.27    2.5  1.3  4.8   7.0  4.5  4.8  7.2
5  MDI  7.5     2.5  1.3  4.3   4.6  4.0  4.3  4.9
6  ETQ  10.6    2.4  1.2  3.6        3.3  3.7
7  PWG  15.33   2.1  1.2  2.2             2.3
8  COV  21.33   1.7  1.2


No contact was made with any target at 1 AU probe radius on repeated attempts.

It is difficult to evaluate the deviation between runs. Repeated runs with slightly different position produced different values: repeated runs with the same position (including zooming and reducing probe radius between runs) produced identical values.

A graph of these results, together with the model prediction, is shown in Figure 3. The fit of prediction with measurement seems good. The constant 85.3 is in no way empirical, but rather derived from first principles.

## Two-Probe Scanning.

A usable model of probe scanning should account for 1–8 probes. Having modeled a single probe, modeling two is the obvious next step.

Because the scanner quadrilaterates, placing multiple probes on top of the target is not helpful: geometry matters. The author has tested this claim experimentally. Placing a second probe directly on top of the first makes almost no difference in scan quality.

In Run 1.2 a second probe was placed atop the first to see how that affected result quality. The null hypothesis was double strength. Slashed entries are 2/1 probes, achieved by recalling the second probe individually. The other columns were not recorded, but showed a similar pattern to radius 2: very small downward changes with 1 probe.

                     64   32   16    8     4      2         1         0.5

1  CFC  0       2.2  3.8  6.5  11.6  22.4 38.0/37.0  48.7/48.1  55.4/55.2
2  ZLM  1.57    1.4  2.8  5.4  10.3  18.1 21.6/21.6
3  WOD  3.5     1.3  2.7  5.1   8.8   9.9
4  KVL  5.27    1.3  2.6  4.8   7.0
5  MDI  7.5     1.3  2.5  4.3   4.6
6  ETQ  10.6    1.3  2.4  3.6
7  PWG  15.33   1.2  2.1  2.2
8  COV  21.33   1.2  1.7


The null hypothesis is rejected: there appears no interesting strength change with multiple probes in a single position.

The next experiment was to evaluate the effect of probe angle in a two-probe setup. The first probe was placed at a fixed distance $$D$$ from the target. The second probe was rotated “around the circle” at this same distance to various angles.

In Run 2 (performed YC 119 about Day 275), return quality was measured as a function of angle to try to understand the trilateration model. Two probes were set up at similar distance from the target, a Mobile Depot placed at a known bookmark. The relative angles of probes were varied and the resulting scan quality recorded. The probe radius was 1 AU. the probe target distance was about 0.2 AU. The results are shown in the table below.

    0°      50%
10°     54%
22°     57%
45°     65%
90°     79%
135°    93%
180°    96%
270°    79%


This data is shown graphically in Figure 4.

Excepting the one outlier, quality appears to vary between 1x and 2x as a function of angle.

## Conclusions and Future Work

The author has not yet done any solid experiments with more than two probes. A hypothesis for the eight-probe model is in development based on Space Wanderer’s model. However, this hypothesis differs in some details. Further experimentation is in the works.

Once a probe scanning model is developed, optimization work can be resumed. The author has a background in computer-aided optimization. The research reported here starte with an attempt to build a software optimizer for probe formations. This research did not go well: it quickly led to the conclusion that an optimizer was not going to make progress without an accurate model. Once the current line of research is complete, it will be time to return to the optimizer and see what it has to say.

One might ask how much better we can expect to do with optimal formations. A seemingly reasonable guess based on the observations so far is that the difference will be small: probably in the 2–5% range. However, it is probably too early to tell for sure. In any case, the knowledge gained will be valuable in its own right. Also, even a small percentage increase can pick up some marginal signatures: it’s worth building a custom formation for.

## Acknowledgments

The contribution of Signal Cartel and its members to this work is gratefully acknowledged. Special thanks to Arataka Research Corporation for providing a venue for the reporting of this work, and to Makoto Priano in particular for helping me to navigate that process.

## Biography

Po Huit has been a Capsuleer for about 3.5 years. He received his training at the Center for Advanced Studies in Cistuvaert. Po has flown with a small private corp, with Provibloc, and with Goonswarm as part of Karmafleet and later Amok. . He joined Signal Cartel at start of YC 119. Soon thereafter, he was invited to be a Director of ‘Splunkworks’, Signal Cartel’s ship-fitting team.