Link between AMDR & ESW

• The Correlation
• Why Care?
• Why not just believe the data?
• What is the AMDR?
• Teaser
• Appendix

 

 Correlation

The sar-l list has recently revisited the AMDR-ESW discussion, and I thought this might be helpful.

The Sweep Width Estimation report (Koester et al. 2004) was released at the 2004 NASAR conference in Oakland. Although it was inconclusive, the authors had found a puzzling correlation between AMDR & ESW.

They didn't state it as an overall correlation, so I plotted all their AMDR & ESW values together. For some reason, I never posted that plot here. Here it is:

For those not familiar with the terminology:

• AMDR = Average Maximum Detection Range. Roughly, an average of 8 readings of the distance at which a known target stops being visible.

• ESW = Effective Sweep Width, a measure of detectability. Let us call it W for short. More details in the Appendix.

Why Care?

To allocate our resources effectively, we want to know how well they will be able to detect the subject (or clues) in the different regions to which we might send them. We need to find some parameter that is a function of: the environment, the target, and the detector. The gold standard has usually been the sweep width, W, though others are possible. (For example, in an email, Alan Washburn suggested time-to-contact.) The problem is that all the meaningful parameters take a long time to measure.

On the other hand, AMDR can be estimated rather quickly. If there were a stable correlation between AMDR and W, it would greatly help searchers to estimate the actual detectability in a region.

Nevertheless, Koester et al. have been extremely cautious in believing such a relationship. Frost has even stated that there is no theoretical link at all -- any relationship will be "just empirical".

Why not just believe the data?

The apparent relationship is puzzling at best. As we see above, W was generally between 1.0 AMDR and 2.0 AMDR, and Koester et al. suggested in fact there were two cases: environments were it was about 1.0 AMDR and those where it was about 2.0 AMDR. The second is quite curious, because only a perfect sensor can have a W of twice the maximum detection range. We know that searchers are not perfect detectors. Indeed, these very experiments showed that quite clearly. So, what's going on?

Several possibilities:

• This is just a fluke.

• The AMDR measurements are too conservative

• AMDR is not MDR

The apparent relationship may be just a fluke. After all, we didn't have that many data points. Also, the measured AMDR may always underestimate the "true" AMDR that would be obtained by measuring it at all points in the region. However, I wouldn't have expected such flukes to be so stable. So I think we should investigate the effect of the following observation: AMDR is not MDR.

The maximum detection range (MDR) is really bounded only by horizon and atmospheric visibility. In the right conditions of sunlight and gaps in the vegetation, detections can be made very far off. Much farther than AMDR.

What is the AMDR?

So the open question is: What is the relationship between AMDR and MDR? Or perhaps, what is the relationship between the AMDR and the LRC? Where does AMDR fall on the LRC? Can we link it to something like the point where only 1% of detections happen outside?

I think that under some specifiable circumstances, there will be a link between AMDR and W. For example, if the AMDR corresponds to some point on the LRC, then given both the LRC and the AMDR, we can get W. Teaser

A searcher walks the line down the middle of field of trees (green dots). A line is drawn whenever the searcher could see a clue (tiny red dot).

Appendix

Background

AMDR as such was invented to help set up experiments to determine W (Koester et al, 2004). The idea was that to measure W, you need to spread the clues widely enough that the farthest should never be detected. So you need an estimate of the maximum detection range. One way is to pick a spot, and average several maximum detection ranges for your clue. AMDR sets the scale for your experiment.

Now, the Northumbrian Rain Dance (Perkins and Roberts) had been used for just such an estimate: the search team walks a circle around a backpack or some other target, adjusting their distance to keep the target just barely in sight, and takes the average distance around the circle. P&R called this estimate the Critical Distance (CD), because they advocated placing searchers at a Critical Separation (CS) of twice the CD.

Clearly the rain dance is also estimating the average, maximum detection range. I credit Koester et al. for the more neutral term (AMDR). I think changing the terminology is a conceptual advance, because it separates out what was estimated from how we use it.

Glossary

Effective Sweep Width -- ESW or just W is the area under a detector's Lateral Range Curve, a curve that describes how detection rate falls off with distance. Since perfect detection has probability 1 for its whole sweep width, and W = area = width X height = width X 1, W will equal the sweep width of a perfect detector. That's why it's called the effective (or equivalent) sweep width.

W is the width of a perfect detector that would "sweep up" (detect) as many clues as your real detector. Now, a real detector misses some clues inside W, and detects others outside W. So in order to detect the same number of clues overall, W has to be the point at which those inside-misses equal the outside-detections, a useful property when measuring W.