SPECIAL REPORT: ELECTRONIC COUNTERMEASURES
The inclusion threshold is hereby defined as the probability that the warning zone includes the ground-truth ECM toggle range.
processed, indicating that the RCIED receiver is outside the ECM protection bubble. At some point in the test, the RCIED receiver will be at a range where the ECM is only intermittently able to prevent reception and processing of the trigger signal (yellow segment in figure 1 (a)). As a side point, use of the word “intermittently” means that repeated trigger tests are required at each test range. Let’s call this the ECM effectiveness toggle range, the range at which the ECM “toggles” between effective and ineffective. A few milliseconds of thought reveals that the outcome of this thought experiment depends on a number of as-yet unstated parameter choices implicit in the problem statement: for example, how far away the trigger man is from the IED receiver, the relative antenna gains for the ECM, threat receiver and threat transmitter, the power of the transmitter, the power of ECM, the ECM waveform type, the type of IED, and a host of other variables. Now suppose the experiment is repeated, but this time the trigger man is moved closer so the trigger signal is more powerful in the IED receiver, and further suppose that nothing else changes. As a result, the ECM protection bubble is smaller, i.e. range at which the ECM is able to prevent the trigger signal from being received and processed is closer than previously. Now suppose we repeat the experiment many times, let’s say 5,000 times, and a different
parameter set is used each time. Generally speaking, each experiment will result in a different ECM toggle range. This population of answers defines the range window in which all observed ECM toggle ranges lie (figure 1 (b)). The best way to present this information is as a probability density function, or pdf (written with small-case letters, the since capital-case version PDF is used to designate a probability distribution function). A pdf is a graph of the relative likelihood that a particular answer is in the population, and an example one is shown in figure 2 (a). One of the properties of a pdf is that the area under the curve adds up to 100% probability, or 1.0. From basic probability theory 101, these curves can be used calculate the probability that an experimental outcome (e.g. ECM toggle range) will lie between two values; it’s just the area under the curve between the two values. At this point it’s useful to introduce the idea of an “inclusion threshold”: The inclusion threshold is hereby defined as the probability that the warning zone includes the ground-truth ECM toggle range. Remember: we do not – and cannot – know the ground-truth ECM toggle range because we do not – and cannot – know all of the specifics of the attack scenario. If we did know all the specifics, that would include the location of the trigger man and the IED itself, and we could avoid or capture both. Instead, the best alternative is to define
FIG. 2: WARNING ZONE INFORMATION IS DERIVED FROM PROBABILITY DENSITY FUNCTIONS
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