Why four is not enough

HEXTA electronic targets have eight sensors, rather than the usual four, to increase both accuracy and reliability. Here’s why.

Acoustic electronic targets (ETs) work by detecting the acoustic waves generated by supersonic projectiles as they pass through the target. In essence, an electronic target system consists of a series of processes working in sequence, rather like ‘links in a chain’. Roughly in order, these processes are:

  1. The impact of the acoustic wave on the sensors in the target
  2. The conversion of acoustic energy to an electrical signal by the sensors
  3. Processing and digitising of the electrical signal
  4. Analysis of the data
  5. Transmission of the data to the monitors at the mound
  6. Display of the data as information on the monitors

Like all physical systems, each of these processes is prone to error. But it is the first three steps – the acoustic wave detection and signal processing – that are by far the least accurate and least reliable ‘links in the chain’.

By comparison, the remaining steps should involve only digital electronics, and should have extensive in-built error checking/correction and redundancy. As a result, the accuracy and reliability of this part of the system should be very high.

How many sensors are necessary?

You only need three acoustic sensors to make an estimate of shot position. The system records the time instants when each of the sensors registers the impact of the acoustic wave. By calculating the time interval between each, and knowing the speed of the wave, the system can estimate the shot position.

In a perfect world, the estimated position would be exactly the same as the actual position. But the real world is full of variations and errors, and there are many things that can affect the accuracy of the measurement.

The first thing you can do to reduce the effects of these errors is to take multiple estimates and calculate an average. Traditionally, ET manufacturers have done this by increasing the number of sensors to four, resulting in a level of redundancy. With four sensors, there are four possible 3-sensor combinations (that is, 1-2-3, 2-3-4, 3-4-1 and 4-1-2), each of which can make an estimate of shot position. These four estimates can then be averaged to give a resultant shot position.

You might think that an average of four estimates would be more accurate than a single estimate. And you’d be right – but only if all four sensors are giving accurate readings. But once again, in the real world acoustic sensors often give inaccurate readings.

Let’s say, for example, sensor number 3 has a significant error in measuring the time instant that an acoustic wave hits it. This error will affect three of the four 3-sensor combinations (1-2-3, 2-3-4, and 3-4-1). And if three out of four estimates of shot position have errors, the average will obviously have an error too.

But it gets worse. With only four sensors, you may not even know if an error has occurred, let alone which sensor (or sensors!) was the culprit. You have no choice but to accept the answer the system reports, correct or not.

What about even more sensors?

So why not add even more sensors? With a 5-sensor target, for example, there are now 10 possible 3-sensor combinations. If the error in sensor number 3 again, four of the 10 estimates would not include sensor 3 (that’s 40% of the total number). It’s an improvement, but not a big one.

By the time you get to an 8-sensor target, there would be 35 three-sensor combinations (of a total of 56) that would not include sensor 3 (62% of the total number). Now we’re getting somewhere.

But there’s more. With so many sensors it’s now possible to identify a sensor that’s causing an error. And once you’ve identified it, you can take steps to reduce the effects of the error. Firstly, you can reject the faulty results before calculating the average. And secondly, if the error is consistent over a number of shots (that is, if it is not random), you can calculate a correction factor and apply it to that sensor, so that the sensor will give correct results for future shots.

These methods are described in more detail in our article HEXTA statistical analysis and correction.

Oh, and by the way, if you’re thinking of building an ET with any of the methods described here, you’d better check with us first, because we have patents on them!

Errors and where they come from

Where to these errors come from? Acoustic waves are inherently ‘noisy’ – nothing like the pure sound wave from a tuning fork – and amidst all that noise the sensor has to find the ‘signal’. The “noise” comes from many sources – waves can be reflected off objects; they travel through solid objects; they cause the target frame to resonate; they can approach a sensor from many different directions; noises can come from other sources (like shots on nearby targets); the amount of energy in a wave varies greatly, depending on projectile calibre, shooting distance and many other variables.

Reliability

So far we’ve been talking about accuracy. Now we come to the question of reliability.

Quite often, acoustic sensors fail to detect an acoustic wave at all, or detect it so poorly that a shot position cannot be resolved. This, again, is due to the large number of variables we’ve already mentioned. If a single sensor fails to register, an 8-sensor target temporarily becomes a 7-sensor target, and a 4-sensor target becomes a 3-sensor target. But if two sensors fail simultaneously to detect (and yes, this happens!), an 8-sensor target temporarily becomes a 6-sensor target, and a 4-sensor target won’t work at all.

Users of traditional 4-sensor electronic targets will already know about ‘lost shots’. This usually happens when more than one sensor fails to detect the shot entirely, or when one or more sensors detect the shot with so great an error that the position could not be resolved.

As we said earlier, the reliability of the acoustic measurement process is much more of a concern than the reliability of the digital electronics that communicate and present the information (provided of course that that the electronics are thoroughly designed). So any improvements in the reliability of acoustic detection will improve the reliability of the ET system as a whole. And it’s pretty clear that using more sensors will also reduce the chances of a ‘lost shot’.

The three-legged stool

Let’s look at some numbers to get a better idea of reliability.

A complete ET ‘system’ is made up of a number of ‘subsystems’ working together, either in series (that is, sequentially, like links in a chain), or in parallel (that is, ‘side by side’). In the simplest terms, an ET system consists of two main subsystems in series – a target subsystem and a digital subsystem. These, in turn, are each made up of further subsystems.

The digital subsystem consists of three subsystems in series – 1) data analysis, 2) transmission of the information and 3) display of the information. The digital subsystem, with its inbuilt error checking/correction and redundancy, has very high reliability; perhaps 99.9%.

A simple three-sensor target subsystem can be thought of as three subsystems (that is, each of the sensors) in series. If one sensor doesn’t work, the target doesn’t work. It’s like a three-legged stool – if one leg breaks the stool falls over. Each leg (or sensor) is necessary in order for the system to work – just like three links in a chain.

An individual sensor may have a reliability of about 95% (by this we mean the probability of the sensor detecting the acoustic wave accurately enough that the shot position can be resolved). The combined reliability of three sensors in series would be 95% x 95% x 95% = 85.7%.

So the combined reliability of the entire ET system (that is, the target subsystem in series with the digital subsystem), is 85.7% x 99.9% = 85.6%.

Now, if we were to add a fourth sensor to the target, it would be more like a four-legged stool – if one leg breaks, the stool probably won’t fall over. This fourth leg (or sensor) is basically a backup for any of the other three legs (sensors); we consider it to be a parallel system to the other legs. To calculate the combined reliability of systems in parallel, we multiply the probability of failure of each.

The probability of failure of a sensor as well as its ‘backup’ sensor is 0.05 x 0.05 = 0.05 2 =  0.0025 (0.25%), equivalent to a reliability of 99.75%. So the reliability of three sensors with a ‘backup’ fourth sensor is 99.75% x 99.75% x 99.75% = 99.25%. And the reliability of the whole ET system is 99.25% x 99.9% = 99.15%. That’s a big improvement over a 3-sensor target system.

With eight sensors, each sensor now has effectively six backup sensors. So the probability of failure of each sensor including its backups is 0.05 6 = 1.56 x 10 -8, equivalent to a reliability of 99.999998%. So the reliability of three sensors each with six backup sensors is 99.999998% x 99.999998% x 99.999998% = 99.999995%. And the reliability of the whole ET system is 99.999995% x 99.9% = 99.89999%. You can see that the overall reliability of an 8-sensor target system would be extremely high. And the reliability of the target itself is – to all practical purposes – one hundred per cent.

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