Speed and distance accuracy
This test measures the combined accuracy of the speed measurement and the pulse output. Measuring the speed accuracy of the SPEEDBOX by comparing the results to those of a reference speed measurement technology was not possible, to do so would require a technology which has proven accuracy much higher than that claimed by the SPEEDBOX, and nothing is available which can provide this. As such, validation of the speed has to be done indirectly.
For the test, two reflective barriers were placed approximately 40 meters apart along a straight section of the test track. A high speed combined laser emitter/detector unit was mounted on the side window to shine out of the vehicle at 90° to the direction of travel, as illustrated below. As the beam hits each of the reflective barriers the laser sensor generates a pulse; producing a pulse at the start and end of the test distance.
Laser and reflective barrier installation
The test system was configured to count the number of pulses output by the SPEEDBOX between the two reflective barriers.
The test consists of driving the test vehicle at a variety of speeds and whilst accelerating and decelerating past the barriers.
If the test vehicle follows an identical path between the barriers and no errors are present in the SPEEDBOX output, the number of pulses counted between the barriers will be identical for every test.
If a scaling error exists on the SPEEDBOX output, the error in the number of pulses counted will vary in proportion to average speed between the barriers.
If significant output latency exists in the SPEEDBOX output, the number of pulses counted will rise or fall depending on the differences in speed between the entrance and exit barriers. The error from latency is approximately 0.44mm / ms latency / mph speed difference between start and end of test, neglecting 2nd order effects. A brake test from 60mph to 0mph with a latency of 10ms would give a distance error of approximately 0.26m
If the SPEEDBOX was fundamentally inaccurate or inconsistent the pulse count would vary in other manners depending on the cause of the problem.
This type of test is exceptionally challenging for any speed measurement device – any deficiencies in the SPEEDBOX GPS, the GPS/accelerometer combining, or the output stages would be very clearly visible. In practice this test is even more demanding than a braking distance test and more clearly highlights any latency problems.
In total 15 tests were carried out under a wide variety of conditions, from almost constant speed to maximum (1g) braking and acceleration. The measured speed profiles between the barriers are shown below (for clarity the steady state tests have been removed).
Measured speed profiles between reflective barriers
A detailed investigation of the results from one test can more clearly demonstrate the test methodology. The illustration below shows the vehicle speed taken from the analogue output and the pulse count from the digital output. The vehicle is accelerated to approximately 70mph and passes the first barrier at (approximately) constant speed. Once past the barrier, maximum braking force is applied, exiting the trap whilst decelerating at approximately 1g. The pulse count starts from zero when the first barrier is passed, and stops as soon as the second barrier is passed.
Vehicle speed and pulse count versus time for one test
The following table is a summary of all 15 tests carried out. The manually measured distance is 48.76m.
|Test||Entry Speed [mph]||Exit Speed [mph]||SPEEDBOX Pulse Count||'''Maximum Acceleration in Test [m/s2]]||Distance Error|
|Absolute Maximum Error||6cm|
|95% confidence limit on error||3.1cm|
From these results the maximum error was 3.1cm with 95% confidence. These errors consist of errors from the SPEEDBOX and measurement errors. Obvious sources of experimental error include:
• Inconsistencies in the driven path
• Latency on the exit barrier response time
• Movement of the barriers (due to air movement)
• Angular movement of the laser/detector in its mounting
Since many of these errors would not be present in a typical braking test, it can be expected that the error in such a test would typically be in the 2cm range (with 95% confidence), which equates to approximately 0.04% error for the 48.76m distance between the reflective barriers used in these tests.
Low speed tests
Low speed tests provide the severest challenge to the accuracy of non-contact speed measurement systems. Errors often show up as high noise when stationary. Many manufacturers remove this noise by implementing a crude zero-clamp on the output, so it is impossible to see any data below 0.5m/s, for example. This is a particular problem with all GPS speed sensing systems as speed errors at rest are normally significantly higher than speed errors when moving (the reason for this is that noise on the speed output becomes a measurement error at speeds below the noise threshold, since a positive scalar speed value is always output).
The illustration below shows the final seconds of a coast down test, showing the vehicle decelerating very slowly to rest and then gently pulling away. From this test it can be seen that the output is not clamped to zero and the stationary error is less than 0.1m/s.
SPEEDBOX stationary noise
This low noise is further demonstrated in the following illustration. The test vehicle is stationary for around 40 seconds, at which time the vehicle pulls away very slowly to a fast walking pace and then slows back to a stop
SPEEDBOX stationary noise
Effect of combining GPS and accelerometer data
There are three key advantages to combining GPS data and accelerometer data:
1. Faster update rates. GPS can be sampled at very high frequencies (there is no theoretical upper limit). However, the noise on the measurement increases along with the sample rate. In a perfect GPS environment up to 100Hz is possible, but at these high sample rates even driving past a tree can cause accuracy problems. In practical situations 20Hz is normally considered a good balance between update rate and low noise. In contrast, accelerometers can be sampled at >1kHz without encountering noise inaccuracies.
2. If the GPS signal is lost for a short period of time the accelerometers are used to “fill in the gaps”. For example, driving under a bridge will stop a GPS receiver working for a few seconds, however no error would be seen on the SPEEDBOX output as the speed data would be filled in by accelerometer information as shown below:
SPEEDBOX output during GPS signal dropout
3. Combining the accelerometer data and the GPS data also has the effect of reducing the noise on the GPS speed signal whilst testing in imperfect GPS conditions. These imperfect conditions could be the result of driving past trees or intermittent lock from some satellites becoming obscured by buildings etc. The following example is very typical of data taken on a highway flanked by buildings. It is important to note that the speed data is not filtered in any way and there is no interpolation of the data, it is simply because the GPS and accelerometer data has been combined and the accelerometers have far lower noise – no dynamics are lost in the combining process.
Typical SPEEDBOX output data recorded along built up highway
This reduction in noise on the speed data is more obvious in the data set shown below, which includes driving past taller buildings which significantly increases the noise on the raw GPS speed data.
Typical SPEEDBOX output with poor GPS reception