When your problem is life ... and statistics

We have been having slight issues with some elements of the race track system, today I decided to have a look at some of our problems using Matlab.

The issue is that there is a lot of noise in our accelerometer readings on the car. This makes distance and speed estimation rather tricky as errors are quickly accumulated and there is no easy way to get rid of them. So far we are implementing speed traps to try and give us defined locations and speeds for the car regularly.

While this does work, the autonomous car still has a tendency to floor the accelerator or brake at very odd points. I had a suspicion that these problems were arising from random noise in the acceleration readings, and set out to use Matlab to simulate a bunch of trials with lots of noise to see what the effect of this noise was.

For the simulations a constant acceleration of 1ms-2 had noise (normally or gaussian distributed with variance of 1) added to it. These acceleration readings were fed in to a set of equations mirroring those that run in the autonomous car and the distance/velocity predictions were recorded after a second. The beauty of using a computer like this is that (provided you have enough time) running a single trial is as easy as running 1000. For those interested the actual result of this test should be a final speed of 1ms and a final distance of 0.5m.

The results, surprise, surprise  seem to follow normal distributions:

Normally distributed with a mean close to the correct value, but an enormous spread of results.

Final velocity predictions were no better, although the mean was rather close

There are several things to note with this small experiment.

Firstly the noise in the acceleration readings was chosen at random, I will need more information from team members before I can make this more accurate. The noise profile is still plausible, if it is noise affecting our results chances are that it follows a normal distribution and a change in our readings of ~1ms is not impossible, given that we are reading from an analog accelerometer connected by long wires passing though an electrically noisy environment (with the car motor and track contact brushes).

Secondly, gaussian noise (the noise modeled) averages out to nothing if you wait long enough. Given how distance and velocity are calculated, this averaging out should be passed on to them in this particular scenario. Thus these two distributions are the best possible we might expect from our car. Ever.

This is a problem as much of the car's decision making relies on it having a good idea of where it is and how fast it is going, getting both of these bits of information wrong would explain some of the weird behaviour we have been seeing.

This is not a deadly problem, my next task will be to test some more complicated scenarios including varied acceleration and then work out a convolution I can use on the readings to try and give a more consistent result.

Until then!