Like everything, inertial navigation has its strengths and weaknesses. While inertial navigation systems are undoubted good at measuring position, orientation and dynamics, the one Achilles heel of basic un-aided inertial navigation systems is drift.
Un-aided means systems that only use accelerometer and gyro measurements to calculate their position. Drift is the term used to describe the accumulation of small errors in the accelerometer and gyro measurements, which gradually cause the INS position estimate to become more and more inaccurate.
What is INS Drift?
Understanding why drift occurs is quite easy. Imagine measuring a length of wood with a single 5 m-long tape measure. If you can read the divisions on the tape to an accuracy of 1 mm, then you could easily declare that this piece of wood is 4 m long ± 1 mm. If on the other hand the only tape measure you could find was 0.5 metres long, and you can still only read it to an accuracy of 1 mm, then by the time you have measured and moved along with the tape measure eight times, you would only be able to say that the wood is 4 m long ± 8 mm. In fact, you might not make it 4 m at all.
Inertial navigation drift accumulates in the same way. Each time an accelerometer or gyro is read, there is a minuscule error in the reading. If we were just taking a single reading to work out how fast we were accelerating or turning, this wouldn’t be a problem. But because the navigation computer is adding up each measurement to work out how it has moved on from the previous position estimate, the minuscule error grows with time.
How drift can accumulate in un-aided INS
This diagram gives a very simplified view of how drift can accumulate in an un-aided inertial navigation system. A great deal of work has been put into systems that minimise the accumulation of these errors, but there’s no getting away from the fact they are there. That does not, however, mean that the principle of inertial navigation systems is useless—or that it’s inferior to GPS for example. Far from it.
Estimation theory
Estimation theory, in the most basic of terms, refers to the way in which a prediction is made based on available data. It is a way of solving the observer problem. The true value of anything can never be known for certain, so we use estimation theory to predict what the true value should be and how good that prediction is. Whilst using data to make a prediction about the true value of something is important, its equally important to know how confident you should be with that prediction. This is because having confidence in a bad prediction can cause more problems than making a known bad prediction in the first place.
Estimation theory allows mathematicians and scientists to make accurate predictions about certain parameters that contain a random component. One of the most relevant examples in the world of inertial navigation comes from how the device calculates its position using other sensors such as a GNSS receiver or more specifically the satellites it’s receiving data from.
For example if an INS is tracking twenty satellites and all twenty of the satellites are providing the same position update, then the INS can be very confident that it is indeed in that position. However, if one of the satellites is suffering from atmospheric interference for instance, and is quoting a position some twenty miles away, how does the INS know to trust the nineteen rather than the one? There needs to be a calculated, methodical way for it to do so.
Now add into the mix other satellites (not just one) giving incorrect readings, and other sensors on a network possibly having their say, and all of a sudden you need a way of analysing all of that data to determine what to trust and what to ignore.
This is where estimation theory comes in – its in essence a theoretical framework for combining information from various sensors and using that data to make accurate predictions about various parameters – like position.
GPS aided INS is the solution
At the beginning of this page, we said that drift was the achilles heel of un-aided inertial navigation systems—so what about aided ones? When you combine an INS with GPS to create a GPS-aided INS (also written as GPS+INS), you solve the problem of drift and also solve the problems that affect GPS too. This is why OxTS can provide customers with the ability to measure with confidence – by providing a complete solution to measure position, orientation and dynamics in all environments. We discuss this in detail in our article ‘What is GNSS?’.
This is one of a series of articles in our ‘What is an inertial navigation system?‘ series.
