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Inertial navigation: dead reckoning

Industry Articles October 5, 2020

Using the measurements taken from three accelerometers and three gyros, the OxTS inertial navigation system keeps track of where it is in three-dimensional space. It does this using a process called dead reckoning.

The actual process of dead reckoning is quite easy to understand; you take information from some source (gyros and accelerometers in this case) and turn them into a movement that can be added to your last known position to see where you are now.

A simplified 2D example of dead reckoning is shown here.

Inertial navigation (INS) dead reckoning


You can see that initially the INS is stationary and aligned squarely to the image, with its x-axis pointing straight up. The image then shows three other positions and the information recorded by the sensors between them. Of course, in reality, the INS would update its position tens or hundreds of times per second, but in this example, position updates are only shown when key changes take place for ease of understanding.

So at time zero, the INS is stationary (and does not know where it is). It then sees an acceleration of 5 m/s² on the x-axis accelerometer for 1 second, which gives it a velocity of 5 m/s (or 18 km/h). It then immediately comes to a complete stop—detecting an acceleration of -10 m/s² for 0.5 seconds. As no other measurements were registered on the other sensors, the strap-down navigator can easily work out that it has moved 3.75 metres in the direction of the x-axis. Again, at this point, the INS doesn’t know where it is as we haven’t given it any position information to begin with.

As soon as the INS stops at position update 1, the z-axis gyro detects a value of 90 °/s for 0.5 seconds; so it knows that it has just turned 45° in a clockwise direction. Again, as soon as that movement is complete the INS again sees acceleration on the x-axis accelerometer. This time it’s 1 m/s² for 10 seconds followed by -5 m/s² for 2 seconds. Using the same techniques as before, the INS can work out that it has now moved 60 metres further on at a 45° angle from where it was at position update 1. This is what was meant earlier on when we talked about the fact that an INS’s position updates were relative to the last known position.
The last movement is different from previous ones. At position update 2, you can see the INS has rotated so it has the same orientation it has initially. When it then moves towards position 3 however, we can that the INS is now moving at an angle to its measurement axis (the IMU frame)—it’s moving backwards and to the right at a bearing of 135°.

Because of this movement, acceleration is registered simultaneously on both the x- and y-axis. There is also no negative acceleration causing the INS to stop—so although the measurements on the accelerometers drop to zero after 1 second, the navigation computer knows that the unit still has a velocity. In this case, it’s moving at 7.07 m/s (about 25 km/h), and position update 3 happens 1.5 seconds after the INS leaves position update 2. In that time the INS has covered 7.95 metres.

Like all things, inertial navigation has its strengths and weaknesses. One of the most important to understand in order to get the most accurate position, orientation and dynamics measurements is drift.

This is one of a series of articles in our ‘What is an inertial navigation system? series.

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