How Do You Know Where You Are Without GPS? Dead Reckoning and Inertial Navigation

Summary

Areas of Science

Electricity & Electronics

Difficulty

Method

Engineering Design Process

Time Required

Average (6-10 days)

Prerequisites

Previous experience with Arduino or another microcontroller is recommended. See our How to Use an Arduino page for tutorials.

Material Availability

A kit is available from our partner Home Science Tools®. Additional items required that are not included in the kit.

Cost

Average ($50 - $100)

Safety

No issues

Credits

Ben Finio, PhD, Science Buddies

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Abstract

Put a meter stick on the ground. Starting at one end of the stick, close your eyes and try to walk exactly one meter. Open your eyes. How close were you? Now try it again with five, ten, or twenty meters. Does it get harder as the distance gets bigger? Without an outside reference from your visual system, it's quite difficult to know exactly how far you've gone!

Electronic navigation systems face the same problem. Without an external reference like the global positioning system (GPS), it's very difficult to know exactly where you are or how far you've gone. If you have taken a physics class, you may remember that if you know an object's velocity, you can calculate how far it has traveled in a certain amount of time. Similarly, if you know an object's acceleration, you can calculate how much its velocity has changed in a certain amount of time. This means that, if you can measure acceleration, you can use it to back-calculate position (from a known starting point), even if you cannot always measure your absolute position with something like GPS. This navigation method is called dead reckoning. 

Acceleration is measured with electronic sensors called accelerometers. Gyroscopes are another type of sensor that can measure angular velocity. Accelerometers and gyroscopes can be combined to form an inertial navigation system that can calculate an object's position and orientation. Originally developed for rockets before the invention of GPS, inertial navigation systems are still used today to reduce reliance on GPS in some cases. Navigation systems may include other sensors, like a compass or magnetometer, that can measure orientation relative to Earth's magnetic field. Computer algorithms combine input from all the different sensors to help with navigation.

However, inertial navigation systems have an inherent problem: drift. Small errors in acceleration will result in small errors in the calculated velocity, which in turn result in small errors in the calculated position. These errors accumulate over time, which can rapidly result in inaccurate position values. Even a highly accurate accelerometer can accumulate errors of several meters over just a few minutes! This means that long-term reliance on inertial navigation alone is not a very accurate way to determine absolute position. 

So, how do you turn all of this into a science project? Science Buddies has many projects based on the Arduino platform - a microcontroller where you can connect an external accelerometer. We also have an assortment of projects for the micro:bit, a smaller board with a built-in accelerometer. Can you use either one for an inertial navigation project? Write a simple program to integrate acceleration to calculate velocity, and then integrate velocity to calculate position. If you keep the accelerometer's orientation fixed (for example, sitting flat on a table), you can do this separately for the X, Y, and Z axes without worrying about changes in orientation. How rapidly does the position drift if the accelerometer is just sitting still on the table? If you slide the accelerometer a known distance (measured with an external reference like a ruler), how accurate is the calculated distance? 

For a more advanced project, can you include readings from a gyroscope to calculate orientation? What about a magnetometer? Look into sensor fusion algorithms to learn how the different sensor readings are combined. This is also an interesting project to pursue if you are interested in learning about how drones use sensors to navigate and stay upright. 

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Global Goals

The United Nations Sustainable Development Goals (UNSDGs) are a blueprint to achieve a better and more sustainable future for all.

This project explores topics key to Industry, Innovation and Infrastructure: Build resilient infrastructure, promote sustainable industrialization and foster innovation.

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