Global navigation satellite system (GNSS) and dead-reckoning today T he red vehicle is close to the blue vehicle, however, some distance away in terms of position and heading. Rotate 30° clockwise, move straight ahead from ( D ) 15.8 m to ( E ) in 5 s.Īt the end of the journey, the blue vehicle should have travelled 88.3 m over 22.5 s (not including time required for rotation).Rotate 135° clockwise, move straight ahead from ( C ) 42.5 m to ( D ) in 9.5 s.Rotate 45° counterclockwise, move straight ahead from ( B ) 22.5 m to ( C ) in 5 s.Move straight ahead from ( A ) 7.5 m to ( B ) in 3 s.Note that inaccuracy and drift is exaggerated for illustrative purposes. As you can see, there are discrepancies between the two trajectories due to limitations in sensor accuracy and a tendency for sensors to drift. That is, the INS accelerometers and gyroscopes are estimating linear acceleration and rate of rotation, with an internal timing clock reference. The red vehicle is an attempt to follow the trajectory of the blue vehicle using dead-reckoning by an INS (Inertial Navigation System) only. The vehicle accelerates from standstill (zero velocity) and back to zero over a period between each change of direction. That is, where we actually want to go by distance, time and heading. The blue variant shows the perfect trajectory.

To keep things simple, the vehicle is able to rotate on its Z-axis. We will use the animation below to illustrate a dead-reckoning being applied to a vehicle using an inertial navigation system (INS). So we invent things that can help us do it. Humans, on the other hand, are not particularly adept at dead-reckoning. Many of them rely on dead-reckoning to quickly and reliably return to a safe haven in the face of danger. Interestingly, there are a great many creatures of land, air and sea that can innately dead-reckon with incredible accuracy. Better still, your torch batteries decide to rescue you. Hopefully you remember your initial route well and your estimates of distance by steps and orientation are accurate until you see the glimmering saviour of light. You go back to what you estimate to be your previous straight line direction and distance, then turn in the reverse direction where you think you last turned and by the same amount and travel an estimated distance and so on. Or, you remember where you were on the map when the light went out – your last known position then attempt to retrace your steps by estimating your position. You might immediately panic and start shouting for help, but the echoes only serve to heighten your panicked state. Suddenly, your torch batteries decide to die and you are left in total darkness without any navigation aids or devices. You make turns and move forward then enter different tunnels and so on. Imagine exploring a cave system, slowly heading through it by map and torchlight.

Dead Reckoning by Michael W. Smart