An Introduction to Inertial Navigation From the Perspective of State Estimation [Focus on Education

Abstract

The objective of navigation is to determine the instantaneous location of a moving vehicle. Historically, sailors estimated the speed of a ship by dropping a log into the water and observing the time for it to float from the bow to the stern [1, pp. 21-38]. Combining this speed information with directional data from a compass yields a velocity estimate. Finally, integrating the velocity estimate with respect to time and using the known initial position yields a position estimate at each instant of time. This procedure is called dead reckoning [2, p. 30], [3] or, when performed by animals without the benefit of calculus and digital computation, path integration [4]. Although not all navigation is based on dead reckoning-for example, celestial navigation uses the stars for position fixing-it is widely used due to its ability to utilize speed, direction, and time data from a variety of sensors. By computing position from velocity data, dead reckoning is an integration process. It is important to stress, however, that, because of the lack of observability, dead reckoning cannot take advantage of an observer and, thus, cannot stabilize the integrator dynamics. Therefore, dead reckoning is an inherently unstable process, regardless of how the velocity and direction data are acquired.