AN APPRECIATION OF THE PROGRESS IN NAVIGATION FROM THE PERSPECTIVE OF KALMAN FILTER

摘要

Navigation has an exciting role in the evolution of human society. Its progress since antiquity can be viewed in three phases namely mythological, medieval, and modern respectively around the millenniums from 10000 BCE up to 900 CE, centuries from 900 CE to 1900 CE, and decades from 1900 CE to the present. Some typical events in the above phases provide a reference view of the progress. The ancients finding the sea route easier and more profitable than over land constructed ships and intuitively used winds, tides, birds, sea depths and later the celestial objects for navigation. The medieval phase involved sun, moon, stars, magnetic compass, astrolabes, cross staff, sextant, together with charts, and later calculus and chronometer helped them to explore the earth more effectively for commerce and conquest. Towards the end of this period the seeds were laid for inertial and radio navigation. The modern phase saw the development of radio, inertial, and satellite navigational systems. The data from many of the systems can be fused using in particular Kalman filter. The approaches during the three phases can be characterized respectively as correlational, calculational and computational (with increasing speed and accuracy) or as intuitive, practical, and modeling. The progress of navigation can also be seen from the perspective of Kalman filter as an expanding knowledge front by assimilating newer information as best as possible. In a Kalman filter the state and measurement quantities are generally different and its operation also needs certain conditions to be satisfied. In navigation the estimated state is position, and if possible velocity and acceleration but generally the measurements are such as angle, acceleration, and arrival time of a signal. The filter has to suppress the effect of noise, fuse and assimilate the measurement data, to improve qualitatively and quantitatively both the system and measurement models. The development of more accurate maps, shape, and tectonic plate movements of the earth is an example of improved state estimation. The modern satellite navigation has to handle the errors introduced by the intervening atmospheric constituents through which the signals propagate which can also be estimated by a proper modeling thus providing an expansion of the scenario. Here the filter estimates the unobserved quantities thus going beyond the position estimation of navigation. An analogy for the filter operation in many aspects of life and society where the observation and inference are different is also provided.