Does a navigation algorithm have to use a Kalman filter?

Complications are known to arise when a Kalman filter is used in the design of navigation algorithms. Many improvements have been introduced over the past thirty years. Still, problems seem to occur when navigation based on a single source data is attempted. Such navigation is then somewhat dependent upon the knowledge of the vehicle's dynamics model. This knowledge is almost never available at a level to satisfy the basic reliability requirements. We seek a solution through an approach different from that of Kalman filtering in so far that no physical modelling is called for. We use a purely mathematical approach based on the laws of mechanics (e.g., Hamilton's principle), applied in a statistical space. The result is a new navigation algorithm (NNA) that relies solely upon the measurements of vehicle's positions (and possibly velocities), and their error statistics. The force field in which non-Newtonian forces are at work is induced simply by confidence regions of the position fixes. It is assumed that instantaneous position fixes and their corresponding error statistics can be obtained by one or more navigation services, such as GPS or Loran C. One promising application of the NNA that will be investigated in the near future is the tracking of evasive targets based on position and/or velocity measurements. The results of the new algorithm are presented for a couple of real-life trajectories and a comparison with the best Kalman filter navigation is shown.