Forced Singular Perturbations as Theoretical Background to a Split-Coordinate Frame Multirate Strapdown Terrestrial Navigation Algorithm

Forced singular perturbations (FSP) are proposed as a theoretical background to Bar-Itzhack´s body−local-level split-coordinate frame multirate scheme intuitively derived for terrestrial strapdown navigation with reduced computations. Forcing the dynamics into distinct time scales caused a degradation of the continuous-time solution, though the loss of accuracy was not significant in comparison with the covered distance. Simulation of ideal sensors undergoing actual operating conditions showed that discretization and use of inertial data in incremental form, however, had a significant impact on navigation acuracy. The interaction between sensor quantization and sensor sampling frequency was investigated. The evaluation of performance in a variety of conditions indicated that the multirate algorithm proposed by Bar-Itzhack, in spite of its elegance and simplicity with reduced computational workload, showed acceptable accuracy in comparison with Savage´s more complex multirate correction terms to coning, sculling, and scrolling errors.