Error Sensitivity Associated with Orbital Hyperbolic-Navigation Schemes and a Suggested Approach for Improvement

摘要

This paper deals with the fundamental mathematical relationships applicable to satellite-linked hyperbolic systems in general (i.e., direct or inverse, the direction of the propagation paths being insignificant). Error expressions are developed for determining the sensitivity of a system to uncertainties in measurement and to satellite geometry. A LORAN satellite system involves obtaining lines of position from the intersection of hyperboloids of revolution with a spherical earth. The resultant second-order equations are solved by a computer using iterative techniques. Solutions in the form of error sensitivities are presented for a number of vehicle-satellite geometric configurations. A particular problem arises when the receiving stations and the propagating sources are located in certain geometrical configurations. Results are presented from the standpoint of navigators' lines of position (LOP's) intersecting at unfavorable angles that can cause the sensitivity to error to become unbounded. The problem becomes more complicated if satellite relative motion is involved because the orientation of the LOP's will change as a function of time. However, results indicate that certain general statements can be made regarding the number of satellites needed and the configurations necessary to meet a specified set of operational requirements. It is pointed out that known satellite velocity information is not being exploited in range only or hyperbolic satellite systems, and it is recommended that further study be directed to the area of the multisatellite, multielement fix-determination processing using range-rate doppler data. (Author)