Automatic Positioning by Redundant Measurements - Böhme, Jahann F. (The International Hydrographic Review, 2015)
The paper investigates a short-range positioning system, e.g. for surveying of rivers, using electromagnetic phase measurements. The system consists o f a transmitter on a ship and three shore based transponders. For computing the initial position for a calibration, differences of ranges to four successive transmitter positions are measured. The differences yield an overdetermined hyperbolic equations system for the unknown coordinates of the transmitter positions. The redundant measurements are used to get a unique solution o f the equations system in almost all situations. The equations system is well adapted for an iterative, numerical solution by means of the secant method. The algorithm o f an automatic positioning system is developed which calls the radio link for suitable measurements, computes the above indicated hyperbolic method for a calibration, uses only two transponders and computes the classic range-range method if the last position is known, checks periodically the result of the range-range method by means of two redundant measurements from the third transponder, restarts the hyperbolic method in the case of an error, and informs the operator when the course should be altered. Some results of numerical experiments and some properties of the algorithm are reported which show that the proposed hyperbolic method can be advantageous in application.