It is well known that in low-frequency hyperbolic navigational systems the phase differences measured by the receiver do not correspond precisely to the hyperbolas on the plotting chart. This is largely because of variations in the terrain over which the waves are propagated. The system service area may be sampled so that the curve distortions can be ascertained at selected points. This article discusses how the whole service area can be calibrated, given a knowledge of the grid distortions at a sample of points. The mathematical treatment takes into account the correlation between the grid distortions at adjacent sampling points by using autocorrelation theory.

The degree to which fixing accuracy is improved by the proposed method of calibration is assessed against the background of an actual set of field measurements.

Mr. Sullivan is Head of the Applied Research Group of the Navigation and Guidance Laboratory at the Institute of Science and Technology. Dr. Porter is Assistant Professor of Electrical Engineering at The University of Michigan, and Head, Analytical Research Group of Navigation and Guidance Laboratory at the Institute of Science and Technology.

In low-frequency ground-wave navigation systems such as Loran-C and Decca, position information is determined from measurements of time and/or phase differences in signals received from several separately located transmitter stations. A pair of stations generates a family of hyperbolic lines which are the loci of points of constant time/phase difference. Two station pairs provide a grid of hyperbolas. By measurement of the time/phase difference between the signals from two transmitters, the receiver is located on a hyperbolic line. The same receiver is located on a second line by similar measurement which uses another pair of stations; the receiver is thus fixed specifically at the intersection of the two lines.