Dr. Joseph L. Ryerson

Peer Reviewed

Abstract: RELATIONSHIPS between positions determined by the intersections of hyperbolae defined by the differences in the times of arrival of pulses from three fixed transmitters and those determined by the intersections of circles centered at two of the transmitters provides the means of estimating the systematic errors in the radii of the circles due to clock bias errors. The radii are determined from a clock located at the fix point which is not synchronized with the clock used to establish the sequence of pulses from the transmitters. This clock is assumed to indicate a known function of the transmitter clock time having stationary but unknown coefficients. These coefficients are estimated by least squares methods from a sequence of hyperbolic fixes outside of the exterior base line regions. After the clock synchronization errors are reduced the random time measurement errors of the hyperbolic and circular systems will become comparable. The spatial errors of the circular fixes will be less than those of the hyperbolic fixes. This is due to the greater spatial displacement of a hyperbolic line of position with a time difference error than that of a circle due to a corresponding error in the time of transmission over the radius.
Published in: NAVIGATION, Journal of the Institute of Navigation, Volume 16, Number 4
Pages: 382 - 389
Cite this article: Ryerson, Dr. Joseph L., "DERIVATION OF CIRCULAR FIXES IN HYPERBOLIC NAVIGATION SYSTEMS", NAVIGATION, Journal of The Institute of Navigation, Vol. 16, No. 4, Winter 1969-1970, pp. 382-389.
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