notes

1. The principles of Hyperbolic Positioning
HiFix was a short range precision positioning system primarily for marine hydrographic survey purposes, capable of
providing a fix with an accuracy of about 1.5m at 30 miles from the shore stations. HiFix was a hyperbolic system using a
chain of three transmitters, one as master and two as slaves. As with most such systems, for example Decca, the operating
principle was that the transmitters radiated a carrier phase locked to an accurate source, and the receiver measured the
difference in phase between the signals received from the three transmitters. Unlike Decca however, where the transmitters
radiated a continuous transmission on different but harmonically related frequencies, HiFix used the time-share principle
where the transmitters radiated on the same frequency, but in sequence. This is explained further in the 'System
Description' section.
The principle on which all hyperbolic navigation and positioning systems operate is essentially the same. If two transmitters
radiating a radio wave in the same phase are located at the ends of a baseline, as shown in the diagram below, then a
receiver in the centre of the baseline will receive the wave in the same phase since the time-of-flight of the wave to the
receiver from both transmitters is the same. It therefore follows that, if the receiver is receiving the two waves in phase,
then it must be located either at the centre of the baseline or somewhere along the perpendicular line l - l'.
If we were to plot points of equal phase difference between the carrier received from the 2 transmitters, we will get a family
of curves instead of a straight line. These curves are referred to as hyperbolae, and a set of hyperbolae generated by the
master and one slave are referred to as a pattern. If, at the receiver, we are receiving signals with a particular phase
relationship then we know that we are somewhere along one of these curves.
In practice, the transmitters are further apart than a single wavelength (which is only about 160 metres in the case of HiFix
on 1900 kHz) so consequently there are many places where the pattern repeats- each repetation is called a 'lane'.
In order to give a navigational 'fix'- i.e. to find out exactly where on the curve we are, we need another pair of transmitters
and to carry out the phase measurement process on the pattern produced by these as well. The hyperbolae from this

2. second pair will overlap those from the first, producing a 'lattice': If we can establish our location along a hyperbola from
each pattern, then we have found our position. In practice, one of the transmitters can be common to both pairs- with
HiFix, this is the Master or A station; those at the ends of the two baselines are the B and C slaves. The diagram below
shows a section of coastline with the 3 sites and their overlapping pattern of hyperbolae. It must be remembered that the
fix was always in relation to the position of the chain transmitters, and these had therefore to be accurately known.
Resolution
Points of zero phase difference are referred to as 'lanes'. It is not necessary to rely on these however since the receiver can
measure phase differences at points in between lanes. The maximum resolution of the system is expressed as the smallest
distance within a lane that can be measured and is limited by a number of factors. In the case of HiFix the maximum
resolution of the system is given as 0.01 lane, which at an operating frequency of 1900kHz would be 1.6 metres. Since the
distance between hyperbolae and hence lanes increases with distance away from the transmitters, the accuracy of the
system reduces in proportion. The operator would have to take this into account when a fix is obtained.
Lane Ambiguity
As stated above, there are actually several points where the same phase relationships can be measured from both the A-B
and A-C sectors of the chain. The result of this is that a fix is not unique. This is a characteristic of hyperbolic systems, and
is referred to as 'lane ambiguity'. Different radio location systems tackle the problem in different ways. Decca, for instance,
periodically broke the normal transmission format and transmitted a signal that enabled the receiver to get a rough fix- to
within a lane. On resumption of the normal transmission, phase measurements were taken and the exact postion within the
lane displayed
HiFix in its simplest form had no inherent capability to resolve lane ambiguity. The receiver did, however, have a 'lane
counter' display. Therefore, a navigator using HiFix always had to start from a known position- perhaps by taking bearings
on visual objects or radio beacons on the shore. As the vessel moved, lane counters incremented every time a complete
lane was crossed. Users would still have to periodically mark a position with a buoy. Ultimately this was a major drawback,
and a system using two radio frequencies was developed (mode B) which could be used to give lane resolution. This used
the fact that at different RF frequencies, the lane pattern shifts. Subtracting one pattern (the higher frequency) from the
other results in a coarse lane pattern that allows the user to fix their position to within half a lane.
Range-Range Operation
An alternative to hyperbolic mode was Range-Range mode. This involved carrying the master transmitter actually aboard
the vessel, whilst the slaves remained ashore. The receiver, also aboard the vessel, would therefore be at zero distance
(and therfore phase difference) from the master transmitter. With this arrangement, instead of hyperbolae, a set of
concentric rings around each slave were obtained, and positional fixes could be obtained where the rings overlapped. The
advantage of this approach was that the spacing of the rings stays the same as the vessel moves away from the shore, so
the resolution may be higher at greater ranges but the angles at which they intercept become less favourable. Nevertheless
under particular conditions, an improvement in accuracy over hyperbolic mode could be obtained.

3. Accuracy and sources of error
Several factors influenced the accuracy obtainable under practical conditions. The first of these was the siting of the master
and slave stations. For best results they would ideally have been located with the baselines at an angle to each other. They
also needed to be located right on the coast, since radio waves refract as they cross the coastline. Also, the accuracy of the
system would have been affected by radio propagation conditions; in particular after dark when the signals become
reflected by the ionosphere and therefore interfence from the sky wave would have occurred. The Hi-Fix antenna system
was designed to minimise sky wave radiation, nonetheless at night it was often possible to receive the chain at greatly
increased range. Navigators were warned not to rely on fixes under these conditions.
Last Modified 21/11/07