Hyperbolic System operating principles
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.Hyperbolic system prnciples
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. Applying this principle in reverse, 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'.
However, 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 will be several points along the baseline where the signal is received in phase. Unlike the simple case outlined above however, when plotted out from the baseline, these points of equal phase will produce 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 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 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
It may have become apparent to you that 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. This is true and the result 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.
Errors
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.
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