GNSS: Principles and Errors

The four systems

There are four main GNSSs:

NAVSTAR GPS — the USA's NAVigation System with Timing And Ranging Global Positioning System;

GLONASS — the Russian GLObal NAvigation Satellite System;

Galileo — the European system, under construction;

BeiDou — the Chinese system, under construction.

All four systems consist, or will consist, of a constellation of satellites which a suitably equipped receiver can use to determine position. The rest of this lesson works through how, mostly on the example the exam prefers: GPS.

Two services, two frequencies

The system serves two audiences; there are two modes of operation:

Standard positioning service (SPS) — for civilian users; originally designed to provide them with a less accurate positioning capability than PPS.

Precise positioning service (PPS) — for authorised users.

The split lives in the radio spectrum: each satellite broadcasts ranging signals on two UHF frequencies, called L1 and L2 (UHF: ultra-high frequency); SPS is a positioning and timing service provided on L1, while PPS uses both L1 and L2. On L1 itself ride two codes: a coarse acquisition (C/A) code and a precision (P) code, and the P code is not used for SPS: the civilian receiver lives entirely on the C/A code on L1.

The signal and the message

What the satellites actually transmit is code: a coded signal used for ranging, for identification (each satellite has an individual PRN code), for timing and for navigation (PRN: pseudo-random noise). The code reaches the carrier by the phase modulation of the propagation lesson: the carrier reverses phase at the code's bit changes, which is how every satellite can share the same two frequencies and still be told apart by its own code. Woven into the transmission, the navigation message carries the receiver's homework:

satellite clock correction parameters;

UTC (Universal Time Coordinated) parameters;

an ionospheric model;

satellite health data.

Two of those deserve a sentence. The ionospheric model is used to calculate the time delay of the signal travelling through the ionosphere, the layer the propagation lesson taught as a bender of radio waves and which here acts as a delayer of them. And behind everything stands the clock: the satellites are equipped with atomic clocks, which allow the system to keep a very accurate time reference. A system that navigates by timing signals is only ever as good as its clocks.

Three segments

Organisationally, a GNSS has three segments:

The space segment — the constellation.

The control segment — comprises a master control station, a ground antenna and monitoring stations, and provides the monitoring of the constellation status, the correction of orbital parameters and the uploading of navigation data to the satellites.

The user segment — every receiver, from the panel of an airliner to a telephone: it only listens.

From ranges to a fix

What the user gets: GNSS supplies three-dimensional position fixes and speed data, plus a precise time reference. The mechanism is timing: the receiver determines the distance to a satellite from the difference between the time of transmission by the satellite and the time of reception. But the receiver's own clock is a cheap quartz one, so the initial distance calculated is called a pseudo-range, because the difference between the receiver's and the satellite's time references initially creates an erroneous range.

Geometry turns ranges into position: each range defines a sphere with its centre at the satellite, and the receiver sits where the spheres intersect. Count the unknowns: there are four unknown parameters, x, y, z and the receiver clock error, so ranges to four different satellites are required to get the position, and in solving them the receiver synchronises itself to the correct time reference when receiving four satellites: the fourth measurement turns the cheap quartz clock into an atomic-grade one, as a by-product of the fix.

Speed and integrity

Speed comes from the same signals: the receiver calculates the aircraft's ground speed using the SV (space vehicle) Doppler frequency shift, or from the change in receiver position over time: the propagation lesson's Doppler once more, this time read off satellites. Trust needs its own machinery: receiver autonomous integrity monitoring (RAIM) is a technique that ensures the integrity of the provided data by redundant measurements, and RAIM is achieved by consistency checks among the range measurements: with more ranges than the fix needs, the receiver can ask whether they all agree. The count matters: basic RAIM requires five satellites, and a sixth is needed to isolate a faulty satellite from the navigation solution: five to notice something is wrong, six to say which one it is and carry on without it.

Between the systems themselves: agreements have been concluded between the appropriate agencies for compatibility and interoperability of the NAVSTAR and GLONASS systems for any approved user, which matters because the different GNSSs use different data with respect to reference systems, orbital data and navigation services: a receiver mixing constellations must reconcile their differing frames before the ranges can share one fix.

The error budget

The most significant factors affecting accuracy, listed for the exam:

ionospheric propagation delay;
dilution of precision;
satellite clock error;
satellite orbital variations;
multipath.

From all of these a user equivalent range error (UERE) can be computed: one number for how wrong a single range may be. The list's head is no accident: the ionospheric delay is the most significant error, and the error from the ionospheric propagation delay (IPD) can be reduced by modelling, using the broadcast model of the ionosphere, or almost eliminated by using two frequencies: the delay depends on frequency, so a receiver hearing both L1 and L2 can measure the ionosphere instead of estimating it. Multipath is the propagation lesson's acquaintance in new clothes: the signal arriving by more than one path, here reflected off the airframe and the ground near the antenna, corrupting the timing. Orbits drift too: errors in the satellite orbits are due to solar winds and the gravitation of the Sun and the Moon, which is why the control segment corrects orbital parameters at all.

Geometry has the last word: dilution of precision arises from the geometry and the number of satellites in view, and is called the geometric dilution of precision (GDOP): ranges from satellites bunched together cross at shallow angles and pin the position poorly, while ranges from a well-spread constellation cross steeply and pin it tight. The UERE in combination with the GDOP allows an estimation of the position accuracy: how wrong each range may be, times how badly the geometry multiplies it.