Sect_3.2.2

3.2.2 The GPS Measurements:

PSEUDO-RANGES MEASUREMENT

Ranging with the PRN Codes

Consider for a moment a perfect system where all satellite clocks are synchronised to the same time system: GPS Time. Furthermore, the ground receiver's clock also maintains the same synchronisation, and none of the clocks drift with respect to the GPST scale. Now suppose the satellite starts transmitting its L1 carrier (modulated with the combined C/A code and navigation data), and at the same instant the receiver begins generating the C/A code corresponding to that particular satellite (see Figure below). Under these circumstances, the satellite and receiver generated C/A codes would be output in unison. However, when the satellite signal is received it will be lagging the receiver generated code due to the signal transit time. Multiplying the time offset required to align the two code sequences within the code-tracking loop (one from the received satellite signal and the other an internally generated code) by the speed of electromagnetic radiation yields the satellite-receiver range.

Figure 1. One-way ranging using PRN codes.

Measuring ranges simultaneously in this fashion to three satellites would fix the receiver's position at the intersection of three spheres of known radii (the satellite ranges), centred at each satellite whose coordinates can be calculated from the Navigation Message, as illustrated in Figure 2.

Figure 2. The geometric problem of 3-D positioning from ranges.

In reality the situation is more complex:

Receivers are generally equipped with quartz crystal clocks that do not necessarily keep the same time as the more stable satellite clocks (these clocks can be approximately synchronised to GPST using the clock correction model transmitted in the Navigation Message -- section 3.3.2). Consequently each range is contaminated by the receiver clock error. This is the reason this range measurement is referred to as a "pseudo-range". Hence, to determine position using pseudo-range data, a minimum of four satellites must be tracked and the position determination problem is therefore one requiring the solution of four equations (one per observation), each containing four unknowns: the three-dimensional position components and the receiver-clock offset (from GPST). This is the basis of GPS (real-time) navigation as described in section1.4.2.
Ranging (and hence receiver position determination) can be carried out using the C/A code or the P code. P code ranging can be performed on either of the two frequencies, or a linear combination of the L1 and L2 pseudo-ranges that largely eliminates the bias due to ionospheric refraction (section 6.2.7). Furthermore, the C/A code resolution is "coarser", and hence the C/A derived ranges are subject to greater measurement "noise". The absence of a C/A code on L2 is intentional, as one of the accuracy limitations of the GPS system. Others are the ability under the policy of Anti-Spoofing to restrict access to the secret Y code to only "authorised" users (such as the military and those working in the "national interest" of the U.S. and its allies), and implementation of the policy of Selective Availability.
This distinction between the ranging codes, and the associated policies for their use (in peacetime and in times of global emergencies), results in the provision of two GPS positioning services: the Precise Positioning Service based on P code (dual-frequency) ranging, and the Standard Positioning Service based on single frequency C/A code ranging.

Recovery of PRN Ranging Codes from the Incoming Signals

The PRN codes are accurate time marks that permit the receiver's navigation computer to determine the time-of-transmission of any portion of the satellite signal. Before examining this in detail it is necessary to consider, in general terms, how the incoming satellite signal is processed within the GPS receiver. Within the electronics of a receiver tracking "channel" the L1 carrier modulated by the C/A code is mixed with a locally generated replica C/A code. The local C/A code is generated on a different time scale to that of the incoming C/A code (due to non-synchronisation of the receiver clock to GPST, and the travel time of the signal from the satellite to the receiving antenna). Alignment of the incoming signal with the receiver generated C/A code is carried out by the code-tracking loop, or the "delay-lock loop" electronics. As soon as the incoming signal and the receiver C/A code sequences are aligned within the receiver (by sliding the received code sequence against that internally generated sequence), the "0"s and "1"s of the two codes cancel, leaving the incoming carrier signal modulated only by the binary Navigation Message. This process is summarised in Figure 3 below.

Figure 3. Recovery of ranging code.

Because of the complexity of the P code sequence (its length and higher chipping rate), a sliding correlation technique as described above for the C/A code cannot be used in practice without a very good estimate of GPST and receiver position. Typically a P code receiver must acquire lock on the C/A code first, then use a timing mark known as the "Handover Word", contained within the Navigation Message, to enable the correct portion of the P code to be generated within the receiver and thus initialise the P code delay-lock loop.

Extraction of the Pseudo-Ranges

As mentioned already, the extraction of the pseudo-range, or more precisely, the determination of the amount by which the receiver generated PRN code must be shifted to align it with the incoming signal, is carried out with the aid of a PRN code correlator in some delay-lock loop scheme (see, for example, TALBOT, 1987; LANGLEY, 1993). How accurate is this carried out? The C/A code has a chip rate of 1.023Mbps, corresponding to a wavelength of about 300m (speed of light divided by the frequency). The P (or Y) code, on the other hand, has a chip rate of 10.23Mbps, and hence a wavelength of about 30m.

As a "rule-of-thumb": the alignment of the incoming and receiver generated codes is generally possible to within about 1-2% of the chipping rate, hence the measurement precision of C/A code ranging is of the order of 3-5m, and for P code ranging it is of the order of 0.3-0.5m. (Modern "narrow correlator" technology has demonstrated 10 times better correlation performance for the C/A code than that above.)

The main advantages gained by using the P code therefore are:

Because of the higher chipping rate, and hence higher measurement precision, P code ranging translates into a more accurate position fix.
The P code is modulated on both the L1 and L2 carriers, hence the ionospheric signal delay can be overcome.
P code receivers are better suited to high dynamic environments and resist signal jamming better than C/A code receivers.

Both the P and C/A code ranges are susceptible to multipath (though the susceptibility is inversely proportional to the signal frequency). Multipath is caused by extraneous reflections from nearby metallic objects or water surfaces reaching the antenna and causing the signal measurement process to become noisy than normal. Some characteristics of multipath are (section 6.2.12):

Multipath can cause "jumps" in the signal measurement of the order of its (effective) wavelength. For pseudo-ranges this could mean tens or hundreds of metres, but of the order of only centimetres for carrier phase measurements.
Multipath is receiver-satellite geometry dependent, and the causes of multipath tend to be permanent features (metallic fences, buildings, chimneys, superstructure, water surfaces, etc.), hence the multipath effect will generally repeat on a daily basis at the same receiver site.
As the receiver-satellite geometry changes (and hence the angle of incidence and reflection of the signal with respect to the reflective surface changes), the multipath effect changes, and generally "averages out" over a period from several minutes to a quarter of an hour, or more. This makes static GPS positioning more accurate and reliable than in the case of positioning a moving GPS receiver (using either pseudo-range or carrier phase data).

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