Sect_6.2.12

6.2.12 Measurement Biases and Errors

MULTIPATH DISTURBANCE & SIGNAL INTERFERENCE

The carrier wave propagates along a straight line (not quite, there are small bending effects due to the presence of the atmosphere). Multipath is caused by extraneous reflections from nearby metallic objects, ground or water surfaces reaching the antenna. This has a number of effects: it may cause signal interference between the direct and reflected signal (see Figure 1 below) leading to noisier measurement, or it may confuse the tracking electronics of the hardware resulting in a biased measurement that is the sum of the satellite-to-reflector distance and the reflector-to-antenna distance.

Figure 1. The multipath effect is a result of signals from a satellite reaching the antenna over more than one path.

The magnitude of the multipath effect on a phase observation can be estimated from the following mathematical relation (HOFMANN-WELLENHOF et al, 1998):

(6.2-18)

where:

_m is the shift in carrier phase of the combined signal received at the antenna due to multipath,

is the phase shift of the reflected signal with respect to the direct signal, and

is a damping factor which varies between 0 (no reflection) and 1 (reflected signal as strong as direct signal).

Some characteristics of multipath are:

Multipath can cause "jumps" in the signal measurement which are a function of frequency. The theoretical maximum multipath bias that can occur in pseudo-range data is approximately half of chip length of the code, that is, 150m for C/A code ranges and 15m for P (Y) code ranges. Typical errors are much lower (generally <10m). The carrier phase multipath does not exceed about one-quarter of the wavelength (when = 1 and = 180° in eqn (6.2-18) ) -- 5-6cm for L1 or L2, 20cm for L5, etc.
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 in a sinusoidal pattern, and generally "averages out" over a period from several minutes to a quarter of an hour, or more (Figure 2 below).
Multipath is receiver-satellite geometry dependent, and the causes of multipath tend to be horizontal, vertical, or oblique planes/objects (such as metallic fences, buildings, chimneys, superstructure, water surfaces, etc.), hence the effect of the multipath error on positioning will generally repeat on a daily basis for the same baseline (Figure 3).
There is no general mathematical model to determine or predict the effect of multipath on a position solution, however its effect on a range observation may be measured using a combination of L1 and L2 carrier phase and pseudo-range data (section 6.4.9).
Multipath will bias the baseline results as a function of the percentage of observed data that is multipath-affected, and the amplitude of the multipath phase disturbance.
The impact of multipath error on kinematic positioning is greater than that on static positioning, because in the former the error propagates into an incorrect position solution (Figure 3), whereas in the case of static positioning the multipath error propagates into the residuals (implying a less precise solution).

Figure 2. Sinusoidal signature of multipath effect on measurement residuals.

Figure 3. Single epoch baseline length solutions for a static baseline on consecutive days.

Some options for reducing the effect of multipath are:

Make a careful selection of antenna site in order to avoid reflective environments.
Use a good quality antenna that is multipath-resistant.
Use an antenna groundplane or choke-ring assembly (section 4.1.2).
Use a receiver that can internally digitally filter out the effect of multipath signal disturbance.
Do not observe low elevation satellites (signals are more susceptible to multipath).
In the case of pseudo-range positioning (single point or differential), averaging the computed results over a period of time will reduce the contribution of multipath errors on the averaged pseudo-range solution.
In the case of carrier phase positioning, longer observation sessions will tend to diminish the impact of multipath on the final baseline results.

Signal Jamming and Interference

There is considerable concern about the effects of intentional and unintentional signal jamming and interference on critical GPS navigation applications. There is much anecdotal evidence, as well as tests results (SLUITER & HAAGMANS, 1995), to indicate that a problem exists in this regard. The disturbance to the incoming signal is a function of the frequency of the disturbing signal (it must be at or close to the GPS carrier frequencies or its harmonics), the distance from the jamming transmitter, and its power. In the surveying context, such signal disturbances are likely to manifest themselves as noisier than normal observations or, in extreme cases, the occasional loss-of-lock on the signal (and subsequent cycle slips). Hence, be suspicious of TV and microwave transmission towers, and various types of radar.

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_m	is the shift in carrier phase of the combined signal received at the antenna due to multipath,
	is the phase shift of the reflected signal with respect to the direct signal, and
	is a damping factor which varies between 0 (no reflection) and 1 (reflected signal as strong as direct signal).