Multipath Effect (Physical Influences of GPS Surveying)

Multipath is the phenomenon whereby a GPS signal arrives at a receiver’s antenna via more than one different paths. Multipath propagation affects both pseudorange and carrier phase measurements. In GPS static and kinematic precise positioning, the multipath effect is an error source that has to be taken into account. Related studies have been carried out for many years to reduce or eliminate the multipath effects (cf., e.g., Braasch 1996; Langley 1998; Hofmann-Wellenhof et al. 1997).

Multipath is a very localised effect, which depends only on the local environment surrounding the antenna. As illustrated in Fig. 5.13, the receiver may receive both the direct transmitted signal and the reflected (indirect) signal. The indirect path is obviously dependent on the reflecting surface and the satellite position. The reflecting surface is usually a static one related to the receiver; however, the satellite moves with time. Therefore, the multipath effect is also a variable of time.

Consider the direct signaltmp2A813_thumbwhere A is the amplitude,tmp2A814_thumbis the angular velocity andtmp2A815_thumbis the phase; then the indirect signal can be represented astmp2A816_thumb where f is a factor which has the physical meaning of reduced energy through reflection and St is the time delay. The multipath effect is indeed the influence of the indirect signal on the observations of the receiver. Because different receiver deals with the signals with a different manner, multipath error is highly dependent upon the architecture of the receivers.


Theoretically (Braasch 1996; Langley 1998), the multipath effect may reach up to 15 meters for P-code measurements and 150 meters for C/A-code. Due to the chip length, P-code is much less sensitive to the indirect signal. Typically, multipath error of the carrier phase is on the order of a few cm.

GPS signals are right-handed circularly polarised (RHCP); therefore, conventional GPS antennas are designed as RHCP antennas. This property helps to reject the multi-path signal because the reflected signal has changed its polarisation. The pure reflected signals received by the RHCP antenna usually have only 1/3 of the signal to noise ratio compared with that of the direct signals (Knudsen et al. 1999). This may also be used for detecting multipath effects. The simplest method to avoid the influence of the multipath effects is to set up the antenna far away from possible reflecting surfaces. Using only the carrier phase measurement is possibly the other method. (Code is usually used for clock error correction for the satellite coordinates computation; this would be accurate enough even if the multipath effects existed in code; for details, see the discussion in Sect. 5.5).

Fig. 5.13.

Geometry of multipath effects

Geometry of multipath effects

In the case of code positioning, a phase smoothed code should be used. This can reduce the maximum multipath effects to a few cm.

An exact method to deal with the multipath effects is to detect the multipath using code-phase data, and then reject the related phase data or set the phase data to a lower weight for phase data processing. Recalling the models of the code and phase observables discussed in Sect. 4.1 and Sect. 4.2, a code-phase difference can be formed by using Eqs. 4.7 and 4.18 as

tmp2A822_thumb

wheretmp2A823_thumbare the measured pseudorange and phase,tmp2A824_thumbis the wave length, te is the GPS signal emission time and tr the signal reception time,tmp2A825_thumbdenotes the ionospheric effects of the stationtmp2A826_thumbis the integer ambiguity parameter,tmp2A827_thumbis the multipath effect of code measurements, and e is error of code measurements. The errors of phase and frequency as well as multipath in phase measurements are omitted here. Using the above formula, multipath effects in code measurements can be determined or detected. Because of the higher noise level of the code measurements, detection over a given period of time is reasonable so that the noise can be smoothed.

GPS-Altimetry, Signals Reflected from the Earth-Surface

The existence of multipath effects indicates that a GPS receiver can be used for receiving the reflected GPS signal. That is to say, through receiving the reflected GPS signal, GPS may be used for measuring the reflecting surface topography. Early in 1993, the European Space Agency’s Manuel Martin-Neira first suggested using a GPS reflected signal as a signal source for measuring. The accidental acquisition of ocean-reflected GPS signals by an airborne receiver was reported by French engineers in 1994. Katzberg and Garrison (1996) discussed how the GPS signal reflected from the ocean can be used for the determination of ionospheric effects in satellite altimetry. Komjathy et al. (1999) used the GPS signal reflected from the ocean to determine the wave height, wind speed and direction. Knudsen et al. (1999) used a downward-pointing GPS antenna to receive the reflected GPS signal to see if it was possible to use it for determining the topography of the sea surface and ice sheet as well as snow covered land. CHAMP satellite has a downward-pointing GPS antenna on board for an experiment of GPS-altimetry.

Usually, profiles of footprints over the sea surface are measured from satellite al-timetry or airborne altimetry; however, by using GPS-altimetry, every profile of footprints has a bandwidth, so that such GPS-altimetry can be used for covering the topography of the reflecting surface. The sea and ice sheet as well as snow covered land are good reflecting surfaces for the GPS signals (Knudsen et al. 1999).

The polarisation of the reflected signal changes after the reflection. A conventional GPS antenna is right-handed circularly polarised; therefore, for receiving the reflected GPS signals a left-handed circularly polarised antenna shall be used (Komjathy et al. 1999; Katzberg and Garrison 1996). Such an antenna has been designed and used in the experiments reported. The power of the reflected signal is then reduced insignificantly.

Fig. 5.14.

Geometry of the reflecting signal

Geometry of the reflecting signal

Reflecting Point Positioning

The method to process the downward-pointing antenna measured GPS data is quite different from the known method to process the GPS data obtained by an upward-pointing antenna. As shown in Fig. 5.14, the GPS signal is transmitted from the satellite to the downward-pointing antenna through the reflecting point R (or more exactly, a small zone surrounding R, cf. Komjathy et al. 1999) of the reflecting surface. The satellite orbit is known. The position of the downward-pointing antenna can be determined by using the data received from an upward-looking antenna. So the purpose of the GPS-altimetry is to determine the unknown point R. The vertical line of the satellite and the antenna forms a plane. Such a plane will intersect with the Earth’s surface and form a curved line. The reflecting point shall be on the line. Due to the principle of reflection, the angle of fall in and the angle of fall out must be equal. In other words, the elevations of the antenna and the satellite related to the reflecting surface at the reflecting point must be the same. Therefore, the reflecting point shall be generally a unique one if the reflecting surface is a fixed surface. Even in a static case, i.e., the GPS antenna does not move, the reflecting point R is a kinematic point because of the movement of the satellite. Different satellites have generally different reflecting points. These points are independent if one does not take the a priori knowledge of the reflecting surface into account.

For every observed satellite of every epoch there are three new coordinate unknowns. A straightforward solution is mathematically impossible. However, suppose the reflecting surface is a geoid or a known sea surface, for example, then the latitude and longitude of the reflecting point can be computed from the satellite position and the known antenna position. Then the left unknown is just one parameter of height. Suppose the reflecting surface is just needed to be determined up to, say, a resolution of two kilometres, then the height of every point located within the one km radius could be considered the same, and in such case the GPS altimetry problem is clearly solvable.

The signal transmitting distance d can be described below:

tmp2A834_thumb

where indices s, r and k denote satellite, reflecting point and downward-pointing GPS antenna, respectively. Of course the transmitting time correction has to be taken into account. Cartesian coordinates x, y and z of the reflecting point can be represented by geodetic coordinates -tmp2A835_thumbof the reflecting point shall fulfil the following linear equation:

tmp2A837_thumb

For any giventmp2A838_thumbbetween valuetmp2A839_thumba relatedtmp2A840_thumbcan be obtained. Then the zero height reflecting point in Cartesian coordinates can be obtained. The zenith distances of the downward-pointing GPS antenna and the GPS satellite related to the reflecting point can be then computed respectively. By using the criteria that both zenith distances shall be the same, a best set oftmp2A841_thumbcan be found. Taking the known coordinates of the zero height reflecting point into account, there is just one parameter of height remaining as an unknown in the Eq. 5.166.

By reducing the resolution rate to every two epochs, i.e., suppose within every two epochs the height of the reflecting point remained the same, the problem including the receiver clock error and ambiguity can be solved with enough redundancies.

Image Point and Reflecting Surface Determination

An alternative method to determine the reflecting surface is proposed below.

The reflecting surface is considered a mirror and the downward-pointing antenna is an image point behind the mirror. If the reflecting surface is a plane, then the image point positioning can be done with the same method used in kinematic positioning of the upward-looking antenna. Usually, the longitude and latitude of the image point can be obtained from the results of the upward-looking antenna; therefore, the image point positioning problem has just one coordinate-unknown height and can be well determined. Now one has two heights, one is the height of the downward-pointing antenna; another is the height of the image point. The average value of these two heights is then the footprint height of the downward-pointing antenna on the reflecting surface. The longitude and latitude of the reflecting point can be determined by using the method discussed in Sect. 5.6.2; therefore in this way, the reflecting point can be determined.

However, the reflecting surface is usually not a plane; therefore, the above-discussed image point positioning result is a kind of average height. For convenience, we define the reflecting point, which has such an average height, as a nominal reflecting point. The distances between the nominal reflecting point and the satellite and downward-pointing antenna can be computed. Comparing the computed value with the true signal transmitting distance, the bias of heights of the real reflecting point and the nominal reflecting point can be determined. In such a way, the reflecting surface can be determined.

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