GPS World, October 2009

INNOVATION Algorithms Methods h θ β δ 2h sinβ γ h δ 2h sinβ a FIGURE 1 a Forward scatter multipath geometry where the red arrows indicate the longer path traveled by the multipath signal relative to the direct signal See Table 1 for definition of terms b Signal amplitudes after including antenna gain pattern green line effects and attenuation upon reflection at a surface see Table 2 for definition of terms GNSS receiver tracks a composite signal which is the sum of the direct or line ofsight signal and one or more multipath signals The composite signal is biased from the direct signal simply because the multipath signal travels a longer path length than the desired direct signal GNSS tracking and positioning rely upon the assumption of direct line ofsight between satellite and receiver thus tracking a composite signal will result in mismeasurement of the carrier and code ranges Why is multipath still an unsolved problem with GNSS positioning As discussed below multipath is a site specifi c phenomenon each GNSS site or satellite or vehicle will have a unique multipath generating environment Multipath is also dynamic errors evolve with motion of the GNSS satellites and change as the refl ecting surfaces such as growing vegetation moving cars dry or damp ground around the receiving antenna also change Multipath errors cannot be simply differenced away multipath at one station will not cancel out upon differencing with observables from another station Nor can multipath always be averaged out with realtime or rapid static GNSS positioning β θ γ 90 b Symbol Term Units Path delay meters Antenna refl ector distance meters Multipath relative phase radians Satellite elevation angle radians Angle of refl ection at surface radians Tilt angle of refl ecting surface radians Signal carrier wavelength meters TABLE 1 Multipath Geometry Terms the spatial and temporal complexity of site specifi c multipath environments can adversely affect position determination Simplified Multipath Model On the most basic level multipath errors are driven by the geometric relationships between the receiving point the GNSS receiver antenna the sending point the GNSS satellite antenna and the refl ecting object We illustrate these geometric relationships using simple ray tracing for a more involved ray tracing technique see the paper Development and Testing of a New Ray Tracing Approach to GNSS Carrier Phase Multipath Modelling listed in Further Reading 60 Ad 0 60 P P PRs Rs Am The geometric relationships between the satellite receiving antenna and refl ecting objects dictate the additional path length traveled by the multipath signal and how this path length changes as the satellite moves In an ideal multipath free world this geometry is described only by the lineof sight betwxeen satellite and receiver which we describe via the azimuth and elevation angle of the satellite relative to the receiver The geometry becomes more complicated when a refl ecting multipath object is introduced TABLE 1 introduces some multipath terms and FIGURE 1 shows how these factors combine to create a forward scatter multipath environment where a single refl ected signal is received by the GNSS antenna This illustration shows an antenna receiving two signals from one GNSS satellite the desired direct ray and a second ray that refl ects off a tilted planar object before reception For this example we assume all angles are coplanar and disregard the third dimension Using the multipath terms listed in Table 1 and the geometric relationships depicted in Figure 1a the additional distance traveled by the refl ected multipath signal relative to the direct one is the GPS World October 2009 www gpsworld com 32