GPS World, October 2009
Algorithms Methods INNOVATION 100 50 0 Elevation angle 15 10 05 0 05 10 15 Error centimeters ρMP δφ 600 500 400 300 200 100 0 10 15 20 25 30 10 5 0 5 10 SNRMP 05 SNR Time hours FIGURE 2 Simulated carrier phase error code error and SNR recorded directplus multipath SNR in green SNR due to multipath alone in blue in linear amplitude units for a horizontal surface 10 meters below the antenna assuming R s 02 reflection coefficient and a choke ring antenna gain pattern path delay The phase of the multipath signal again relative to the direct signal is the angular equivalent of path delay 1 Already we see that the path delay and multipath relative phase are a function of the antenna refl ector distance h and the angle of refl ection from the surface and that the same multipath object will result in different multipath phases for different GNSS signals due to the dependence on As discussed below the time varying nature of multipath is key to understanding and mitigating its effects Thus we examine the multipath frequency that is the rate of change of the multipath phase 2 If we assume a single stationary refl ecting object the only time varying factor in Figure 1 is the satellite as the satellite moves relative to the receiving antenna the refl ection point also moves changing the path delay and multipath relative phase Substituting the angular relationships see Figure 1a between the satellite receiver and refl ecting object into the previous equation makes this more obvious Symbol Term Units Multipath signal amplitude volts Direct signal amplitude volts R s Attenuation coeffi cient of refl ecting surface unitless Incoming signal power volts TABLE 2 Multipath Signal Terms www trimble com GNSS Inertial www gpsworld com October 2009 GPS World 33
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