Positioning and Navigation Using the Russian Satellite System
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Pseudorange and carrier phase measurements were logged every second for approximately one hour each, of which some forty minutes were common to both receivers. One of these receivers was used as reference station, the other was treated as the user station. Its position was de- termined and compared to its known coordinates in this example. Observation epochs at both receivers were not exactly synchronized. The data are the same as already used for the single difference example. The plot shows the deviation from the known location of the antenna of the user station in the horizontal plane. GPS positions were computed from carrier smoothed L 1 C/A-code pseudorange measurements. GLONASS positions were computed from carrier smoothed dual-frequency P-code measurements. Wher- ever possible, the ionospheric free linear combination was formed. These observables used are not really identical for GPS and GLONASS, but with P-code and dual-frequency measurements readily available on GLONASS, the best possible results for each system are determined. GLONASS satellite positions at the time of signal transmission were converted from PZ-90 to WGS84 using the transformation according to (Roßbach et al., 1996). For the combined GPS/GLONASS double difference, the system of Eqs. (8.1.65) to (8.1.69) has been employed. Like in the single difference case, the large deviations from the true position due to GPS S/A have been eliminated by the differencing of observations, but not completely, due to the imperfect synchronization of measurements at reference and user station. Again, this is most clearly visible in North/South direction, where the S/A effects on the absolute and single difference positioning also were most obvious. Standard deviations of the computed positions from GPS only are 4.1 m in North/South direction and 1.5 m in East/West direction. This is even slightly more than in the single difference case, due to the increased 102 8 OBSERVATIONS AND POSITION DETERMINATION 550 560 570 580 590 600 610 620 141000 141500 142000 142500 143000 143500 Ellipsoidal Heigh t [m] GPS Time [s] GPS only GLONASS only GPS + GLONASS Figure 8.6: GPS, GLONASS and combined GPS/GLONASS double difference positioning, height com- ponent. noise level of the double difference observations. Since there is no S/A on GLONASS, its effects cannot remain in the differenced positioning solution even with imperfect synchronization of measurements. Consequently, positions computed only from GLONASS range measurements scatter much less. Here the standard deviations are 1.4 m in North/South direction and 1.2 m in East/West direction. Again, slightly more than in the single difference example. For the combined GPS/GLONASS positioning, all satellite measurements were weighted equally. These results are still affected by GPS S/A due to imperfect synchronization, but to a much less extent than the GPS only results. Standard deviations are 1.8 m in North/South direction and 0.8 m in East/West direction. This is better than in the single difference case. The height components of the processing results are displayed as a time series in Figure 8.6. Again it can be seen that the GPS solution oscillates very much due to remaining S/A effects, caused by the imperfect synchronization of measurement epochs. However, the mean GPS height solution of 591.3 m is closest to the true height, which is 594.5 m. Standard deviation of the GPS height component is 6.5 m. Again, there are no oscillations on the GLONASS solutions. These positions are more stable. However, one can notice a clear bias in the GLONASS height solution, especially during the first two thirds of the observation period. The increasing oscillations towards the end of the observation period are most likely caused by multipath effects, together with a change in satellite geometry. Track to one satellite was lost at 143328 s GPS time, leading to an increased VDOP value and thus increased noise of the height solution. Mean GLONASS height is 586.0 m, standard deviation is 3.9 m. Over a large extent of the observation period, the combined GPS/GLONASS height solution is more stable than the GPS or GLONASS only solutions. This definitely is caused by the more favorable VDOP of the extended satellite geometry. However, one can also notice a bias in the combined solution. Mean GPS/GLONASS height is 587.7 m, which is closer to the true height than the GLONASS only solution. Standard deviation of the height component is 3.8 m and thus only slightly better than that of the GLONASS only solution. Figure 8.7 shows the computed single difference receiver inter-system hardware delay ∆δt U R,HW , as used in the system of Eqs. (8.1.65) to (8.1.69). It can be clearly seen that this bias is not constant. Its 8.2 Carrier Phase Measurements 103 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 141000 141500 142000 142500 143000 143500 Hardw are Bias [ns] GPS Time [s] Figure 8.7: GPS/GLONASS double difference inter-system hardware delay. absolute value increases with time, until it obviously reaches some kind of saturation after approximately fifteen minutes. Even then, it oscillates strongly around this value. 8.2 Carrier Phase Measurements 8.2.1 Single Point Observation Equation Analogously to GPS, carrier phase measurements to GLONASS satellites can be used to determine user positions even more precisely than by means of pseudorange measurements. The observation equation for carrier phase measurements from receiver R to satellite S can be written as: ϕ S R = 1 λ S S R +N S R +f S ·(δt R +L R,GLO )−f S ·δt S +f S ·δt S,T rop R −f S ·δt S,Iono R +f S ·δt S R,ICB +ε S R (8.2.1) with S R = (x R − x S ) 2 + (y R − y S ) 2 + (z R − z S ) 2 and x R Position vector of receiver x S Position vector of satellite λ S Wavelength of carrier signal of satellite S Φ S r Carrier phase measurement of receiver R to satellite S N S R Carrier phase ambiguity of receiver R to satellite S f S Frequency of satellite signal δt R Receiver clock offset with respect to system time L R,GLO Common frequency-dependent hardware delay for GLONASS satellites δt S Satellite clock offset with respect to system time δt S,T rop R Tropospheric delay of signal δt S,Iono R Ionospheric advance of signal δt S R,ICB Inter channel bias for measurement of receiver R to satellite S ε S R Measurement noise 104 8 OBSERVATIONS AND POSITION DETERMINATION It should be noted that, due to the dispersive character of the ionosphere, the carrier signal is accelerated in the ionosphere, contrary to the code signal, which is delayed. Units in Eq. (8.2.1) are cycles. Scaled to units of length, this equation reads Φ S R = S R + λ S N S R + c · (δt R + L R,GLO ) − c · δt S + c · δt S,T rop R − c · δt S,Iono R + c · δt S R,ICB + λ S ε S R (8.2.2) where c Speed of light in vacuum Φ S R = λ S ϕ S R Carrier phase measurement scaled to distance Like in the case of the pseudorange observations Eq. (8.1.8), the tropospheric delay δt S,T rop R has to be determined using a suitable model, e.g. a Modified Hopfield model, if possible supported by measurements of the actual temperature, air pressure and humidity at the time of observation. The ionospheric acceleration δt S,Iono R also can be modeled using e.g. the GPS Klobuchar model, adapted Download 5.01 Kb. Do'stlaringiz bilan baham: 
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