GPS World, September 2016

AUTOMATED VEHICLE the number p of free parameters to be estimated p 3 for negligible tropospheric error p 4 to estimate a single additional tropospheric parameter and the number of carrier frequencies broadcast by each of the satellites 1 2 or 3 along with each carriers wavelength The model is highly accurate for single epoch AR but only approximate for multiple epochs with accuracy degrading as the data interval lengthens The models inaccuracy results from its assumption that overhead satellites remain static from epoch to epoch which yields pessimistic results for even fairly short data capture intervals for example 30 seconds Fully accounting for satellite motion in an analytical model for P z z is an open problem which is why studies that wish to account for satellite motion resort to simulation FIGURES 1 and 2 show single epoch single frequency results from the analytical P z z model for parameters 34 GPS WORLD WWW GPSWORLD COM SEPTEMBER 2016 approximately reflecting the mass market use case The most important conclusion to draw from these figures is that for single epoch single frequency AR to be even moderately reliable P T 09 over the next few years the ionospheric uncertainty σ ι must be held under 2 millimeters This will relax somewhat as more Galileo and MEO BeiDou satellites come online but signal blockage in built up areas will raise the effective elevation mask angle significantly above the 15 degrees assumed here reducing the number of available satellites Thus sub 2 mm ionospheric uncertainty remains desirable for urban environments even as GNSS constellations become fully populated FIGURES 3 and 4 offer results for a dual frequency L1 L2 single epoch scenario All other scenario parameters are held as for the single frequency scenario except that in an attempt to be somewhat more pessimistic P m is based only on GPS satellites It is assumed that from each satellite the user can extract dual frequency measurements As with the single frequency case it is evident that dual frequency P T is strongly dependent on σ ι The dual frequency case is more forgiving but substantial performance improvement can still be had by reducing σ ι to under 2 mm Corrections Uncertainty and Network Density This section is posted in the online version gpsworld com murrian FIGURE 2 Total probability of a correct fix for the scenario of Figure 1 as a function of ionospheric uncertainty σ ι FIGURE 4 Total probability of a correct fix for the scenario of Figure 3 as a function of ionospheric uncertainty σ ι FIGURE 1 Single epoch single frequency ambiguity fixing Blue traces left axis indicate the probability P z z of correctly resolving all integer ambiguities with a single epoch of data as a function of the number of satellites m Each trace represents P z z for a different value of ionospheric uncertainty σ ι Green bars right axis represent the probability mass function P m for the number of satellites above an elevation mask angle of 15 degrees assuming 31 GPS 14 Galileo and 3 WAAS satellites projected mid 2017 Each blue trace is marked with the total probability of correct integer resolution P T a function of both the trace itself and P m Other parameters of the scenario geometry factor f g 25 standard deviation of undifferenced phase measurements σ ϕ 3mm standard deviation of undifferenced pseudorange measurements σ ρ 50cm and number of estimated parameters p 3 FIGURE 3 As Figure 1 except for dual frequency L1 L2 measurements and the probability mass function P m corresponds only to a constellation of 31 GPS satellites The elevation mask angle is again taken to be 15 degrees It is assumed that dual frequency measurements can be obtained from every GPS satellite