## 4 L1-L5 Dual-Frequency WAAS  
As described in the first section, GPS will add a new civil frequency, L5 at 1176.45 MHz, in the ARNS band. This new civil GPS signal combined with current L1 will improve the performance for GPS users by enabling them to estimate and mitigate the ionosphere delay. Recall that ionospheric delay currently is the largest obstacle for the GPS to become the primary navigation aid in civil aviation. An L1-L5 dual-frequency GPS user avionics sensor can estimate the ionospheric delay directly (_i.e._, no ionosphere correction needed from WAAS) and then subtract this estimation from the pseudorange measurements. This direct use of the L1-L5 dual-frequency will be more accurate and offer higher availability [12; 13; 14]. WAAS should be modernized to take advantage of these new and stable signals. The major changes will be in the WAAS ionosphere model (algorithm). The detailed changes of the L1-L5 dual-frequency WAAS algorithms are specified in [13]. For an L1-L5 dual-frequency GPS/WAAS user avionics sensor, the weighting matrix, \(W\), is a diagonal matrix and the inverse of the \(i^{th}\) diagonal element is given by the variance for the corresponding satellite, \(\sigma^{2}_{i,\,\text{dual}}\) as calculated in Equation (6) [13]:  
\[\sigma^{2}_{i,\,\text{dual}}=\sigma^{2}_{i,\,\text{{ft}}}+\sigma^{2}_{i,\, \text{air, L1-L5}}+\sigma^{2}_{i,\,\text{{propo}}} \tag{6}\]  
where  
\(\sigma^{2}_{i,\,\text{{ft}}}\) and \(\sigma^{2}_{i,\,\text{{propo}}}\) are defined in the same manner as in Equation (2), and  
\(\sigma^{2}_{i,\,\text{{air, L1-L5}}}\) is the L1-L5 dual-frequency airborne receiver error confidence, which is the confidence bound on ionospheric-free receiver measurements for an L1-L5 dual-frequency GPS/WAAS user avionics sensor and is derived in [13]. Note: Because the calculation of \(\sigma^{2}_{i,\,\text{{air, L1-L5}}}\) already considers both the L1-L5 dual-frequency user ionosphere range error confidence and the airborne multipath and noise error confidence, there is no need for additional terms accounting for these errors in Equation (6) [13]. Figure 6 shows the comparison of the error components between the L1 single frequency GPS/WAAS user (_i.e._, Equation (2)) and the L1-L5 dual-frequency GPS/WAAS user (_i.e._, Equation (6)). The specific numbers used in the calculations are based on the nominal observations of WAAS. For the L1 single frequency GPS/WAAS user avionics sensor, the minimum \(\sigma_{i,\text{{ft}}}\) term is based on the minimum User Differential Range Error (UDRE) [7] of 2.25 m [11], the minimum \(\sigma_{i,\text{{U}}\text{{I}}\text{{R}}\text{{E}}}\) term is based on the minimum GIVE value of 3 m [7], the \(\sigma_{i,\text{{air}}}\) term uses the Airborne Accuracy Description (AAD-B) model defined in [7], and the calculation of \(\sigma_{i,\text{{propo}}}\) term is defined in [7]. For the L1-L5 dual-frequency GPS/WAAS user avionics sensor, the \(\sigma_{i,\text{{ft}}}\) and \(\sigma_{i,\text{{propo}}}\) terms are identical to those of the L1 single frequency GPS/WAAS user, and the \(\sigma_{i,\text{{air,L1-L5}}}\) term is defined in [13] which is larger than \(\sigma_{i,\text{{air}}}\) but is significantly smaller than \(\sigma_{i,\text{{U}}\text{{I}}\text{{R}}\text{{E}}}\). As indicated in Figure 6, the \(\sigma_{i,\text{{ft}}}\) term is the dominant error component for the L1-L5 dual-frequency GPS/WAAS user avionics sensor. Figure 7 shows the VPL contour of the L1-L5 dual-frequency GPS/WAAS user. As shown in Figure 7, the VPL values are less than 20 m (APV II VAL) in most of CONUS, Alaska, and Canada. This is a significant improvement from Figure 3, 4 or 5 (single frequency WAAS), however, the VPL contour shown in Figure 7 still falls short of meeting the CAT I requirement (CAT I VAL = 12 m). In the next section, this paper will seek additional improvement that could be possible made in the dual-frequency WAAS user avionics sensor algorithm, and examine if the dual-frequency WAAS could meet CAT I requirement (VAL = 12 m).