Data-Replay Analysis of LAAS Safety during Ionosphere Storms

As reported in [2,4,5], previous Stanford research has identified the potential for severe ionosphere spatial gradients to affect Local Area Augmentation System (LAAS) integrity. In previous work [1], real-time position-domain geometry screening was used to maximize LAAS availability in the presence of ionosphere anomalies by broadcasting an inflated value of σ vig so that the maximum-ionosphere-induced-error-invertical (MIEV) for all viable airborne “subset” geometries (subsets of the set of satellites visible to and approved by the LGF) is below a pre-determined safe limit. The results of this work are based on the LAAS ionosphere spatial-gradient “threat model” established and validated with ionosphere storm data observed from WAAS and IGS since 2000 [2,4]. This previous approach leads to marginal availability of the required integrity (95 to 99 percent) and does not give the higher availability that is desired (99.9 percent or higher). In this paper, data from the Ohio cluster of CORS stations on November 20, 2003 and the North Carolina cluster of CORS stations on October 29, 2003 from [6] are used to perform “data-replay” analysis for several independent station pairs with separations from 23 to 75 km. These separations are significantly further than the effective LAAS user-to-LGF separation at the CAT I decision height. Comparisons of the result of data-replay analysis with the result of worst-case simulation in the manner of [1] are made. The conclusion derived from these comparisons is that CAT I ionosphere analysis performed by worst-case simulation is conservative but not unreasonable. 1.0 INTRODUCTION The Local Area Augmentation System (LAAS) was designed to insure the integrity of broadcast pseudorange corrections by monitoring of measured satellite pseudoranges within the LAAS Ground Facility (LGF). This monitoring allows the LGF to ensure that errors in the LGF pseudorange corrections are bounded (to the required integrity probability) by the nominal error sigmas that are broadcast with them (within the LGF, measurements that fail one or more monitors are excluded so that they cannot be applied by LAAS users). This procedure allows aircraft receiving LAAS corrections to compute “protection levels” and thus determine the integrity of any set of satellites visible at the aircraft as long as each satellite has a pseudorange correction, sigma values, and “B-values” broadcast for it [1]. One of the residual errors that can build up for the user of a differential GPS system like LAAS is ionosphere spatial decorrelation error. This error is caused by the fact that two GPS signals are passing through different regions of the atmosphere, and the resulting ionosphere delays cannot be completely canceled out even after applying differential corrections. Under severe ionosphere storm conditions, these errors can grow large enough to pose a threat to user integrity. Several ionosphere storms of concern have occurred since the April 2000 storm that first alerted us to this potential hazard. Among them, the two largest ones were on October 29-30, 2003 and November 20, 2003. Figure 1 shows a snapshot of the ionosphere delay map over CONUS on October 29, 2003 between 20:00 to 20:45 UT. The x-axis and y-axis represent longitude and latitude, respectively. The color scale indicates the magnitude of the vertical ionosphere delay [2]. Dark red represents about 20 meters of delay, and dark blue represents about 2 meters. As can be seen, there are some sharp transitions between the dark red and the blue, which indicates sharp spatial gradients in those areas. By comparing the subplots, it appears that the storm did not move much (relative to the continental scale shown) during the 45 minutes covered by the subplots. An ionosphere movie made to show that period with finer time resolution also indicates that the anomaly may have been “near stationary” at specific locations and times. Figure 2 shows the November 20, 2003 storm in a similar fashion. This time, only the eastern half of the U.S. is shown. The large anomaly feature appears different than what was seen previously (i.e., it has a distinctive “finger shape” in it), and it appears to move faster in general. However, additional sharp gradients between dark red and blue zone are observed [2]. Figure 1: Ionosphere Spatial Anomalies Observed during October 29, 2003 Storm As described in our previous work (see [5,9,10]), ionosphere anomalies are modeled as linear wave fronts in order to study their impact on a LAAS user. Figure 3 illustrates this simplified model. The gradient represents a linear change in vertical ionosphere delay between the “high” and “low” delay zones. Four parameters are used to characterize the anomaly: gradient slope (in mm/km), gradient width (in km), front speed (in m/s), and maximum delay difference (in m), which is simply the product of gradient slope and width. Upper bounds on each of these parameters have been determined based on analysis of past storms, including the October 29-30 and November 20, 2003 storms. Note that the maximum delay difference is also expressed as an upper bound in this model, and it constrains the slope and width values through their product (i.e., values of slope and width which are within their respective bounds but exceed the maximum-delay-difference bound when multiplied together are not a valid combination) [2,4]. Figure 2: Ionosphere Spatial Anomalies Observed during November 20, 2003 Storm Figure 3: Simplified Model of Ionosphere Anomaly While almost all anomalies that pose a threat to LAAS can be mitigated completely within the range domain, severe ionosphere spatial anomalies must be handled differently. Very large ionosphere spatial gradients observed in CONUS during ionosphere storms in October and November 2003 could have created range-domain errors of several meters before being detected by LGF monitoring [2,5]. The magnitude of these potential errors exceeds what can be bounded in the range domain. In other words, aircraft satellite geometries that appear usable due to the vertical protection level (or VPL) being below the specified “safe” vertical alert limit (or VAL) for CAT I precision approaches (VAL = 10 meters at the minimum CAT I decision height of 200 ft) are safe with respect to nominal conditions and almost all failure modes but may not be safe in the presence of a worst-case ionosphere anomaly. Therefore, satellite geometry screening, or position-domain verification that each geometry potentially usable at the aircraft is safe in the presence of the worst-case ionosphere-anomaly threat, is required. Our previous paper demonstrates that positiondomain geometry screening in LAAS can fully mitigate the CONUS ionosphere spatial decorrelation threat model [1]. A summary of this screening procedure is shown on the left-hand side of Figure 5. Figure 5: Simulation versus Data-Replay Analysis Figure 6: Ionosphere Anomaly Threat Model (Slope Bounds Last Updated in March 2007) As noted above, the parameters in the simplified model of ionosphere anomaly are estimated using data collected on ionosphere stormy days, and they can be summarized by an ionosphere anomaly “threat model”. The current threat model (most recently revised in March 2007) is as shown in Figure 6, in which the ionosphere slope is 375 mm/km for low satellite elevation and 425 mm/km for high satellite elevation (the bounds on speed, width, and maximum delay difference remain the same as the numbers given in [1]). Next, LAAS mitigations such as the LGF code-carrier divergence (CCD) monitor, which detects high ionosphere rates-of-change that are observable to the LGF, and any sigma/P-value inflation implemented for geometry screening are applied. Then, LAAS impact simulations are performed to get the worstcase vertical protection error (VPE), which is commonly known as the maximum ionosphere error in vertical position (or MIEV) are conducted. The “Pierce Point Plucking” or “PPP” method described in [1], which is the current method used in ionosphere mitigation simulation, considers worst-case ionosphere impacts on all possible pairs of satellites and is thus seen to be conservative. As originally conceived in previous work (see [2,3]), a process known as “data-replay analysis” has been developed to demonstrate that the results obtained by simulation (based on the conservative approach described above) can reasonably approximate the result that is achieved by using observed anomalous data between two fixed WAAS or CORS reference-station locations that were also used to estimate the parameters of the ionosphere threat model. Therefore, actual ionosphere data from the same ionosphere anomaly database was picked for pairs of CORS stations to compute unsmoothed DGPS Range Errors. Applying “baseline” geometry screening (meaning that sigmas are not inflated to further constrain user geometries), VPE for each usable subset geometry and histograms of VPE over subset geometry and time were obtained. Finally, the worst-case VPE (or MIEV) is obtained and is compared to the worst-case VPE obtained by simulation. 2.0 DATA AND ANALYSIS PROCEDURE