WAAS Precision Approach Metrics
The first concept, accuracy, fits well with intuition when measured as the difference between the corrected navigation fix and the true position. Any viable navigation aid is enabled by its inherent accuracy. As a baseline, a WAAS implementation is obliged to quantify the accuracy of wide-area differentially corrected navigation solution. Accuracy is most critical in the vertical dimension for aircraft precision approach. Moreover, in satellite navigation the vertical dimension is the most difficult due to inherently weaker vertical geometry.
Accuracy or more specifically, Navigation Sensor Error (NSE) is defined as the difference between the position estimated by the navigation sensor and the true position of the aircraft which is only exceeded 5% of the time in the absence of system failures.
The second two concepts, integrity and continuity, address performance of the navigation system in the presence of failures or rare natural events. Integrity measures the ability of the system to protect the user from inaccurate position estimates in a timely fashion. Continuity measures the navigations system's ability to complete an operation without raising an alarm. These are the instantaneous metrics of flight safety and are computed at 1 Hz.
Integrity risk is defined as the probability that the NSE exceeds either the Horizontal or Vertical Alert Limits (HAL and VAL) and the navigation system alert is silent beyond the time-to-alarm. On the other hand, continuity risk is defined as the probability that the navigation system alarm will drop during the operation (precision approach in this case). These are competing constraints on the system; integrity failures shall not lead to Hazardously Misleading Information (HMI) favoring a small alert limit but continuity failures lead to False alarms favoring a large alert limit.
The final metric for the WAAS system is availability which emphasizes the operational economy of the navigation system. It is computed as the fraction of time the WAAS system is providing position fixes to the specified level of accuracy, integrity and continuity. The Minimum Operational Performance Standards (MOPS) for WAAS specify the computation of the Vertical Protection Level (VPL) and Horizontal Protection Level (HPL) of the differentially corrected navigation solution which must be met at a probability of 99.99999%. Thus the true error must not exceed the protection level more than once in 107 seconds. If the computed protection level exceeds the corresponding alert limit then the alarm is dropped and the operation cannot proceed. If the operation has already begun this condition is a continuity breach and a missed approach must be conducted. Otherwise the system is declared unavailable for that epoch.
The histogram of Figure 1 reports the horizontal system metrics provided by Stanford University's real-time WAAS implementation on the National Satellite Test Bed (NSTB) to a static user at Stanford, CA. The horizontal axis is the true error in the WAAS navigation solution with respect to the surveyed antenna location. The vertical axis is the protection level computed for each and every navigation solution. Each bin tabulates the number of occurrences of a specific (error, protection level) pair and the color of each grid indicates the total number of epochs that pair occurred. Note that the color scale is logarithmic and the bins are quantized into 0.125m bins.
The HAL for Category I precision approach, indicated by the horizontal and vertical lines, is set in the WAAS System Specification at 30m. Points with HPL above the HAL raise the alarm condition and constitute at least a loss of availability and possibly a continuity failure. Points with HPL less than the HAL but error greater than the HAL indicate a breach of integrity. In any case, the true error should always be less than the HPL and any points in violation are considered HPL failures of the navigation system. The long-term availability requirement of the WAAS system is 99.9% and hence at least 999 out of 1000 points should lie in the ``Normal Operation'' region. Here, the system maintained greater than 99.999% availability in horizontal positioning.
Figure 2 shows the vertical system performance corresponding to the horizontal data presented above. The WAAS correction in the vertical dimension has not only poorer performance than the horizontal due to weaker geometry but also more stringent alert limits with the VALs specified at 12m and 20m. These two VALs correspond to the Category I and proposed Instrument Precision with Vertical guidance (IPV) approach procedures. Nevertheless, the navigation system met all three safety metrics (accuracy, integrity, and continuity) with an availability of 99.671%.
More detail on our WAAS architecture can be found in the papers from the WADGPS Laboratory or contact us directly if you have a particular interest. Be sure to stop back for the latest developments. You may also want to hit our system description to learn more about wide-area differential GPS and our real-time WAAS implementation on the NSTB.
MATLAB was used to generate these plots. We have made the m-file scripts vplstat.m and hplstat.m available for download. Included in these functions is exemplar code for collecting the positioning data to be rendered by the m-files. You will also need the bound.m and bound2.m files in the download directory. For those who have visited this page before or seen our ``Innovations'' article in GPSWorld, we do still compute the older histogram form of the accuracy, integrity, and availability metrics.