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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.
The histogram below is an example of the accuracy realized by the Stanford WAAS implementation running on data from the NSTB network. The differentially corrected navigation solution at the passive monitor in Atlantic City, NJ (FAA Technical Center) was compiled over 24 hours 29 July 1997. The top histogram in Figure 1 reports the distribution of vertical error on a semi-log scale along with the mean, 95%, and 99% statistics.
An aircraft on final approach cannot quantify the accuracy of guidance information since there is no truth reference. The critical concept in such a safety of life operation is integrity. The position estimate provided by the navigation system will always have some error. In order to protect the integrity of the aircraft it is the responsibility of the system to provide a confidence interval on the error in the position estimate which bounds the true position error. This is the essential contract between system provider and aircraft and it must be upheld.
Stanford's approach is to quantify integrity by the ratio of true error to predicted error (confidence interval). To analyze the integrity of the system whose accuracy was tabulated in Figure 1, the ratio (true error)/(sigma) was compiled on each and every position estimate. The integrity ratio is reported in the middle histogram. Of significance is the red parabola which identifies the equivalent (equal area) Gaussian distribution. If the avionics presume Gaussian error sources then the distribution of the integrity ratio must always have tails shorter than the red curve in order to protect integrity. Again the histogram of occurrences of a particular value of the integrity ratio are reported on a semi-log scale to highlight the tails of the distribution.
The last specification addressed by our trio of metrics is availability. The fundamental quantity that determines availability is the confidence interval, that is, the denominator in the integrity ratio. Note this is the only number in any and all system metrics which the in flight avionics will actually receive from the WAAS system. The fact that the confidence interval for satellite navigation will be a time dependent quantity is a major departure from the specification of previous navigation aids. The bottom histogram in Figure 1 reports the distribution of the confidence interval over 29 July 1997.
In the end, availability is the trade-off quantity which pays in the integrity contract. For example, integrity can always be protected by simply inflating the denominator in the integrity ratio. Procedurally this is unacceptable because all aircraft on approach have an alarm limit based on the confidence interval (the denominator) which indicates go--no go for landing. If the confidence interval is too large then the system is unavailable and the aircraft must wait until the confidence interval is adequately tight to safely conduct an approach. The need to make the denominator as small as possible is clear--maximize availability.
Choosing, for example, a vertical alarm limit (VAL) of 15(m) at a probability of 99.99999% on the Gaussian over-bound the one sigma confidence interval can be translated to the 99.99999% interval with a multiplier of about K = 5. Thus if we need a system with 99.9% availability, sigma needs to be less than three at least 99.9% of the time.
Figure 2 provides concrete evidence of the viability of wide-area differential GPS navigation for precision approach. The three system metrics were computed at the Stanford, CA passive monitor which was using the exact same 250 bit WAAS message stream as the Atlantic City monitor a continent away. The accuracy and sigma distributions did have significant differences over the day. However, around Atlantic City, NJ and Stanford CA the Stanford WAAS implementation exceeded 99.9% availability while maintaining integrity. The contribution of the NSTB will be to show this across continental geographies on day/month/year time scales.
A more detailed description of the 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.
