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GNSS Horizontal Integrity Limit/ Horizontal Protection Level is a measure of GNSS position error/integrity that's very important in RNP operations and RAIM, but it has an obtuse definition in aviation regulations like DO-229D that's hard to apply in practice:

[HPL] describes the region assured to contain the indicated horizontal position. It is a horizontal region where the missed alert and false alert requirements are met for the chosen set of satellites when autonomous fault detection is used.

Is there a simpler definition that is equivalent for most equipment? It seems like a 1 - 10-X% accuracy bound, given pessimistic assumptions about satellite availability, but given the description it's hard to be sure?

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The true position of an aircraft in flight can be measured, but the accuracy of any measurement is limited. The actual measured position is the actual true position plus the actual measurement error. Each error of position measurement is 3dimensional. If observed over a long time, the distribution of the errors will have a shape and size that is characteristic for the measurement method.

For GNSS receivers, the measurement of the latitude and longitude measurements depend on each other, while the vertical measurement of altitude does not correlate much with the horizontal measurement. This is why the usual model to describe is a cylinder:

HPL/VPL diagram Image source: ESA

The Horizontal Protection Level (HPL) is simply a horizontal cut through the cylinder where the aircraft is located with an acceptable level of probability. The cross section of a cylinder is a circle, and the radius of this circle is the horizontal performance requirement.

The HPL is just a geometric definition. It is useless without acceptance levels and performance requirements, which are not part of its definition. Those emerge from the performance of an GNSS augmentation system like WAAS for GPS or EGNOS for Galileo, and the requirements for the use in aviation. Here below is a table of GNSS augmentation performance requirements by FAA for different phases of flight:

enter image description here Image source: ICAO

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  • $\begingroup$ So does the HIL/HPL signal output by an aviation-grade GPS receiver change based on the performance requirements? That seems to be what's suggested in your answer. $\endgroup$
    – Cody P
    Jan 15, 2020 at 20:32
  • $\begingroup$ @CodyP I don't think I wrote that. HIL/HPL are geometric figures. They are pointless without performance requirements, but they do not change depending on the actual requirements. Which sentence do you find wrong or confusing? Maybe I can change something. $\endgroup$
    – bogl
    Jan 15, 2020 at 22:17
  • $\begingroup$ Sorry for the confusion and thanks for the help. The thing that's unclear to me is what the "acceptable level of probability" and "accptance levels and performance requirements" are, and why if its something simple like 1-2x10^-7 per approach it isn't stated more prominently. $\endgroup$
    – Cody P
    Jan 16, 2020 at 20:05
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    $\begingroup$ No worries! I am not aware if or how navigation units handle actual performance requirements. The figures in the table, like the 1-2x10^-7 (=99.99998%) per approach are just arbitrary trade-offs between feasibility, cost, and acceptable risk. At least that is my limited understanding. I would be happy if there was another answer that could shed more light on this aspect, or maybe it is worth a dedicated question. $\endgroup$
    – bogl
    Jan 17, 2020 at 12:39

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