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I understand that this is some sort of on-board navigation monitoring and alerting...what is it used in? Do the Garmin G500s, G1000s, or the G430s use it? Where can you find it? I know nothing about this and I am trying to figure out what it is.

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    $\begingroup$ RNP and RNAV are implementations of the overall idea of performance-based navigation. The principle is to increase navigation accuracy to enable more efficient uses of the airspace (more direct and optimized routes). This can be summarized this way. $\endgroup$ – mins Mar 5 '16 at 22:21
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    $\begingroup$ See also What is a SAAAR instrument approach? where the answer from DeltaLima includes a description of RNAV and RNP and a link to a very interesting presentation of RNP by FAA. $\endgroup$ – mins Mar 5 '16 at 22:40
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RNP (Required Navigation Performance) is a standard which avionics manufacturers may choose to design/certify their products for. It guarantees a particular level of navigation performance that routes and procedures can be designed around, and not have to worry about how the navigation is being conducted, but only that it will meet requirements.

A particular product may be certified to various levels such as RNP10, RNP5, RNP2, RNP1, RNP0.3, etc. (accurate to within 10NM, 5NM, 2NM, 1NM, 0.3NM, etc.).

To see if a particular unit is certified for RNP, and to what level, you would need to look in the aircraft flight manual / supplement and see what it says (note that this is installation specific too, as it involves antennas and "full system" performance, not just the capability of one piece of the puzzle).

The FAA has an advisory circular caled AC 90-101A - Approval Guidance for Required Navigation Performance (RNP) Procedures with Authorization Required (AR) Including Change 1 if you want more technical information on it.

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