3. The RNP Concept

3. THE RNP CONCEPT
3.1. DEFINITIONS
The definition of the  navigation error components is given in the drawing below (in a simplified manner) assuming that the AP is used.

The PDE has been demonstrated negligible, provided there is no systematic error such as navigation database coding error or error due to inadequate geodesic reference (other than WGS84).
The FTE is a characteristic of the pilot performance using FD or the Auto-Pilot guidance performance in the steering of the aircraft on the FMS defined flight path. The FTE has a cross-track statistical distribution.
The NSE is the error made by the navigation system in the computation  of the aircraft position. The NSE has a circular statistical distribution around the aircraft true position. From this circular distribution, it is possible to derive a cross-track component of the NSE, which is relevant for the RNP lateral navigation.
The Total System Error (TSE) is defined as follows:
TSE=√(FTE)2+(NSE)2+(PDE)2
For the purpose of further development in this document  the following simplified equation will be considered:
TSE=√(FTE)2+(NSE)2 (1)
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3.  The RNP Concept
Getting to grips with RNP AR

The TSE, which is calculated with equation (1) above has consequently as well a statistical distribution in cross-track direction as illustrated below. 

TSE probability distribution

3.2.  THE LATERAL NAVIGATION REQUIREMENTS OF MASPS ED-75/DO-236
The three requirements of MASPS ED-75/DO-236 on lateral navigation performance for RNP are:
1°Accuracy:
Each aircraft operating in RNP airspace shall have Total System Error components in the cross-track and along track directions that are less than the RNP value for 95% of the flying time.
The TSE must be < RNP value for 95% of the flying time. 2°Containment Integrity
The probability that the Total System Error of each aircraft operating in RNP airspace exceeds the specified cross track containment limit without annunciation shall be less than 10-5/FH. The cross track containment limit is twice the RNP value.
Containment limit

The probability of TSE > Containment limit must be < 10-5/FH. 3°Containment Continuity The probability of annunciated loss of RNP capability shall be less than 
10 /FH.
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3. The RNP Concept

3.3.  THE VERTICAL NAVIGATION REQUIREMENTS OF MASPS ED-75/DO-236
The along track navigation error on a descending vertical flight path induces a component of
the vertical error called Horizontal Coupling Error (HCE). 
The pilot performance using FD, or the performance of the guidance system, to control the
　
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