# Celestial navigation explained - page 9

## Random errors - a solution

Random errors are inevitable.

With random errors, there is a 75% probability for True Position to be outside the cocked hat.

How to trust the ship position drawn on the chart, then?

More helpful than the cocked hat or the MPP (Most Probable Position) by itself is the confidence ellipse.
The confidence ellipse defines the area within which the True Position lies with a given probability (95% or 99% for instance).
A statistical analysis is needed to be able to draw this ellipse.

Confidence ellipse characteristics:

• its centre is the MPP
• its size depends on the size of the random errors and on the chosen probability
• its shape depends on the number of observations and distribution of the azimuths.

The confidence ellipse will normally overlap the cocked hat partly.
Another advantage of the confidence ellipse is that this ellipse can be drawn for any number of LOPs and therefore give a visual representation where the cocked hat fails to do so.

A program like ASNAv is able to draw the confidence ellipse around the MPP. It gives also the radius of the circle of equivalent probability (as this is easier to plot on the chart).