What information is available to indicate the degree of accuracy of the GPS data at any given time?

What information is available to indicate the degree of accuracy of the GPS data at any given time? What is the criteria used to establish HDOP, is it only related to satellite location and signal strength?

We provide HDOP and EHPE in MID 41 as an indication of position accuracy. HDOP is computed only from satellite geometry – azimuth and elevation and number of satellites – there is no signal strength factor (attached DOP formula). See attached document on position error for a better understanding