How is accuracy achieved in Inertial Positioning? Is it possible to get 10 or 11 digits of accuracy without transmission of real-time corrections from a base (known) station? Is post-processing simultaneous data of Ref. & Rover required for getting the precise (10 & 11 digit) coordinates?
Inertial navigation is separate from GPS navigation. Inertial navigation senses accelleration and uses that to estimate changes in velocity and hence estimate changes in position. GPS is a GNSS system that determines position from timing of satellite signals. There's no such thing as Inertial GPS although there are systems marketed as sat-nav which can use inertial navigation when GPS is unavailable (e.g. when driving through a tunnel).
Digits are about precision not accuracy. Any sat-nav or GNSS receiver can produce location digits to much greater precision than their accuracy.
The number of digits, and their implications regarding accuracy and precision, depends on the units being presented. For example, I have a handheld GNSS receiver that I set to display UK Grid-references for convenience in conjunction with Ordnance Survey maps. The meaning of the 10th and 11th characters in terms of positional precision is therefore different.
TQ 395012 775012
In this case, the 10th digit is something like kilometers north of the OS origin. Accuracy of ±1 Km can certainly be achieved by unaugmented GNSS.
It is probably better to state a desired accuracy in terms of distance on the ground - for example many handheld GNSS receivers will display something like "Accuracy: 23 feet".
All GNSS receivers (including GPS, GLONASS, Galileo etc) use multiple satellites to determine their position. Typically three or four are required for a fix. Pure GNSS receivers don't use base stations.
SBAS capable receivers (such as those that can use WAAS, EGNOS, etc) use additional satellites to achieve higher accuracy. They do not directly use base stations on the ground. The additional satellites transmit positional corrections that have been gathered from ground stations but the GNSS receivers do not receive data directly from the ground stations.
Higher accuracy GNSS units are used by, for example, site surveyors. These are larger and more expensive and in some cases do use ground base stations for greater accuracy.
Generally, I don't think aviators have any use for knowing their aircraft location to centimeter accuracy in flight.
A GNSS with SBAS (e.g. GPS + WAAS) can provide the accuracy needed for precision flight approaches but Garmin state "Currently, GPS alone does not meet the FAA's navigation requirements for accuracy, integrity and availability"
- GNSS = Global Navigation Satellite System.
- GPS = Global Positioning System, US operated GNSS.
- Galileo = EU operated GNSS.
- GLONASS = Global Navigation Satellite System, Russian operated GNSS.
- BDS = BeiDou Navigation Satellite System, China operated GNSS.
- SBAS = Satellite Based Augmentation Systems.
- WAAS = Wide Area Augmentation System = US operated SBAS.
- EGNOS = European Geostationary Navigation Overlay Service, EU SBAS.
- GBAS = Ground Based Augmentation Systems.
Rather than talking to (a single) base station, most aviation units will use signals from additional satellites to apply corrections. In North America, the system is WAAS.
For a standard (civilian, single-frequency) GPS unit, the largest contributor to the positional error is the ionosphere model used. (See GPS Error Analysis page). WAAS transmits data that allows the unit to apply a real-time correction to that model for locations over North America. (Similar systems exist to do the same in other regions of the world).
Actual performance measurements of the system at specific locations have shown it typically provides better than 1.0 metre (3 ft 3 in) laterally and 1.5 metres (4 ft 11 in) vertically throughout most of the contiguous United States and large parts of Canada and Alaska.