How accurate is inertial positioning?
"Inertial GPS"

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).

10th Character

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".

Base stations

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.

Aviation

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"

Glossary


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.