We don't say "erroneous position" for GPS data, but "innacurate". This is because, being a measurement, it'll always have an amount of error, no matter what one does. What one can do is work around these errors, that is, define an acceptable Margin of Error and try to bring your derived positions to within it.
There is, however, very equipement-specific. There is no simple statistical filtering one can do here (if that is what you're looking for). There are three ways to bring you precision up:
1. Use a better signal: There are two types of signals in GPS - open, civilian-use signals, and encrypted, military-use signals. The open signals give much lower precision than the encrypted ones, and there isn't really much you can do about it if you're using a civilian receptor.
2. Work with phase information: The codes themselves can only take you so far, for the extra mile you have to derive your final position using carrier phase differentiation. This is what the talk about "base station" you read was referring to. This, however, is only an option on survey-grade receivers, which yours isn't. Again, nothing you can do about it.
3. Correct for outside errors sources: There are many sources of error in the GPS system that accumulate. Some of them can be calculated by external stations, and either transmited to your receiver for real-time corrections, or post-processed. These transmissions can be done through other satellites (SBAS) or direct point-to-point radio (GBAS). Of these, your receiver accepts two SBAS providers, WAAS and EGNOS. These, however, will only work at North America and Europe, respectively.
Given your receiver, turning on SBAS is your best approach here. A typical code-only receiver should give about 15m of precision, with SBAS you can expect something like 3m on a good day. If that is good enough for you, then you're set. If not, then you'll need to upgrade your equipment, to a much more expensive one at that. Sadly, it's the limitations of the system.