Get the probable right location from multiple points

Question

I have a location collection tool which send me location data of our survey. Surveyors send multiple data of a single item. Such as they send numarous data for a school like the following image. From the image we can clearly identify few locations those are actually not collected properly or inaccurate location came due to GPS accuracy. Here I have marked red circle which location need to be excluded and the green circle indicates this is the probable location. IF we create a centroid based on all points then it will not indicates the probable correct location due to few highly inaccurate data. I wonder, if any method or tool can exclude the wrong location and create a cluster based on densed location points to create a centroid then the centroid can be established as probable right location of the surveyed item. I have millions of item those have hundreds of location each. I came to know that k-means do something like that but it does not do on a single item. I have four column in table.

1. fid
2. item_id
3. item_name
4. geom

Is there any method to create item wise clustering where every cluster have a value which indicates its containing points to get the probable right location?

Answer 1

ST_GeometricMedian should compensate for outliers in MultiPoint geometries, e.g. sth. like:

SELECT ST_GeometricMedian(ST_Collect(geom)) AS geom
FROM   <your_table>
GROUP BY
       item_id
;

General info on the concept, and difference to weighting (i.e. ST_Centroid).

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As an alternative, using

ST_ClusterDBSCAN(geom, <eps>, 1) OVER(PARTITION BY item_id)

allows for cluster assignement over item_id and with an <eps> distance representing e.g. the specific GPS devices' standard margin of error; getting the centre of the highest populated cluster should be a precise approximation.