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Geospatial databases generally consist of measurements related to points (or pixels in the case of raster data), lines, and polygons. In recent years, the size and complexity of these databases have increased significantly and they often contain erroneous measurements or noise. In this paper, we address the problem of detecting erroneous and suspicious values in a database consisting of point measurements. We use a database of measurements of anomalies in the Earth's gravity field that we have complied as a test case, and we found that the standard methods of detecting erroneous measurements - based on regression analysis - do not work well. As a result, experts use manual methods to clean such databases that are very time-consuming. In this paper, we propose a (natural) "localized" version of regression analysis as a technique for automatic cleaning of the database and illustrate its efficiency in the case of this gravity database. We believe that this approach will prove to be useful when dealing with many other types of point data.