A user equipment (UE) receives assistance data for positioning that includes relative position information for anchor points, such as base stations and/or sidelink UEs. The relative position information may include, for example, distances or angles between anchor points. The UE performs positioning measurements for reference signals received from the anchor points. The UE performs outlier rejection of the positioning measurements using the relative position information. Positioning measurements selected by the UE using the relative position information are provided to a location server. The location server may perform UE-assisted positioning using the selected position measurements and the actual locations of the anchor points. Accordingly, the outlier rejection of the position measurements may be off loaded from the location server to the UE while maintaining confidentiality of the actual locations of the anchor points.