Disclosed is a method for providing a Global Navigation Satellite System (GNSS) navigation position solution with guaranteed integrity in non-controlled environments, the method including processing a (GNSS) signal including multiple satellites generating at least one signal to obtain carrier phase and pseudorange measurements; pre-processing the measurements to detect and characterize local errors in the measurements, wherein the local errors cannot be ascertained a priori, the characterization including providing error bounds estimated by measuring the carrier phase and pseudoranges measurements, thereby providing a set of measurements rejections when the characterization is not possible; and using the estimated error bounds, together with error bounds provided by the GNSS signal concerning satellite and ionospheric errors, to build in each measurement an estimated noise level in the measurements as input to a weighted Receiver Autonomous Integrity Monitoring (RAIM) algorithm in order to compute position coordinates and associated protection levels in the non-controlled environments.