A method for radar altimeter integrity monitoring, the method comprising: obtaining one or more global navigation satellite system, GNSS, measurements, or one or more hybridized GNSS /inertial navigation system, INS, measurements, in an earth-centered-earth-fixed, ECEF, coordinate frame for a vehicle; obtaining one or more altitude measurements from one or more radar altimeters on the vehicle; transforming the one or more altitude measurements into the ECEF coordinate frame using a terrain map and a GNSS or hybridized GNSS/INS based position estimate with ensured integrity, wherein the transformed one or more altitude measurements are given by the following equation: ρ ̃ RA, transformed = ρ ̃ RA + ρ ^ TERMAP where ρ̃ RA is the radar altimeter measurement, and ρ̂ TERMAP is an estimate of orthogonal distance between an ECEF frame origin and a terrain at a point given by a horizontal position of the vehicle and the terrain map; computing one or more characteristics of the transformed one or more altitude measurements, including orthogonal distance ρ TERMAP moments, wherein a mean value of the orthogonal distance ρ TERMAP is computed as: ρ ^ TERMAP = E ρ TERMAP = function 1 ρ ^ HOR map, where ρ̂ HOR is a horizontal position estimate of the vehicle and map is the terrain map, wherein the mean of orthogonal distance is computed on the basis of horizontal position moments and terrain map properties; determining a full solution estimate of position for the vehicle based on the transformed one or more altitude measurements, and the one or more GNSS or hybridized GNSS/INS measurements; determining one or more sub-solution estimates of position for the vehicle based on a subset of the transformed one or more altitude measurements, and the one or more GNSS or hybridized GNSS/INS measurements; comparing the full solution estimate with the one or more sub-solution estimates using statistical analysis; and determining an altitude protection level for the vehicle based on a probability of hazardous misleading information and a probability of false detection. obtaining one or more global navigation satellite system, GNSS, measurements, or one or more hybridized GNSS /inertial navigation system, INS, measurements, in an earth-centered-earth-fixed, ECEF, coordinate frame for a vehicle; obtaining one or more altitude measurements from one or more radar altimeters on the vehicle; transforming the one or more altitude measurements into the ECEF coordinate frame using a terrain map and a GNSS or hybridized GNSS/INS based position estimate with ensured integrity, wherein the transformed one or more altitude measurements are given by the following equation: ρ ̃ RA, transformed = ρ ̃ RA + ρ ^ TERMAP where ρ̃ RA is the radar altimeter measurement, and ρ̂ TERMAP is an estimate of orthogonal distance between an ECEF frame origin and a terrain at a point given by a horizontal position of the vehicle and the terrain map; computing one or more characteristics of the transformed one or more altitude measurements, including orthogonal distance ρ TERMAP moments, wherein a mean value of the orthogonal distance ρ TERMAP is computed as: ρ ^ TERMAP = E ρ TERMAP = function 1 ρ ^ HOR map, where ρ̂ HOR is a horizontal position estimate of the vehicle and map is the terrain map, wherein the mean of orthogonal distance is computed on the basis of horizontal position moments and terrain map properties; determining a full solution estimate of position for the vehicle based on the transformed one or more altitude measurements, and the one or more GNSS or hybridized GNSS/INS measurements; determining one or more sub-solution estimates of position for the vehicle based on a subset of the transformed one or more altitude measurements, and the one or more GNSS or hybridized GNSS/INS measurements; comparing the full solution estimate with the one or more sub-solution estimates using statistical analysis; and determining an altitude protection level for the vehicle based on a probability of hazardous misleading information and a probability of false detection.