A positioning device comprising: - a correction data generation unit to receive reinforcement information including integrity information; - an observation noise calculation unit to calculate observation noise used in positioning calculation by using integrity information included in reinforcement information that is used to correct a satellite positioning error; - a positioning calculation unit to perform positioning calculation by using the observation noise calculated by the observation noise calculation unit; and - an observed data screening unit to repeat an operation of selecting m, m ≥ 4 and m < n, pieces of observed data from among n, n ≥ 5, pieces of observed data, each piece of observed data transmitted from a corresponding positioning satellite, and generate k, k ≥ 4 and k ≤ n, data sets each of which is formed of the m pieces of observed data selected at different repetition, and that has a different combination of the m pieces of observed data, wherein the positioning calculation unit is adapted to perform, for each data set, observation update calculation on the m pieces of observed data making up the data set as a part of the positioning calculation, and to select any data set from among the k data sets on the basis of a variance of a residual before the observation update calculation of each data set and a variance of a residual after the observation update calculation of each data set, wherein the residual for each data set is a difference between an actual observation amount and an estimated observation amount; wherein the observation update calculation includes applying a Kalman gain to the residual for each data set; and wherein the observation noise is included in a denominator of a Kalman gain. - a correction data generation unit to receive reinforcement information including integrity information; - an observation noise calculation unit to calculate observation noise used in positioning calculation by using integrity information included in reinforcement information that is used to correct a satellite positioning error; - a positioning calculation unit to perform positioning calculation by using the observation noise calculated by the observation noise calculation unit; and - an observed data screening unit to repeat an operation of selecting m, m ≥ 4 and m < n, pieces of observed data from among n, n ≥ 5, pieces of observed data, each piece of observed data transmitted from a corresponding positioning satellite, and generate k, k ≥ 4 and k ≤ n, data sets each of which is formed of the m pieces of observed data selected at different repetition, and that has a different combination of the m pieces of observed data, wherein the positioning calculation unit is adapted to perform, for each data set, observation update calculation on the m pieces of observed data making up the data set as a part of the positioning calculation, and to select any data set from among the k data sets on the basis of a variance of a residual before the observation update calculation of each data set and a variance of a residual after the observation update calculation of each data set, wherein the residual for each data set is a difference between an actual observation amount and an estimated observation amount; wherein the observation update calculation includes applying a Kalman gain to the residual for each data set; and wherein the observation noise is included in a denominator of a Kalman gain.