This paper analyzes the pseudorange relationship between different frequency signals, and proposes a multifrequency receiver autonomous integrity monitoring (RAIM) algorithm. Aimed at the problems that measurement error covariance matrix is not diagonal, the paper proposes a new prewhitening method which can easily be implemented in a receiver. In addition, the paper analyzes the RAIM algorithms from different frequency points. The simulation results show that the multiplefrequency algorithm can eliminate the ionosphere error so that the positioning error can be reduced to less than 10 m. In addition, when the pseudorange deviation is less than 50 m, multifrequency RAIM algorithm can still be applied in detecting and identifying fault satellite. And the triplefrequency RAIM algorithm is in an advantageous position compared to dual algorithm, which would have a tempting theoretical and practical value for the future research of multifrequency receiver autonomous integrity algorithm research.