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We propose a dual-recursion particle filter for global navigation satellite system (GNSS) calculations that separates the positioning and velocity estimations. The proposed filter can cover the state space more adequately with the same number of particles, and hence, it provides better positioning accuracy. Additionally, considering the vulnerability of GNSS, an improved receiver autonomous integrity monitoring (RAIM) method is proposed for spoofing detection and spoofing identification. This method is able to resist attacks from one or many spoofing satellites. Using the improved RAIM, the proposed particle filter can correct the positioning under spoofing attacks.