This paper describes the first of a two-part research effort to find the optimal detector and estimator that minimise the integrity risk in Receiver Autonomous Integrity Monitoring (RAIM). In this first part, a new method is established to determine a piecewise linear approximation of the optimal detection region in parity space. The paper presents examples suggesting that the optimal detection boundary lays in between that obtained using chi-squared residual-based RAIM, and that provided by

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... ution Separation (SS) RAIM, as one varies the alert limit requirement. In addition, these examples indicate that for realistic navigation requirements, the SS RAIM method approaches the optimal detection region. The SS RAIM detection tests will be employed in the second part of this work, which focuses on the design of non-least-squares estimators to reduce the integrity risk in exchange for a slight increase in nominal positioning error.