We propose a new protection level computation algorithm, where a nonlinear optimization problem derived from conventional RAIM is just once solved for a bias vector, such that satisfies its lower and upper bounds as constraints. This algorithm does not limit a number of assumed faulty measurements, while avoiding combinatorial increase of computational load which is usually problematic in RAIM and ARAIM as the number of fault modes increase. Also the upper and lower bounds of bias vector can be applied as a part of integrity assistance data which is being standardized in 3GPP and RTCM.