  Global Navigation Satellite Systems (GNSS) aided Inertial Navigation System
(INS) is a fundamental approach for attaining continuously available absolute
vehicle position and full state estimates at high bandwidth. For transportation
applications, stated accuracy specifications must be achieved, unless the
navigation system can detect when it is violated. In urban environments, GNSS
measurements are susceptible to outliers, which motivates the important problem
of accommodating outliers while either achieving a performance specification or
communicating that it is not feasible. Risk-Averse Performance-Specified (RAPS)
is designed to optimally select measurements to address this problem. Existing
RAPS approaches lack a method applicable to carrier phase measurements, which
have the benefit of measurement errors at the centimeter level along with the
challenge of being biased by integer ambiguities. This paper proposes a RAPS
framework that combines Real-time Kinematic (RTK) in a tightly coupled INS for
urban navigation applications. Experimental results demonstrate the
effectiveness of this RAPS-INS-RTK framework, achieving 85.84% and 92.07% of
horizontal and vertical errors less than 1.5 meters and 3 meters, respectively,
using a smartphone-grade Inertial Measurement Unit (IMU) from a deep-urban
dataset. This performance not only surpasses the Society of Automotive
Engineers (SAE) requirements, but also shows a 10% improvement compared to
traditional methods.
