This article presents a Contemplative Realtime (CRT) framework to resolve a vector of carrier phase integer ambiguities existing in Real-Time Kinematic GPS aided inertial navigation systems (RTK GPS/INS). Within this CRT framework, a Maximum-a-Posteriori (MAP) estimation method is derived to represent the RTK GPS/INS problem, and solved by Nonlinear Mixed Integer Least Square (NMILS) approach. This approach allows the utilization of multiple epochs of GPS data with INS defined motion constraints over a time interval. The NMILS approach over time intervals allows hypothesis testing on each interval to contemplate alternative fault detection hypotheses. The objectives are to enhance reliability and accuracy. Implementation results are included that demonstrate the performance of the proposed method achieving centimeter position accuracy.