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Connected and Autonomous Vehicles (CAV) require positioning that is consistently reliable and accurate. This is achieved through the choice of sensors and the real-time selection of high-quality measurements. Global Navigation Satellite Systems (GNSS) are the foundation to achieve accurate absolute positioning. GNSS Common-mode Errors (CME)mitigation can be realized with Differential GNSS (DGNSS) approach and Precise Point Positioning (PPP) techniques. With the evolution of the International GNSS Service (IGS) Multi-GNSS Experiment (MGEX), Real-time PPP (RT-PPP) corrections for multi-GNSS have only recently become accessible. GNSS measurements are prone to outliers. This results in an inherent performance versus risk trade-off in CAV state estimation applications. Recently proposed Risk-Averse Performance Specified (RAPS) methods address this trade-off by optimally selecting a subset of measurements to minimize risk while achieving a target performance. The existing RAPS literature presents cases where the performance specification is stated for the full information matrix. However, those methods are not computationally efficient as required for real-time and do not address situations where that specification is infeasible. This dissertation focuses on the Diagonal Performance-Specified RAPS (DiagRAPS) formulation. This dissertation begins with a review of GNSS measurement models and real-time CME mitigation techniques, such as DGNSS, PPP, and Virtual Network DGNSS (VN-DGNSS). It then develops the theory of DiagRAPS for both binary and non-binary measurement selection variables. Algorithms suitable for real-time applications are proposed within Linear Programming (LP) and Mixed-Integer Linear Programming (ILP) optimization frameworks, achieving polynomial time complexity. The convergence and computation costs of these algorithms are discussed. For binary DiagRAPS, a novel convex reformulation is derived, leading to a globally optimal solution that can be solved using existing tools. Additionally, a soft constraint optimization approach is proposed for situations when the specified performance is unfeasible. Finally, this dissertation evaluates DiagRAPS state estimation approaches using real-world multi-GNSS data from challenging environments for both DGNSS and RT-PPP applications. The results reveal that the locally optimal approach achieves state estimation performance comparable to the global solution. Both binary and non-binary DiagRAPS outperform traditional methods. Notably, the non-binary approach yielded the lowest computation cost and the best overall performance.