Navigation system integrity monitoring is crucial for mission (e.g. safety) critical applications. Receiver autonomous integrity monitoring (RAIM) based on consistency checking of redundant measurements is widely used for many applications. However, there are many challenges to the use of RAIM associated with multiple constellations and applications with very stringent requirements. This paper discusses two positioning techniques and corresponding integrity monitoring methods. The first is the use of single frequency pseudorange-based dual constellations. It employs a new cross constellation single difference scheme to benefit from the similarities while addressing the differences between the constellations. The second technique uses dual frequency carrier phase measurements from GLONASS and the global positioning system for precise point positioning. The results show significant improvements both in positioning accuracy and integrity monitoring as a result of the use of two constellations. The dual constellation positioning and integrity monitoring algorithms have the potential to be extended to multiple constellations.