A signal of opportunity (SOP)-aided inertial navigation system (INS) framework provides various technical solutions to technical problems facing GNSS implementations. A mobile receiver, whether handheld or vehicle-mounted, has access to Global Navigation Satellite System (GNSS) signals, multiple unknown terrestrial SOPs, and IMU measurements, which are used to estimate receiver states. When GNSS signals become unreliable, the mobile receiver continues to navigate using the SOP-aided INS. The SOP-aided INS produces bounded estimation errors in the absence of GNSS signals, and the bounds are dependent on the quantity and quality of exploited SOPs.