A system and associated methods for mutual-aiding and mutual-calibrating positioning and navigation that fuse self-contained and referenced displacement measurements to provide position, velocity, and attitude estimates. In one embodiment the system includes a dead-reckoning device, a radio signal receiver, and a computational device that performs integration with mutual aiding and mutual calibration, leading to a position, velocity, and attitude solution. In another embodiment the system further includes auxiliary sensors. In one embodiment the method that performs fusion of dead-reckoning and radio signal measurements includes dead-reckoning mechanization, estimation of radio signal parameters including signal strength, code phase, and carrier phase, coarse initialization of navigation states with code phase and signal strength measurements, refinement of navigation estimation using temporal carrier phase differences, and estimation of dead-reckoning and radio measurement error terms. In another embodiment the method also includes identification and estimation of non-line-of-sight multipath signals for mitigation and removal.