Positioning system and method with inertial navigation and position estimate

A navigation system comprises an inertial subsystem configured to determine a plurality of relative positions of the system from a reference position based on the speed and/or acceleration and/or direction of the system, and/or changes to these parameters. The system also includes a position estimator subsystem configured to estimate the absolute position of the system based on at least two received signals. The system further comprises a processor, the processor configured to define a first track 700 based on the plurality of relative positions determined during a first period of time and to cause the position estimator to generate a plurality of estimates 704 of the absolute position of the system during the first period of time. The processor defines a second track 702 based on the plurality of estimates of absolute position by calculating a best fit using the estimates, the second track approximating the same shape as the first track. The processor may then determine a deviation in position and/or orientation of the first track based upon the second track and update or generate a new reference for the inertial subsystem.