A navigation system for a machine is disclosed. The navigation system may have a navigation unit configured to measure a position of a machine at a first time and at a second time, and at least a first sensor configured to generate at least a first signal indicative of a speed and a heading of the machine during a time period from the first time to the second time. The navigation system may also have a controller configured to estimate a position of the machine at the second time based on the measured position of the machine at the first time and the at least a first signal, and to make a comparison of the measured position of the machine at the second time with the estimated position of the machine at the second time. The controller may also be configured to determine an integrity of the navigation unit based on the comparison.