A navigation system is disclosed comprising a navigation device (2a) with a navigation sensor unit (3) and a magnetic field sensor unit (4), the navigation device is arranged to be moved. The navigation sensor unit (3) is arranged for providing a navigation signal with navigation information (ā, θ). The magnetic field sensor unit is arranged for providing a magnetic field signal (H) indicative for a magnetic field strength. The navigation system further comprises a first integration unit (6a) for integrating the navigation signal (ā, θ) and for providing a first integration result (p), a second integration unit (6b) for calculating a path-integral of the magnetic field signal using the navigation signal, and for providing a second integration result (m), a first auxiliary integration unit (6c) for providing a first coefficient (α), a second auxiliary integration unit (6d) for providing a second coefficient (φ), and a proximity detector (5) for providing a proximity signal (Snc) indicative whether a distance between the navigation device (2a) and a reference position is less than a predetermined value. A matrix solving unit (8) for solves a set of equations based on the first integration result, the second integration result, the first coefficient and the second coefficient.