Navigation system comprising - a navigation device with a navigation sensor unit and a magnetic field sensor unit, the navigation device being arranged to be moved, - the navigation sensor unit being arranged for providing a navigation signal with navigation information ( a, θ) - the magnetic field sensor unit being arranged for providing a magnetic field signal indicative for a magnetic field strength, - a first integration unit for integrating the navigation signal ( a,θ) and for providing a first integration result (p), the first integration result being an estimated position, - a second integration unit for calculating Ampere's integral of the magnetic field signal along the path (O 1 - O 2) followed by the navigation system as estimated on the basis of the navigation signal ( a, θ),and for providing a second integration result (m), - a first auxiliary integration unit for providing a first coefficient (α), by a double integration of a normalization constant in time over a time-interval (T 1 - T 2) in which the estimated path was followed, - a second auxiliary integration unit for integrating a normalization constant in time over said time-interval, for multiplying an integration result obtained therewith by the measured magnetic field and for integrating the product obtained therewith in time over said time-interval, wherein the integration result of this integration is a second coefficient ( φ), - a proximity detector for providing a proximity signal (Snc) indicative whether a distance between the navigation device and a reference position is less than a predetermined value, - a data storage unit for storing the first integration result, the second integration result, the first coefficient and the second coefficient for states wherein the proximity signal is positive, - a matrix solving unit for solving a set of equations based on the first integration result, the second integration result, the first coefficient and the second coefficient retrieved from the data storage unit, the set of equations including at least a first equation in which the estimated position (p 1 1) is expressed as the product of the first coefficient (α) with a bias ( b) in the acceleration, and a second equation wherein Ampere's integral is expressed as the product of said bias ( b) with the second coefficient (φ), and wherein the matrix solving unit estimates said bias by solving the set of equations, - a controller for controlling the first integration unit, the second integration unit, the first auxiliary integration unit, the second auxiliary integration unit data storage unit, the data storage unit and the matrix solving unit. - a navigation device with a navigation sensor unit and a magnetic field sensor unit, the navigation device being arranged to be moved, - the navigation sensor unit being arranged for providing a navigation signal with navigation information ( a, θ) - the magnetic field sensor unit being arranged for providing a magnetic field signal indicative for a magnetic field strength, - a first integration unit for integrating the navigation signal ( a,θ) and for providing a first integration result (p), the first integration result being an estimated position, - a second integration unit for calculating Ampere's integral of the magnetic field signal along the path (O 1 - O 2) followed by the navigation system as estimated on the basis of the navigation signal ( a, θ),and for providing a second integration result (m), - a first auxiliary integration unit for providing a first coefficient (α), by a double integration of a normalization constant in time over a time-interval (T 1 - T 2) in which the estimated path was followed, - a second auxiliary integration unit for integrating a normalization constant in time over said time-interval, for multiplying an integration result obtained therewith by the measured magnetic field and for integrating the product obtained therewith in time over said time-interval, wherein the integration result of this integration is a second coefficient ( φ), - a proximity detector for providing a proximity signal (Snc) indicative whether a distance between the navigation device and a reference position is less than a predetermined value, - a data storage unit for storing the first integration result, the second integration result, the first coefficient and the second coefficient for states wherein the proximity signal is positive, - a matrix solving unit for solving a set of equations based on the first integration result, the second integration result, the first coefficient and the second coefficient retrieved from the data storage unit, the set of equations including at least a first equation in which the estimated position (p 1 1) is expressed as the product of the first coefficient (α) with a bias ( b) in the acceleration, and a second equation wherein Ampere's integral is expressed as the product of said bias ( b) with the second coefficient (φ), and wherein the matrix solving unit estimates said bias by solving the set of equations, - a controller for controlling the first integration unit, the second integration unit, the first auxiliary integration unit, the second auxiliary integration unit data storage unit, the data storage unit and the matrix solving unit.