An inertial device for determining a walking direction of a pedestrian carrying the inertial device, said inertial device comprising: an acceleration sensor which is operable to output accelerations in a horizontal and a vertical direction, said acceleration sensor being a three-axis acceleration sensor associated with a device coordinate system (X', Y', Z'); a coordinate system conversion unit configured to convert accelerations in the device coordinate system (X', Y', Z') obtained from the acceleration sensor into accelerations in an absolute coordinate system (X, Y, Z) having an axis extending in a vertical direction and mutually perpendicular first and second axes extending in respective horizontal directions (X, Y); characterized in that the inertial device further comrpises: a detection unit configured to detect turning points in a waveform representing the acceleration in the vertical direction with respect to time and to detect time at the turning points, wherein the turning points in question mark local minima in case a positive vertical axis is chosen to point in the downward vertical direction, a turning point corresponding to a first half of a mid stance phase of a step of the walking motion of the pedestrian in which a lifting foot passes a pivoting foot; a calculation unit configured to calculate a velocity in the horizontal plane using the acceleration in the horizontal directions (X, Y) in a predetermined period centering on the time at a respective turning point; a determination unit configured to determine whether the velocity is less than or equal to a threshold value; and an estimation unit configured to estimate a walking direction into which the pedestrian carrying the inertial device moves using the velocity in response to a determination by the determination unit that the velocity is less than or equal to the threshold value; wherein the walking direction is estimated for each step of the pedestrian based on a resultant vector (V 0 ' + V 1 '), which resultant vector is calculated based on at least two velocities (V 0, V 1) in the horizontal plane that are associated with respective first halves of consecutive mid stance phases of the walking motion of the pedestrian. an acceleration sensor which is operable to output accelerations in a horizontal and a vertical direction, said acceleration sensor being a three-axis acceleration sensor associated with a device coordinate system (X', Y', Z'); a coordinate system conversion unit configured to convert accelerations in the device coordinate system (X', Y', Z') obtained from the acceleration sensor into accelerations in an absolute coordinate system (X, Y, Z) having an axis extending in a vertical direction and mutually perpendicular first and second axes extending in respective horizontal directions (X, Y); characterized in that the inertial device further comrpises: a detection unit configured to detect turning points in a waveform representing the acceleration in the vertical direction with respect to time and to detect time at the turning points, wherein the turning points in question mark local minima in case a positive vertical axis is chosen to point in the downward vertical direction, a turning point corresponding to a first half of a mid stance phase of a step of the walking motion of the pedestrian in which a lifting foot passes a pivoting foot; a calculation unit configured to calculate a velocity in the horizontal plane using the acceleration in the horizontal directions (X, Y) in a predetermined period centering on the time at a respective turning point; a determination unit configured to determine whether the velocity is less than or equal to a threshold value; and an estimation unit configured to estimate a walking direction into which the pedestrian carrying the inertial device moves using the velocity in response to a determination by the determination unit that the velocity is less than or equal to the threshold value; a detection unit configured to detect turning points in a waveform representing the acceleration in the vertical direction with respect to time and to detect time at the turning points, wherein the turning points in question mark local minima in case a positive vertical axis is chosen to point in the downward vertical direction, a turning point corresponding to a first half of a mid stance phase of a step of the walking motion of the pedestrian in which a lifting foot passes a pivoting foot; a calculation unit configured to calculate a velocity in the horizontal plane using the acceleration in the horizontal directions (X, Y) in a predetermined period centering on the time at a respective turning point; a determination unit configured to determine whether the velocity is less than or equal to a threshold value; and an estimation unit configured to estimate a walking direction into which the pedestrian carrying the inertial device moves using the velocity in response to a determination by the determination unit that the velocity is less than or equal to the threshold value; wherein the walking direction is estimated for each step of the pedestrian based on a resultant vector (V 0 ' + V 1 '), which resultant vector is calculated based on at least two velocities (V 0, V 1) in the horizontal plane that are associated with respective first halves of consecutive mid stance phases of the walking motion of the pedestrian.